Trivalent Praseodymium-Doped Yttrium Lithium Fluoride Visible Lasers Pumped by Gallium Nitride Series Laser Diodes

Trivalent Praseodymium-doped Yttrium Lithium Fluoride Visible Lasers Pumped by Gallium Nitride Series Laser Diodes

August 2018

Hiroki Tanaka

Abstract

This study deals with the demonstration of continuous-wave and passively Q-switched trivalent praseodymium (Pr3+)-doped solid-state lasers directly pumped by indium gallium nitride (InGaN)-based blue laser diodes 3+ (LDs). As the laser gain medium, Pr -doped yttrium lithium fluoride (LiYF4, YLF) was adopted in this study.

Recent progress of InGaN-based blue LDs are remarkable, and nowadays, an output power of 5 W is available around 450 nm from a 9-mm CAN single emitter device. By utilizing the high power blue LDs, the pump power was increased up to 20 W, the highest pump level for visible Pr3+ lasers ever reported, and continuous output powers of 6.7 W and 3.7 W were obtained from Pr3+:YLF lasers operated at 640 and 607 nm, respectively. The onset of strong negative thermal lensing for π-polarization inhibited the scaling at 523 nm. The highest efficiency of 640-nm diode-pumped Pr3+:YLF laser was achieved by directly exciting the 479-nm line by a cyan-blue LD providing 1-W pump power. The highest slope efficiency of 62.9% was obtained. Using a fiber-coupled pump module provided >20 W pump power at 445 nm, the pump-limited scaling of an end-pumped Pr3+:YLF laser at 640 nm was demonstrated. The laser performance exhibited an onset of strong thermally-induced diffraction loss when high transmission output couplers were used. Using an output coupler of 1.1% transmission, an output power of 3.4 W was obtained with a slope efficiency of 25%.

For passive Q-switching of Pr3+ visible lasers, a variety of transition-metal-doped crystals were experimentally investigated as saturable absorbers. tetravalent chromium- and divalent cobalt-doped oxide crystals were mainly 4+ 2+ focused on. Cr in Y3Al5O12 (YAG) and Mg2SiO4 (forsterite), and Co in MgAl2O4 spinel, LiGa5O8, and

Gd3Ga5O12 (GGG) exhibited attractive saturable absorption for passive Q-switching. Passive Q-switching 3+ 4+ 2+ 2+ of diode-pumped Pr :YLF visible lasers were achieved using Cr :YAG, Co :MgAl2O4, and Co :GGG saturable absorbers. The proposed rate equation model showed a good agreement with the experimental results. The numerical models allow to optimize laser parameters and to examine the possibility to obtain Q-switching of other gain media.

Frequency doubling and tripling were applied to continuous-wave and passive Q-switching Pr3+:YLF lasers at 640 nm to generate ultraviolet. Intracavity frequency doubling of Pr3+:YLF laser is a promising approach to efficiently generate continuous-wave ultraviolet laser. Using a lithium triborate3 (LiB O5, LBO), a 320-nm output power of 880 mW was obtained at an absorbed pump power of 5.9 W. Intracavity frequency doubling was also applied to a passive Q-switching Pr3+:YLF laser, and 50-ns ultraviolet pulses were successfully generated with a repetition rate of 52-kHz. The numerical model for passive Q-switching were extended for frequency doubling. 213-nm deep ultraviolet pulse generation as third harmonic of visible laser was realized for the first time. The use of visibly oscillating frond end enables to simplify the conversion processes. The 213-nm deep ultraviolet has conventionally been achieved as fifth harmonic of 1-µm lasers, and requires three conversion steps, while 640-nm laser can reach 213 nm by only two steps of conversion. In the proof-of-concept demonstration, 213-nm deep UV pulses were successfully generated from an actively Q-switched Pr3+:YLF laser which only provided a pulse energy of 56 µJ.

i Acknowledgements

The work presented in this thesis was carried out in the group of Prof. Dr. Fumihiko Kannari at the Graduate School of Science and Technology in Keio University. I am highly grateful to him for giving me the opportunity to conduct this research in his group. He kindly accepted me in his group from my master course even though I had never learnt the laser physics and engineering before. He was always available to discuss on experiments and results although he was always busy. Through the discussions with him, I could learn a lot from him not only things related to my research.

I would like to thank Prof. Dr. Hiroyuki Sasada, Prof. Dr. Hiroyuki Tsuda, and Prof. Dr. Takasumi Tanabe for being the vice chairs in my dissertation committee, and for carefully reviewing and giving advices and corrections to improve this thesis.

I would like to thank Dr. Kenichi Hirosawa, a previous research associate in the group of Prof. Kannari, for his knowledge on laser engineering. I could learn a lot of know-how through experiments with him.

A part of work presented in this thesis was conducted from August 2017 to January 2018 in the Center for Laser Materials of Leibniz Institute for Crystal Growth (Institut für Kristallzuchtung, IKZ) in Berlin. I would like to express my appreciation to Dr. Christian Kränkel, the group leader of the Center for Laser Materials, for accepting me as a visiting student of his group. Although he was always busy, he occasionally gave me lectures on physics in laser materials and was always available for discussing on results and ideas.

I also thank Elena Castellano-Hernández, a Ph.D. student in the Center for Laser Materials in IKZ, for helping me when I got difficulties in the institute. I appreciate her effortto excavate old crystals at the Institute of Laser-Physics in Hamburg University to be investigated.

I would also like to thank Maxim Demesh, a visiting student at IKZ from Beralusian National Technical University, for allowing me to use a Cr:forsterite crystal for my measurements.

I would like to acknowledge to all the members of Kannari laboratory. Particularly, Ryosuke Kariyama, Kodai Iijima and Shogo Fujita, who had been working together for praseodymium lasers, were huge help for completing this thesis. I would also like to thank Aruto Hosaka, a Ph.D. student in the lab., for his insightful advices on my experiments and results. His comments at meetings were always helpful.

I am grateful to Nichia Corp. for providing high-power GaN blue laser diodes. These were indispensable devices to accomplish all the laser experiments presented in this thesis.

I would like to thank all the technical staffs in the manufacturing center of Keio University. I frequently used the facility to make mechanical pieces to be integrated in laser setups. The facility and support of the technical staffs were important to carry out experiments.

I would like to express my appreciation to the Program of Leading Graduate Schools of Keio University for “Science for Development of Super Mature Society” for its financial support for travels expenses of international

ii conferences, for article publication fees, and for the six-month research visit at the Leibniz Institute for Crystal Growth in Berlin. Help and supports of the project professors and staffs are appreciated.

I would like to acknowledge the colleagues participating as research assistants in the Program of Leading Graduate Schools of Keio University. Although we have completely different research backgrounds, discussion with them were always exciting, and allowed me to keep my motivation for research.

I would like to express my sincere gratitude to Yuri Yamamoto for her mental support allowing me to complete this Ph.D. study.

Finally, I express my gratitude to my family for allowing me to continue my whole student life.

iii List of Abbreviations

AOM Acousto-Optic Modulator AR Anti-Reflection β β BBO -Barium Borate ( -BaB2O4) BRF Birefringent Filter BS Beam Splitter

BYF BY3F10

CLBO Cesium Lithium Borate (CsLiB6O10) CMOS Complimentary Metal-Oxide-Semiconductor CW Continuous-Wave DM Dichroic Mirror DUV Deep Ultraviolet ESA Excited State Absorption FWHM Full Width at Half Maximum GaN Gallium Nitride

GAP Gallium Aluminum Perovskite (GaAlO3)

GGG Gadolinium Gallium Garnet (Gd3Ga5O12) GSA Ground State Absorption HR High Reflectivity

KYF KY3F10 LASER Light Amplification by Stimulated Emission of Radiation

LBO Lithium Triborate (LiB3O5) LD Laser Diode LED Light Emitting Diode

LGO LiGa5O8

LLF Lutetium Lithium Fluoride (LiLuF4)

LuAP Lutetium Aluminum Perovskite (LuAlO3)

MALO MgAl2O4 MOPA Master Oscillator Power Amplifier NA Numerical Aperture NIR Near-Infrared OC Output Coupler OPO Optical Parametric Oscillator OPSL Optically Pumped Semiconductor Laser PBS Polarizing Beam Splitter PD Photo-Detector PID Proportional-Integral-Differential PM Plane Mirror PMT Photomultiplier Tube

iv QD Quantum Dot QPM Quasi Phase Matching RE Rare Earth RF Radio Frequency SH Second Harmonic SHG Second Harmonic Generation

SRA Strontium Hexaaluminate (SrAl12O19) UV Ultraviolet VECSEL Vertical External Cavity Surface Emitting Laser

YAG Yttrium Aluminum Garnet (Y3Al5O12)

YAP Yttrium Aluminum Perovskite (YAlO3)

YLF Yttrium Lithium Fluoride (LiYF4)

ZBLAN ZrF4-BaF2-LaF3-AlF3-NaF

v Physical Constants

Speed of light c = 2.998 × 108 m/s Planck constant h = 6.626 × 10−34 J · s Reduced Planck constant ℏ = h/2π −12 −1 Electric constant ε0 = 8.854 × 10 F · m Elementary charge e = 1.602 × 10−19 C −31 Electron mass me = 9.109 × 10 kg −23 −1 Boltzmann constant kB = 1.380 × 10 J · K

vi List of Symbols

A21 Einstein’s A coefficient A˜ A-element of ABCD matrix B Racah B parameter

B12,B21 Einstein’s B coefficient B˜ B-element of ABCD matrix C Racah C parameter C˜ C-element of ABCD matrix Dq Crystal field strength D˜ D-element of ABCD matrix E Energy E′ Young modulus F Fluence of laser pulse f Focal length fp Ratio of excited state absorption cross section to ground state absorption cross section g gain coefficient g˜i=1,2 Degeneracy of ground (i = 1) and excited state (i = 2) Hˆ Hamiltonian h′ Boyd-Kleinman factor I Optical intensity J Total angular momentum quantum number of ion K Thermal conductivity L Total orbital angular momentum quantum number of ion li Angular momentum quantum number lc Cavity length lg Length of gain medium lSA Length of saturable absorber M 2 Beam quality factor mi Magnetic quantum number N Population density of energy level

Ntot Total density of active ions in gain medium ∆N Population inversion density nes Population density of excited state in saturable absorber ngs Population density of ground state in saturable absorber ntot Total density of absorption centers in saturable absorber ni Principal quantum number P Power q q-parameter of Gaussian beam

vii R Reflectivity

Rni,li Radial part of wavefunction for given quantum numbers ni, li rb Radius of laser rod S Total spin angular momentum quantum number of ion si Spin angular momentum quantum number T Transmittance T ′ Temperature U Complex envelope function of beam

Wp Pumping rate w Beam radius Y mi Spherical harmonic function for given quantum numbers l , m li i i Z Atomic number zR Rayleigh range of Gaussian beam α Absorption coefficient

αT Thermal expansion coefficient Γ Irreducible representation of symmetry

ηC Coupling efficiency of laser

ηQ Quantum efficiency of laser

ηStokes Stokes efficiency of laser

ηm Mode matching efficiency of laser λ Wavelength µ Moment operator ν Frequency ν˜ Wavenumber ρ(ν) Photon energy density

σgs Ground state absorption cross section

σes Excited state absorption cross section

σst Stimulated emission cross section σ′ Mechanical stress

τc Cavity lifetime

τf Fluorescence lifetime

τR Radiative lifetime

τSA Recovery time of saturable absorber Φ˜ Distribution function ϕ Photon number density Ψ Multi-electron wavefunction

ψ0 Single-electron wavefunction

viii Contents

Abstract i

Acknowledgements ii

List of Abbreviations v

Physical Constants vii

List of Symbols ix

1 Introduction 1

1.1 Context ...... 1

1.2 Background ...... 2

1.2.1 Pump sources ...... 2

1.2.2 Visibly emitting solid-state lasers ...... 4

1.2.3 Ultraviolet solid-state lasers ...... 6

1.2.4 Saturable absorbers for passive Q-switching and mode-locking of visible lasers ...... 8

1.3 Objective ...... 11

2 Fundamentals 13

2.1 Energy structure of rare earth and transition metal ions in solid hosts ...... 13

2.1.1 Energy levels in a free ion ...... 13

ix CONTENTS x

2.1.2 Energy structure of 4f n orbital of rare earth ions ...... 16

2.1.3 Energy structure of 3dn orbital of transition metal ions ...... 17

2.1.4 Selection rules ...... 19

2.2 Interaction of light and matter ...... 20

2.3 Laser principles ...... 22

2.3.1 Two-level system ...... 22

2.3.2 Three-level and four-level lasers ...... 24

2.3.3 Lasing threshold ...... 25

2.3.4 Mathematical description of four-level lasers ...... 26

2.4 Optical resonator ...... 28

2.4.1 Gaussian beam ...... 28

2.4.2 Resonator design ...... 30

3 Continuous-wave Pr3+:YLF visible lasers 33

3.1 Pump laser diodes ...... 33

3.1.1 Single-emitter InGaN blue and cyan-blue laser diodes ...... 33

3.1.2 Fiber-coupled blue LD module ...... 37

3.2 Crystalline hosts for Pr3+ visible lasers ...... 37

3.2.1 Yttrium lithium fluoride (YLF) ...... 40

3.3 Spectroscopic properties Pr3+-doped YLF crystal ...... 41

3.3.1 Ground-state absorption (GSA) ...... 42

3.3.2 Excited-state absorption (ESA) ...... 43

3.3.3 Emission spectroscopy ...... 44

3.3.4 Lifetime ...... 44

3.4 Diode-pumped continuous-wave Pr3+:YLF lasers ...... 46

3.4.1 Single-emitter-blue-diode-pumped Pr3+:YLF laser ...... 46 CONTENTS xi

3.4.2 Single-emitter-cyan-blue-diode-pumped Pr3+:YLF laser ...... 50

3.4.3 Fiber-coupled-diode pumping ...... 51

3.5 Summary ...... 57

4 Characterization of transition-metal-doped saturable absorbers 60

4.1 Methods ...... 60

4.2 Sample preparation ...... 65

4.3 Cr4+-doped oxide crystals as saturable absorbers ...... 65

4+ 4.3.1 Cr :Y3Al5O12 (YAG)...... 66

4+ 4.3.2 Cr :Mg2SiO4 (forsterite) ...... 73

4.4 Co2+-doped oxide crystals as saturable absorbers ...... 79

2+ 4.4.1 Co :MgAl2O4 (MALO, spinel) ...... 79

2+ 4.4.2 Co :LiGa5O8 (LGO) ...... 85

4.4.3 Co2+-doped garnets ...... 89

2+ 4.4.4 Co :LiAlO2 ...... 94

2+ 4.4.5 Co :Ca2MgSi2O7 (åkermanite) ...... 96

4.5 Summary ...... 97

5 Passive Q-switching of Pr3+:YLF visible lasers 101

4+ 5.1 Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber ...... 101

5.1.1 Determination of saturation parameters of Cr4+:YAG saturable absorbers ...... 101

5.1.2 Passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorbers ...... 104

5.1.3 Rate equation analysis ...... 107

5.1.4 Design of Pr3+:YLF/Cr4+:YAG microchip Q-switched laser ...... 108

2+ 5.2 Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber ...... 110

5.2.1 Co2+:MALO crystal for passive Q-switching ...... 110 5.2.2 Passively Q-switched Pr3+:YLF laser with Co2+:MALO saturable absorber ...... 112

5.2.3 Rate equation analysis ...... 113

5.3 Passive Q-switching with Co2+-doped garnet saturable absorber ...... 115

5.4 Summary ...... 118

6 Frequency conversion of Pr3+:YLF lasers for ultraviolet generation 120

6.1 Continuous-wave ultraviolet Pr3+:YLF laser at 320 nm ...... 120

6.1.1 Experiment ...... 120

6.1.2 Rate equation analysis ...... 122

6.2 Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser ...... 123

6.2.1 Experiment ...... 123

6.2.2 Rate equation analysis ...... 127

6.3 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser ...... 131

6.3.1 Diode-pumped 640-nm Pr3+:YLF laser actively Q-switched by acousto-optic modulator . 131

6.3.2 Frequency tripling using optically active quartz for successive Type-I phase matching . . . 132

6.4 Summary ...... 138

7 Conclusion 140

Bibliography 144

List of Publications 158

xii List of Tables

1.1 Reported saturable absorbers in the visible region ...... 9

2.1 Number of 4f electrons and ground-state notation of trivalent rare earths ions from atomic

number of 58 to 71...... 17

2.2 Number of 3d electrons and ground-state notation of divalent, trivalent and tetravalent transition

metal ions. Notation of ground-state is for the case of no crystal field...... 18

2.3 ABCD matrices for common optical elements and media ...... 32

3.1 Nominal parameters of single-emitter InGaN LDs used in this thesis. Beam divergence is defined

as full angle at 1/e2 from peak intensity...... 34

3.2 Structual, optical, and mechanical properties of YLF crystal ...... 41

3.3 Wavelength, polarization, and termination level of major emission lines from Pr3+:YLF . . . . . 45

3.4 Nominal parameters of single-emitter InGaN LDs used in this thesis...... 47

3.5 Summary of demonstrated diode-pumped Pr3+:YLF visible lasers in continuous-wave operation. 59

4.1 Peak position and width of Cr4+:YAG absorption ...... 68

4.2 Summary of measured and determined parameters of Cr4+:YAG crystals ...... 72

4.3 Summary of parameters of green absorption in Cr4+:forsterite ...... 77

4.4 Summarized parameters of Co2+:MALO ...... 86

4.5 Summary of saturation characteristics of investigated Cr4+- and Co2+-doped oxide crystals . . . 100

5.1 Determined parameters of Cr4+:YAG crystals ...... 102

xiii 5.2 Parameters for simulating passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorber109

5.3 Parameters of Co2+:MALO used fro passive Q-switching experiments ...... 111

5.4 Parameters for simulating passively Q-switched Pr3+:YLF laser with Co2+:MALO saturable ab-

sorber ...... 116

6.1 Parameters for simulating passively Q-switched SHG Pr3+:YLF laser with Cr4+:YAG saturable

absorber ...... 129

6.2 Parameters of Type–I BBO, Type–II BBO, and Type–I LBO as candidates for SHG at 640 nm. . 133

xiv List of Figures

1.1 Summary of lasers from UV to NIR regions ...... 3

1.2 Evolution of InGaN-based semiconductor lasers ...... 3

1.3 Schematic of frequency-doubled optically-pumped semiconductor laser (2ω-OPSL) ...... 4

1.4 Schematic structures of conventional Nd3+-based and Pr3+-based UV lasers ...... 7

1.5 Schematic view of thesis structure ...... 12

2.1 Ligand field arrangement and crystal field splitting of d1 electron ...... 19

2.2 Absorption, spontaneous emission, and stimulated emission in two-level system...... 21

2.3 Simplified energy levels of three-level system and four-level system...... 24

2.4 Simplified laser schematic ...... 26

2.5 Propagating Gaussian beam with associated parameters...... 29

3.1 3D image of mechanical design of LD mount ...... 34

3.2 Power characteristics of blue LDs ...... 35

3.3 Emission spectrum of 5-W blue LD with respect to forward current and temperature ...... 35

3.4 Variation of beam radius of 5-W blue LD ...... 36

3.5 Power characteristic and spectrum of 478-nm cyan-blue LD ...... 36

3.6 Variation of beam radius of 1-W cyan-blue LD ...... 37

3.7 Power characteristic of fiber-coupled blue LD module at◦ 25 C...... 38

3.8 Emission spectrum of fiber-coupled blue LD module ...... 38

xv LIST OF FIGURES xvi

3.9 Energy diagram of the lowest energy levels of Pr3+ in fluoride crystalline hosts ...... 40

3.10 Crystal strucuture of LiYF4 (YLF) ...... 41

3.11 Polarization-resolved absorption spectrum of Pr3+:YLF crystal in the blue region ...... 42

3.12 Polarization-resolved absorption spectrum of Pr3+:YLF crystal in the orange region ...... 43

3.13 Energy diagram Pr3+ in YLF crystal and associated absroptions, emissions, and cross-relaxations 44

3.14 Fluorescence decay of Pr3+:YLF ...... 45

3.15 Schematic image of Pr3+:YLF laser pumped by four single-emitter blue LDs ...... 46

3.16 Output characteristics of Pr3+:YLF laser pumped by four single-emitter blue laser diodes oper-

ated at 640 nm and 607 nm ...... 49

3.17 Output characteristic and power stability of Pr3+:YLF laser at 640 nm ...... 49

3.18 Schematic image of Pr3+:YLF laser pumped by a cyan-blue LD at 479 nm ...... 50

3.19 Output characteristics of cyan-blue-diode-pumped Pr3+:YLF laser operated at 640 nm ...... 51

3.20 Experimental setup for evaluating thermal lens in Pr3+:YLF crystal ...... 52

3.21 Transmitted pump beam profile undergone thermal lens in end-pumped3+ Pr :YLF crystal for

varied absorbed pump powers ...... 53

3.22 Experimental setup of Pr3+:YLF laser at 640 nm end-pumped by fiber-coupled blue LD module 54

3.23 CW and quasi-CW output characteristics of Pr3+:YLF laser at 640 nm pumped by fiber-coupled

blue LD module ...... 55

3.24 Tempral output of quasi-CW Pr3+:YLF laser pumped by fiber-couple blue LD module ...... 55

3.25 Calculated temperature distribution in Pr3+:YLF crystal ...... 56

3.26 Overview of recently reported continuous-wave Pr3+:YLF lasers operated at 640 nm ...... 58

4.1 Four-level model for saturable absorbers ...... 61

4.2 Experimental setup of pump-probe measurement ...... 62

4.3 Experimental setup of Z-scan measurement ...... 63

4.4 Transmission of hypothetical saturable absorber as a function of incident pulse energy for Gaus-

sian and top-hat distributed pump beams ...... 64 LIST OF FIGURES xvii

4.5 Schematic image of fitting parameter space ...... 65

4.6 Crystal structure of Y3Al5O12 (YAG) ...... 66

4.7 Absorption spectra of Cr4+:YAG crystals ...... 67

4+ 4+ 3+ 4.8 Energy diagram of Cr (Td), Cr (Oh), and Cr (Oh)...... 67

4.9 Resolved absorption spectrum of Cr4+:YAG crystals ...... 69

4.10 Results of pump-probe measurements of Cr4+:YAG crystals ...... 70

4+ 4.11 Results of pump-probe measurements of Cr :YAG crystal (λP = 450 − 580 nm) ...... 71

4.12 Absorption recovery in Cr4+:YAG pumped at 450 nm ...... 71

4.13 Transmission of Cr4+:YAG crystals as a function of incident pulse fluence ...... 71

4.14 Crystal structure of Mg2SiO4 (forsterite) ...... 73

4.15 Polarization-resolved absorption spectrum of Cr:forsterite ...... 74

4.16 Energy diagram of tetrahedrally coordinated Cr4+ in forsterite ...... 75

4.17 Result of pump-probe measurement of Cr4+:forsterite crystal pumped at 570 nm ...... 75

4.18 Transmission of Cr:forsterite as a function of incident pulse fluence in the green–yellow region .76

4.19 Transmission of Cr4+:forsterite as a function of incident pulse fluence at 640 nm ...... 77

4.20 Result of Z-scan measurement of Cr4+:forsterite at 720 nm ...... 78

4.21 Crystal structure of MgAl2O4 spinel ...... 80

4.22 Absorption spectrum of Co2+:MALO ...... 80

4.23 Tanabe-Sugano diagram and simplified energy diagram for2+ Co ...... 81

4.24 Fluorescence spectrum of Co2+:MALO pumped at 532 nm ...... 82

4.25 Result of pump-probe measurement of Co2+:MALO crystal pumped at 640 nm ...... 83

4.26 Fluorescence decay of Co2+:MALO pumped at 607 nm ...... 83

4.27 Transmission of Co2+:MALO as a function of incident pulse fluence ...... 84

4.28 Crystal structure of LiGa5O8 ...... 86

4.29 Absorption spectrum of Co2+:LGO ...... 87 LIST OF FIGURES xviii

4.30 Result of pump-probe measurement of Co2+:LGO ...... 88

4.31 Fluorescence spectrum of Co2+:LGO pumped at 532 nm ...... 88

4.32 Fluorescence decay from Co2+:LGO pumped at 607 nm ...... 89

4.33 Absorption spectra of Co2+-doped garnets ...... 91

4.34 Result of pump-probe measurement of Co2+-doped garnets ...... 92

4.35 Two-dimensional transmission in Co2+:YAG...... 92

4.36 Transmission of Co2+:GGG as a function of incident pulse fluence ...... 93

γ 4.37 Crystal structure of -LiAlO2 ...... 94

4.38 Polarization-resolved absorption spectrum of Co:LiAlO2 crystal ...... 95

4.39 Result of Z-scan measurement of Co:LiAlO2 ...... 95

4.40 Crystal structure of Ca2MgSi2O7 (åkermanite) ...... 96

4.41 Absorption spectrum of c-cut Co2+:åkermanite ...... 96

4.42 Result of pump-probe measurement of Co2+:åkermanite ...... 97

4.43 Transmission of Co2+:åkermanite as a function of incident pulse fluence at 607 nm ...... 98

5.1 Result of Z-scan measurement of Cr4+:YAG crystals for passive Q-switching experiments . . . . 103

5.2 Experimental setup of diode-pumped Pr3+:YLF laser passively Q-switched by a Cr4+:YAG sat-

urable absorber ...... 104

5.3 Calculated cavity mode radius of V-shaped cavity ...... 104

5.4 Averaged output power of passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable ab-

sorber at 640 nm ...... 106

5.5 Pulse width of passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorber at 640 nm106

5.6 Pulse repetition rate of passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorber

at 640 nm ...... 106

5.7 Transmission spectrum of Co2+:MALO for passive Q-switching experiments ...... 111

5.8 Experimental setup of diode-pumped Pr3+:YLF laser passively Q-switched by a Co2+:MALO

saturable absorber ...... 112 LIST OF FIGURES xix

5.9 Averaged output power of passive Q-switched diode-pumped Pr3+:YLF laser with Co2+:MALO

saturable absorber ...... 113

5.10 Pulse width of passive Q-switched diode-pumped Pr3+:YLF laser with Co2+:MALO saturable

absorber ...... 113

5.11 Pulse repetition rate of passive Q-switched diode-pumped Pr3+:YLF laser with Co2+:MALO

saturable absorber ...... 114

5.12 Experimental setup of 2ω-OPSL-pumped Pr3+:YLF laser Q-switched by Co2+:GGG saturable

absorber ...... 117

5.13 Q-switched pulse train and waveform from Pr3+:YLF laser Q-switched by Co2+:GGG saturable

absorber ...... 117

6.1 Experimental setup of intracavity frequency-doubled Pr3+:YLF laser in CW operation ...... 121

6.2 Calculated beam radius of V-shaped cavity for intracavity frequency-doubled Pr3+:YLF laser . . 122

6.3 Power characteristic of intracavity frequency-doubled continuouse-wave Pr3+:YLF laser . . . . . 122

6.4 Experimental setup of 320-nm Q-switched SHG Pr3+:YLF laser ...... 124

6.5 Calculated cavity mode radius for frequency doubling passively Q-switched Pr3+:YLF laser . . . 124

6.6 UV output power with respect to absorbed pump power ...... 125

6.7 Q-switched pulse width (FWHM) and pulse repetition rate of passively Q-switched SHG laser at

320 nm ...... 126

6.8 Pulse train and pulse shape of passively Q-switch SHG laser at 320 nm ...... 126

6.9 Beam quality of passively Q-switched SHG laser at 320 nm ...... 127

6.10 Simulated Q-switched pulse width with varied SHG conversion coefficient ...... 130

6.11 Simulated peak power and pulse energy with varied SHG conversion coefficient ...... 130

6.12 Schematic of actively Q-switched Pr3+:YLF laser at 640 nm ...... 131

6.13 Actively Q-switched pulse train ...... 132

6.14 Spectrum of actively Q-switched laser at 640 nm ...... 132

6.15 Beam quality of actively Q-switched laser at 640 nm ...... 133 6.16 Experimental setup for 213-nm third harmonic generation ...... 133

6.17 Pulse shape and spectrum of second harmonic ...... 134

6.18 Reflectivity of 320-nm second harminic from silica glass for varied incident angle . .135

6.19 Pulse shape of second harmoinic and third harmonic detected by biplanar phototube ...... 136

6.20 Photograph of spatially dispersed fundamental wave, second harmonic, and third harmonic . . . 137

6.21 Relation between pulse energy and integrated signal of GaP-photodiode ...... 137

xx Chapter 1

Introduction

1.1 Context

Albert Einstein predicted the possibility to generate highly coherent photons, which do not exist in the natural world, by means of stimulated emission in 1916 [1]. However, the first laser realized after 44 years from the

3+ Einstein’s prediction. In 1960, Theodore Maiman finally succeeded to demonstrate the ruby (Cr :Al2O3) laser at 694.3 nm [2] (LASER is the acronym of Light Amplification by Stimulated Emission of Radiation).

After his great invention, laser technologies have been rapidly progressed, and nowadays, lasers are spread in various fields, not only in scientific use but also industry. Practically used lasers in our society aremainly near-infrared (NIR) solid-state lasers based on neodymium, erbium, and ytterbium or semiconductors. The development of these NIR lasers have been accelerated by the successful power scaling of gallium arsenide

(GaAs) based pump laser diodes (LDs). Although the first laser, ruby laser, was realized in the visible region, development of visibly emitting lasers have been limited mainly owing to the lack of efficient pump sources.

Various trivalent rare-earth ions enable to generate visible radiation according to their energy structure [3], but they have to be excited with blue or ultraviolet (UV) light sources. So far, visibly emitting lasers have been based on either gas or dyes as active media. Furthermore, frequency doubled NIR solid-state lasers or semiconductor lasers have alternatively been used.

Visible laser sources are of considerable interest for various applications. It is straightforward to use them for laser displays. High-brightness RGB lasers, providing superior color reproduction, are required for entertainment field, such as laser cinema. Short wavelength lasers are advantageous for some medical treatments, suchasthe surgery of retina without affecting the ocular lens [4]. Metals, such as copper and gold, are highly reflective for

NIR light, and this complicates laser processing of the metals with NIR lasers. Visible lasers are expected to improve the processing efficiency of these metals due to their relatively high absorbance in the visible region.

1 1.2. Background 2

1.2 Background

1.2.1 Pump sources

Historically, flash-lamps were mainly employed for optical pumping of laser crystals in 1970s, however, the absorption efficiency of flash lamp pumping is poor due to the limited spectral overlap between theabsorption flash lamps and doped ions, especially rare earth ions. The resulting absorption efficiency of flash-lamp pumping is typically a few percent. Nowadays, pumping with laser diodes (LDs) is a main stream of solid-state lasers.

The emission spectrum of LDs is relatively narrow, and it enables to obtain a good spectral overlap with the absorption lines of rare earth ions, resulting in absorption efficiency more than 80%. It is noteworthy that LDs are recognized as ideal devices enabling efficient electrical-to-optical conversion. Therefore, the direct diode pumping has dramatically improved the efficiency of a total laser system.

For near infrared (NIR) lasers based on RE3+ such as neodymium (Nd3+), erbium (Er3+), and ytterbium

(Yb3+), the optical pumping is accomplished by utilizing gallium arsenide (GaAs)-based LDs emitting in the spectral range of 800–1000 nm (see Fig. 1.1). The fact that high power GaAs LD modules became available has been accelerating the development of these solid-state NIR lasers. Slightly shorter wavelength around 780 nm is achieved with AlGaAs, but the spectral coverage of GaAs-based LDs does not cover the visible region.

LDs in the red wavelength have been demonstrated using the aluminum gallium indium phosphide (AlGaInP) semiconductor, and their emission is typically 630–640 nm [5]. However, the AlGaInP semiconductor cannot cover even shorter wavelength.

Gallium nitride (GaN) is a III-VI semiconductor material enables to generate violet and blue light due to its large direct bandgap. In 1996, Nakamura et al. first reported pulsed laser operation at 405 nmin

InGaN/GaN/AlGaN-based heterostructure at room temperature [6]. Subsequently, the same group succeeded continuous-wave (CW) operation with lifetime as long as 1,000 [7] and 10,000 hours [8] at room temperature.

Finally in 1999, commercially available products of violet InGaN-based LDs were reported [9]. The bandgap of GaN can be controlled between 2.0 to 6.2 eV by mixing indium nitride (InN) and aluminum nitride (AlN) crystals, corresponding to the wavelength of 200–620 nm. Thus, InGaN-LDs potentially cover the wide range of the visible region. The development of InGaN LDs successfully paved the unexploited spectral region, and now, InGaN, AlGaInP and GaAs semiconductor lasers cover from UV to NIR.

Recently, InGaN-based blue LDs around 450 nm have been rapidly progressed for the application of laser displays. In 2013, Masui et al. reported an output power of 3.75 W from a 450-nm InGaN single emitter blue

LD [10]. Nowadays, an output power of ∼5 W is obtained at a current of 3.0 A from a single emitter blue LD around 450 nm [11]. The electrical-to-optical efficiency at 442 nm was higher than 40%. The recent progress of

InGaN-based LDs are summarized in Fig. 1.2. These figures are provided by Nichia Corp. 1.2. Background 3

ArF laser Ar laser HeNe laser Nd3+:YAG laser (193 nm) (488 nm) (633 nm) (1064 nm)

KrF laser Ar laser 3+ Er :fiber laser CO2 laser (245 nm) (514 nm) (1550 nm) (10,600 nm) XeCl laser (308 nm) XeF laser THG SHG (351 nm) (355 nm) (532 nm)

400 nm 700 nm Ultraviolet Visible Infrared

GaN-based AlGaInP-based GaAs-based laser diode laser diode laser diode (630 – 640 nm) (800 – 1000 nm) (400 – 500 nm)

Figure 1.1: Summary of lasers from UV to NIR regions

Even higher power is obtainable by spatially combining several blue LDs. Recently, fiber-coupled modules providing >20-W output power at 450 nm are commercially available for the application of metal processing.

The blue lasers are advantageous for the application because metals have higher absorption coefficient at blue wavelength compared to the NIR. Further power scaling was experimentally demonstrated by combining 64 LDs in free space, and achieved a combined output power of 250 W [12].

Figure 1.2: Evolution of output power of single-emitter InGaN blue LD at 450 nm (left), and wavelength coverage (provided by Nichia Corp.).

In addition to the InGaN-base LDs, technologies of optically pumped semiconductor lasers (OPSLs) opened the way to achieve the visible region. OPSLs are also called optically-pumped vertical external cavity surface emitting lasers (VECSELs). An OPSL consists of an InGaAs semiconductor gain chip and an optical cavity. In the gain chip, a distributed Bragg reflector (DBR) is integrated behind the quantum well gain layers, and which forms one of cavity mirrors. A NIR pump beam is focused on the front surface of the gain chip for the optical pumping. The OPSL technology enabled to cover a broad spectral range from the NIR to the mid-infrared

(MIR) [13]. The gain of InGaAs is typically 800–1000 nm, and therefore the blue and cyan blue spectral range 1.2. Background 4 can be accessed by applying intracavity frequency doubling. Because of the very broad gain spectrum of InGaAs semiconductors, 2ω-OPSLs do not have any limitations in wavelength tunability. The simplified configuration of a 2ω-OPSL is depicted in Fig. 1.3.

Output coupler

BRF

Nonlinear crystal Lens

Highly reflecting Gain chip mirror

Heat sink

Figure 1.3: Schematic of frequency-doubled optically-pumped semiconductor laser (2ω- OPSL).

1.2.2 Visibly emitting solid-state lasers

Many RE3+ have visible radiative transitions, and their energy levels were presented by Dieke et al. [3]. So far, visible lasers with trivalent praseodymium (Pr3+), neodymium (Nd3+) [14], samarium (Sm3+) [15], europium

(Eu3+) [16, 17, 18], terbium (Tb3+) [19, 20], dysprosium (Dy3+) [21, 22, 23], holmium (Ho3+) [24, 25], erbium

(Er3+) [26, 27, 28], and thulium (Tm3+) [29] doped gain media have been demonstrated. In fact, among the 13

RE3+, only cerium (Ce3+), gadolinium (Gd3+), and ytterbium (Yb3+) do not have visible transitions (Ce3+ in garnets exceptionally has a broad visible emission corresponds to 5d → 4f transition). Kränkel et al. presented a comprehensive review on the latest progress of RE3+-doped visible lasers [30]. Although many RE3+ exhibit visible transitions, most of them are spin-forbidden, resulting very small absorption and emission cross sections.

In fact, the visible emissions in Pr3+, Nd3+, Pm3+ (trivalent promethium), Ho3+, and Er3+ are spin-allowed.

In addition, the visible radiative transitions in Er3+ and Ho3+ at ∼540 nm terminate at the ground-state, so the lasers with these ions are three-level systems. Moreover, Pm3+ lasers are practically useless because among the 36 Pm isotopes, only three isotopes have a half-life longer than a year [31]. Consequently, Pr3+ is the only candidate for a four-level laser with large cross sections. Most importantly, Pr3+ lasers can directly be excited by high power blue LDs emitting around 450 nm. These are the reasons why Pr3+-doped solid-state lasers have been extensively studied rather than other ions, so far. 1.2. Background 5

Praseodymium lasers

3+ 3+ The first Pr lasing was reported by Yariv et al. using a Pr :CaWO4 crystal after only two years after the 3+ invention of the ruby laser [32]. The Pr :CaWO4 was pumped by a Xe flash lamp and oscillated at 1046.8 nm. However, the demonstrations of visible lasing were reported ∼30 years later. Allain et al. first demonstrated

3+ a continuous-wave (CW) visibly emitting Pr :ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF) fiber laser in 1991 [33]. They realized lasing at 610, 635, 695, 715, 885 and 910 nm with the pump source of an argon (Ar) gas laser at 476.5 nm. In the same year, Smart et al. demonstrated a Pr3+:ZBLAN fiber laser oscillating at 491, 520,

605, 635, and 715 nm. Visible lasing in Pr3+-doped bulk medium at room temperature was first reported by Sandrock et al. [34]. Since the invention of InGaN-based blue LDs, the absorption band of Pr3+ around

450-nm has been directly addressed. The first diode-pumped visible laser was realized by Richter et al. in

Pr3+-doped yttrium lithium fluoride (YLF) pumped by a 25-mW blue LD [35]. Subsequently, Hashimoto et al. reported a power scaling of the diode-pumped Pr3+:YLF laser up to >100-mW output at 639 nm using a

500-mW blue LD [36]. Moreover, Richter et al. first adopted a2ω-OPSL at 479 nm for pumping of Pr3+:YLF laser [37]. In last decade, many groups reported efficient visible3+ Pr lasers with fluoride host media, such as YLF [35, 37, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46], LLF (LiLuF4) [37, 38], LiGdF4 [38], KYF (KY3F10)

[47], BYF (BY3F10) [45], LaF3 [48], and ZBLAN [49, 50, 51] and AlF3 [52, 53, 54, 22] glasses. The use of the fluoride hosts are advantageous because of their small phonon energy. Owing to the relatively small energygap

3 1 between the upper laser level P0 and the underlying D2 level, the multiphonon relaxation leads to depopulate 3+ the upper laser level in host media of moderate phonon energy. Pr doped in Y3Al5O12 (YAG) crystal, a common crystalline oxide laser host, exhibits the fluorescence lifetime of ∼8 µs [55], while the lifetime in fluorides is typically longer than 30 µs. However, fluoride crystalline hosts in general not suitable forhigh power operation due to their poor thermal and mechanical properties compared to oxide hosts. For instance, the thermal conductivity of YLF crystal is approximately half of YAG crystal. Very recently, hexaaluminate crystals, such as SrAl12O19 [56, 57, 58, 59], CaAl12O19 [60], LaMgAl11O19 [61], and Sr1-xLaxMgxAl12-xO19 [62] were recognized as good host materials for Pr3+, because those simultaneously satisfy the requirement of low phonon energy and good thermal and mechanical properties.

So far, the most successful laser performances have been obtained with Pr3+:YLF crystal as a gain medium.

Metz et al. demonstrated the high power continuous-wave operation of Pr3+:YLF laser at 523, 546, 604, 607,

640, 698, and 720 nm using a 479-nm 2ω-OPSL providing 5-W pump power, and obtained >1-W output for all the operated wavelengths [44]. The highest output power at 523 nm was achieved by Ostroumov et al. They realized 4.3 W output from a Pr3+:YLF laser double-end-pumped by two 479-nm 2ω-OPSLs. Using an InGaN blue LD module delivering ∼8-W pump power, Luo et al. achieved efficient lasing with Pr3+:YLF at 523, 604,

607, 640, 698, and 720 nm [46].

3+ Fibrich et al. made large efforts on diode-pumped Pr :YAlO3 (YAP) lasers [63, 55, 64, 65]. They found out that 1.2. Background 6

YAP is a good crystalline host for Pr3+-doping, and suitable for high power operation due to its high thermal conductivity (>11 Wm−1K−1) and excellent hardness (Mohs scale: 8.5–9) [63]. The phonon energy in YAP is relatively small compared to in YAG, and the fluorescence lifetime of 3+a Pr :YAP crystal of 0.6 at.% doped concentration was measured to be 13.8 µs [55]. At the emission wavelength of 747 nm, the slope efficiency with respect to the absorbed pump power higher than >40% was recorded. They also achieved a green laser emission at 547 nm with a cryogenically cooled laser crystal [65]. Very recently, Liu et al. performed a spectroscopy and a Judd-Ofelt analysis of a Pr3+:YAP crystal, and showed that it has a very large emission cross section at

∼620 nm for the polarization parallel to the crystal’s b-axis [66].

3+ 2+ 3+ The first visible laser operation with Pr , Mg :SrAl12O19 (Pr :SRA) was reported by Merkle et al. [56]. They used a 466-nm dye laser as the pump source, and demonstrated a red laser at room temperature and a cyan-blue laser at cryogenic temperature. The diode-pumping was first reported by Fechner et al. in 2011 [57].

By utilizing a 1-W InGaN blue LD, they achieved CW laser operation at 643.5 nm with a slope efficiency of

47%. In 2012, Reichert et al. performed the laser experiments at 525.3, 622.8, 643.6, and 724.4 nm at room temperature using a 486-nm 2ω-OPSL [48]. The Pr3+:SRA exhibited a suppressed concentration quenching, because of its low cation density. Therefore, high doping is possible without affecting the upper state lifetime.

Moreover, since the absorption band around 445-nm of Pr3+:SRA is relatively broad, it does not require a severe wavelength control of pump diodes. By fully benefiting these characteristics, Voss et al. demonstrated the first thin-disk Pr3+:SRA laser pumped by twenty four 1-W InGaN blue LDs [58].

In addition to Pr3+-doped bulk crystalline lasers, several reports on Pr3+-doped fluoride fiber lasers could be found. The first report was from Smart et al. that a 250-mW output at 635 nm with a Pr3+:ZBLAN glass fiber pumped by an argon laser [67]. Richter et al. also demonstrated the lasing at 635 nm with a 2ω-OPSL

[49]. It is well-known that the ZBLAN glass exhibits high water solubility resulting an unreliable practical use.

Fujimoto et al. developed a water proof fluoroaluminate glass (WPFG) fiber for better chemical stability [22], and experimentally demonstrated an efficient operation of3+ Pr -doped WPFG fiber laser [54, 53].

1.2.3 Ultraviolet solid-state lasers

Conventionally, UV lasers have been achieved by means of high harmonic generation of NIR lasers, including frequency-tripled 355-nm Nd3+-based lasers. In general high peak power lasers are used to obtain a high conversion efficiency, therefore Q-switched or mode-locked NIR lasers have been utilized for high harmonic generation (HHG). Thus, efficient CW UV lasers were challenging.

Lasers directly emitting in the visible region have an advantage to reach the UV region via a single frequency conversion, while NIR lasers need more than two conversion steps to reach the UV (see Fig. 1.4). It is significantly important that visible lasers can directly be extended to UV lasers by means of intracavity second harmonic 1.2. Background 7 generation (SHG). In this scheme, laser systems do not require an additional conversion stage. It is noteworthy that CW UV lasers are difficult to achieve as frequency-converted NIR solid-state lasers, since multiple frequency conversion steps generally require pulsed laser with high conversion efficiency. Thus, intracavity SHG of visibly emitting lasers is the only way to get efficient CW UV source. Up to now, novel solid-state UV lasers havebeen demonstrated by applying the intracavity frequency doubling to visibly emitting Pr3+ lasers. Furthermore, the use of visible lasers are beneficial to reach the deep UV region. For instance, 213-nm deep UV pulses, which have been generated by means of fifth-harmonic of 1064-nm Q-switched Nd3+ lasers, can be accesses as the third harmonic of red-emitting lasers, such as Pr3+ lasers (see Fig. 1.4).

Richter et al. presented an efficient 320-nm UV generation from a2ω-OPSL-pumped Pr3+:YLF and BYF lasers with a lithium triborate (LiB3O5: LBO) chosen as a nonlinear crystal [68], and achieved 19-mW CW output power at 320 nm with ∼9% optical-to-optical efficiency from the absorbed pump power. A year later, they succeeded the power scaling up to 364 mW and 262 mW using Pr3+:YLF and LLF crystals, respectively.

Furthermore, the SHG of green emission enabled to reach the deep UV region. Gün et al. first demonstrated intracavity frequency doubling of a diode-pumped Pr3+:YLF laser at 523 nm using a β-barium-borate (BBO), and obtained a 481 mW CW output power at 261.3 nm [69]. The further power scaling up to >1-W output at

261 nm was reported by Ostroumov et al. [39].

Q-switched Nd3+ laser

Nonlinear crystal

SHG SFG 355 nm 1064 nm Nd3+-doped 532 nm crystal Q-switch SHG SHG SFG 213 nm 266 nm Intracavity frequency doubling Pr3+ laser

SHG ~320 nm ~260 nm Pr3+-doped Nonlinear crystal crystal

Q-switched Pr3+ laser

640 nm SHG SFG 213 nm Pr3+-doped 320 nm crystal Q-switch

Figure 1.4: Schematic structures of conventional Nd3+-based and Pr3+-based UV lasers. 1.2. Background 8

1.2.4 Saturable absorbers for passive Q-switching and mode-locking of visible lasers

A saturable absorber is an optical component in which the transmission reduces at high optical intensity.

Saturable absorbers or effective saturable absorber actions, e.g. Kerr-lens with an aperture, are responsible for pulsed operations of lasers, i.e. Q-switching and mode-locking. Q-switching is categorized into active or passive.

Active Q-switching is accomplished by using an electronically controlled active devices, such as a Pockels cell and an acousto-optic modulator (AOM). For driving these active Q-switching components, external high-voltage source (for Pockels cell) or radio frequency (RF) oscillator is necessary. On the other hand, passive Q-switching is accomplished simply by inserting a saturable absorber into an optical resonator, and basically any external power supply is not required (that is why called “passive”).

Techniques of passive Q-switching was well established for NIR lasers including Nd3+-, Yb3+-, and Er3+-based solid-state lasers. However, there are only a few media recognized as saturable absorbers in the visible region, since visibly emitting lasers have only recently been developed. The saturable absorbers which can be used in the visible region reported so far are summarized in Table 1.1. 1.2. Background 9 2 – – [78] Black phosphorus ∼ 500 GW/cm – – Gold nanoparticle – QD [76] [77] Low CdTe/CdS ) 2 2 2 , MoS 2 [75] ∼ mJ/cm 2D-materials ∼ 1.5 GW/cm (e.g. WS 2 >GW/cm 2 ∼ 100 mJ/cm 2 able 1.1: Reported saturable absorbers in the visible region. :spinel SESAM Graphene T [71] [72, 73] [74] 2+ ∼ MW/cm 2 AG Co :Y [70] 4+ Cr ∼ 20 kW/cm Operation References Saturation Recovery time 4–5 µs >450 ns <10 ps sub-ps a few ps sub-ps – tensity or fluence wavelength (nm) 600–650 520–670 >600 Broadband Broadband Broadband <600 Broadband Damage threshold High High Low High in 1.2. Background 10

4+ 2+ Q-switching or mode-locking of visible lasers have been demonstrated by Cr :Y3Al5O12 (YAG) [70], Co :

MgAl2O4 spinel [71], semiconductor saturable absorber mirror (SESAM) [72, 73], graphene [74], transition- metal dichalcogenides including WS2, and MoS2 [75], CdTe/CdS-based quantum dots [76], gold nanoparticle [77], and black phosphorus [78]. Cr4+:YAG is a popular saturable absorber for 1-µm lasers, and its saturation properties have extensively been studied by many groups [79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89]. It is well- known that this saturable absorber enabled to generate high peak power pulses from a Nd3+:YAG/Cr4+:YAG microchip [90, 91, 92]. Recently, the saturation in the visible region was observed and passive Q-switching of a diode-pumped Pr3+:YLF laser at 640 nm was demonstrated [93, 70]. The detailed saturation characteristics of

4+ 2+ Cr :YAG in the visible region is dealt in this thesis. Divalent cobalt ion (Co )-doped MgAl2O4 (MALO) has been recognized as a saturable absorber for 1.5-µm lasers mainly based on Er3+-doped media [94, 95]. Demesh

2+ et al. first reported that the visible absorption in divalent cobalt ion(Co )-doped MgAl2O4 (MALO) can be bleached, and demonstrated a passively Q-switched Pr3+:YLF laser at 523, 607, and 640 nm [71]. SESAM is a semiconductor based passive optical element [96], and its saturation parameters can be controlled. The technologies of SESAM have been developed for NIR lasers using GaAs-based semiconductors [96]. Recently, by utilizing a GaInP-quantum well-based SESAM, passive mode-locking of red Pr3+:YLF lasers pumped by a 2ω-OPSL [72] and InGaN blue LDs [73] were reported. In addition ot GaInP, CdTe/CdS quantum dots were recognized as good candidates of visible saturable absorbers. Xu et al. applied this quantum dots to a

Q-switched Pr3+:YLF laser at 607, 640, and 720 nm, and obtained <300-ns pulses [76]. Graphene theoretically shows saturable absorption due to its zero-bandgap energy structure. The saturable absorption in graphene can be explained by the electronic transition between the valence band and the conduction band. The saturation intensity theoretically increases for shorter wavelength, the application of the graphene saturable absorbers have mainly been limited to NIR lasers such as Nd3+ and Yb3+-based laser at 1 µm [97, 98, 99, 100], Er3+ lasers at

1.5 µm [101, 102, 103, 104], and Tm3+-based lasers at 2 µm [105, 106]. However, the graphene saturable absorber can be even shorter wavelength. Mode-locking of Ti:sapphire laser generating 70-fs pulses was reported by Baek et al. [107], and Kajikawa et al. reported passive Q-switching of Pr3+:WPFG laser [74]. Two dimensional transition-metal dichalcogenides (TMDs) such as WS2, MoS2, and MoSe2 are recently recognized as broadband saturable absorbers owing to their unique optical properties. Layered TMDs have direct bandgap in the visible region, and Luo et al. demonstrated the first passively Q-switched Pr3+:ZBLAN fiber laser with TMDs in polyvinyl alcohol (PVA) film at 635 nm [75]. Moverover, Li et al. reported the passively Q-switched visible

3+ fiber laser at 607 nm [108]. Furthermore, Zhang et al. demonstrated passive mode-locking of a Pr :LiGdF4 ∼ laser at 523, 607 and 640 nm generating 50-ps pulses using MoS2 layers [109]. In addition to the above mentioned saturable absorbers, gold nanoparticle and black phosphorus were applied to passive Q-switching of a Pr3+ fiber laser at 635 nm [77, 110]. 1.3. Objective 11

1.3 Objective

This study aims to establish Pr3+ visible laser technologies for profiting high power InGaN blue LDs. The development of high power blue LD modules has been significantly progressing. Currently, by combining 64 single-emitter blue LDs, a 250-W module was reported [12]. By using blue LD arrays or stacks together with combining techniques, high power modules providing more than kilowatt output power are expected to be soon realized. Therefore, blue-diode-pumped solid-state laser technologies need to be developed for profiting the future kilowatt-level pump sources. Moreover, blue LDs can potentially replace blue LEDsin the lightning application, since the electrical-to-optical efficiency of LEDs sharply drops at high-current level, so-called “efficiency droop.” Even though the efficiency of blue LEDs at low-current levelis ∼70%, it decreases down to <20% at an input power density of a few kilowatts per square centimeter. Thus, blue LEDs require large areas of expensive semiconductors for scaling. On the other hand, the efficiency of blue LDs is constantly

∼30% at high current level [111]. If blue LED-based lighting equipment will be replaced by blue LD-based one, the cost of blue LDs will dramatically be reduced by the mass production. Therefore, blue-diode-pumped solid-state lasers will potentially be the cheapest coherent light sources in the future.

This work focuses on the demonstration of a high power CW operation and passive Q-switching of visibly emitting Pr3+ lasers with the crystalline host of YLF, the most efficient host material 3+for Pr doping. High power laser experiments were performed to clarify limitations and further scalability. In addition to the CW operation, passively Q-switched Pr3+:YLF lasers are experimentally examined. Even though passive Q-switching is well-established technology in the NIR region, saturable absorbers in the visible region are limited. A variety of transition-metal-doped oxide crystals were investigated as saturable absorbers in the visible region, and some of them were applied for Q-switched Pr3+:YLF lasers. Pr3+-doped gain media are not capable to generate high energy pulses by Q-switching due to their relatively short fluorescence lifetime; instead, Q-switched Pr3+ lasers can be operated at high repetition rate with moderate pulse energy. The work on the investigation of novel transition-metal-doped solid-state saturable absorbers will be applied to the development of high-energy passively Q-switched visible lasers based on rare earth ions with spin-forbidden transitions, such as Eu3+ and

Tb3+, exhibiting millisecond lifetime. The Pr3+:YLF lasers in CW and passive Q-switching operations were further extended to UV directly by applying intracavity second harmonic generation.

Structure of thesis

Chapter 2 gives the theoretical background of spectroscopy and laser physics required for this study. Chapter 3 describes CW Pr3+:YLF visible lasers. The details of the pump sources and laser crystals used in this study are also presented. Chapter 4 is devoted to the experimental characterization of various transition-metal-doped 1.3. Objective 12 visible saturable absorbers. Experiments of passively Q-switched Pr3+:YLF lasers are described in Chapter 5 together with rate equation based numerical simulations. Frequency doubled and tripled Pr3+ lasers operated in the UV region are presented in Chapter 6. Conclusions of the thesis are presented in Chapter 7. Figure 1.5 schematically illustrates the structure of this thesis.

Chapter 1 Introduction

Chapter 2 Fundamentals

Chapter 3 Continuous-wave Chapter 4 Characterization of transition- Pr3+:YLF visible lasers metal-doped saturable absorbers

Chapter 5 Passive Q-switching of Pr3+:YLF visible lasers

Chapter 6 Frequency conversion of Pr3+:YLF lasers for ultraviolet generation

Chapter 7 Conclusion

Figure 1.5: Schematic view of thesis structure. Chapter 2

Fundamentals

In this chapter, a brief introduction to theoretical background related to this work is described. The following fundamentals are based on some textbooks [112, 113, 114].

2.1 Energy structure of rare earth and transition metal ions in solid

hosts

Solid-state lasers are based on crystals, glasses or ceramics in which rare earth or/and transition metal ions are doped. The energy levels of the doped ions undergo the influence of crystal field. It is convenient to introduce to review the interactions responsible to determine energy levels of a free ion. The descriptions for a free ion is further extended for an ion in a solid host.

2.1.1 Energy levels in a free ion

The energy eigenvalues of electronic systems are given by the time-independent Schrödinger equation as follows:

Hˆ |Ψ⟩ = E |Ψ⟩ , (2.1) where Hˆ is the Hamiltonian, E the energy of the system, and Ψ the wave function representing the state of electron. By ignoring the relativistic effects of moment, the Hamiltonian for an isolated ion containing N ′ electrons is written in the form:   ′   ∑N ℏ2 Ze2 ∑N e2 Hˆ = − ∇2 − + , (2.2)  2m i 4πε r 4πε r  i=1 e 0 i j>i 0 ij

13 2.1. Energy structure of rare earth and transition metal ions in solid hosts 14

where Z is the atomic number, e the electron charge, me the electron mass, ri the distance between the i-th electron and the nucleus, and rij the distance between i-th and j-th electrons. The terms on the right hand respectively represent the kinetic energy, Coulomb potential in the field of the nucleus, and electron-electron repulsion. Due to the third term, it is not possible to decompose the Hamiltonian of N ′-electron system into

N ′ equivalent single-electron systems. It is not feasible to solve directly Eqs. (2.1) and (2.2) due to its huge computational cost. Once it is realized that a large part of the electron repulsion (third term in Eq. (2.2)) is in the radial direction, an effective centrosymmetric potential V0(ri) is introduced. This potential depends only on the radial distance from the nucleus. Then, the Hamiltonian given by Eq. (2.2) is modified as follows:

Hˆ = Hˆ0 + Hˆre, (2.3) where ′ { } ∑N ℏ2 Hˆ = − ∇2 + V (r ) , (2.4) 0 2m i 0 i i=1 e   ′  ′  ∑N Ze2 ∑N e2 Hˆ = − + − V (r ) . (2.5) re  4πε r 4πε r 0 i  i=0 0 i j>i 0 ij

Hˆ0 is the centrosymmetric field Hamiltonian, and Hˆre the residual electrostatic interactions. Here, one assumes that the residual electrostatic interaction is sufficiently small so that one can treat it as a perturbation to Hˆ0. It is then clear that the Schrödinger equation can be decomposed into single-electron systems. The wave function

Ψ is now considered as a product of single electron wave functions ψ0(ri) as follows:

Ψ(r1, r2, r3,..., rN ) = ψ0(r1)ψ0(r2)ψ0(r3) . . . ψ0(rN ′ ) (2.6)

The single electron wave function is a solution of the single-electron Schrödinger equation given by

Hˆ0ψ0(ri) = Eiψ0(ri). (2.7)

It is well-known that the solutions under the central potential given by Eq. 2.4 are of the form

ψ (r ) = R (r )Y mi (θ, ϕ), (2.8) 0 i ni,li i li where R (r ) is the radial part of the wavefuction, and Y mi (θ, φ) the well-known spherical harmonic function. ni,li i li ni and li are the principal quantum number and the orbital angular momentum quantum number, respectively.

A set of the quantum numbers ni, li gives an electronic configuration.

So far the non-centrosymmetric residual electrostatic interaction and other interactions has been ignored. The largest in the ignored interactions is the spin-orbit interaction which arises from the interaction between the 2.1. Energy structure of rare earth and transition metal ions in solid hosts 15 magnetic dipole moment of an electron and the magnetic field. The electron experiences the magnetic field when the electron moves in the electric fields due to the nucleus and other electrons. The Hamiltonian forthe spin-orbit interaction for a single electron is written in the form:

Hˆso = ξ(ri)li · si, (2.9)

where ξ(ri) is the function of the position of the electron, and li and si are respectively the orbital and spin angular momenta of the electron. The resulting Hamiltonian Hˆion is then written as follows:

Hˆion = Hˆ0 + Hˆre + Hˆso, (2.10)

The neglected interactions, the residual electrostatic interaction and the spin-orbit interaction, are then treated as perturbations of the centrosymmetric field Hamiltonian (Eq. (2.4)).

Once ions are incorporated in a solid, one needs to take into account an interaction with neighboring ions, so-called crystal field. The Hamiltonian of the crystal field interaction Hˆcf is written in the form:

Hˆcf = −eVcf , (2.11)

where Vcf is the electrostatic potential of the crystal field. The interaction with crystal field in general leadsto splitting and shifting of energy levels from their position in the case of free ions, so called the Stark effect. The crystal field has a symmetry generally designated by an irreducible representation given by group theory[115].

The following three cases can be considered regarding the strength of the crystal field compared to that of the spin-orbit and residual electrostatic interactions.

ions is considered to be small. Because of the small shifting and splitting of energy levels, one can still

label the manifolds by the terms for the free ions. Energy levels of 4f configurations of rare earth ions are

categorized into this case, further presented in Section 2.1.2.

account as a perturbation on the terms formed by the residual electrostatic interaction. The spin-orbit

interaction further leads to splitting and shifting of energy levels. For the intermediate field, one can no

longer label the energy levels neither by Russel-Saunders notation nor the irreducible representations of

group theory.

actions only act as small perturbations on the energy levels formed by the crystal field interaction. The

energy levels formed by the interaction reflect the symmetry of the crystal field. The levels are labeledby

irreducible representation of group theory. This strong field approximation is applied to energy levels of

3d configurations of transition metal ions, further presented in Section 2.1.3.

2.1.2 Energy structure of 4f n orbital of rare earth ions

Atoms with the atomic number from Z = 57 (lanthanum: La) to Z = 71 (lutetium: Lu) are called lanthanides.

Because scandium and yttrium have similar chemical properties with the lanthanides, the two ions are often categorized into a same group as lanthanides, called rare earths. Lanthanides typically form triply ionized states in doped solids. Therefore lanthanides atoms lose three outer shell electrons or chemical bonding. Trivalent lanthanides have electronic configurations of [Xe](4f)n where [Xe] = 1s22s22p63s23p63d104s24p64d105s25p6 is the electronic configuration of xenon. Consequently, trivalent lanthanides have only an unoccupied 4f orbital, and transitions in this orbital contribute to laser actions. It is noteworthy that rare earth ions also have electrons in outer shells, such as 5s and 5p shells. The outer shell electrons electronically shield the 4f shell from external fields, so an influence of crystal field on the energy levelsof 4f electrons is relatively weak. Thus, this is the situation corresponding to the weak field case. Consequently, the spin-orbit interaction term is dominant over the crystal field term of the Hamiltonian. As mentioned in Section 2.1.1, one can still use the notationfor free ions to designate energy levels. For designating energy terms, capital letters with a system of superscripts

2S+1 and subscripts are used for spectroscopy. The symbol characterizing a term is written as LJ , where L is the total orbital angular momentum quantum number, S is the total spin angular momentum quantum number, and J is the total angular momentum quantum number given by J = L + S. The total orbital angular momentum quantum number L are expressed by the capital letters S, P, D, F, G, H, I, A, … corresponding to

L = 0, 1, 2, 3, 4, 5, 6, 7,... and this notation is conventionally used in spectroscopy. The left sided superscript

2S + 1 represents the multiplicity of the term due to possible orientation of the resultant spin S. For instance, a one-electron system, corresponding to S = 1/2, has a multiplicity of 2. Using this spectroscopic notation of energy terms, 4f n energy structures are represented. For trivalent rare earth ions, their number of 4f electrons and notation of ground-states are summarized in Table 2.1.

2S+1 The energy terms labeled by LJ are further undergone a slight shift in the energy and splitting owing to the effect of the crystalline field. According to the degeneracy of the energy terms, the maximum numberof

2S+1 split component for each LJ state is 2J + 1. The actual number of split components is given by take into account the local symmetry of the doped ion. 2.1. Energy structure of rare earth and transition metal ions in solid hosts 17

Table 2.1: Number of 4f electrons and ground-state notation of trivalent rare earths ions from atomic number of 58 to 71.

Atomic number Z Trivalent rare earth, RE3+ Number of 4f electrons Notation of ground-state 3+ 2 58 Cerium, Ce 1 F5/2 3+ 3 59 Praseodymium, Pr 2 H4 3+ 4 60 Neodymium, Nd 3 I9/2 3+ 5 61 Promethium, Pm 4 I4 3+ 6 62 Samarium, Sm 5 H5/2 3+ 7 63 Europium, Eu 6 F0 3+ 8 64 Gadolinium, Gd 7 S7/2 3+ 7 65 Terbium, Tb 8 F6 3+ 6 66 Dysprosium, Dy 9 H15/2 3+ 5 67 Holmium, Ho 10 I8 3+ 4 68 Erbium, Er 11 I15/2 3+ 3 69 Thulium, Tm 12 H6 3+ 2 70 Ytterbium, Yb 13 F7/2 3+ 1 71 Lutetium, Lu 14 S0

2.1.3 Energy structure of 3dn orbital of transition metal ions

Transition metal ions have frequently been used as dopants for tunable solid-state lasers and saturable absorbers.

Atoms designated by the term “transition metal” are varied due to its several possible definitions. In the context of laser physics, the term typically designates atoms with the atomic number from Z = 21 (scandium: Sc) to

Z = 30 (zinc: Zn). They have an unoccupied 3d shell when ionized. Optical transitions take place between the energy levels in the orbital. It should be noted that the 3d orbital of the transition metals is the outermost shell. Consequently, the energy structure of the 3d orbital undergoes a strong influence of the crystal field due to the lack of outer electrons for electronic shielding as 4f-shell of RE ions.

In a doped crystal, the transition metal ions form different valence states depending on their substitution sites. In most cases, the transition metals prefer to form divalent, trivalent or tetravalent states. Number of 3d electrons and ground-states of divalent, trivalent and tetravalent transition metals in the case of free ion are summarized in Table 2.2. For 4f n levels of rare earth ions, an external crystal field can be considered as a perturbation

2S+1 of each LJ levels. On the other hand, the crystal field is stronger than the spin-orbit interaction for 3d

2S+1 electrons so that one can no longer label energy levels by the notation of LJ . As mentioned in Section 2.1.1, the energy levels of 3d electrons of transition metal ions in solids are designated by irreducible representation given by group theory [115]. An applied crystal field splits and shifts the degenerated energy terms, andthe energy position after applying the crystal field strongly depends on the local site symmetry and the crystal field strength.

The energy shifting and splitting are simply described for one 3d-electron case, such as Ti3+ and V4+. Let assume an ion with one 3d-electron in an octahedral site (see Fig. 2.1). For the 3d1 state, five-fold degenerated 2.1. Energy structure of rare earth and transition metal ions in solid hosts 18

Table 2.2: Number of 3d electrons and ground-state notation of divalent, trivalent and tetravalent transition metal ions. Notation of ground-state is for the case of no crystal field.

Transition metal Number of 3d electrons Notation of ground-state Divalent Trivalent Tetravalent – Ti3+ V4+ 1 2D Ti2+ V3+ Cr4+ 2 3F V2+ Cr3+ Mn4+ 3 4F Cr2+ Mn3+ Fe4+ 4 5D Mn2+ Fe3+ Co4+ 5 6S Fe2+ Co3+ Ni4+ 6 5D Co2+ Ni3+ Cu4+ 7 4F Ni2+ Cu3+ Zn4+ 8 3F Cu2+ Zn3+ – 9 2D orbitals are form in the case of free ion. The form of the orbitals are the spherical harmonic functions given

ml − − by Yl with l = 2 and ml = 2, 1, 0, 1, 2. The orbitals dz2 and dx2−y2 are directed to the ligands in the octahedral site, so these orbitals undergo a stronger electrostatic potential than orbitals dxy, dyz, dxz directed between the ligands. Consequently, the originally five-fold degenerated multiplet splits into a triplet2g stateT and a doublet state Eg. Their energy shift depends on the crystal field parameter Dq. The energy splitting of 1 the d electron in typical symmetries, octahedral (Oh), tetrahedral (Td) and cubic, are shown in Fig. 2.1. The crystal field strength Dq for the tetrahedral and octahedral symmetries are related to that for the octahedral symmetry. Assuming the same distance between the central ion and ligands for these symmetries, the relation between the crystal field strengths are as follows:

9 9 Dq = − Dq = Dq . (2.12) oct 4 tet 8 cube

The crystal field splitting in the tetrahedral and cubic symmetries are smaller than that in the octahedral symmetry. The minus signs in the equation indicates that the triplet state T2g is the higher lying level in the tetrahedral and cubic symmetries.

The case of ions with more than one 3d electrons is complicated, because the electron-electron interactions must be taken into account. Tanabe and Sugano calculated the energy of the state of 3dn ions (n = 2 − 8) as a function of the crystal field for octahedral coordination, so-called Tanabe-Sugano diagram. The diagram is useful to interpret absorption and emission spectra of transition metal ions in a variety of crystalline hosts. The

2S+1 Tanabe-Sugano diagram shows how the energy terms LJ split and shift as a function of parameter Dq/B, where Dq is the crystal field strength, and B the Racah parameter. 2.1. Energy structure of rare earth and transition metal ions in solid hosts 19

Octahedral Tetrahedral Cubic

z y

x Eg

T2g 6Dqoct T2g 4Dqcube 4Dqtet

6Dq 4Dqoct tet 6Dqcube Eg T2g

Figure 2.1: Arrangement of ligand ions (black spheres) surrounding a central ion (gray sphere) and crystal field splitting of d1 electron in different symmetries.

2.1.4 Selection rules

The probability of a transition depends on the electric dipole matrix element µif given as follows:

⟨ | | ⟩ µif = Φf µe Φi , (2.13)

where Φi is the initial state, Φf the final state, µe the electric dipole moment operator given by er. Transitions induced by interactions of the electric dipole element with the incident optical electric field are so-called electric dipole transitions. Thus, electric dipole transitions happen when the matrix element µif is not zero. Since the operator er has odd parity, the matrix element µif is not zero only when the initial and final states of transition have the opposite parity, well-known as Laportes selection rule. It should be noted that optical centers in some crystals do not rigorously obey this rule.

Even though a transition is forbidden by an electric dipole process, it is still possible by a magnetic dipole process. Transitions induced by interactions of the ion with the incident magnetic field are so-called magnetic dipole transitions. For magnetic dipole transition, the matrix element µif is given as follows:

⟨ | | ⟩ µif = Φf µm Φi , (2.14)

where µm is the magnetic moment operator given by µm = e2m(l+2s). Magnetic dipole transitions are allowed only when the initial and final states of transition have the parity, since the magnetic moment operator has 2.2. Interaction of light and matter 20 even parity. Thus, a forbidden electric dipole transition is allowed by a magnetic dipole process, and vice versa.

However, magnetic dipole transitions are much weaker than electric dipole transitions by a factor of ∼ 105.

For the radiative transitions of rare earth ions, 4f-electrons are responsible, and their energy terms are in general

2S+1 labeled by LJ as mentioned in Section 2.1.2. Because the initial and final states of 4f − 4f transitions have the same parity, electric dipole transitions are prohibited according to Laportes selection rules. However, according to the Judd-Ofelt theory [116, 117], a part of the 5d wavefunctions are added to the 4f states of ions in non-inversion symmetric sites, and therefore, the matrix elements do not vanish. The resulting electric dipole transitions are subject to the following selection rules:

• ∆l = 1,

• |∆S| = 0,

• |∆L| ≤ 2l,

• |∆J| ≤ 2l, except J = 0 → J = 0.

The above mentioned selection rules are further modified by crystal field. The consideration of local symmetry of optical centers are important to understand optical transitions of 3d electrons of transition metal ions, and polarization dependent transitions.

The initial and final states of a transition belong to the irreducible representations, Γi and Γf in the group symmetry of the optical center. These irreducible representations are used to label the energy levels associated with these states. This labeling is usually used for energy terms of 3d electrons of transition metals. The selection rules are well-established by the group theory as follows:

• The matrix elements are nonzero only if the direct product Γi × Γµ contains the irreducible representation

Γf .

Here, Γµ is the irreducible representation that the moment operator µ belongs to. The above mentioned rule is simply equated as follows:

Γi × Γµ ⊂ Γf . (2.15)

2.2 Interaction of light and matter

When light is irradiated to a matter, light undergoes several interactions, including reflection, refraction, scattering and absorption. In addition to absorption, other inelastic interactions (interactions in which energy is not conserved) between light and matter should be introduced to understand the laser process. There are three 2.2. Interaction of light and matter 21 inelastic processes between light and matter; absorption, spontaneous emission, and stimulated emission. As laser is the acronym of light amplification by stimulated emission of radiation, the last process is essential for laser process.

In laser processes, light interacts with ions. Before introducing the three processes, an ideal two-level system is first considered. The two-level system describe a ground state E1 and an excited state E2 of an ion, where the energy separation between the levels is ∆E = E2 − E1. When a photon with energy hν is irradiated to an ion in the ground state, and if the photon energy is equal to ∆E (∆E = hν), absorption happens with a certain probability. This process is sometime also called stimulated absorption. Here, the photon energy is given by the Planck’s constant h and photon’s frequency ν. Once the absorption happens, the ion is lift from the ground state to excited state. This process is illustrated in the left hand of Fig. 2.2. Because an ion in the ground state absorbs the photon, this is called ground state absorption (GSA), and furthermore, the probability of GSA is characterized by its ground state absorption cross section σgs. Since a two-level system is described here, there is no energy state above the excited state, but if multiple energy level system is assumed an absorption from the excited state to other higher lying levels can happen. This is called excited state absorption (ESA). Ions practically have more than three energy levels, so the ideal two-level system is not realistic. The excited ion

E2 E2 E2

E1 E1 E1

Spontaneous Stimulated Absorption emission emission

Figure 2.2: Illustration of absorption (left), spontaneous emission (center), and stimulated emission (right) in ideal two-level system. cannot permanently remain in the upper level. The excited ion relaxes to the ground state by releasing its energy ∆E. Assuming that phonon-induced relaxation and interionic processes do not take place, the energy is released as an emitted photon. Again, the photon energy is equal to the energy difference between the levels ∆E.

This process is called spontaneous emission depicted as center of Fig. 2.2. The relaxation rate with spontaneous emission is given by 1/τR, the inverse of radiative lifetime τR. This description is based on classical theory, but in quantum theory, spontaneous emission is considered as stimulated emission due to the vacuum fluctuation.

Stimulated emission is described below. It is noteworthy that the parameters of emitted photon, including wave vector, polarization, and phase are random. Assuming the situation that an ion is in the excited state, when a photon of energy ∆Eis irradiated to the excited ion, the photon induces the ion to emit a photon of the same energy ∆E. This process is called stimulated emission. The photon generated through this process can be seen 2.3. Laser principles 22 as a copy of the incoming photon, because all the parameters, frequency or wavelength, wave vector, phase, and polarization, are same. Therefore, the stimulated emission provides a phase-coherent amplification. The proof of this fact is beyond the scope of this section, and for the understanding, a quantum mechanical treatment of light-matter interaction is required.

2.3 Laser principles

A laser consists of two components; a gain medium which enables light amplification and an optical resonator.

In short, there are two requirements to obtain laser oscillation. First requirement is that a gain medium has an optical gain. The second requirement is that the optical gain of a system becomes higher than losses of the optical resonator. In this subsection, a general description of conditions to obtain lasing, and detailed mathematical modeling of four-level lasers are presented.

2.3.1 Two-level system

As presented in the previous section, stimulated emission is essential for light amplification. Here, a conditions to obtain the light amplification are presented. The three processes of light-matter interactions, stimulated absorption, spontaneous emission, and stimulated emission, result in temporal evolution of the population in the energy levels. Transition rate of these processes are characterized by Einstein’s A and B coefficients. Here, the population per unit volume, or population density, in the ground and excited state of the ideal two-level system (illustrated in Fig. 2.2) are respectively written as N1 and N2.

The absorption rate is proportional to the incoming photon energy density ρ(ν) and the population density in the ground state N1. The temporal evolution of the ground and excited state population density due to the stimulated absorption written as the following equation:

∂N ∂N − 1 = 2 = B ρ(ν)N . (2.16) ∂t ∂t 12 1

3 2 The coefficient B12 is called Einstein’s B coefficient in [cm /(s ·J)]. The transition rate due to the spontaneous emission is independent of the applied electric field and given by the equation:

∂N ∂N 1 = − 2 = A N . (2.17) ∂t ∂t 12 2

−1 The coefficient A12 is called Einstein’s A coefficient in [s ]. This differential equation is easily solved and the solution is N2(t) = N2(0) exp(−A12t). From this solution, it is clear that the coefficient A12 represents the 2.3. Laser principles 23 lifetime of the excited state:

τ = 1/A12. (2.18)

The stimulated emission can be considered as the inverse process of the stimulated absorption, and the temporal evolution owing to the stimulated emission is given as follow:

∂N ∂N 1 = − 2 = B ρ(ν)N . (2.19) ∂t ∂t 21 2

Phase-coherent light amplification is achieved by stimulated emission, not by spontaneous emission. Photons generated by spontaneous emission are not phase-coherent with the applied electric field, and therefore, the process of spontaneous emission does not contribute to laser action. However, it should be noted that the stimulated emission cannot take place without a photon, so a part of photons generated through the spontaneous emission have role as an initial trigger to induce the stimulated emission. By combining Eqs. (2.16), (2.17), and

(2.19), the following equation is derived:

∂N ∂N 1 = − 2 = B ρ(ν)N − B ρ(ν)N + A N . (2.20) ∂t ∂t 21 2 12 1 12 2

Eq. (2.20) tells us that the upward transition and downward transition are balanced at steady-state (∂N1/∂t =

∂N2/∂t = 0). At thermal equilibrium, the ratio of population in the ground- and excited state is described by

Boltzmann distribution given by ( ) − N2 g˜2 −E2 E1 = exp ′ , (2.21) N1 g˜1 kBT

′ where kB is the Boltzmann constant, T is temperature, and g˜1 and g˜2 are degeneracy of the ground- and excited state, respectively. From Eq. (2.20) and (2.21), the photon energy density ρ(ν) is given by

A /B ρ(ν) = 21( 21 ). (2.22) g˜1 B12 hν exp ′ ) − 1 g˜2 B21 kBT

By comparing Eq. (2.21) with the Planck’s black body radiation law given by Eq. (2.23), the Einstein’s relations

(Eq. (2.24) and (2.25)) are obtained.

8πν2dν hν ρ(ν)dν = ( ) (2.23) c3 hν exp ′ − 1 kBT

3 A21 8πhν = 3 (2.24) B21 c

g˜1 B21 = B12 (2.25) g˜2 c in Eqs. 2.23 and 2.24 is speed of light. The Einstein’s relations tell us that the coefficients B12 and B21, 2.3. Laser principles 24 determining the probability of stimulated absorption and emission process, are equal for non-degenerated system.

According to the Boltzmann distribution, the population in higher lying levels is always fewer than that in lower lying levels. Therefore, the absorption process is dominant, and consequently, light amplification does never happen at thermal equilibrium. For light amplification, the population in the excited state should bemore than that in the ground state. This situation called a population inversion. The population inversion per unit volume ∆N, so-called population inversion density, defined as the difference of population density between the levels, is defined as follows:

∆N = N2 − N1. (2.26)

The theoretical descriptions above are all based on the ideal two-level system for simplicity. However, in the two-level system, a population inversion can never exist in steady-state. For instance, if all the ions are in the excited state at a moment, an optical gain is instantaneously obtained and the dominant stimulated emission process vanish the population inversion. Thus, more than three energy levels are required for laser operation.

2.3.2 Three-level and four-level lasers

All lasers can be categorized in three-level or four-level lasers. Their simplified energy level systems are illustrated in Fig. 2.3. The three-level system consists of ground-state, meta-stable pump level, and upper laser level. In addition to these energy levels, the four-level system has lower laser level.

Pump level N3 Pump level N3

Upper laser level Upper laser level

N2 N2

Pump Laser Pump Laser transition transition transition 21 transition 20 20

N1 Lower laser level N0 N0 Ground-state Ground-state

Three-level system Four-level system

Figure 2.3: Simplified energy levels of three-level system (left) and four-level system (right).

In the three-level system, the population inversion density is defined by N2 − N0. For producing a population inversion, ions in the ground state is optically or electrically pumped to the pump level. Because the lifetime of the meta-stable pump level is so short, the population in the pump level can be considered to be zero.

Therefore, for obtaining light amplification, more than half of the all ions have to be excited to upperlaser level. Consequently three-level lasers have a high lasing threshold. In the four-level system, the population inversion density is defined by N2 − N1. Theoretically, a population inversion can be formed only by exciting 2.3. Laser principles 25 one ion to the upper laser level because the population in the lower laser level is considered to be zero owing to its very short lifetime. This fact results in a low lasing threshold on four-level lasers. In Section 2.3.4, more detailed mathematical description of the four-level laser is presented.

2.3.3 Lasing threshold

Here, conditions for lasing are described. Again, a laser consists of a gain medium and optical resonator. Gain media contain optically active centers which are responsible for absorption and emission of light. For simplicity, a straight resonator comprised of two mirrors is considered, as shown in Fig. 2.4. Light propagates between mirrors and is amplified when passing through the gain medium. Lasing is achieved when the gain perround- trip becomes larger than the loss per round-trip, including cavity mirrors, scattering and absorption in the gain medium. One of the mirrors is an output coupler from which laser output is extracted. The reflectivity is therefore less than 100%; otherwise no output is obtained. The other mirror is a highly reflecting mirror at the wavelength of the laser, and the reflectivity is ideally 100%. The gain medium of a length of lg is pumped by an appropriate pump source, and a population inversion is formed. The gain coefficient is then given as g = σst∆ where ∆N is the population inversion density, and σst is the stimulated emission cross section. The light propagates in the gain medium is amplified by a factor by exp(glg). At the lasing threshold, the gain is equal to the cavity loss, represented by the following equation:

R1R2 exp[2(g − α)lg] = 1, (2.27)

where R1 and R2 are reflectivity of mirror (see Fig. 2.4), and α is the effective attenuation coefficient to take into account the losses in the gain medium. Equation (2.27) can be transformed into the following form:

2glg = − ln R1R2 + 2αlg, (2.28)

The second term on the right-hand side is the resonator loss per round-trip. If the gain coefficient g is constant, the light propagating in the resonator continues to be amplified, and the laser output continues to increase; however, in reality, at a given pump power, the laser output is converged to a certain value owing to the gain saturation. During the amplification process, the population inversion density is consumed and the decreased down to the value in which the gain coefficient is equal to the resonator loss. Therefore, the gain coefficient is the highest when the intracavity light is absent. The highest gain coefficient is so-called small-signal gain coefficient g0. The gain saturation is represented by the following equation:

g g = 0 , (2.29) 1 + I/Isat 2.3. Laser principles 26

where I is the optical intensity at the gain medium. In the case of four-level lasers, the saturation intensity Isat is given as follows: hν Isat = . (2.30) σstτf

Thus, the saturation characteristic is determined by parameters of gain media.

High-reflectivity Output (HR) mirror, 1 Pump coupler, 2

Laser output

Gain medium,

Figure 2.4: Simplified schematic of laser system consisting of a gain medium andhigh reflectivity (HR) mirror and output coupler.

2.3.4 Mathematical description of four-level lasers

Dynamics of lasers are described by differential equations of intracavity photon number density ϕ and population density of ions in each energy level. The differential equations are called rate equations of laser. As mentioned in the previous subsection, lasers are categorized into three- and four-level lasers. In this subsection, rate equations for four-level lasers are introduced, since all lasers dealt in this thesis are described by the four-level system.

In the schematic of a four-level system shown in Fig. 2.3 (right). The population density of the energy levels, ground-state, upper laser level, lower laser level, and meta-stable pump level are respectively N0, N1, N2 and

N3. In general, the relaxation from the pump level to the upper laser level is very fast, the population in the pump level n3 is considered to be zero. In fact, the relaxation time of non-radiative decay is typically

−8 −11 10 − 10 s. The rate equations of population in the lower laser level N1, and upper laser level N2 are given as follows:

dN1 N2 N1 = (N2 − N1)σstϕc + − , (2.31) dt τ21 τ10 ( ) dN2 N2 N2 = WpN0 − (N2 − N1)σstϕc − + , (2.32) dt τ21 τ20 where Wp is the pumping rate and c the speed of light. The population in the ground-state is calculated by

N0 = Ntot − N1 − N2, because N3 is assumed to be zero. Here, Ntot is the total ionic population density of active centers, Wp is the pumping rate from the ground-state to the pump level, and σst is the stimulated emission cross section. The population in the lower laser level N1 is determined by its lifetime τ10. Most cases 2.3. Laser principles 27

the relaxation to the ground-state can be considered to be instantaneous, and therefore, the lifetime τ10 is approximately zero. Consequently, in addition to the pump level, the population in the lower laser level is also considered to be zero. This approximation leads to

N0 = Ntot − N2. (2.33)

Population inversion density ∆n is defined by ∆N = N1 − N2. Because N1 is approximately zero, the rate equation for the population inversion density is same as that for the upper laser level given by Eq. (2.32).

Moreover, Eq. (2.32) is further simplified to

d∆N dN2 ∆N = = WpN0 − ∆Nσstϕc − , (2.34) dt dt τf

−1 where τf is the fluorescence lifetime given by τf = (1/τ20 + 1/τ21) .

Temporal evolution of the intracavity photon number densityϕ is given by the following equation:

dϕ ϕ = cϕσst∆N − + S. (2.35) dt τc

τc is the photon lifetime (or cavity lifetime) given as follows:

2lc τc = , (2.36) c(TOC + Li)

where TOC is the transmission of the output coupler, lc the cavity length, and Li the intrinsic resonator losses. S is the contribution of the spontaneous emission. By applying a steady-state condition to these rate equations, the analytical form of continuous-wave (CW) operation is calculated. In steady state (d∆N/dt = dϕ/dt = 0),

Eq. (2.34) and (2.35) are set to zero and the following simultaneous equations:

∆N Wp(Ntot − ∆N) − ∆Nσstϕc − = 0, (2.37) τf

ϕ cϕσst∆N − = 0. (2.38) τc

From Eq. (2.38), the population inversion density in the steady-state is given as follows:

1 ∆N = . (2.39) cσstτf

Theoretically, the population inversion density no longer changes above the lasing threshold. At a given pumping 2.4. Optical resonator 28 rate, the intracavity photon density is then derived with the steady-state population inversion density as follows:

[ ] 1 ∆N ϕ = Wp(Ntot − ∆N) − . (2.40) cσst∆N τf

The laser output can be calculated from the intracavity photon density and the reflectivity of output coupler.

2.4 Optical resonator

An optical resonator is an essential component of a laser. In this subsection, a representative method of optical resonator design using ABCD matrices is described. This method is based on Gauss beam optics. Before presenting the practical method of ABCD matrix, fundamentals of Gaussian beam are described.

2.4.1 Gaussian beam

Hermite-Gaussian beam is one of solutions of the paraxial Helmholtz equation under the slowly varying envelope approximation given by Eq. (2.41). The solution of lowest order mode is called Gaussian beam.

∂U ∇2U − j2k = 0. (2.41) ∂z where U is the complex envelope function. Here, the beam is considered to propagate along z-axis (optical axis). The complex amplitude of an electric field is written as U(r) exp(−jkz). The complex envelop function of a Gaussian beam is as follows: [ ] U r2 U(r) = 0 exp −jk , (2.42) q(z) 2q(z) √ 2 2 where U0 is the amplitude coefficient, and r is the distance from the optical axis (r = x + y ) The parameter q in the equation is called q-parameter by given by

q(z) = z + jzR. (2.43)

2 The parameter zR is the Rayleigh range defined by zR = πw0/λ, where λ is the wavelength of the beam. Here, one introduces two functions, R(z) and w(z) respectively defined as follows:

[ ( ) ] z 2 R(z) = z 1 + R , (2.44) z

[ ( ) ]1/2 z 2 w(z) = w0 1 + . (2.45) zR 2.4. Optical resonator 29

R(z) and w(z) are wavefront’s radius of curvature and beam radius of a Gaussian beam, respectively. w0 is the smallest beam radius, and the position where w(z) is equal to w0 is called beam waist. The smallest beam diameter 2w0 is often called the beam spot size. The coordinate z has its origin at the beam waist, and therefore R(z) diverged to infinity at the beam waist. Using these functions, the q-parameter (Eq. (2.43)) is rewritten in the following form: 1 1 λ = − j . (2.46) q(z) R(z) πw(z)

The intensity distribution of Gaussian beam’s cross section is Gaussian, and its beam radius w(z) is defined as the width where the intensity drops to 1/e2 of that at the peak. When the coordinate z is large enough, the beam radius w(z) can be considered to increase linearly with z, and the beam is approximately considered as a cone with a half angle θ. This angle is called the divergence angle of a Gaussian beam given by the following equation: λ θ = . (2.47) πw0

It should be noted that the divergence angle is inversely proportional to w0. Propagation of a Gaussian beam is depicted in Fig. 2.5. When the beam propagates a distance zR from the beam waist, the beam radius becomes √ to 2w0.

Figure 2.5: Propagating Gaussian beam with associated parameters.

Practically, the function w(z) is often written in the form:

√ ( ) λz w(z) = w0 1 + 2 . (2.48) πw0

In most cases lasers do not exhibit an ideal Gaussian beam, because the beams generally contains the higher order modes. However, it is known that the mathematical treatments described above can be applied by introducing the beam quality factor M 2 for non-ideal Gaussian beams. The beam quality factor M 2 is defined as follows: πw θ M 2 = 0 (2.49) λ

It is clear that M 2 is equal to unity for the ideal Gaussian beam, by comparing with Eq. (2.47). For a given beam spot size, the divergence angle of a non-ideal Gaussian beam with M 2 > 1 is larger than that of an ideal 2.4. Optical resonator 30

Gaussian beam with a factor of M 2. In other words, for a given divergence angle, the spot size of a non-ideal

Gaussian beam is larger with a magnitude of M 2 with respect to that of an ideal Gaussian beam. Using this

M 2 factor, the evolution of beam radius given by Eq. (2.48) is modified as follows:

√ ( ) M 2λz 2 w(z) = w0 1 + 2 . (2.50) πw0

2 2 Consequently, Rayleigh range of a non-ideal Gaussian beam is rewritten as zR = (πw0)/(M λ). For experimental evaluation of a beam quality, M 2 is determined so that Eq. (2.50) fits to experimental data.

2.4.2 Resonator design

ABCD matrices are originally introduced for ray optics. Paraxial optical rays are characterized by the distance y and angle θ with respect to the propagation axis. An optical ray is written as t[y θ]. Any optical treatments, including propagation, refraction and reflection, are represented by transformations with2×2 matrices, called

t t ABCD matrices. For an arbitrary optical treatment, the input [y1 θ1] transforms into [y2 θ2] as follows: [ ] [ ][ ] y A˜ B˜ y 2 = 1 . (2.51) θ2 C˜ D˜ θ2

Typical ABCD matrices useful for designing an optical resonator are shown in Table 2.3. Optical transformations of Gaussian beams are also described by using the ABCD matrices. It is known that ABCD matrices transform q-parameters as follows:

Aq˜ 1 + B˜ q2 = , (2.52) C˜q1 + D˜ where q1 and q2 are q-parameters of the input and output of an optical element. The four coefficients are matrix elements of ABCD matrices listed in Table 2.3. Based on Eq. (2.52), one can arbitrary design optical resonators. For a stable optical resonator, its q-parameter at any position has to be preserved after a round-trip.

Therefore, one calculates an ABCD matrix for one resonator round-trip MRT once a configuration of resonator is given. Using the matrix elements A˜ and D˜ of the round-trip ABCD matrix MRT, the stability condition of the resonator is given as follows:

|A˜ + D˜| < 2, (2.53)

Only if this condition is satisfied, the q-parameter is preserved after a round-trip. This fact is represented by the following equation: Aq˜ + B˜ q = , (2.54) C˜q + D˜ 2.4. Optical resonator 31

This quadratic equation for q−1 is easily solved, and the solution is given as follows:

√ 1 D˜ − A˜ j = + 4 − (A˜ + D˜)2. (2.55) q 2B˜ 2B˜

Once a q-parameter at a position is obtained, one can easily calculate q-parameters for any resonator’s position using Eq. (2.52). Accordingly, the beam size and wavefront’s radius of curvature can be calculated using

Eq. (2.46). 2.4. Optical resonator 32

Table 2.3: ABCD matrices for common optical elements and media [118, 119].

[ ] 1 d Propagation of homogeneous 0 1 medium: length d z1 d z2 [ ] 1 0 Thin lens: focal length f (f > 0 −1/f 1 convex lens, f < 0 concave lens) f

[ ] 1 0 Plane interface (normal inci- 0 n1/n2 dence): refractive index: n1, n2 n1 n2

[ ] 1 0 Spherical interface: Radius R − n2 n1 n /n n1 n2 n R 1 2 R 2 [ ] 1 0 Spherical mirror: curvature ra- −2/R 1 dius R R

[ ] cos θ2 cos θ 0 Angled plane interface θ θ2 1 1 0 n1 cos θ2 n2 cos θ1 n1 n2 Chapter 3

Continuous-wave Pr3+:YLF visible lasers

3+ In this chapter, the demonstration on visibly emitting Pr -doped LiYF4 (YLF) lasers in continuous-wave (CW) operation are described. The lasers were directly pumped by indium-gallium-nitride (InGaN) blue laser diodes

(LDs). First, the details of the pump sources used in this study are presented. Then the properties, including spectroscopic measurements, of the gain medium, Pr3+-doped YLF crystal, are described. The Pr3+:YLF lasers were demonstrated with several pump sources: single-emitter InGaN blue LDs, and a fiber-coupled module.

3.1 Pump laser diodes

3.1.1 Single-emitter InGaN blue and cyan-blue laser diodes

In this section, details of pump sources used in this thesis is described. In this work, two kinds of InGaN blue

LDs, single-emitter LDs and fiber-coupled LD module, are used for exciting3+ Pr -doped laser crystals.

The employed single-emitter LDs are standard ϕ 9-mm CAN multimode diodes (Nichia Corp.). Regarding the absorption spectrum of Pr3+-doped crystals, the three different samples were employed as listed in Table 3.1.

InGaN blue LDs emitting around 450 nm (NDB7A75T and NDB7N75T) are the most successful in terms of 3+ 3 → power scaling, and they are suitable to pump the absorption line of Pr corresponding the transition H4 3 3+ P2. The wavelength of the blue LDs were selected regarding the absorption spectrum of Pr -doped YLF crystal, a laser crystal mainly adopted in this work. Because the crystal has its absorption peak respectively at

444 and 442 nm for polarization parallel to crystal’s c- and a-axes, the samples emitting at these wavelength at

33 3.1. Pump laser diodes 34

Table 3.1: Nominal parameters of single-emitter InGaN LDs used in this thesis. Beam divergence is defined as full angle at 1/e2 from peak intensity.

Item Nominal Nominal Operating Operating Beam divergence number wavelength power current voltage (deg.)

(nm) (W) (A) (V) θ∥ θ⊥

NDB7A75T 442 or 444 3.5 2.3 ∼4.3 ∼14 ∼44

NDB7N75T 442 or 444 5.0 3.0 ∼4.0 ∼10 ∼46

NDA7175E 478 1.0 0.9 ∼4.0 ∼12 ∼47

25°C were selected. The LDs were driven by a LD controller supplying up to 5 A (LDC4005, Thorlabs). The

LDs were mounted on an aluminum plate, and the temperature of the plate was controlled by a PID controller via a Peltier module. The temperature was measured with a K-type thermocouple. The reverse side of the

Peltier module was cooled by a water-cooled copper heat sink. The 3D schematic of the LD mount is shown in

Fig. 3.1.

Water-cooled copper heatsink

Laser diode Tube fitting

Thermocouple Peltier module (attached on the aluminum plate) (sandwiched between aluminum plane and copper heatsink)

Figure 3.1: Schematic 3D image of mechanical design of LD mount.

The output power of the 5-W single emitter InGaN blue LD nominally emitting at 25◦C (NDB7N75T) with respect to forward current is shown in Fig. 3.2. The LD was driven by a LD controller supplying up to 5 A

(LDC4005, Thorlabs). The emission wavelength of semiconductor lasers without any feedbacks depend on temperature and forward current. The emission spectra of the LD for varied forward current at a controlled temperature of 25◦C, and for varied temperature at a forward current of 3 A are shown in Fig. 3.3. As the temperature or forward current increased, the emission wavelength red-shifted. The spectral width (full-width at half maximum: FWHM) of the blue LD was ∼1.2 nm. The tunability of the spectrum by temperature was approximately ∼0.6 nm/◦C.

The beam quality of the output beam was evaluated by using CMOS camera. The CMOS camera was scanned around the beam waist of the focused beam. The beam radii for both planes were plotted and shown in Fig. 3.4. 3.1. Pump laser diodes 35

(a) 4 (b) 3.5 5.0

3 4.0 2.5 3.0 2

1.5 2.0 Output power (W)

1 Output power (W) 1.0 0.5

0 0.0 0 0.5 1 1.5 2 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Forward current (A) Foward current (A)

Figure 3.2: Power characteristic of 3.5-W (a) and 5-W (b) blue LDs.

(a) 1 0.5 A (b) 1 10qC 1.0 A 15qC 1.5 A 20qC 2.0 A 25qC 0.8 2.5 A 0.8 30qC 3.0 A 35qC 40qC 45qC 0.6 0.6

0.4 0.4 Intensity (arb. units) 0.2 Intensity (arb. units) 0.2

0 0 438 439 440 441 442 443 444 445 446 441 442 443 444 445 446 447 448 Wavelength (nm) Wavelength (nm)

Figure 3.3: Emission spectrum of 5-W blue LD around 444 nm with respect to forward current at a temperature of 25◦C (a), and with respect to temperature at a forward current of 3.0 A (b). The spectra were measured by a spectrometer (USB4000, Ocean Optics). 3.1. Pump laser diodes 36

The beam waist positions for the vertical and horizontal planes are different as seen in this figure, because the output beam from the LD had an astigmatism. The solid lines in Fig. 3.4 were resulting fitting curves governed by Eq. (2.50).

1500 measurement (vertical plane) measurement (horizontal plane) 2 (µ m) best fit (M =1.90) 1000 best fit (M2=22.05)

500

Beam radius 1 mm 0 -30 -20 -10 0 10 20 30 Position (mm)

Figure 3.4: Variation of beam radius of 5-W blue LD around beam waist in vertical and horizontal planes. Beam profile at z = −30 is shown on the right hand.

The best fit for the 5-W blue LD was obtained with M 2 = 1.9 and 22.1 for vertical and horizontal planes, respectively. Note that the beam quality of LDs was power-dependent. The results shown in Fig. 3.4 was measured at the full power. The beam quality of a 3.5-W blue LD was measured to be 1.5 and 12.9 for vertical and horizontal planes, respectively.

(a) (b) 1.0 150 mA 1000 200 mA 300 mA 400 mA 0.8 500 mA 800 600 mA 700 mA 800 mA 0.6 900 mA 600

400 0.4 Intensity (arb. units) Output power (mW) 200 0.2

0 0 0 200 400 600 800 1000 474 475 476 477 478 479 480 Forward current (mA) Wavelength (nm)

Figure 3.5: (a) Power characteristic and (b) emission spectra of 478-nm cyan-blue LD at 25◦C.

In addition to ∼440-nm blue LDs, samples emitting at 478 nm were also used, since the Pr3+:YLF crystal has a narrow but strong absorption peak at 479 nm. The pumping at longer wavelength is advantageous because of a higher Stokes efficiency. The output power and spectrum as a function of forward current wereshownin

Fig. 3.5. The temperature of the cyan-blue LD was set to 25◦C. The beam quality factor M 2 of the cyan-blue

LD at the forward current of 900 mA in vertical and horizontal planes were respectively measured to be 2.2 and

7.9, as shown in Fig. 3.6. 3.2. Crystalline hosts for Pr3+ visible lasers 37

1200 measurement (vertical plane) 1000 measurement (horizontal plane) Gauss beam fit (M2=2.2) 800 Gauss beam fit (M2=7.9) 600 400 200 Beam radius ( µ m) 1 mm 0 0 20 40 60 80 100 120 140 Position (mm) Figure 3.6: Variation of focused beam radius of 1-W cyan-blue LD at 900-mA current in vertical and horizontal planes. Temperature was set to 25◦C. Beam profile at z = 0 mm is shown on right.

3.1.2 Fiber-coupled blue LD module

A fiber-coupled module (BLUE IMPACT, Shimadzu) was also used as the pump source3+ ofPr lasers. The module delivered the output higher than 20 W from a multimode fiber of 100-µm core diameter and 0.2 numerical aperture (NA). The beam quality of the output was determined by the delivering fiber. Therefore, its beam quality was calculated to be M 2 ∼ 70 using the following equation:

πd { } πd (NA) M 2 = core tan sin−1(NA) ≈ core , (3.1) 2λ 2λ

where dcore is the fiber core diameter, NA the numerical aperture of the fiber,and λ the wavelength. In the fiber-coupled module, 3.5-W blue LDs (NDB7A75T) spatially combined into the fiber. The temperature ofthe

LDs was controlled by one Peltier module between 25 to 40◦C. It was important to keep the good spectral overlap of the pump spectrum with the absorption spectrum of laser crystals. Therefore, 3.5-W blue LDs emitted at the same wavelength were adopted for the module. The power characteristic of the fiber-coupled module operated at 25◦C is shown in Fig. 3.7. At the highest forward current of 7.5 A, the highest output power of 23.9 W was obtained. The emission spectra for varied operating current and temperature are shown in Fig. 3.8. The spectral width was measured to be ∼2.2 nm at FWHM.

3.2 Crystalline hosts for Pr3+ visible lasers

Triply ionized praseodymium ion (Pr3+) has two electrons in the 4f shell, and the 4f electrons determine spectral characteristics. The energy band structure of Pr3+ exhibited many visible radiative transitions, and therefore Pr3+ is recognized as an attractive active ion for visible lasers. Figure 3.9 depicts the energy diagram of Pr3+. In the blue spectral region, Pr3+-doped materials have absorption lines corresponding to the transitions 3.2. Crystalline hosts for Pr3+ visible lasers 38

Output power (W) 5

0 0 1 2 3 4 5 6 7 8 Forward current (A)

Figure 3.7: Power characteristic of fiber-coupled blue LD module at◦ 25 C.

1 1 A 1 25°C (a) 2 A (b) 30°C 3 A 35°C 4 A 40°C 0.8 5 A 0.8 6 A 7 A 7.5 A 0.6 0.6

0.4 0.4

Intensity (arb. units) 0.2 Intensity (arb. units) 0.2

0 0 438 440 442 444 446 448 450 442 444 446 448 450 Wavelength (nm) Wavelength (nm) Figure 3.8: Emission spectra of fiber-coupled LD module with respect to forward current at a operating temperature of 25◦C (a) and with respect to operating temperature at a forward current of 7.5 A (b). The spectra were measured by a spectrometer (USB4000, Ocean Optics). 3.2. Crystalline hosts for Pr3+ visible lasers 39

3 → 3 3 →3 H4 PJ . The absorption transition H4 P2 around 450 nm can be addressed by high power InGaN LDs [11]. Moreover, direct pumping of the 480-nm absorption is possible by utilizing frequency-doubled optically pumped semiconductor lasers (2ω-OPSLs), as presented in the previous chapter. The fluorescence from3+ Pr - doped crystals cover the wide range the visible region, so Pr3+ crystals enable to realize red, orange, green, and cyan blue emitting lasers.

The dashed lines shown in Fig. 3.9 are the possible cross-relaxation channels. Due to these channels, an ion in the excited-state can relax by transferring its energy to a neighbor ion in the ground-state. This interionic process is called cross relaxation. The cross relaxation leads to depopulate the excited state, and the process becomes significant when3+ Pr is highly doped. Consequently, the higher the doping concentration, the shorter the fluorescence lifetime of3+ Pr ions. This effect is so-called fluorescence concentration quenching. The doping concentration of Pr3+ is typically limited below 1 at. %.

3 3 The lifetime of the excited-state P0 is mainly determined by the multiphonon relaxation from P0 level to 1 the underlying D2 level. For a host material of high phonon energy, necessary number of phonons for the downward transitions is fewer. Consequently the multiphonon relaxation becomes much more likely. Thus, as host materials for Pr3+, crystals of low phonon energy are required. Moreover, the excited-state absorption at laser wavelengths should be absent or small for efficient laser operations. If the excited-state absorption cross section is larger than the emission cross section at the laser wavelength, one can never get a net gain. In some crystalline hosts, Pr3+ exhibits a strong excited-state absorption [120]. This absorption has been attributed to transitions to 4f 15d1 levels. It should be noted that the 4f n to 4f n−15d transitions exhibits a large cross section since the transitions always satisfy Laportes selection rules. Because the 5d shell is not shielded by outer-shell electrons as 4f shell, the energy position of the 4f 15d1 levels strongly depends on the host crystal. In crystalline hosts of strong crystal field, the energy of 4f 15d1 levels shift downward, or ”depressed,” and approach to the

3 n−1 PJ manifolds. The amount of energy downward shift of 4f 5d levels are characterized by the parameter often called crystal field depression. Dorenbos gave a comprehensive review on the location of the lowest level of the triply ionized rare earth ions in various crystalline hosts [121]. Thus, the use of host crystals with small crystal field depression is essential for3+ Pr visible lasers.

So far, use of Pr3+-doped fluorides have been the main stream for visible lasers because of their low phonon energy compared to that in oxide crystals. However, it is often said that fluorides have severe drawbacks such as low thermal conductivity and low fracture limit, resulting potential issues for power scaling. Very recently, some of oxide crystals were found to be an attractive host material for Pr3+ doping due to their relatively small phonon energy. 3.2. Crystalline hosts for Pr3+ visible lasers 40

3 P2 3P , 1I 3 1 6 P0 20 ) 1 - 1 D2 cm

3 15 450 nm 450 480 nm 480 nm 480 nm 520 nm 605 nm 640 nm 700 nm 720

10 1 Energy Energy (10 G4

3 3 F4 F3 3 5 F2 3 H6

3 H5

3 0 H4

Figure 3.9: Energy diagram of the lowest energy levels of Pr3+ in fluoride crystalline hosts. The solid arrows are absorption and emission transitions in the visible region. The dashed lines are possible cross-relaxation channels.

3.2.1 Yttrium lithium fluoride (YLF)

Yttrium lithium fluoride (LiYF4 or YLF) is known as a common laser host. It has been mainly adopted as a host crystal of Q-switched Nd3+ lasers because its low phonon energy results in a longer fluorescence lifetime.

This crystal is commercially available and doping of various rare earth ions is possible. YLF has a tetragonal crystal structure as shown in Fig 3.10, so-called CaWO4 (Sheelite) structure. It is categorized in the space group 6 of C4h in the Schönflies notation. Thus, YLF has an anisotropy resulting in a strong polarization dependence on spectroscopic properties of doped ions. Doped rare earth ions typically substitute the Y3+ sites and form triply

3+ ionized state. The symmetry of the Y site is reduced to S4. Structural, optical and mechanical properties of YLF crystal are summarized in Table 3.2. The properties of YLF is very similar to lithium lutetium fluoride

(LLF), However, large rare earth ions including Pr3+ are most likely inducing a lattice stress in LLF rather than YLF because the ionic radius of Lu3+ in LLF is slightly smaller than that of Y3+ in YLF.

In general, phonon energy in fluoride crystals is smaller than that in oxide crystals. The phonon energy inYLF crystal is in fact approximately half of Y3Al5O12 (YAG) crystal, a famous oxide laser crystal. Therefore, the use of YLF crystal is expected to be advantageous for rare earth doping because the repressed multiphonon relaxation process results a longer upper state lifetime.

A main drawback of YLF crystal is its relatively poor thermal and mechanical properties compared to oxide crystalline hosts. The thermal conductivity is much smaller that YAG, a conventional oxide host. However

YLF has been recognized as a good laser host owing to its attractive feature of the thermal lensing [123]. The temperature dependence of refractive index (dn/dT ) of YLF is negative for both polarizations. In the end- 3.3. Spectroscopic properties Pr3+-doped YLF crystal 41

Li+ Y3+

F-

Figure 3.10: Structure of LiYF4 (YLF) crystal (drawn by VESTA [122]). pumping scheme, the bulging of the crystal facets acting as a positive lensing cancels out the negative lensing effect of temperature induced refractive index change for σ-polarization (polarized parallel to the crystal’s a- axis). Consequently, YLF has been recognized as an attractive laser host in terms of its capability to suppress the thermal lensing effect. The main limiting factor of laser power scaling with YLF is its low fracture limit

(∼40 MPa)[124], which is much lower than that of YAG crystal ∼140 MPa [125].

Table 3.2: Structural, optical, and mechanical properties of YLF crystal [126, 127, 124, 128, 129, 130, 131, 132].

Crystal system Tetragonal 6 Space group (Schönflies) I41/a (C4h) 3+ Symmetry of Y site S4 Lattice constants (Å) a = 5.160 c = 10.850 Thermal expansion coefficient (K−1) 13.3 × 10−6 (along a-axis) 8.3 × 10−6 (along c-axis) Thermal conductivity (W/m·K) 5.8 (along a-axis) 7.2 (along c-axis)

Refractive index (at 578 nm) no = 1.455

ne = 1.477 dn/dT (K−1) −4.3 × 10−6 (π-polarization) −2.0 × 10−6 (σ-polarization) Effective phonon energy (cm−1) 460 Density (g/cm3) 3.99 Mohs hardness 4–5

3.3 Spectroscopic properties Pr3+-doped YLF crystal

In this section, experimental results on spectroscopy of the laser crystal used in this study, Pr3+-doped YLF, are presented. 3.3. Spectroscopic properties Pr3+-doped YLF crystal 42

3.3.1 Ground-state absorption (GSA)

A polarization resolved absorption spectroscopy was performed using a double beam spectrometer (UV3600plus,

Shimadzu or LAMBDA1050, Perkin Elmer). The beams of the spectrometer in the sample chamber were larger than samples to be investigated. Therefore, for each beam, a circular aperture of 3-mm diameter was placed for accurately measuring the absorption coefficient. Since the laser gain media used in this study wereboth anisotropic crystals, a Glan-Thompson polarizer (GTH10M, Thorlabs) was placed before the sample on each beam line. To resolve the fine structure in absorption spectrum, the spectral resolution of the spectrometer, determined by the slit width, was set to 0.2 nm.

For the absorption spectroscopy, a 0.2 at. % Pr3+-doped YLF crystal (VLOC) was used. Figure 3.11 shows the polarization-resolved absorption spectrum in the blue region. To take into account the Fresnel reflections on the uncoated facets, the Sellmeier equation for undoped YLF was used [126].

6.0 E ||a E ||c 4.0

2.0

Abs. coefficient (/cm) 0.0 430 440 450 460 470 480 490 Wavelength (nm)

Figure 3.11: Polarization-resolved absorption spectrum of 0.2 at. % Pr3+:YLF crystal in the blue region.

It was possible to estimate the absorption cross sections using the nominal doping concentration. However, the doping concentration strongly depends on the parameters and environment of crystal growth. Therefore, absorption cross sections were not derived from Fig. 3.11. According to an earlier work on the spectroscopy

[133], the absorption cross sections were reported. Using the reported cross section values, the effective dopant density was calculated to be ∼ 3.2 × 1019 cm−3, which was higher than the nominal density of 2.8 × 1019 cm−3.

Therefore, the sample’s effective doping concentration was calculated tobe ∼0.23 at. %. The absorption peaks 3 →3 around 440 nm correspond to the transition H4 P2. The peaks for both polarizations are clearly seen, because this transition is allowed by electric dipole moment for the both polarizations in group symmetry of S4. Therefore, one can employ a polarization-combined pump sources of ∼440 nm. On the other hand, the peaks 3 →3 3 →3 around 468 and 479 nm, respectively corresponding to the transitions H4 P1 and H4 P0, are allowed by electric dipole moment only for the polarization parallel to the crystal’s c-axis. That is reason why the absorption peaks for polarization parallel to crystal’s a-axis for these transitions are so small. 3.3. Spectroscopic properties Pr3+-doped YLF crystal 43

1.0 E ||a E 0.8 ||c

0.6

0.4

0.2

Abs. coefficient (/cm) 0.0 560 570 580 590 600 610 620 Wavelength (nm)

Figure 3.12: Polarization-resolved absorption spectrum of 0.2 at. % Pr3+:YLF crystal in the orange region.

The polarization-resolved absorption in the orange region (560–620 nm) is shown in Fig. 3.12. These orange 3 →1 absorption peaks are attributed to the transition H4 D2. The orange GSA is detrimental for the laser lines in the orange region at 604 and 607 nm. Even though the absorption looks approximately zero at 607 nm, the laser performance at 607 nm, presented in the following chapter, showed the existence of non-negligible absorption resulting a large loss for laser cavity.

3.3.2 Excited-state absorption (ESA)

Even though many trivalent rare earth ions have emission in the visible region, laser operations are often

3 −1 prohibited due to ESA. Above the energy levels PJ , there is no 4f-energy level up to 40,000 cm [3]. However, ESA is often observed in the visible region due to transitions to 4f5d levels. The energetic position of 4f n−15d levels are determined by crystal field depression, one of parameters of crystalline hosts [121]. For example,in 3+ 3 1 ∼ Pr :Y3Al5O12 (YAG), strong ESA from P0 and D2 levels were observed in the blue-green region ( 480– 570 nm). Therefore, lasing in the green region is not realistic with Pr3+:YAG crystal. It should be noted that transitions to 4f n−15d bands are, in general, very strong, since the transitions always satisfy the selection rules.

Fluoride hosts are known to exhibit small crystal field depression. Richter examined the ESA spectrum of

Pr3+:YLF, and confirmed that the ESA to 4f5d level takes place below 400 nm, so the ESA in YLF does not affect the laser performances [133]. Oxide hosts, in general, exhibit much larger crystal field depression and the energetic position of 4f5d level is lowered. However, perovskites, including YAP, LuAlO3 (LuAP: lutetium aluminum perovskite), and GdAlO3 (GAP: gadolinium aluminum perovskite) crystals, showed much smaller crystal field depression compared to other oxide crystals such as garnets [121]. To the best ofauthor’s knowledge, Pr3+:YAP lasers have been operated at 662, 720, and 747 nm at room temperature, and the 547-nm green operation has been demonstrated only when the crystal was cryogenically cooled. 3.3. Spectroscopic properties Pr3+-doped YLF crystal 44

3.3.3 Emission spectroscopy

Emission characteristics of Pr3+ in YLF are investigated by other groups [133, 44]. The energy diagram of

Pr3+:YLF is shown in Fig. 3.13.

3 P2 3P , 1I 3 1 6 P0 20 ) 1 - 1 D2 ) nm ) nm ) cm ||c ||a ) ) ) ) ) ) ) 3 ||c ||c ||c ||c ||c ||c 15 ||a (E ), 444 444 (E ), ), 607 (E ), 607 ||a ||c 546 (E nm 546 523 523 nm (E 479 479 nm (E (E nm 479 698 698 nm (E 720 nm 720 640 640 nm (E

Energy Energy (10 10 1 442 442 (E 604 604 (E G4

3 F4 3 F3 3 5 F2 3 H6

3 H5

3 0 H4

Figure 3.13: Simplified energy diagram with major absorption and emission 3+lines ofPr in YLF crystal. Black dashed lines are possible cross-relaxation channels.

Pr3+:YLF has many radiative transitions covering from cyan-blue (∼479 nm) to deep-red (∼720 nm). Since

YLF is a strongly anisotropic crystal, the emission of Pr3+:YLF, of course, exhibited polarization dependence.

The polarization of the major emissions are also indicated in Fig. 3.13. Wavelength, stimulated emission cross section, polarization, and terminating level of the emission lines of Pr3+:YLF are summarized in Table 3.3.

3.3.4 Lifetime

The emission lifetime of a Pr3+:YLF crystal was experimentally measured. For the excitation of the crystal, the fiber-coupled blue LD module (see Section 3.1.2) was electrically modulated to observe the temporal decay of the fluorescence. The LD module was modulated at 100-Hz repetition rate with a duty ratio of 95%. Ideally, nanosecond-pulse lasers, such as a Q-switched laser or an optical parametric oscillator, should be adopted for lifetime measurement. The fall-time of the modulated blue LD module was measured at 1.2 µs, and the observed

3 3+ fluorescence decay from P0 manifolds of Pr in YLF crystal was sufficiently long compared to the fall-time of the pump.

A 12-mm long 0.3 at. % Pr3+:YLF crystal (Unioriental Optics) was adopted for the lifetime measurement. The 3.3. Spectroscopic properties Pr3+-doped YLF crystal 45

Table 3.3: Wavelength, polarization, and termination level of major emission lines from Pr3+:YLF [44, 45].

Wavelength Emission cross section (nm) (10−20 cm2) Polarization Termination level

3 479 19.4 E||c H4

3 523 2.6 E||c H5

3 546 0.8 E||c H5

3 604 9.8 E||c H6

3 607 13.6 E||a H6

3 640 21.8 E||a F2

3 698 5.2 E||c F3

3 720 8.8 E||c F4 fluorescence was collected by a lens of 75-mm focal length and focused into a photodiode (S3883, Hamamatsu) through a spherical lens of 100-mm focal length. The scattered blue pump light was filtered out by a yellow- color glass filter. The output of the photodiode was connected to an oscilloscope and the fluorescence decay was recorded. The fluorescence decay curve in log scale is shown in Fig. 3.14. The fluorescence lifetimewas determined to be 42.7 µs.

e0 experiment fitting e-1

e-2

e-3 µ τf = 42.7 s e-4 Intensity (arb. units) e-5

e-6 0 50 100 150 Time (µs)

3 3+ Figure 3.14: Fluorescence decay curve of P0 level in 0.3 at. % Pr :YLF. Red symbols are experimental results. Black lines are fitting curves.

3 Due to the small phonon energy, the non-radiative multiphonon relaxation from P0 manifolds to under lying 1 D2 was reduced compared to oxide crystalline hosts. The fluorescence lifetimes of 0.16, 0.33, and 0.65 at.% Pr3+ in YAG crystals were measured at 13.3, 11.2, and 9.8 µs, respectively [134]. It should be commented that these values may be longer than the actual lifetimes due to the radiation trapping [135], because the photoluminescence at 610 nm, at which the ground-state absorption takes place, was detected. The lifetime of 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 46 a 0.6 at. % Pr3+:YAP crystal was measured at ∼ 13.8 µs [63].

It has bee known that Pr3+ exhibit a fluorescence quenching with high doping level owing to the possible cross relaxation channels. Richter studied the quenching effect of3+ Pr in YLF crystal, and the fluorescence lifetime of a 1.35 at. % crystal was measured at 21.4 µs, while the radiative lifetime was estimated to be 50 µs [133].

3.4 Diode-pumped continuous-wave Pr3+:YLF lasers

In this section, the performances of the diode-pumped Pr3+:YLF lasers are presented. As the pump sources, blue LDs around 440 nm, a cyan-blue LD at 479 nm, and a fiber-coupled blue LD module were employed.

3.4.1 Single-emitter-blue-diode-pumped Pr3+:YLF laser

First, laser experiments using single-emitter blue LDs (NDB7N75T, Nichia Corp.), providing a nominal output power of 5 W as the pump source, were performed. In the experiments, four single-emitter LDs were employed for pumping a Pr3+:YLF crystal. The experimental setup of the Pr3+:YLF laser pumped by the single-emitter blue LDs is depicted in Fig. 3.15. As a gain medium, a 0.3 at. % Pr3+-doped YLF crystal rod (Unioriental

Optics Co., Ltd.) cut perpendicular to the crystal’s a-axis was adopted. The diameter and length of the laser rod were 5 and 12 mm, respectively. The crystal facets were uncoated. The laser crystal was mounted on a copper heat sink in which cooling water was circulating. The air-gap between the heat sink and crystal was filled with 0.1-mm thick indium foil for better thermal contact.

Blue laser diode (442 nm) Cylindrical Isolator expander HWP Aspherical lens (x 5) (f = 3.1 mm)

DM HWP Cylindrical Blue laser diode (plane) a DM expander c (444 nm) Cylindrical (plane) (x 5) Blue laser diode expander a Isolator (442 nm) (x 5) PBS Lens Pr3+:YLF (f = 120 mm)

Aspherical lens Lens PBS OC Cylindrical (f = 3.1 mm) (f = 150 mm) Blue laser diode (R = 100 mm) expander (444 nm) (x 5)

Figure 3.15: Schematic image of Pr3+:YLF laser pumped by four single-emitter blue LDs.

Characteristics of the four blue LDs are summarized in Table 3.4. The absorption of anisotropic Pr3+:YLF crystal is polarization dependent, and the absorption peak wavelength locates at ∼444 and ∼442 nm for polarization parallel to the crystal’s c- and a-axes, respectively. Even though the LDs at a nominal operating temperature of 25◦C exhibited good spectral overlap with the absorption spectrum, to further improve absorption efficiency, the wavelength of each LD was optimized by tuning their temperatures using Peltier modules. The optimized 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 47 temperature and peak emission wavelength together with the resulting absorption efficiency and effective absorption coefficient of each LD are listed in Table 3.4. For the 442-nm LDs, optical isolators wereintroduced because the absorption coefficient for E∥a is ∼60% of that for E∥c, and thus ∼500 mW of each 442-nm pump beam was transmitted and focused to the LD of the other side without the isolators.

The beam quality of the LDs were measured by using a complementary metal-oxide-semiconductor (CMOS) beam profiler. Because the LDs have a rectangle stripe shaped planar waveguide structure (Fig. 3.4),beam quality factor M 2 along the fast axis was measured at <2 and that along the slow axis was measured at >17.

To improve mode-matching efficiency with the astigmatism-free cavity mode, each LD’s beam was extended along its slow axis at a factor of five by a cylindrical lens pair (f = 20 and 100 mm). It should be noted that the cylindrical expanders compensated the astigmatism of the pump beams; otherwise, the beam waist in both planes separated when focused as shown in Fig. 3.4.

The expanded 444- and 442-nm beams were then combined at the polarizing beam splitters (PBSs) and focused by spherical lenses (f = 120 and 150 mm) into the laser crystal through the dichroic mirrors. Each LD’s pump power incident to the Pr3+:YLF crystal was measured and is listed in Table 3.4. The total incident pump power and absorbed pump power was 17.0 and 15.0 W, respectively, under the non-lasing condition. A part of the pump power from each LD was lost due to the pump shaping optics and the dichroic mirrors. Even though the optics had an anti-reflection coating for the visible region, the loss was still not negligible since eachpump beam passes through ten coated surfaces. The measured absorbed pump power corresponded to a total effective absorption efficiency of 91.6%. The change in the absorbed pump power between the lasing and non-lasing conditions was negligible.

Table 3.4: Nominal parameters of single-emitter InGaN LDs used in this thesis.

Operating Peak Half Measured Output Incident Absorption Absorption temperature wavelength width beam quality M 2 power pump power coefficient efficiency ◦ 2 × 2 ( C) (nm) (nm) Mx My (W) (W) (/cm) (%) LD1 (444 nm) 24 444.2 0.9 24.3 × 2.3 5.16 4.24 2.79 96.5 LD2 (442 nm) 15 441.8 1.0 18.6 × 1.9 5.00 4.15 1.71 87.2 LD3 (444 nm) 15 444.8 1.1 17.4 × 1.5 4.96 4.41 3.15 97.7 LD4 (442 nm) 18 442.1 0.9 24.2 × 1.8 4.96 4.26 1.95 90.0

The laser resonator consisted of three mirrors, two plane dichroic mirrors (DMs) and an output coupler (OC) with a curvature radius of 100 mm. The dichroic mirrors had a high reflectivity (>99.5%) for 520–650 nm and high transmission (>98%) for 430–450 nm. For operating at 640 nm, a 5.2%-transmission output coupler was used. Any lasing at other wavelengths was not observed at the same time because the emission cross section at 640 nm was the largest. For 607-nm operation, an output coupler of 10.8%-transmission, in which the transmission at 640 nm was >90% to suppress the parasitic lasing at 640 nm, was used. It is noteworthy that 3+ 3 →1 the Pr :YLF has a ground-state absorption in the range of 580–610 nm corresponding to transition H4 D2, 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 48 resulting a relatively a high intracavity loss. Therefore, output couplers with higher transmission for 607-nm oscillation provided efficient operation.

The cavity length was optimized to obtain maximum output power. For both wavelengths, maximum output power was achieved with a cavity length of ∼72 mm because a large cavity mode volume resulted in high mode-matching efficiency with the population inversion distribution. Output power with respect to absorbed pump power at 640 and 607 nm is shown in Fig. 3.16. Maximum output power at a maximum absorbed pump power of 15 W was 6.7 and 3.7 W at 640 and 607 nm, respectively. The slope efficiency with respect to the absorbed pump power was calculated to be 45.5 and 30.0% at 640 and 607 nm, respectively. In the vicinity of the 607-nm transition line, there is an emission line at 604 nm. However, a lasing at the wavelength was not observed even though the reflectivity of the output coupler was almost same for these two wavelengths. Infact, the emission cross section at 604 nm (9.8×10−20 cm2) is slightly smaller than at 607 nm (13.6×10−20 cm2) [44].

Moreover, the 607-nm light has σ-polarization (polarized along the crystal’s a-axis), while the 604-nm light has

π-polarization (polarized along the crystal’s c-axis). It is well known that YLF crystal exhibits strong negative thermal lens due to the negative and large refractive index change against temperature dn/dT for π-polarization

(4.3 × 10−6 K−1), which leads to destabilization of the laser cavity. On the other hand, a weak positive thermal lens is formed for σ-polarization despite a negative dn/dT (2.0 × 10−6 K−1) because the bulged end facet of the end-pumped crystal, acting as a positive lens, compensates the negative lens formed by the negative dn/dT

[136]. Thus, the strong negative thermal lens for π-polarization might also contribute to lasing suppression at

604 nm.

The laser operation at 523 nm was also attempted with the same cavity configuration. However, a stable lasing was not achieved at the maximum pump power. The highest output power of 1.8 W with a slope efficiency of 38.2% at an absorbed pump power of 5.4 W was obtained using a 2.5%-transmission output coupler. This unsuccessful result was attributed to the strong negative thermal lens for the π-polarized 523-nm light and the small emission cross section at 523 nm. The emission cross section at 523 nm (∼ 2.6 × 10−20 cm2) is in fact much smaller than that at 640 nm (21.8 × 10−20 cm2) and 607 nm (13.6 × 10−20 cm2) [44]. The cavity loss induced by the thermal aberration did not strongly affect the output performance for the 640- and 607-nm operations since the large emission cross sections made the lasers less sensitive to cavity loss. However, even a small cavity loss critically degraded the laser performance at 523 nm.

Although a YLF crystal exhibits a weak positive thermal lens for σ-polarization, the output beams at 640 and

607 nm were strongly aberrated, as shown in the far-field profiles in Figs. 3.16(a,b). Clarkson experimentally demonstrated that the effective focal length of thermal lenses varies radially, and this results in non-parabolic phase aberration [137]. Therefore, phase aberration is, in general, suppressed by reducing the cavity mode volume with respect to the pump beam size in the gain medium. However, smaller cavity mode sizes result in lower mode-matching efficiencies. In our cavity configuration (the cavity length was ∼72 mm), the cavity mode 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 49

(a) 7 (b) 4 6 η = 45.5% 3 η = 30.0% 5 sl,abs sl,abs

4 2 3

Output power (W) Output power (W) 1 1

0 0 0 5 10 15 0 5 10 15 Absorbed pump power (W) Absorbed pump power (W)

Figure 3.16: Output characteristics of Pr3+:YLF laser pumped by four single-emitter blue laser diodes operated at (a) 640 nm and (b) 607 nm. diameter in the gain crystal was calculated at 190 µm by means of ABCD matrices, while the pump beam spot diameter was estimated to be (20–25)×(65–85) µm2 for the four LDs. The maximum mode-matching efficiency was numerically estimated to be ∼70–75% for all the pump LDs. We experimentally examined this trade-off between beam quality and mode-matching efficiency for the 640-nm operation. The cavity length was changed from ∼72 mm to ∼102 mm, resulting in a cavity mode diameter of ∼120 µm in the laser crystal. Figure 3.17 illustrates the absorbed pump power dependence of the output power. The maximum output power and the slope efficiency slightly decreased to 6.3 W and 43.5%, respectively, presumably due to the slightly decreased mode-matching efficiency. However, as we expected, the beam profile shows that the fundamental transverse mode dominated over the higher order modes. We could not properly evaluate beam quality factor M 2 at the highest output power because the conventional Gaussian beam fitting was not suitable.

The temporal power stability of the laser was examined with the cavity length of ∼102 mm. The output power was recorded for >60 minutes as shown in Fig. 3.17(b), and the peak-to-peak and RMS fluctuations were <1.5% and <0.25% , respectively.

(a) 7 (b) 7 6 6

5 ηsl,abs = 43.5% 5 4 4 3 3 2 2 Output power (W) Output power (W) 1 1 0 0 0 5 10 15 0 10 20 30 40 50 60 Absorbed pump power (W) Time (min.)

Figure 3.17: (a) Output characteristic of Pr3+:YLF laser at 640 nm with improved output beam profile. (b) Output power stability recorded for 60 minutes. 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 50

3.4.2 Single-emitter-cyan-blue-diode-pumped Pr3+:YLF laser

Subsequently, the cyan-blue LD (see Figs. 3.5 and 3.6) is used for pumping a Pr3+:YLF laser. The highest absorption peak at 479 nm (see Fig. 3.11) has been only accessed by 2ω-OPSLs. The pumping at longer wavelength improves the Stokes efficiency, and accordingly reduces the thermal load. The experimental setup of a Pr3+:YLF laser operated at 640 nm is shown in Fig. 3.18. As shown in Fig. 3.5(b), the emission wavelength of cyan-blue LD was shorter than the absorption peak. Therefore, the temperature of the LD was optimized to obtain the highest possible absorption. The highest absorption efficiency was attained when the temperature was set to 42◦C. For the laser experiments, two 0.3 at. % 12-mm long Pr3+:YLF crystals from two different companies (AC Materials and Unioriental Optics), respectively named Crystal A and B, were used. Even though the two crystals nominally have the same amount of dopant, the absorption coefficient of Crystal A was larger.

In the absorption spectroscopy, Crystal A was revealed to have the doping level of ∼ 0.36 at. %. The effective absorption coefficient for the cyan-blue LD was measured at 1.87 and 1.26 /cm for Crystal A and B, respectively.

The output from the LD was collimated by an aspheric lens (f = 3.1 mm) and expanded along its slow axis by a factor of five using a cylindrical expander consisting of a concavef lens( = −20 mm) and a convex lens

(f = 100 mm). The pump power incident into the laser crystal was varied using half-wave plate (HWP) and a polarizing beam splitter (PBS) rather than changing the forward current of LD, since the emission spectrum strongly depended on the forward current.

The simple straight cavity was formed by a plane dichroic mirror (DM) and a concave output coupler. Three output couplers were adopted to examine the output characteristics: transmittance T = 2.5% (radius of curvature R = 75 mm), T = 5.2% (R = 100 mm), and T = 8.6% (R = 75 mm). The cavity length was optimized so that the highest output power was obtained at the highest pump power. The output characteristics with two different laser crystals are shown in Fig. 3.19.

Aspherical lens (f = 3.1 mm) Damper

DM (plane) a Blue laser diode c Cylindrical (479 nm) a expander HWP (x 5) PBS Pr3+:YLF Lens (f = 75 mm) Concave OC (T = 75 or 100 mm)

Figure 3.18: Schematic image of Pr3+:YLF laser pumped by by a cyan-blue LD at 479 nm.

The highest output power of 266 mW was obtained when Crystal A and the output coupler of 2.5% transmission were used. The slope efficiency was high as the output coupling. The highest slope efficiency was obtainedwith

Crystal B. The highest slope efficiency was 62.9% when the output coupler of 8.6% transmission was used.This is the highest slope efficiency of diode-pumped3+ Pr lasers ever reported. Due to the much better beam quality 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 51

(a) 300 (b) 250 T OC = 2.5%, ηsl = 53.3% T OC = 2.5%, ηsl = 58.7% 250 T = 5.2%, η = 56.4% T = 5.2%, η = 60.8% OC sl 200 OC sl T OC = 8.6%, ηsl = 57.3% T OC = 8.6%, ηsl = 62.9% 200 150 150 100 100

Output power (mW) Output power (mW) 50 50

0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 Absorbed pump power (mW) Absorbed pump power (mW)

Figure 3.19: Output characteristics of cyan-blue-diode-pumped Pr3+:YLF laser operated at 640 nm with Crystal A (a) and B (b) of the 2ω-OPSL, Metz et al. achieved a slope efficiency of 68% at 640 nm [44]. The lower slope efficiencyis attributed to the lower mode matching efficiency of the pump LD.

The intrinsic cavity losses were estimated from lasing threshold using Findlay-Clay analysis [138]. Those with

Crystal A and B were respectively determined at ∼ 1.0% and ∼ 0.8%. Therefore, the higher slope efficiency with Crystal B could be explained by its better crystal quality. The coupling efficiency was calculated tobe

>90% with the 8.5% output coupling for both crystals.

Slope efficiency is given as the product of Stokes efficiency ηStokes, quantum efficiency ηQ, coupling efficiency

ηC, and mode-matching efficiency ηm. Assumed that the quantum efficiency was unity, the upper limit of slope efficiency is equal to Stokes efficiency. The Stokes efficiency3+ ofthePr :YLF laser at 640 nm pumped at

479 nm is 74.8%. Therefore, the product ηCηm was calculated at ∼ 84% from the experimentally obtained slope efficiency and the Stokes efficiency for Crystal B, and the output coupler of 8.6% transmission. Consequently, the mode matching efficiency was calculated to be >90%.

3.4.3 Fiber-coupled-diode pumping

Power scaling of the Pr3+:YLF laser at 640 nm was performed using a fiber-delivered spatially combined blue

LD source described in Section 3.1.2. Power scaling of lasers with fluoride crystalline hosts is often hindered due to their low fracture limit. Therefore, the maximum tensile stress in the Pr3+:YLF crystal was estimated to determine the optimum doping concentration before performing the laser experiments. The maximum tensile stress in the vicinity of the front facet was simply estimated by the following equation based on Peng et al.

[139]:   ( )2 w2 ′ ′ ηthPinα  − 1 p  σmax = αTE 1 , (3.2) 4πK 2 rb

′ where αT is the thermal expansion coefficient, E the Young modulus (85 GPa for YLF), ηth the thermal load, 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 52

Pin the incident pump power, α the absorption coefficient, K the thermal conductivity, wp the radius of the pump beam spot, and rb the radius of the laser rod. The smaller thermal conductivity (5.8 W/(m·K)) and larger thermal expansion coefficient (13.3 × 10−6 K−1) along the a-axis of the anisotropic YLF crystal was used

[132] to estimate the maximum possible tensile stress. The pump spot radius was set to 150 µm at the entrance surface. For absorption coefficient α, the experimentally obtained value was used. The minimum thermal load was the fraction of absorbed pump power that could never convert to light, the so-called quantum defect heating, corresponding to 1 − ηStokes, where ηStokes is the Stokes efficiency for 640-nm lasing. For a 0.5 at. %doping concentration crystal exhibiting an experimental absorption coefficient of 2.0 /cm for the fiber LD module, the maximum tensile stress was ∼20 MPa, which is smaller than the fracture limit of 40 MPa, when quantum defect heating was assumed [139]. The maximum thermal stress under non-lasing was expected to be much larger than that for lasing and, moreover, possible multiphonon relaxation may induce additional thermal load. In fact, a 0.5 at. % crystal fractured at an incident pump power of ∼20 W under non-lasing. Therefore, a crystal of 0.3 at. % doping concentration was adopted to avoid the risk of fracture during the experiment.

To qualitatively evaluate thermal lensing effect in an end-pumpedPr3+:YLF crystal, pump-probe experiment was performed in the setup depicted in Fig. 3.20.

Dumper

HeNe laser PBS HWP Blue cut DM a c filter Fiber-delivered CMOS blue pump beam a camera

Pr3+:YLF

Figure 3.20: Schematic image of experimental setup for qualitative evaluation of thermal lens in Pr3+:YLF crystal.

As the probe laser, a helium-neon (HeNe) laser at 632.8 nm was used. Because thermal lens in Pr3+:YLF crystal was polarization dependent, the output of the HeNe laser was linearly polarized by a polarizing beam splitter.

Then, the polarization was rotated by a half-wave plate so that the polarization of the probe beam became parallel to the crystal’s a- or c-axis. The pump and probe beams were combined by a dichroic mirror (DM) and launched into a 0.3 at. % Pr3+:YLF crystal of 5-mm long. In this experiment, the crystal was mounted in a water-cooled copper heat sink in which the temperature of circulating water was set to 18◦C. Then, the transmitted probe beam was profiled by a CMOS camera. The fiber-coupled LD module was operated◦ at25 C, and its peak wavelength was measured at ∼445.9 nm at the highest output power (see Fig. 3.8). The output from the delivering fiber was imaged to the3+ Pr :YLF crystal through spherical lenses (f = 60 and 200 mm), resulting a top-hat shaped pump spot of ∼330-µm diameter. The transmitted pump beam was filtered out 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 53 by a yellow colored glass filter. The beam size of the probe beam around the crystal’s position was measured at 670×710 µm2 (vertical × horizontal) in radius. The distance between the crystal and CMOS camera was

∼ 950 mm. The profiles of the transmitted probe beam with varied pump powers for the both polarizations were shown in Fig. 3.21.

Unpumped Pabs = 2.1 W Pabs = 4.1 W Pabs = 7.8 W Pabs = 10.4 W

polarization 1 mm - c σ polarization - π

Figure 3.21: Transmitted pump beam profile undergone thermal lens in end-pumped Pr3+:YLF crystal for varied absorbed pump powers. Figures in upper and lower column are profiles for σ and π-polarized probe, respectively. The size of images are all 4.61 × 3.69 mm2.

The results clearly showed that thermal lens in Pr3+:YLF crystal was strongly polarization dependent, and also anisotropic. For σ-polarization (polarization parallel to crystal’s a-axis), the crystal exhibited a positive lens along a-axis. The lensing along c-axis was negligibly small. The focal length of the positive lens was estimated to be ∼5 m at the highest absorbed pump power. On the other hand, for π-polarization, a strong negative lens along a-axis was formed. Moreover, the lens in c-axis was small and positive, therefore, the thermal lens of the

Pr3+:YLF crystal induces a strong astigmatism for π-polarization than for σ-polarization. Note that thermal lens under non-lasing condition is much stronger than that under lasing condition.

The nature of thermal lensing in YLF crystal has been studied by several groups [123, 132]. The obtained results did not contradict with the previously reported results. The special feature of thermal lensing in YLF crystal, that the sign of lenses for σ- and π-polarization were different, is explained by the end-bulge of facets andthe temperature dependent refractive index change dn/dT . The bulging of end-facets due to thermal expansion is always acting as a positive lens. However, dn/dT is always negative in YLF crystal. For σ-polarization, due to relatively small dn/dT (2.0 × 10−6 K−1), the positive contribution of the end-bulged facets were slightly larger, and consequently, resulted in a weak positive thermal lens. For π-polarization, dn/dT (4.3 × 10−6 K−1) is much larger than that for σ-polarization, and therefore, a negative lens was formed while the bulged facets slightly offset this negative lens.

The schematic view of the laser setup of the fiber-coupled-LD-end-pumped 3+Pr :YLF laser is shown in Fig. 3.22.

A 0.3 at. %, 12-mm long Pr3+:YLF crystal (Unioriental Optics) was used in this experiment. The crystal was cut perpendicular to crystal’s a-axis, and the facets were uncoated. 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 54

Lens (f = 60 mm) Lens (f = 200 mm) DM (plane)

Fiber-delivered Pr3+:YLF blue pump beam

OC HR (plane) (R = 300 mm)

Figure 3.22: Experimental setup of Pr3+:YLF laser at 640 nm end-pumped by fiber- coupled blue LD module.

As depicted in Fig. 3.22, the fiber output was imaged to the laser crystal through the two convex spherical lenses with at a magnifying power of 3.3, resulting a pump spot diameter of ∼330 µm. The laser cavity consisted of three mirrors: a dichroic mirror (DM), a highly reflecting (HR) concave mirror with a 300-mm curvature radius, and a plane output coupling mirror. The concave HR mirror’s incident angle was set to ∼7◦ to minimize cavity astigmatism. The distance between DM and HR mirrors L1 was fixed to ∼300 mm. The cavity mode size in the Pr3+:YLF crystal placed in the vicinity of the DM varied by changing the distance between the HR and

OC mirrors L2. The laser performance was evaluated with three OC mirrors with transmission of 1.1%, 1.4%, and 9.1% at 640 nm. In this experiment, the Pr3+:YLF crystal was water-cooled similarly as in the previous section.

At the highest incident pump power of 22.3 W, the absorbed pump power was 15.6 W corresponding to the absorption efficiency of 72.6% in which the Fresnel reflection at the crystal’s entrance surface was takeninto account. For all of the OC mirrors, the maximum output power was obtained when L2 was set to ∼255 mm. In this case, the gain medium’s spot diameter was calculated to be ∼280 µm by ABCD matrices. For this calculation, thermal lensing in the gain medium was also taken into account. The calculated cavity mode size did not change even when the thermal lens for the non-lasing condition was assumed. In fact, the thermal lens under the lasing condition is much smaller than that for non-lasing. Assuming a top-hat and a Gaussian shaped pump profile, the highest mode-matching efficiency was 47 and 56%, respectively. The CW output powerwith respect to the absorbed pump power is shown in Fig. 3.23(a). When L2 was shorter, resulting in a larger mode volume in the gain medium, a strongly aberrated output beam profile was obtained. On the other hand, the output power decreased due to reduced mode-matching efficiency with a longer L2 resulting a smaller mode size in the gain medium. The beam profile at the highest output power is also shown in Fig. 3.23(a), andthebeam quality M 2 was evaluated at <1.7.

The highest output power and slope efficiency was obtained with the OC mirror of the lowest transmission. The maximum absorbed pump power was 15.6 W and the output power was 3.4 W. In general, the slope efficiency increases as the output coupling increases, but our experimental result does not agree with the general laser 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 55

4 5 (a) η (b) TOC = 1.1% ( sl,abs = 25.0%) TOC = 1.1% (ηsl,abs = 25.2%) TOC = 1.4% (ηsl,abs = 22.3%) TOC = 1.4% (ηsl,abs = 24.8%) (η = 18.1%) 4 TOC = 9.1% sl,abs T = 9.1% (η = 24.5%) 3 OC sl,abs

3 2 2

Output power (W) 1 Output power (W) 1

0 0 0 5 10 15 0 5 10 15 20 Absorbed pump power (W) Absorbed pump power (W)

Figure 3.23: (a) CW and (b) quasi-CW output characteristics of Pr3+:YLF laser at 640 nm pumped by fiber-coupled blue LD module for three output coupling mirrors. For quasi-CW operation pump diode module was electrically modulated and operated with duty ratio of 25% and repetition frequency of 100 Hz. characteristic. The pump source operated in quasi-CW mode by directly modulating the forward current of the fiber LD module with a duty ratio of 25% and a repetition frequency of 100 Hz to reduce the thermal load.To perfectly remove the heat generated by the previous pump pulse, the repetition rate should be reduced. The output characteristics of the Pr3+:YLF laser in quasi-CW operation were plotted for the three OC mirrors, as shown in Fig. 3.23(b). The absorbed pump power and output power were both multiplied by a factor of four for easy comparison with the CW results (Fig. 3.23(a)). For the result with 9.1% OC transmission, the slope efficiency improved from 18.1 to 24.5% in the quasi-CW operation. Moreover, the temporal changein the quasi-CW output power with the OC mirror was monitored by a Si-photodetector, and the output power decreased in time as shown in Fig. 3.24. The initial spike just after the laser reached the threshold was due to the relaxation oscillation. It can be seen in Fig. 3.24(a) and (b) that the output power gradually decreased for a few milliseconds after the relaxation oscillation finished. This indicated the existence of a heat-induced loss even at the quasi-CW operation.

(a) 1.0 (b) 1.0 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Intensity (arb. units) Intensity (arb. units) 0.0 0.0 0 5 10 15 20 0 5 10 15 20 Time (ms) Time (ms)

Figure 3.24: Temporal output of quasi-CW Pr3+:YLF laser with 1.1% (a) and 9.1% OC (b) at the highest pump power. Pump sources was driven at 100-Hz repetition rate with duty ratio of 50%.

The temperature distribution in the Pr3+:YLF crystal was calculated using finite-element analysis software

(COMSOL Multiphysics®) as shown in Fig. 3.25. The temperature in the vicinity of the front surface dramatically increased and the highest temperature difference with respect to the crystal’s side boundary was estimated 3.4. Diode-pumped continuous-wave Pr3+:YLF lasers 56

∼80◦C, assuming the quantum defect heating. It should be noted that the strong natural birefringence of the

YLF crystal eliminated the heat-induced depolarization problem.

(K) (a) (b) (K)

Figure 3.25: Numerically calculated temperature distribution in Pr3+:YLF crystal. (a) 3D schematic image and (b) 2D temperature map in XZ plane.

The experimental results shown in Fig. 3.23 definitely reflect the increase in the cavity loss caused by strong thermal aberration. However, there should be additional physics to fully interpret Fig. 3.23 since the slope efficiency with higher output coupling was still lower even when the thermal load was reduced in thequasi-CW operations. Metz et al. investigated the dependence of the slope efficiency on the output coupling fora2ω-

OPSL-pumped Pr3+:YLF lasers at 523, 604, 607, 640, 698, and 720 nm. The lasers were operated in quasi-CW mode to minimize thermal load. They obtained the highest slope efficiency with output couplings between

2% to 6% for 523, 640, 698, and 720 nm. This results do not agree with the prediction by the laser theory.

Then, Metz et al. proposed nonlinear inversion dependent loss as a reason why the slope efficiency at higher output couplings decreased [44]. Higher population densities of the laser upper state at higher output couplings may induce some loss at the lasing wavelength in some way. Further detailed investigations are necessary for understanding this loss mechanism.

The slope efficiencies in CW and quasi-CW operation were unchanged for the 1.1% output coupling. Thus, the thermal load did not limit the laser performance in the CW operation with such a low output coupling.

The relatively low slope efficiency of 25% could be explained by the limited mode-matching efficiency and comparatively low transmission of the OC mirror. Further improvement in the laser performance will be obtainable when the cavity loss decreases, including using a high-quality laser crystal, so that the laser is optimized at a low output coupling.

Since strong thermal aberration limiting the laser output power was observed as shown in Fig. 3.23, the reduction of thermal load is essential for further power scaling of Pr3+:YLF lasers. For the longitudinal end-pumping, the use of undoped end-caps is effective to reduce the thermal load. Moreover, the undoped end-cap significantly decreases the maximum tensile stress in the vicinity of the entrance surface. The use of gain media with lower 3.5. Summary 57 doping concentrations is also advantageous in heat reduction; however, the gain media become longer to obtain sufficient pump absorption. Thus, this solution is not compatible with end-pumping by low brightness sources.

Therefore, other pumping configurations including a side pumping scheme could be a solution when high-power diode-bars are developed.

3.5 Summary

In this chapter, the characteristics of pump sources and laser crystals adopted in this work were presented in detail. In this thesis, the cutting-edge 5-W output single emitter blue LDs were employed. In addition, cyan-blue 3 →3 3+ LDs at 478-nm of 1-W output power were used to directly pump H4 P0 absorption line of Pr :YLF crystal, for the first time. >20-W fiber-coupled module was also adopted for power3+ scalingofPr -doped solid-state lasers.

The emission cross sections of Pr3+:YLF at 607 and 640 nm are in the order of 10−19 cm2. In general, fluoride crystalline hosts have low thermal conductivity and low fracture limit than oxide crystalline hosts. However, fluorides are attractive as a host for Pr3+ doping due to their very low phonon energy, resulting in a relatively

1 long fluorescence lifetime owing to the suppression of the multiphonon relaxation to the underlying D2 level. Use of low field crystals, including fluorides, are advantageous also in terms of excited-state absorption (ESA).

The position of 4f5d levels is strongly affected by crystalline field. Thus, it is essential to use host crystalsof low crystal field depression for3+ Pr lasers.

Using 5-W single-emitter blue LDs at ∼440 nm, continuous-wave Pr3+:YLF lasers operated at 523, 607, and

640 nm were demonstrated. Using four pump LDs, the highest output power of 6.7 and 3.7 W was obtained at 640 and 607 nm, respectively. These output characteristics were the highest in ever reported diode-pumped

Pr3+-doped solid-state lasers. At these operating wavelengths (σ-polarization), YLF crystal exhibited a small positive thermal lens while the thermo-optic coefficientdn/dT ( ) is negative. The strong negative thermal lens for π-polarization inhibited the power scaling at 523 nm. The highest output power was 1.8 W at the absorbed pump power of 5.4 W.

It was necessary to consider the limitation in doping concentration of gain medium, since the thermal fracture was observed when a 0.5 at. % Pr3+:YLF crystal was pumped by a fiber-coupled blue LD module delivering

>20 W pump power. The maximum tensile stress in 0.3 at. % crystal was calculated at ∼20 MPa when the quantum defect heating was assumed. The calculated tensile stress was half of the fracture limit (40 MPa).

Under non-lasing condition, the thermal load should be larger than that under lasing condition. Therefore, the doping level needed to be limited around this level in end-pumping geometry.

Using the fiber-coupled pump module, a pump limited output power of 3.4 W was obtained with anoutput 3.5. Summary 58 coupler of 1.1% transmission. The laser exhibited a degradation in the slope efficiency as the output coupler’s transmission, which contradicts with the classical laser theory. A part of the degradation could be attributed to the thermal effect because the slope efficiency could be improved when the pump source was operatedin quasi-CW mode. The thermally induced diffraction loss was also may take place. Despite of the effortsto minimize the thermal load, the highest slope efficiency was still obtained with the output coupler of thelowest transmission (T = 1.1%). This observation was tentatively attributed to an inversion dependent loss mechanism.

Further investigations are required to fully understand the observations.

Table 3.5 summarizes the obtained CW laser results. Figure 3.26 shows schematically summarizes the recently reported results of CW Pr3+:YLF lasers operated at 640 nm. The output power of 6.7 W at 640 nm was the highest ever reported. The optical-to-optical efficiency is comparable with the previously reported results. To the best of author’s knowledge, the demonstration of Pr3+:YLF laser with fiber-combined low brightness pump sources has never been reported. It should be noted that the brightness of the used fiber-coupled blue LD module was >100-times lower than that of the 5-W single emitter blue LD.

In the end-pumping geometry presented in this chapter, the power of Pr3+:YLF lasers is limited due to the low fracture limit of the crystalline host. The thermally induced tensile stress can be reduced by adopting crystals of lower doping concentration; however, lower absorption coefficient tends to reduce mode-matching efficiency with low brightness pump sources. It is believed to be effective to use an undoped end-cap. Regarding >100-W pump power, the use of oxide crystalline hosts needs to be considered for further power scaling.

7.5 [This work] Single-emitter GaN-LD 5

2ω-OPSL [This work]

Output power (W) [44] Fiber-coupled 2.5 [46] GaN-LD

[42] Single-emitter [37] GaN-LD

0 5 10 15 20 25 Pump power (W)

Figure 3.26: Overview of recently reported continuous-wave Pr3+:YLF visible lasers operated at 640 nm. The triangle and square symbols represent results of 2ω-OPSL and GaN-LD pumping, respectively. The star expresses the result with a combined low brightness pump LD. The color of symbols correspond to the wavelength of pump sources, i.e. blue and cyan-blue symbols respectively correspond to the pump wavelength of sim450 and 479 nm. The numbers in the vicinity of each symbol indicates a corresponding reference. The gray chain lines indicate optical-to-optical efficiency with respect to the power of pump sources. 3.5. Summary 59 t :YLF visible lasers in 3+ highest power. highest power. highest slope efficiency with diode pumping. highest power with combined low brightness pump. Commen The The The The Output 640607640 6.7640 3.7 0.27 45.5 3.4 30.0 63 25.0 (nm) (W) (%) avelength Power Slope efficiency W 8 20 20 2 × × × 2 M 2 2 ∼ 70 ∼ ∼ ∼ able 3.5: Summary of demonstrated diode-pumped Pr T continuous-wave operation. source Pump 479 1 (nm) (W) ∼ 440 20 ∼ 440 20 ∼ 445 23.9 avelength Power Beam quality W Chapter 4

Characterization of transition-metal-doped saturable absorbers

In this chapter, experimental characterization of transition-metal-doped solid-state saturable absorbers are presented. First, the methods for determine the saturation parameters of saturable absorbers are described.

The investigated samples are mainly tetravalent chromium ion (Cr4+) and divalent cobalt ion (Co2+) –doped oxide crystals.

4.1 Methods

Dynamics of saturable absorbers are in general described by a four-level model as depicted in Fig. 4.1. This model is valid only if there is no intermediate levels between the ground and the excited states so that the population change in the excited state is characterized by a single exponential decay. Saturable absorbers modeled by this four-level system have three parameters: recovery time τ, ground state absorption (GSA) cross section σgs, and excited state absorption (ESA) cross section σes. The transmission of a saturable absorber modeled by this four-level system is given as:

T = exp [− (σgsngs + σesnes) lSA] , (4.1)

where nes is the population density in the excited state, and lSA the thickness of the saturable absorber.

60 4.1. Methods 61

The relaxation from the meta-stable level E3 to the excited state E2 is assumed to be very fast, so that the population density of the meta-stable level E3 is considered to be zero. An ESA from E2 to E4 is taken into account, otherwise the transmission of saturable absorber can be 100% when perfectly bleached. The lifetime of the upper lying E4 is considered to be infinitely short so that the ESA never bleaches, so the ESA represents the residual absorption, so-called non-saturable loss, of saturable absorbers.

The small signal transmission, or initial transmission, of the saturable absorber is given when all the absorption centers are in the ground state. Moreover, the highest transmission of the saturable absorber, so-called the saturated transmission, is given when the ground state is empty. Thus, the small signal transmission, or initial transmission, T0 and the saturated transmission Tsat of the saturable absorber are respectively written as follows:

T0 = exp (−σgsntotlSA) , (4.2)

Tsat = exp (−σesntotlSA) , (4.3)

where ntot is the total density of absorption center. The largest possible transmission change ∆T = Tsat − T0 is defined as modulation depth of saturable absorber.

E3 nes E2 excited-state

ngs E0 ground-state

Figure 4.1: Four-level model for saturable absorbers.

The recovery time was measured by pump-probe measurements. The schematic of the optical layout for the measurements are illustrated in Fig. 4.2. As the pump pulsed laser, an optical parametric oscillator (OPO)

(versaScan, SpectraPhysics) which enabled wavelength tuning from 206 to 2550 nm. The OPO was pumped by a frequency-tripled Q-switched Nd:YAG laser at 355 nm (Quanta-Ray INDI, SpectraPhysics). The pulse energy of the OPO was >10 mJ, and the pulse duration was ∼5 ns for the wavelength range of 400–700 nm.

As the probe laser, a continuous-wave (CW) helium-neon (HeNe) laser at 632.8 nm provided an output power of ∼5 mW, since all the samples investigated in this study had a GSA at this wavelength. The pump and probe beams are respectively focused so that the two beam were spatially overlapped in the samples. Note that the probe beam size was kept smaller than that of the pump beam. The transmitted probe beam was 4.1. Methods 62 directed to a Si-photodetector (PD). The temporal change in the output signal of the PD, which was equivalent to the transmitted probe power, was monitored by an oscilloscope. Just before the PD, a narrow bandpass filter transmitting only around 632.8 nm was placed to suppress the unwanted scattered or reflected pumplight.

Although the bandpass filter was used, the signal without the probe beam was recorded, and this pump-only- signal was subtracted from the signal of the pump and probe to further avoid noises owing to the unwanted pump light. Note that the oscilloscope was synchronized with the pump laser for this signal processing. The

PD and the oscilloscope was connected with a shielded BNC cable because an unshielded BNC cable acting as an antenna received a radio frequency (RF) noise from the flash-lamp for the Q-switched Nd:YAG laser.

HeNe laser (632.8 nm)

Lens

Lens Sample

Lens Photo- Bandpass detector filter

Figure 4.2: Experimental setup of pump-probe measurement to estimate recovery time.

The time-dependent transmission of a saturable absorber is equated as follows:

[{ ( ) ( )} ] t t T (t) = exp −σ (n − n (t = 0)) exp − − σ n (t = 0) exp − l , (4.4) gs tot es τ es es τ SA where τ is the recovery time. In this equation, the optical excitation was considered to be instantaneous. The first and second terms on the right hand side represent respectively the GSA and the ESA. Eq. (4.4)isthen transformed as follows:

[ ( )] T (t) t ln ln = − + ln [(σgs − σes)neslSA] . (4.5) T0 τ

This equation tells us that the recovery time can be determined from the slope −1/τ of the processed signal.

As far as the output signal voltage of the PD, V (t), is proportional to the transmission T (t), T (t)/T0 can be replaced by V (t)/V0, where V0 is the output signal of the PD corresponds to the initial transmission T0.

For determining GSA and ESA cross sections, Z-scan measurements and numerical fitting were performed. The optical layout of the Z-scan measurements is depicted in Fig. 4.3.

The wavelength tunable OPO was again used as the pump source. Because the output beam was strongly 4.1. Methods 63

Energy meter 1 Cylindrical lens

Sample Energy meter 2

1:1 BS Lens Scanning by motor- controlled stage

Figure 4.3: Experimental setup of Z-scan measurement. astigmatic, a cylindrical lens was used to compensate the astigmatism at the focus. The beam was split into two by the 1:1 beam splitter (BS). One of beams was directed to an energy meter (PE25-C, Ophir) to monitor the fluctuation of the pulse energy. The other beam was focused into a sample, and the energy of thetransmitted pulse was measured by another energy meter (PE25-C, Ophir). The sample was translated using a motor- controlled translation stage around the focus to vary the incident pulse fluence. The transmission versus the position (coordinate Z) was recorded with an automated LabVIEW (National Instrument) program.

The GSA and ESA were determined by numerically reproducing the obtained curve of transmission versus position, so-called Z-scan curve. The used numerical model is governed by the following equation:

∫∫ [ ( )] ∂Ep EpΦ˜ p = −(1 − fp)Fsaαp0 1 − exp − dxdy − αp0fpEp, (4.6) ∂z Fsa

where Ep is the pulse energy as a function of coordinate z representing the position in the sample, Fsa the saturation fluence of the sample, fp the ratio of GSA and ESA cross sections (σes/σgs), αp0 the small signal absorption coefficient, and Φ˜ p the spatial distribution function. The beam profile of the focused pump beam was measured by a CMOS beam profiler (CMOS-1202, CINOGY). The profile had a Gaussian-like distribution rather than a top-hat distribution, so the spatial distribution was considered as a Gaussian given as:

( ) ( ) 2 2 ˜ 2 − 2x · 2 − 2y Φp(x, y) = 2 exp 2 2 exp 2 (4.7) πwpx(z) wpx πwpy(z) wpy

where wpx(z) and wpy(z) are the pump beam radius in x and y directions in the sample. It is noteworthy that the ESA cross section is always overestimated when a top-hat pump distribution is assumed [87]. For a hypothetical saturable absorber, the transmission as a function of an incident pulse energy was calculated and shown in Fig. 4.4 with a Gaussian and a top-hat pump distributions. It is clearly seen that the transmission at the saturation regime (Ein > 50 µJ) is much higher for the top-hat beam compared to the Gaussian beam, since the non-uniform distribution of the Gaussian shaped beam has a low fluence component at the tail. Thus, for a given experimental result, a best fitting is obtained with a higher ESA cross section. 4.1. Methods 64

0.9

0.8

0.7

0.6

Transmission 0.5

0.4 Gaussian Top-hat 0.3 0 50 100 150 200 250 300 Incident pulse energy (µJ)

Figure 4.4: Transmission of hypothetical saturable absorber as a function of incident pulse energy for Gaussian and top-hat distributed pump beams. Parameters used for Fig. 4 in [87] were adopted for this hypothetical saturable absorber.

In a numerical model used for the fitting, the variation of pump beam size in the samples were taken into account. However, all the samples were much shorter than the confocal length of the pump beams, and the calculated results did not change even if the variation of the beam size was ignored. Therefore, a pulse fluence could be defined simply as the pulse energy divided by the beam cross section at the sample’s incident facet.

For making the fitting procedure systematic, the best numerical fitting was defined as a set of parameters which minimize the fitting error given as follows:

∑n | k − | ϵ = Tm(Z) Tﬁt(Z) , (4.8) k=1

k k where Tm is the set of measured transmission, and Tﬁt the set of calculated transmission at a relative position of the sample Z. However, it is practically challenging to determine uniquely the pair of the GSA and ESA cross sections, because the pairs resulting the minimum fitting error are always somehow broadened inthe two-dimensional parameter space as depicted in Fig. 4.5. It was practically confirmed that a slight increase in the GSA cross section could be compensated by a slightly increased ESA cross section. This uncertainly (∆σgs and ∆σes in Fig. 4.5) in the fitting procedure could be minimized by measuring the transmission ofsamples with a wide range of incident pulse fluence. For instance, if transmission data in the low fluence regime are only obtained, typically show a linear characteristic (up to 20–30 µJ in Fig. 4.4), infinite sets of cross sections enables to fit the result. Thus, it was important to perform Z-scan measurements with the longest scanning range to widely vary the incident pulse fluence.

The small signal absorption coefficient αp0 was directly measured by an absorption spectroscopy with a double- beam spectrometer (UV3600plus, Shimadzu or LAMBDA1050, Perkin Elmer). Even while it was possible to determine this parameter from the Z-scan measurement, the αp0 directly measured by the spectrometer was expected to be much accurate, since the pump beam used in the Z-scan measurement was too energetic to 4.2. Sample preparation 65

Parameter space resulting minimum fitting error ESA cross section cross ESA

GSA cross section

Figure 4.5: Schematic image of fitting parameter space. Grayed area represents pairs of GSA and ESA cross sections resulting minimum fitting error. determine the small signal transmission. Moreover, it was not favorable to reduce the incident pulse fluence for estimating the small signal transmission, because the energy meter did not support the accurate measurements with such small pulse energy. Please see Section 3.3.1 for the detailed method of absorption spectroscopy. In several previous studies on characterization of saturable absorbers, the incident pulse fluence was varied directly by changing the incident pulse energy rather than the beam size [71]. However, the incident pulse fluence should be varied by the beam size due to its capability to vary in a wider range of fluence. In fact, the range which can be varied by changing the energy was limited due to a dynamic range of pulse energy meters.

4.2 Sample preparation

The samples investigated in this study were all cut from as-grown boules. The as-grown boules were first cut into a slice by utilizing a wire-saw, and the both facets of the slice were then polished by a polishing machine.

The surface roughness was reduced down to ∼1 µm. Note that none of efforts to achieve a good parallelism were made. It was experimentally confirmed that the scattering at the polishing surfaces was sufficiently suppressed with the roughness of ∼1 µm. However, this order of surface roughness is not enough for laser experiments, since laser cavities are very sensitive to small scattering losses. Furthermore, to insert into laser cavities, facets should be kept parallel otherwise the uncoated facets induces large insertion losses.

4.3 Cr4+-doped oxide crystals as saturable absorbers

4+ 4+ 4+ As mentioned in Section 1.2.4, Cr -doped oxides such as Cr :Y3Al5O12 (YAG) and Cr :Mg2SiO4 (forsterite) have been employed as passive Q-switching materials for 1-µm lasers such as Nd3+ and Yb3+ lasers. In this 4.3. Cr4+-doped oxide crystals as saturable absorbers 66 section, the investigation of visible absorption in Cr4+:YAG and Cr4+:forsterite were presented.

4+ 4.3.1 Cr :Y3Al5O12 (YAG)

Yttrium aluminum garnet (Y3Al5O12, YAG) is a one of the most common laser crystalline host. YAG has a well-known garnet crystal structure as shown in Fig. 4.6.

2- O Tetrahedral Al3+ site

Y3+ Octahedral Al3+ site

Figure 4.6: Crystal structure of YAG (drawn by VESTA [122]). Yellow, blue, and red spheres are trivalent yttrium cations (Y3+), trivalent aluminum cations (Al3+), and diva- 2– 2– 2– lent oxygen anions (O ). AlO4 -tetrahedrons and AlO6 -octahedrons are respectively colored by green and blue.

It is known that doped Cr ions substitute to octahedrally and tetrahedrally coordinated Al3+, regarding the ionic radii of Cr and Al ions. If there is no co-dopant for charge compensation, doped Cr ions mainly form trivalent state (Cr3+). To form tetravalent state in YAG, charge compensating ions, such as Ca2+ and Mg2+ respectively substitute to Y3+ and Al3+ site, are in general necessary. In this study, two samples of (111)-cut

Cr4+:YAG were investigated. These samples were both grown in CEA Grenoble. The absorption spectrum of these samples are shown in Fig. 4.7. The Fresnel reflections on the uncoated facets were taken into account using Sellmeier equation of undoped YAG [140]. The spectra were normalized at 1064 nm for comparison.

The absorption coefficient of Sample 1 and 2 at 1064 nm were 6.38 and− 9.21cm 1, respectively. Owing to the

4+ 4+ 4+ existence of several kinds of possible absorption centers, such as Cr in the tetrahedral site (Cr (Td)), Cr

4+ 3+ 3+ in octahedral site (Cr (Oh)), and Cr in octahedral site (Cr (Oh)), absorption spectra are different from sample to sample. The energy diagram for the three absorption centers are shown in Fig. 4.8. The symmetry

2– of the tetrahedron CrO4 is reduced to S4, but it is approximately considered to be D2d by only taking into account the closest ligands. Although YAG has a cubic crystal structure, the local distortion of the tetrahedron induces a polarization dependence [80]. The absorption around 600-680 nm has been attributed to transition 3 3 → 3 3 4+ B1( A2g) E( T1g) of Cr (Td).

However, in this range, absorption bands of the other absorption centers are overlapping. In fact, the Cr3+

4+ (Oh) has an absorption centered at ∼600 nm, and the absorption centered at ∼480 nm of Cr (Oh) is very 4.3. Cr4+-doped oxide crystals as saturable absorbers 67

15 Sample 1 Sample 2

(arb. units) Sample 1 Sample 2

Normalized abs. coeff. 0 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)

Figure 4.7: Absorption spectra of Cr4+:YAG crystals. Absorption coefficients were normalized at 1064 nm.

35 3 T1 1 A1 30

25 )

1 4 - T1g

cm 3 20 T2 3

1 1 A1 A2 4T 1 2g 15 3E E2 1 2 T Eg 3 2 T1 1 B1 1 3E E 1 Energy Energy (10 10 3T A1 2 3A 3 2 B2 482 482 nm 600 600 nm 278 278 nm 432 nm 5 896 896 nm 1117 nm 1117 653 653 nm 616 nm 1025 nm 1025 3 3 3 4 0 A2 B1 T1 A2g Td D2d O Oh Cr4+ Cr4+ Cr3+ (tetrahedral) (octahedral) (octahedral site)

Figure 4.8: Energy diagram of tetrahedrally coordinated Cr4+, octahedrally coordinated Cr4+, and octahedrally coordinated Cr3+ in YAG, and associated absorption transitions. 4.3. Cr4+-doped oxide crystals as saturable absorbers 68

4+ broad. Thus, it is important to estimate the amount of absorption owing to the Cr (Td). For this purpose, the absorption spectra shown in Fig. 4.7 were resolved using the data of peak positions and widths [86]. These parameters are listed in Table 4.1. Because the authors of the reference [86] estimated and subtracted the

3+ 3+ amount of absorption due to the Cr by using a fully reduced sample, the absorption peaks for Cr (Oh) are not listed. They adopted a one-side truncated function given by the following equation for resolving the absorption peaks.

(δ/2π) 1 Φ(˜˜ ν) = I × [ ] (4.9) 0 2 2 − − (ν˜ − ν˜0) + (δ/2) (˜ν ν˜0) δ/2 1 + exp δ/2

ν˜ is the wavenumber, ν˜0 the center wavenumber, and I0 the peak intensity. The peak wavenumber is at

ν˜p =ν ˜0 + 0.07δ, the peak’s full width at half maximum is ν˜FWHM, and the integrated intensity is defined as ∫ ∞ ˜ ∼ I = 0 Φ(˜ν)dν˜ = 0.60544I0. The peak intensity I0 for peaks No. 1 5 are preserved as Table 4.1.

Table 4.1: Peak positions and widths of Cr4+:YAG after [86].

Peak number Attributed absorption center Peak position Peak width (cm) (cm−1)(cm−1) 4+ 1 Cr (Td) 1117 8955 330 4+ 2 Cr (Td) 1025 9755 1730 4+ 3 Cr (Td) 896 11160 1540 4+ 4 Cr (Td) 653 15310 1240 4+ 5 Cr (Td) 616 16245 615 4+ 6 Cr (Oh) 482 20740 4410 7 Cr4+ Not assigned 406 24625 6950 8 Cr4+ Not assigned 361 27710 6350 4+ 9 Cr (Oh) 278 35900 4850

4+ The absorption transitions around 1 µm are purely originated from Cr (Td). Therefore, it was expected that the amount of the orange-red absorption was obtained by fitting around 1 µm. The intensity of other peaks were independently determined; otherwise a good fitting was never obtained. The resulting resolved spectra of

Sample 1 and 2 are shown in Fig. 4.9. The estimated absorption coefficient at 607 and 640 nm owing4+ toCr

−1 −1 (Td + Oh) are 11.0 and 11.3 cm for Sample 1, and 17.4 and 17.9 cm for Sample 2, respectively. In the resolved absorption spectrum for Sample 1, a major discrepancy between the experimental and fitting results

3+ was observed around ∼600–800 nm. This may be owing to the absorption originated from Cr (Oh), and impurities. Also in the resolved absorption spectrum of Sample 2, a relatively large discrepancy was observed around 600–800-nm range. In addition to this, a relatively large discrepancy is clearly seen at ∼400 nm. This

3+ may be due to the absorption owing to Cr (Oh) which expected to have an absorption around this wavelength range (see Fig. 4.8).

Subsequently, pump-probe measurements were performed to determine the recovery time. The measurements 4.3. Cr4+-doped oxide crystals as saturable absorbers 69

80 (a) experimental peak No. 1 peak No. 2 peak No. 3 60 Sample 1 peak No. 4 peak No. 5 peak No. 6 peak No. 7 40 peak No. 8 peak No. 9 fit result 20 Abs. coeff. (/cm) 0 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)

experimental (b) 140 peak No. 1 peak No. 2 120 peak No. 3 Sample 2 peak No. 4 100 peak No. 5 peak No. 6 80 peak No. 7 peak No. 8 60 peak No. 9 fit result 40 20 Abs. coeff. (/cm) 0 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)

Figure 4.9: Resolved absorption spectrum of Cr4+:YAG crystals. (a) Sample 1, and (b) Sample 2. were conducted with two pump wavelength, 607 and 640 nm. The results are shown in Fig. 4.10. The pump pulse energy was set to ∼3 mJ for the both pump wavelengths. The vertical axis was the normalized output voltage from the photodetector V (t)/V0, corresponding to the normalized transmission T (t)/T0. The inset figures are calculated ln(ln(V (t)/V0)) . For both samples, a fast relaxation component owing to the concentration quenching was observed regard less of the pump wavelength. This fast relaxation was much obvious for Sample 2 because of its higher doping concentration. From the inset figures, the recovery time of Sample 1 was estimated tobe

4.20.2 µs, and 4.10.2 µs when pumped at 607 and 640 nm. For Sample 2, it was 4.40.5 µs and 4.30.5 µs at 607 and 640 nm, respectively.

The pump wavelength was further tuned to the shorter wavelength, and it was confirmed that4+ Cr :YAG can be used as a saturable absorber down to ∼580 nm. Owing to the small transmission in the wavelength range of 450–600 nm, a (100)-cut crystal of low doping concentration (Scientific Materials, Inc.) (named Sample

3 in this chapter) was used. Interestingly, the Cr4+:YAG exhibited a drop in transmission after the pump irradiation, and this phenomenon was enhanced as the pump wavelength was shorter as shown in Fig. 4.11.

This observation was attributed to the ESA to the conduction band of the crystalline host, and the subsequent color center formation, which is the common phenomenon for UV-pumped lasers such as Ce3+-doped fluoride lasers [141]. The transmission change of Sample 3 pumped at 500 nm recorded over 20 ms is shown in Fig. 4.12.

Assuming a single exponential decay of the color center, its lifetime was estimated to be ∼7 ms. The bleaching 4.3. Cr4+-doped oxide crystals as saturable absorbers 70

1.60 1.60 (a) 0.0 (b) 0.0 1.50 -1.0 1.50 -1.0 ) ) 0 0 -2.0 -2.0 1.40 1.40 -3.0 -3.0 0 0 ln(ln( V(t)/V 1.30 ln(ln( V(t)/V -4.0 1.30 -4.0

-5.0 -5.0 V(t)/V V(t)/V 1.20 1.20 -6.0 -6.0 -2 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 4 6 8 10 12 14 16 18 20 1.10 Time (µs) 1.10 Time (µs)

1.00 1.00

0.90 0.90 -2 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 4 6 8 10 12 14 16 18 20 Time (µs) Time (µs)

1.25 1.30 (c) -1.0 (d) 0.0

1.20 -2.0 1.25 -1.0 ) ) 0 0 -2.0 -3.0 1.20 1.15 -3.0

0 -4.0 0

ln(ln( V(t)/V 1.15 ln(ln( V(t)/V -4.0 1.10 -5.0 -5.0

V(t)/V V(t)/V 1.10 -6.0 -6.0 1.05 -2 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 4 6 8 10 12 14 16 18 20 Time (µs) 1.05 Time (µs)

1.00 1.00

0.95 0.95 -2 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 4 6 8 10 12 14 16 18 20 Time (µs) Time (µs)

Figure 4.10: Results of pump-probe measurements of Cr4+:YAG crystals. Sample 1 pumped at 607 nm (a), and at 640 nm (b). Sample 2 pumped at 607 nm (c), and at 640 nm (d). in absorption became negligibly small when pumped at 520–530 nm, however, the bleaching became again larger for even shorter pump wavelength. Regarding the excitation spectrum of Cr4+:YAG crystal presented by Kück

4+ et al. exhibited a dip around 525 nm [142]. This may indicate that Cr (Oh) may contribute to the saturable

4+ absorption because the bleaching could be still observed below 525 nm even while the absorption of Cr (Td) is absent.

Finally, Z-scan measurements of the Cr4+:YAG crystals, Sample 1 and 2, were performed at 607 and 640 nm to estimate the GSA and ESA cross sections at these wavelengths. The samples were scanned ∼100 mm using the stepping motor translation stage. The pulse energy was optimized for the accurate numerical fitting process so that the input pulse fluence was high enough to record the characteristic in the saturation regime. However, the samples were damaged when the pulse energy was higher than ∼3 mJ at the focus, corresponding to the incident pulse fluence of ∼2.5 J/cm2, so the pulse energy was kept below 3 mJ in these measurements. The transmission characteristics of Sample 1 and 2 as the function of the input pulse fluence (in which the Fresnel reflection at the uncoated front facet was taken into account) for pump wavelength of 607 nm and 640nmwere shown in Fig. 4.13.

Then numerical fitting was performed for each curve. The resulting parameters exhibiting the minimum fitting error were summarized together with the other material parameters in Table 4.2. The solid lines in Fig. 4.13 are 4.3. Cr4+-doped oxide crystals as saturable absorbers 71

1.05

1 580 nm 560 nm

0 540 nm 0.95 530 nm 520 nm V(t)/V 510 nm 0.9 490 nm 470 nm

450 nm 0.85 -5 0 5 10 15 20 25 Time (µs)

Figure 4.11: Results of pump-probe measurements of Cr4+:YAG crystal pumped from 580 to 450 nm. Incident pulse energy was fixed to ∼3 mJ for all the wavelengths.

1.01 1.00 0.99 0.98 0 0.97 0.96 V(t)/V 0.95 0.94 0.93 0.92 0 5 10 15 Time (ms)

Figure 4.12: Transient and normalized photodetector output voltage V (t)/V0 recorded over 20 ms measured at 450 nm.

(a) 0.50 (b) 0.50 0.45 0.45

0.40 0.40

0.35 0.35

0.30 0.30 Transmission Transmission 0.25 0.25

0.20 0.20 Sample 1 (T0 = 24.0%) Sample 1 (T0 = 26.7%) Sample 2 (T = 17.9%) Sample 2 (T = 19.5%) 0.15 0 0.15 0 0 0.5 1.0 1.5 2.0 0 0.2 0.4 0.6 0.8 1.0 1.2 Fluence (J/cm2) Fluence (J/cm2)

Figure 4.13: Transmission of Cr4+:YAG crystals as a function of incident pulse fluence pumped at (a) 607 nm, and (b) 640 nm. The pulse energy at 607 and 640 nm were respectively 3.0 and 2.8 mJ. Symbols are experimentally obtained results. Solid lines are results of numerical fitting with the minimum fitting error. 4.3. Cr4+-doped oxide crystals as saturable absorbers 72

Table 4.2: Summary of measured and determined parameters of Cr4+:YAG crystals.

Wavelength (nm) 607 640 Sample 1 2 1 2

T0 0.240 0.179 0.267 0.195 −1 α0 (cm ) 17.95 26.17 16.60 24.87 4+ −1 α0 (Cr ) (cm ) 11.01 17.41 11.30 17.88 3+ −1 α0 (Cr )(cm ) 6.94 8.76 5.30 6.99 −18 2 σgs (×10 cm ) 4.5–4.8 4.7–4.9 4.6–4.8 4.6–4.8 −18 2 σes (×10 cm ) 0.90–1.03 1.97–2.11 1.47–1.58 2.28–2.42

fp(= σes/σgs) 0.200–0.215 0.420–0.430 0.320–0.330 0.495–0.505 n (×1018 cm−3) 2.29–2.45 3.55–3.70 2.35–2.46 3.73–3.89

Tsat 0.477–0.484 0.344–0.348 0.488–0.492 0.349–0.353 the best fitting curves obtained with these parameters. For the both samples, the almost identical GSAcross sections were determined for 607 and 640 nm. As shown in Fig. 4.5, the minimum fitting error was obtained with certain sets of parameters for each result. Theoretically, the density of absorption center n at 607 and 640 nm is thought to be same. This was confirmed by the almost identical n for each sample. The determined ESA cross sections were largely varied for the two samples. Sample 2 exhibited much larger effective non-saturable loss owing to the larger ESA cross section. This may indicate the estimation of absorption coefficients originated from Cr4+ and Cr3+ are not perfect. However, it should be noted that the determination of the GSA cross section was not affected by this imperfection, because the parasitic absorption3+ duetoCr can effectively be considered as a part of the non-saturable loss of Cr4+. For the accurate determination of the ESA cross section of a pure Cr4+ in YAG, a sample in which the accurate doping concentration is known may be required.

The saturation fluence Fsat could be calculated be using the determined GSA cross sections as follows:

hν Fsat = , (4.10) σgs and determined at ∼70 mJ and ∼65 mJ at 607 and 640 nm, respectively. Moreover, the saturation intensity

Isat could be also estimated by using the experimentally determined recovery lifetime of ∼4 µs as Isat = Fsat/τ. The saturation intensity was calculated at ∼17.5 and ∼16.3 kW at 607 and 640 nm, respectively.

The saturable absorption in Cr4+:YAG at 1 µm has been known to be polarization dependent, and the saturation characteristics are different for samples of different cut angles [79, 89, 143]. It is known that an incidentlight at 1064 nm polarized parallel to the crystal’s [100]-direction is absorbed only by Cr4+ in the tetrahedrons stretched in [100]-direction. This can be easily confirmed by applying the selection rules to the transition 3 →3 3 B1(2 A2g) A2( T1g). On the other hand, an incident light at 600–680 nm polarized parallel to the crystal’s [100]-direction is absorbed only by Cr4+ in the tetrahedrons stretched in [010]- or [001]-directions. Thus, the 3 →3 3 saturable absorption of the transition B1(2 A2g) E( T1g) must be also polarization dependent. According 4.3. Cr4+-doped oxide crystals as saturable absorbers 73 to the work of Sato et al. [143], the polarization is the most clearly seen in a (100)-cut crystal. However, the samples used in the measurements were both (111)-cut. To observe the polarization dependence, the samples were rotated for various incident fluence. However, no transmission change was obvious when rotated. This can be explained by the too high excitation level. The polarization dependence is in general observed as a relatively low excitation level, and a continuous-wave (CW) source was employed in previous reports [79, 143].

The highly energetic pulse source may not suitable to check the polarization dependence, and it is believed that the polarization dependence will be further confirmed by using a CW excitation source.

4+ 4.3.2 Cr :Mg2SiO4 (forsterite)

4+ ∼ Cr -doped Mg2SiO4 (forsterite) is recognized as a laser gain medium at 1.2 µm. Owing to its broad emission spectrum, Cr4+:forsterite exhibits a wide wavelength-tuning range [144, 145], and moreover, femtosecond pulse generation by means of mode-locking has been reported [146, 147]. The Cr4+:forsterite laser is pumped by 1-µm lasers such as Nd3+ or Yb3+-based solid-state lasers. Since the saturable absorption at this pump wavelength was observed, the Cr4+:forsterite has been employed also as a saturable absorber for 1-µm lasers.

Because the saturable absorption of the tetrahedrally coordinated Cr4+ in YAG was experimentally confirmed, it was worthwhile to investigate other crystalline hosts in which tetrahedral Cr4+ can be formed. As presented in the previous section, the co-existence of several kinds of absorption centers in YAG is problematic, and so a host crystal of limited valence and site is required. From this aspect, the forsterite crystal is attractive because of its limited substitution sites. The crystal structure of the forsterite is depicted in Fig. 4.14.

Tetrahedral Si4+ site

O2-

Octahedral Mg2+ site (II) Octahedral Mg2+ site (I)

Figure 4.14: Structure of Mg2SiO4 (forsterite) crystal (drawn by VESTA [122]). Orange, blue and red spheres are Mg2+, Si4+ and O2– ions. There are two symmetry site for Mg2+: Mg2+ site (I) with inversion symmetry and Mg2+ site (II) with mirror symmetry.

Forsterite is categorized in the space group of Pbnm, and has only two sites, tetrahedrally coordinated Si4+ and octahedrally coordinated Mg2+. There are two types of Mg2+ sites: Mg2+ (I) with inversion symmetry and Mg2+ (II) with mirror symmetry. According to the reports on the crystal growth of Cr:forsterite, the 4.3. Cr4+-doped oxide crystals as saturable absorbers 74 substitution of Cr4+ in the tetrahedral Si4+ sites and the substitution of Cr3+ in the octahedral Mg2+ sites were found, despite of the large difference between the ionic radii [148, 149].

A sample used in this work was a 1.08-mm thick Cr4+:forsterite crystal cut perpendicular to the crystal’s c-axis.

The measured polarization-resolved absorption spectrum is shown in Fig. 4.15. The Fresnel reflections on the uncoated facets were taken into account using the reported refractive index of Cr:forsterite [150]. The intense absorption peaks around 550 nm for polarization parallel to the crystal’s a-axis (E||a) and around 700 nm for 4+ polarization parallel to the crystal’s b-axis (E||b) can be explained by tetrahedrally coordinated Cr . The 2– CrO4 tetrahedrons undergo the uniaxial distortion along the crystal’s a-axis and the resulting symmetry is reduced to C3v. Furthermore, the tetrahedrons are stretched along the c-axis and the symmetry is further reduced to Cs [151]. The energy levels for symmetries of Td, C3v, and Cs and associated splitting are illustrated in Fig. 4.16.

20 E ||a E 15 ||b

5 Abs. coeff. (/cm) 0 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)

Figure 4.15: Polarization-resolved absorption spectrum of b-cut Cr:forsterite crystal. Sample’s thickness was 1.08 mm.

3 3 →3 3 The visible absorption corresponding to A2( F) T1( F) in Td symmetry is split into three in the reduced symmetry of Cs. The visible and NIR absorption peaks respectively for E||a and E||b correspond to the GSA 3 3 3 →3 3 3 represented by the upward red allow (transition A”( A2( A2)) A”( A2( T1))) and the green allow (transition 3 3 3 →3 3 3 A”( A2( A2)) A”( E( T1))). Because the sample was cut perpendicular to c-axis, the absorption spectrum of E||c could not be measured. As shown the energy diagram (Fig. 4.16), the peak of the visible absorption for

E||c is located around 650 nm [151].

In the absorption spectrum (Fig. 4.15), small but broad absorption peaks are found in the visible region. These have been attributed to the co-existing Cr3+ in tetrahedral sites. Jia et al. performed the site-selective excitation spectroscopy, and obtained separately the excitation spectra of Cr4+, Cr3+ (I) (with inversion symmetry) and

Cr3+ (II) (with mirror symmetry) [148]. According to their excitation spectra, the small peak at ∼460 nm

3+ 3+ existing both for E||a and E||b are assigned to the absorption of Cr (II). The Cr (II) also has the broad absorption centered at ∼700 nm. Therefore, the tail in the longer wavelength side of the visible absorption for

3+ E||a broadened up to ∼800 nm may be partly attributed to the Cr (II). 4.3. Cr4+-doped oxide crystals as saturable absorbers 75

3 3 T1( P)

20 ) 1 - 3 3 A2 A’’

cm 3 3 3 15 T1( F) A’ 3 3 E 3A’’

3 3 A1 A’ 3 3 3 10 T2( F) A’ 3E 3A’’ Energy (10 5 E||a E||b,c E||a E||b E||c

3 3 3 3 0 A2( F) A2 A’’

Td C3v Cs Cr4+:forsterite (tetrahedral)

Figure 4.16: Energy diagram of tetrahedrally coordinated Cr4+ in forsterite after [151]. Energy levels for Td, C3v, and Cs symmetries, and associated electric-dipole-allowed absorption transitions are shown as upward arrows.

Pump-probe measurements were performed for both polarizations E||a and E||b. Since the polarization of the used HeNe laser was not stabilized, no polarization filtering optic was used to make a linearly polarized probe beam. The result with the pump wavelength of 570 nm (E||a) is shown in Fig. 4.17. The time-dependent transmission indicated a single exponential recovery of the ground state, and the recovery time was estimated to be ∼2.5 µs, which was good agreement with the previously reported fluorescence lifetime at room temperature

[152]. The recovery time was unchanged when the sample was pumped at 640–720 nm (E||b).

1.05 -2.0

-3.0

1.04 ) 0 -4.0

1.03 -5.0 ln(ln( V ( t )/ 0 -6.0 1.02 -7.0 -1 0 1 2 3 4 5 6 7 8 9 V ( t )/ Time (µs) 1.01

1.00

0.99 -1 0 1 2 3 4 5 6 7 8 9 Time (µs)

Figure 4.17: Result of pump-probe measurement of Cr4+:forsterite crystal pumped by 570-nm pulses linearly polarized along the crystal’s a-axis (E||a). Inset figure is calculated ln(ln(V (t)/V0)) according to Eq. (4.5).

Z-scan measurements were first performed for E||a. The bleaching was clearly observed from for the green absorption band spanning from 510 to 590 nm. The transmission as a function of incident pulse fluence at 4.3. Cr4+-doped oxide crystals as saturable absorbers 76

523 nm (the wavelength of Pr3+:YLF laser), 545 nm (the wavelength of Tb3+:fluoride laser), and 570 nm

(absorption peak) are shown in Fig. 4.18.

0.8 0.8 experiment experiment (a) 0.82 best fit (b) (c) best fit 0.7 0.7 0.80 0.6 0.5 0.6 0.78 0.4 Transmission Transmission Transmission 0.3 0.76 0.5 0.2 experiment best fit 0.74 0.4 0.1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Fluence (J/cm2) Fluence (J/cm2) Fluence (J/cm2)

Figure 4.18: Transmission of Cr:forsterite as a function of incident pulse fluence at (a) 523 nm, (b) 545 nm, and (c) 570 nm. Incident pulse energy was set to ∼2.5 mJ.

The solid lines in these figures are the results of the numerical fitting with the smallest fitting error.The resulting parameters exhibiting the minimum fitting error were summarized together with the other material parameters in Table 4.3. The transmission change was relatively small at 523 nm, and the minimum fitting error could be obtained for relatively large area in the parameter space. Consequently, the error in the numerical fitting at 523 nm was less accurate compared to these at 545 and 570 nm. As a 4+result, theCr density n determined from the results at 545 and 570 nm was reliable compared to that determined at 523 nm.

The transmission of the perfectly bleached sample at 570 nm was estimated to be ∼84% while the small signal transmission was only 15.8%. The parameter fp, the ratio of the ESA cross section with respect to the GSA cross section, is often used as a figure of merit (FOM) of saturable absorbers. The parameter fp at 570 nm was only ∼0.1. The determined ESA cross sections were comparable for the three wavelengths. This may indicate that the existence of a parasitic absorption in the green spectral region. This can be attributed to the Cr3+ (I) and Cr3+ (II). The Cr3+ (I) and Cr3+ (II) respectively have two broad absorption bands centered at ∼430 nm and ∼580 nm, and ∼470 nm and ∼680 nm [148]. Thus, the saturation characteristics of Cr:forsterite may be strongly affected by the growth conditions and treatments such as annealing. Chen et al. studied the formation mechanism of Cr4+ and Cr3+ in forsterite and the effect of oxidizing annealing [149]. Their experimental results indicate that crystal of low Cr concentration is favorable to suppress the Cr3+ (I and II).

Subsequently, the saturation characteristics for even longer wavelength for the same polarization (E||a) was experimentally examined by Z-scan measurements. As seen in the polarization-resolved absorption spectrum shown in Fig. 4.15, the sample had an absorption in the orange-red spectral region for E||a. Moreover, according to the site-selective excitation spectrum of Cr4+ presented in [148], the Cr4+ could be excited in the range 600–

750 nm. However, the bleaching observed at 607 nm was negligibly small while the incident fluence was varied from 0.05 to 1.5 J/cm2. A bleaching could no longer observed for even longer wavelength for this polarization

(E||a). 4.3. Cr4+-doped oxide crystals as saturable absorbers 77

Table 4.3: Summary of parameters of green absorption in Cr4+:forsterite for polarization parallel to the crystal’s a-axis (E||a)

Wavelength (nm) 523 545 570

T0 0.746 0.423 0.158 −1 α0 (cm ) 2.72 7.99 17.12 −18 2 σgs (×10 cm ) 1.8–2.6 5.5–5.8 11.0–11.4 −18 2 σes (×10 cm ) 1.12–1.68 1.18–1.31 1.05–1.14

fp(= σes/σgs) 0.620–0.645 0.215–0.255 0.095–0.100 n (×1018 cm−3) 1.05–1.51 1.38–1.45 1.50–1.56

Tsat 0.829–0.830 0.827–0.828 0.834–0.836

For the polarization parallel to the crystal’s b-axis (E||b), a Z-scan measurement was first conducted at 607 nm. However, the sample did not show any transmission change. This was simply because the excitation spectrum of

Cr4+ has a dip for the orange region. Subsequently, the pump wavelength was tuned to 640 nm, and a saturable absorption was clearly observed. The calculated fluence versus transmission is shown in Fig. 4.19. Owing to the relatively high small signal transmission resulting a small modulation depth, the experimental results were fluctuated.

0.92 experiment best fit 0.91

0.90

0.89

0.88 Transmission

0.87

0.86 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Fluence (J/cm2)

Figure 4.19: Transmission of Cr4+:forsterite as a function of incident pulse fluence at 640 nm for polarization parallel to the crystal’s b-axis.

The solid line in Fig. 4.19 is the resulting fitting curve exhibiting the minimum fitting error obtained withthe following range of parameters:

−18 2 • σgs = (0.8 − 1.1) × 10 cm

−18 2 • σes = (0.45 − 0.68) × 10 cm

corresponding to the parameter fp of 0.57–0.62.

Moreover, an even stronger saturable absorption was observed for even longer pump wavelength. A Z-scan was conducted at 720 nm, and the transmission increased up to ∼78% from the small signal transmission of 69.5% 4.3. Cr4+-doped oxide crystals as saturable absorbers 78 as show in Fig. 4.20. The horizontal axis is the position of the sample with respect to the focus. Although the saturable absorption was sufficiently clear, the numerical fitting was not performed, because multiple focused beam spots appeared due to the non-perfect anti-reflection coating of the employed optics at this wavelength.

In fact, the optics used in the Z-scan measurements were all optimized for the visible region, specifically from

400 to 700 nm, and the reflections between optics made a secondary pump spot of the comparable energy.

Therefore, the beam cross section could not be measured at this wavelength. For determining the GSA and

ESA cross sections at 720 nm for E||b, the optics should be replaced with those optimized for this wavelength. 4+ From the result (Fig. 4.20), it could be at least said that the absorption of Cr :forsterite for E||b spanning from 600 to 800 nm can be bleached, and potentially used for Q-switching solid-state lasers, such as the deep-red

Pr3+ lasers (typically oscillate at 720–750 nm) and the alexandrite laser.

Due to the cut angle of the samples, the saturation characteristics were not investigated for the polarization parallel to the crystal’s c-axis in this work. However, Cr4+:forsterite is expected to be used as a saturable absorber also for polarization parallel to the crystal’s c-axis (E||c). For this polarization, the crystals may act as a saturable absorber in the orange-red region. Thus, Cr4+:forsterite may potentially cover the spectral range from the green to deep-red by appropriately selecting a polarization direction. Since the absorption coefficient at 640 nm for E||c is much larger than that for E||b, the performance as the red saturable absorber may be much better for E||c.

0.8

0.75

E Transmission = 2.2 mJ

0.7 -10 0 10 20 30 40 50 60 70 80 90 100 Z (mm)

Figure 4.20: Transmission with respect to sample’s position at 720 nm for polarization parallel to the crystal’s b-axis. 4.4. Co2+-doped oxide crystals as saturable absorbers 79

4.4 Co2+-doped oxide crystals as saturable absorbers

Divalent cobalt ion (Co2+)-doped oxide crystals have an absorption in the near-infrared (NIR) range around

1.5 µm, and these have been used as saturable absorbers for erbium (Er3+) solid-state lasers [94, 95]. Recently,

2+ Demesh et al. experimentally revealed that the visible absorption in Co -doped MgAl2O4 (MALO, spinel) exhibits a saturable absorption, and demonstrated passive Q-switching of a 2ω-OPSL-pumped Pr3+:YLF laser at 523, 607, and 640 nm [71]. To the best of my knowledge, the visible absorption in other Co2+-doped media have never been investigated before, and it was expected that a Co2+-doped saturable absorber of better performance of saturable absorption than Co2+:MALO. In this work, the six following Co2+-doped oxide crystals were experimentally investigated and their saturation parameters were determined.

2+ • Co :MgAl2O4 (MALO, spinel)

2+ 4+ • Co , Si :LiGa5O8

2+ 4+ • Co , Si :Y3Al5O12 (YAG)

2+ 4+ • Co , Si :Gd3Ga5O12 (GGG)

2+ 4+ • Co , Si :LiAlO2

2+ • Co :Ca2MgSi2O7 (åkermanite)

2+ 4.4.1 Co :MgAl2O4 (MALO, spinel)

The MgAl2O4 spinel is a cubic crystal belonging to space group of O7h in Schönflies notation. The crystal structure is shown in Fig. 4.21. In the crystal, there are two coordination sites: octahedral Al3+ site and tetrahedral

Mg2+ site. Doped Co ions can substitute the both sites, and octahedrally coordinated Co3+ and tetrahedrally coordinated Co2+ are formed. Both the substitutions are likely because of their small mismatch in ionic radii

2+ ∗ 2+ 3+ 3+ (RCN=4(Co ) = 0.58 Å, RCN=4(Mg )= 0.57 Å, RCN=6(Co )= 0.545 Å, RCN=4(Al )= 0.535 Å)[153]. How- ever, the absorption and emission spectra were dominated by the latter, possibly owing to the missing inversion symmetry for the tetrahedral site.

Demesh et al. determined the GSA and ESA cross sections at 523, 607 and 640 nm [71]. However, the spatial distribution of the pump beam was not taken into account in the numerical model for the fitting, so their determined ESA cross sections may be overestimated. In addition, they did not take into account the beam size variation in the sample, while the green pump beam was strongly focused.

∗Ionic radius for a given coordination number (CN) 4.4. Co2+-doped oxide crystals as saturable absorbers 80

Tetrahedral Mg2+ site

O2-

Octahedral Al3+ site

Figure 4.21: Crystal structure of MgAl2O4 spinel (drawn by VESTA [122]). Orange, blue and red spheres are Mg2+, Al3+, and O2– , respectively. Octahedrons and tetrahedrons are respectively colored by blue and green.

For the measurements, a 2.98-mm thick Co2+:MALO crystal (Northrop Grumman, Inc.) was employed. The facets were uncoated. The measured absorption spectrum is shown in Fig. 4.22. The Fresnel reflections on the uncoated facets were taken into account in the reported dispersion of undoped MALO [154].

2.0

1.5

1.0

0.5 Abs. coeff. (/cm) 0.0 400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 4.22: Absorption spectrum of Co2+:MALO. Thickness of sample was 2.98 mm.

4 4 → 4 4 The broad NIR absorption broadened from 1200 to 1600 nm corresponds to transition A2( F) T1( F), ∼ 4 4 →4 4 and the strong visible absorption centered at 600 nm corresponds to the transition A2( F) T1( P). The broadening of the absorption bands are caused by the spin-orbit coupling. Deren et al. calculated the crystal field strength Dq, and Racah parameters B and C from the absorption measurements at cryogenic temperature, and obtained Dq = 402cm−1, B = 815cm−1, and C = 3266cm−1 [155]. Kuleshov et al. also determined these parameters as Dq = 400cm−1, B = 730cm−1, and C = 3500cm−1 [156]. The Tanabe-Sugano diagram of d3 and the simplified energy diagram for the tetrahedrally coordinated2+ Co are shown in Fig. 4.23. The horizontal and vertical axes of the Tanabe-Sugano diagram are both in unit of Racah parameter B.

In the Tanabe-Sugano diagram shown in Fig. 4.23(a), the vertical line corresponds to Dq = 0.493B calculated using the crystal field parameter Dq and the Racah parameter B reported by Deren et al. [155]. The lowest 4.4. Co2+-doped oxide crystals as saturable absorbers 81

25 (a) 4 4 (b) T1 ( P)

2A (2G) 1 2 2 T1 ( H) 20 2 2 4 4 T2 ( G) T1 ( F) ) 2 2

1 A ( G)

- 1 2F 4T (4P) 1 2T (2G)

cm 1 2T (2G) 15 2 2 2 3 E ( G) 4 4 T2 ( F)

2D 1000 nm 1000

2 2 2 2 nm 700 H, P T1 ( G) - 2 2 10 -

E ( G) nm 750 800 - 2 4 4 500 G T1 ( F)

4 600 P Energy (10

5 4 4 T2 ( F) 2500 nm 2500 1600 nm 1600 1500 nm 1500 - - - Dq(B) = 0.493 4 4 A2 ( F) nm 2000 1100 1100 2000 > 4A (4F) 1100 4F 0 2 Co2+ (tetrahedral)

Figure 4.23: (a) Tanabe-Sugano diagram of d3 for tetrahedrally coordinated d7 system. Spin quartet levels and spin doublet levels are drawn as solid lines and dashed lines, respectively. The vertical black line corresponds to Dq = 0.493B calculated using the reported values in [155]. (b) Simplified energy diagram of tetrahedrally coordinated2+ Co with associated absorption and emission transitions shown as upward and downward allows. Arrows with solid line are electric dipole transitions, and those with dashed line are only magnetic dipole allowed transitions. 4.4. Co2+-doped oxide crystals as saturable absorbers 82

2 2 4 4 doublet state E( G) is believed to locate above the level T1( P), otherwise a narrow emission with a long 4 4 lifetime is observed. In fact, a broad emission from the level T1( P) with a relatively short lifetime was 4 4 observed. As seen in Fig. 4.23(b), many emission transitions are expected to occur when the level T1( P) is excited. Figure 4.24 shows the fluorescence spectra of the2+ Co :MALO pumped by a CW green laser at 532 nm.

Compared with the emission of Co2+:MALO at 77 K reported by Kuleshov et al. [156], the intensity of the

NIR emissions was much smaller than the visible emission. Moreover, the emission above 2 µm corresponding 4 4 →4 4 to the transition T2( F) A2( F) could not be observed.

4 4 Since the recovery of the population of the ground state A2( F) is no longer characterized by a single exponential, the conventional four-level model depicted in Fig. 4.1 is not suitable. For the rigorous modeling, lifetime of

4 4 4 4 4 4 the energy levels T1( P), T1( F) and T2( F), and the branching ratios into these levels have to be known.

1.0 Ocean USB4000 x50 0.8 Spectral Evolution FL-2500

0.6

0.4

0.2

0.0 Fluorescence (arb. units) 750 1000 1250 1500 1750 2000 2250 2500 Wavelength (nm)

Figure 4.24: Fluorescence spectrum of Co2+:MALO pumped at 532 nm. Above 750 nm, the fluorescence was scaled up with a factor of 50. The fluorescence was detected bytwo spectrometers (USB4000, Ocean Optics and FL-2500, Spectral Evolution).

The pump-probe measurements were performed at various pump wavelengths, but the results were independent from the pump wavelength. The results with the pump wavelength of 640 nm are shown in Fig. 4.25. The transient output signal a priori seems to be a single exponential decay, but the calculated ln(ln(V (t)/V0)) (inset in Fig. 4.25) could not be fit with a straight line. Therefore, as expected, the conventional four-level modelis

2+ not suitable for Co :MALO. From the slope of the calculated ln(ln(V (t)/V0)), the effective recovery time was estimated to be in the range of 450–700 ns.

For directly measuring lifetime of each energy level, the fluorescence lifetime was measured using a monochromator (1000M, HORIBA) and photomultiplier tubes (PMTs) (R13456 and R5108, Hamamatsu Photonics). The slit width of the monochromator was set to 2 mm to improve the signal-to-noise ratio (SNR). When the level 4 4 2+ ∼ T1( P) of Co :MALO was excited, three major emission bands were observed, roughly centered at 660 nm, ∼900 nm, and ∼1300 nm. Therefore, the fluorescence lifetime was measured at 660, 900, and 1300 nm.The recorded time-dependent fluorescence intensities in log scale are shown in Fig. 4.26. 4.4. Co2+-doped oxide crystals as saturable absorbers 83

1.25 -1.0

-2.0 1.20 -3.0 ) 0 -4.0 1.15 -5.0 0

ln(ln( V ( t )/ -6.0 1.10 -7.0 V ( t )/ -8.0 1.05 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time (µs)

1.00

0.95 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time (µs)

Figure 4.25: Result of pump-probe measurement of Co2+:MALO crystal pumped at 640 nm. Inset figure is calculated ln(ln(V (t)/V0)) according to Eq. (4.5). Black dashed line in inset figure is a fitting result with recovery time of680ns.

e0 660 nm 900 nm 1300 nm e-1

e-2

e-3

-4

Intensity (arb. units) e

e-5 0 200 400 600 800 Time (ns)

Figure 4.26: Time-dependent fluorescence intensity in log scale at 660 nm, 900 nm,and 1300 nm. 4.4. Co2+-doped oxide crystals as saturable absorbers 84

For all the wavelengths, the strong quenching was observed. The fluorescence lifetime was estimated tobe

∼170 ns, ∼310 ns, and ∼330 ns, at 660, 900, and 1300 nm, respectively. It should be noted that the estimated lifetimes at 660 and 1300 nm are believed to be longer than the actual lifetime, because the emission spectrum was overlapped with the absorption spectrum at 660 nm and 1300 nm, and this induced a radiation trapping which effectively lengthens the emission decay. For more accurate measurements, the pinhole method should be used [135]. Interestingly, the observed fluorescence lifetimes were much shorter than the measured effective recovery time of ∼680 ns. This may indicate the existence of a level of even longer lifetime. In fact, the

4 4 4 4 emission around 900–1000 nm corresponds to the transition from T1( P) to T2( F). Therefore, the energy 4 4 level T2( F) was populated. Due to the lack of PMTs for the wavelength >1.5 µm, the emission corresponding 4 4 4 4 to T2( F) → A2( F) was not investigated. However, it is known that the transition is not electric dipole 4 4 transition, and therefore the lifetime of T2( F) is expected to be much longer than the other levels.

Finally, Z-scan measurements were performed to determine the GSA and ESA cross sections. The sample was investigated at 523, 545, 607, and 640 nm. The transmission versus incident pulse fluence was plotted for each pump wavelength in Fig. 4.27.

0.935 0.87 experiment (a) (b) 0.86 best fit 0.930 0.85 0.84 0.925 0.83 0.82 Transmission Transmission 0.920 0.81 0.80 0.915 0.79 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Fluence (J/cm2) Fluence (J/cm2)

0.90 0.84 experiment experiment (c) best fit (d) best fit 0.85 0.82

0.80 0.80

0.75 0.78 Transmission Transmission 0.70 0.76

0.65 0.74 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 Fluence (J/cm2) Fluence (J/cm2)

Figure 4.27: Transmission of Co2+:MALO as a function of incident pulse fluence at (a) 523 nm, (b) 545 nm, (c) 607 nm, and (d) 640 nm. Solid lines in (b,c,d) are fitting curve exhibiting the minimum fitting error.

At 607 and 640 nm, the transmission monotonically increased with the incident fluence. However, the transmission dropped approximately from the incident fluence of 1 J/cm2. This may be due to a multiphoton excited 4.4. Co2+-doped oxide crystals as saturable absorbers 85 state absorption (ESA) or a multiphoton charge transfer (CT) transition, owing to the very high peak intensity of the pump laser. In fact, at the pulse fluence of cm1 J/ 2, the peak intensity was calculated at 0.2 GW/cm2.

If the multiphonon ESA is assumed, it may correspond to the transition to the conduction band of the crys-

4 4 talline host, because there is no spin quartet state above the level T1( P) (see Tanabe-Sugano diagram in Fig. 4.23(a)), and the nature of the spin forbidden transition to the spin doublet states does not explain such strong ESA. The Z-scan measurement of the Co2+:MALO was further performed with longer pump pulses at 527 nm to reduce the peak intensity. The used laser system was a frequency-doubled actively Q-switched

Nd3+:YLF laser (Evolution-15, Coherent, Inc.). The pulse duration was measured at 276 ns at FWHM. As a result, the transmission of the Co2+:MALO monotonically increased while the incident fluence was increased up to ∼12 J/cm2. Demesh et al. neither observed the drop in transmission at 523.5 nm with 30-ns pulses [71].

Therefore, the observed drop in the transmission with the 5-ns pump pulses can be addressed to its too high peak intensity. Further investigations will be needed to understand the mechanism.

The solid lines in Fig. 4.27 are the results of the numerical fitting. The resulting parameters which exhibited the minimum fitting error were summarized in Table 4.4. The calculated saturated transmission Tsat at 607 nm was as high as 95%, resulting a modulation depth of ∼20%. However, Tsat at 640 nm was much below compared to that at 607 nm, due to the relatively high residual absorption. Yumashev et al. presented the ESA spectrum of a Co2+:MALO, and a broad ESA centered at ∼730 nm was confirmed [95]. Thus, this broad ESA may benot perfectly absent at 640 nm. The determined ESA cross section at 640 nm reported in [71] was also larger than that at 607 nm. The estimated Tsat at 545 nm was comparable with that at 607 nm, but the modulation depth was smaller owing to the smaller GSA cross section. For an accurate Z-scan measurement in the green region, pump pulses of 20–30 ns duration, sufficiently shorter than the recovery time, but not so high peak intensity, are expected to be suitable. The estimated GSA cross sections were all larger than the previously reported values [71]. This may be due to the difference in the numerical model used for fitting.

2+ 4.4.2 Co :LiGa5O8 (LGO)

2+ The Co -doped LiGa5O8 (LGO), so-called lithium gallate spinel, has been used for passive Q-switching of NIR lasers such as Nd3+ and Er3+-based solid-state lasers [157], since it has similar optical characteristics with

2+ the Co :MALO. LGO has an inverse spinel structure corresponding to space group of O6 in the Schönflies notation. A single cubic cell contains four formula units. The crystal structure is shown in Fig. 4.28.

On half of the Ga3+ is in the tetrahedral site, while the other half of the Ga3+ is in the octahedral site. Doped

Co ions are believed to substitute mainly for the tetrahedral Ga3+ sites and to form Co2+, and the other valence and site symmetries were not evident from the spectra [158]. It should be noted that the local symmetry of

2+ Co in the tetrahedral site is reduced from Td to C3 due to the lattice distortion caused by the relatively large 4.4. Co2+-doped oxide crystals as saturable absorbers 86

Table 4.4: Summarized parameters of Co2+:MALO. Because of abnormal characteristics in saturation at 523 and 545 nm (Figs. 4.27(a,b)), GSA cross sections at 523 and 545 nm (*2) were directly calculated using the value of Co2+ density estimated from the results at 607 and 640 nm (*1). In the numerical fitting at 545 nm, the ESA cross section was determined with the fixed GSA cross section. The fitting was performed so thatagood fitting was obtained in the low fluence regime (<0.5 J/cm2). The numerical fitting was not performed with the result at 523 nm due to its large fluctuation.

Wavelength (nm) 523 545 607 640

T0 0.920 0.795 0.705 0.749 −1 α0 (cm ) 0.278 0.768 1.174 0.968 −19 2 ∗2 ∗2 σgs (×10 cm ) 3.1–3.3 8.7–9.1 13.5–14.0 11.0–11.5 −19 2 ∗3 σes (×10 cm ) – 2.7–3.1 1.96–2.17 5.94–6.27 ∗3 fp(= σes/σgs) – 0.31–0.34 0.145–0.155 0.540–0.545 n (×1019 cm−3) – 8.4–8.8∗1 8.4–8.7 8.4–8.8

Tsat – 0.925–0.932 0.947–0.951 0.854–0.856

O2- Octahedral Octahedral Ga3+ site Li+ site

Tetrahedral Ga3+ site

Figure 4.28: Crystal structure of LiGa5O8 (drawn by VESTA [122]). Light-green, purple and red spheres are Li+, Ga3+, and O2– . Octahedrons and tetrahedrons are colored by blue and green, respectively. 4.4. Co2+-doped oxide crystals as saturable absorbers 87

2+ 3+ gap in ionic radii (RCN=4(Co )= 0.58 Å, RCN=4(Ga )= 0.47 Å) [153].

The sample used in this study was small pieces of a heavily doped Co2+:LGO crystal. The crystal orientation was unknown. Since the Sellmeier equation of LGO has not been reported, a two samples of different thickness were used to take into account the Fresnel reflection. The measured absorption spectrum is shown in Fig. 4.29.

Because the samples were very small, apertures of 1-mm diameter were used. The absorption coefficient in the visible region was as high as ∼40 cm−1.

10 Abs. coeff. (/cm) 0 400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 4.29: Absorption spectrum of Co2+:LGO.

The absorption spectrum was very similar to that of the Co2+:MALO shown in Fig. 4.22, but the absorption bands in the visible and NIR regions were both red-shifted compared to the Co2+:MALO, probably due to the lower symmetry of the tetrahedral Co2+ site and the smaller crystal field strength.

The results of the pump-probe measurements with pump wavelengths of 523, 545, 607, and 640 nm are shown in Fig. 4.30. The sample of 1.3-mm thick was used in the measurements. It was experimentally confirmed that the whole absorption in Co2+:LGO bleaches, and therefore, Co2+:LGO can potentially be used as a broadband visible saturable absorber. The recorded time-dependent transmission shown in the figures exhibited a low signal-to-noise ratio (SNR), since the transmission for the probe beam at 632.8 nm was only 3.2% due to the very high doping concentration.

The calculated ln(ln(V (t)/V0)) shown as the inset figures indicated that the effective recovery time ofthe Co2+:LGO was ∼200 ns, regardless the pump wavelength. However, it is expected that the conventional four- level model is not suitable for the Co2+:LGO as Co2+:MALO due to the possible multi-relaxation channels. Due to the very low transmission at the probe wavelength, the longer relaxation components could not be observed in the pump-probe measurements.

When the Co2+:LGO crystal was excited with a visible light, the fluorescence similar to2+ Co :MALO was observed. Figure 4.31 shows the fluorescence spectrum of the2+ Co :LGO pumped at 532 nm. Three emission bands were clearly observed. The whole emission spectrum was blue-shifted compared to that of the Co2+:MALO

(Fig. 4.24). The fluorescence lifetime was measured at 690, 900, and 1300 nm using the monochromator andthe 4.4. Co2+-doped oxide crystals as saturable absorbers 88

1.40 1.70 (a) 0.0 (b) 0.0 1.35 -1.0 1.60 -1.0 ) ) 0 -2.0 0 -2.0 1.30 1.50 -3.0 -3.0 1.25

ln(ln( V ( t )/ 1.40 -4.0 ln(ln( V ( t )/ -4.0 0 1.20 0 -5.0 1.30 -5.0 1.15 V ( t )/ -6.0 V ( t )/ -6.0 -250 0 250 500 750 1000 1.20 -250 0 250 500 750 1000 1.10 Time (ns) Time (ns) 1.05 1.10 1.00 1.00 0.95 0.90 -500 0 500 1000 1500 2000 -500 0 500 1000 1500 2000 Time (ns) Time (ns)

2.60 2.80 (c) 1.0 (d) 1.0 2.40 0.0 2.60 0.0

-1.0 -1.0 ) ) 0 2.20 2.40 0 -2.0 -2.0 2.20 2.00 -3.0 -3.0 ln(ln( V ( t )/ ln(ln( V ( t )/ 0 0 2.00 1.80 -4.0 -4.0 -5.0 1.80 -5.0 -6.0

1.60 V ( t )/

V ( t )/ -6.0 -500 0 500 1000 1500 2000 1.60 -500 0 500 1000 1500 2000 Time (ns) Time (ns) 1.40 1.40 1.20 1.20 1.00 1.00 0.80 0.80 -500 0 500 1000 1500 2000 -500 0 500 1000 1500 2000 Time (ns) Time (ns)

Figure 4.30: Time-dependent PD signal V (t)/V0, which is equivalent to normalized trans- 2+ mission T (t)/T0 of Co :LGO pumped at (a) 523 nm, (b) 545 nm, (c) 607 nm, and (d) 640 nm. Inset figures are calculated ln(ln(V (t)/V0)).

1.0 Ocean USB4000 x25 0.8 Spectral Evolution FL-2500

0.6

0.4

0.2

0.0 Fluorescence (arb. units) 750 1000 1250 1500 1750 2000 2250 2500 Wavelength (nm)

Figure 4.31: Fluorescence spectrum of Co2+:LGO pumped at 532 nm. Above 750 nm, the fluorescence was scaled up with a factor of 25. The fluorescence was detected bytwo spectrometers (USB4000, Ocean Optics and FL-2500, Spectral Evolution). 4.4. Co2+-doped oxide crystals as saturable absorbers 89

PMTs, as described in the previous subsection. The recorded time-dependent fluorescence intensities at the three emission wavelengths are shown in Fig. 4.32. Strong quenching was observed at all the detected wavelengths.

The lifetime was estimated to be ∼350 ns, ∼750 ns, and ∼350 ns at 690 nm, 900 nm, and 1300 nm, respectively.

e0 690 nm 900 nm e-1 1300 nm

e-2

e-3

e-4

Intensity (arb. units) e-5

e-6 0 500 1000 1500 Time (ns)

Figure 4.32: Time-dependent fluorescence intensity in log scale at 690 nm, 900 nm,and 1300 nm.

These estimated fluorescence lifetimes were all longer than the measured effective recovery timeof ∼200 ns. It may be due to the strong quenching in the heavily doped sample, which is evident from the fluorescence decay as shown in Fig. 4.32. Again, because of the small transmission at the probe wavelength, the longer relaxation components were not observed in the pump-probe measurements. Thus, the recovery lifetime of Co2+:LGO is expected to be longer than the measured effective recovery time, and it will be measured with a sample of moderate doping concentration.

Since the used samples were very small (∼1.1-mm wide), it was not possible to vary the fluence in the Z-scan measurements. It was practically possible to vary the fluence by controlling the pulse energy instead ofthe beam size on the sample. However, this method did not enable to measure accurately the transmission in the low fluence regime, since the recorded value in the energy meters were less accurate for small pulse energies.

4.4.3 Co2+-doped garnets

2+ In this subsection, the experimental investigation of Co -doped garnet crystals, Y3Al5O12 (YAG) and Gd3Ga5O12 (GGG), is presented. The crystal structure of YAG was presented in Fig. 4.6. GGG has the same structure but consists of Gd3+ and Ga3+ instead of Y3+ and Al3+. As described in Section 4.3.1, there are two Al3+ or Ga3+ sites. Wood presented the detailed spectroscopic investigation of tetrahedral Co3+ and Co2+ in garnet crystals

[159]. Doped Co ions substitute for both the octahedral and tetrahedral Al3+/Ga3+ sites in YAG/GGG, and two kinds of valence states, Co2+ and Co3+, were evident from the absorption spectrum when no charge compensating ions were co-doped. It should be noted that the tetrahedrally coordinated Co2+ and Co3+ ions are dominant in emission and absorption spectra owing to the lack of inversion symmetry. To reduce the valence of 4.4. Co2+-doped oxide crystals as saturable absorbers 90

Co3+ to Co2+ is accomplished by co-doping tetravalent charge compensating ions, such as Si4+. The samples used in this study are as follows:

• Co2+:YAG (Sample A): 1 wt. % Co, Si doped YAG (L = 3.05 mm)

• Co2+:YAG (Sample B): 1.5 wt. % Co, Si doped YAG (L = 1.80 mm)

• Co2+:GGG (Sample C): 0.1 wt. % Co, Si doped YAG (L = 0.60 mm)

The doping concentration were the amount in melt. For all the samples, Si4+ was co-doped for the charge compensation to form Co2+. Sample A and C were bluish colored while Sample B was greenish. The difference in color may be due to the charge compensation and the different doping level.

The measured absorption spectra of the three samples are shown in Fig. 4.33. The Fresnel reflections on the uncoated facets were taken into account using the reported dispersion for undoped YAG and GGG [140, 160].

According to the work of Wood [159], the visible absorption band centered around 600 nm is attributed to the 4 4 →4 4 2+ transition A2( F) T1( P) of Co in the tetrahedral site. In the NIR region, the absorption of tetrahedral Co2+ and Co3+ are coexisting. The NIR absorption due to Co3+ in tetrahedral site has major peaks at ∼1050 nm and ∼1200 nm in YAG. That due to Co2+ in tetrahedral site is spanning from ∼1200 nm to ∼1700 nm in YAG.

In the absorption spectra of Sample A and B, the Co3+ is evident from the peak at ∼1050 nm, but the ratio

Co3+/Co2+ of Sample A was much smaller than that of Sample B. In Sample C, no absorption due to Co3+ was evident, and this indicates that Co3+ was perfectly reduced by the charge compensation. On the longer wavelength side of the visible absorption of Sample A, a small shoulder was observed. However, this shoulder was not detected in Sample B, while Sample B consisted of both Co2+ and Co3+. Therefore, this small shoulder may be due to other impurity ions contained during the crystal growth. The absorption in the ultraviolet region is attributed to a charge transfer transition.

The absorption spectrum of Co2+ in the garnets are similar to that in MALO and LGO, while the crystal field is much stronger in the garnets. Moreover, the tetrahedron in garnet crystals is distorted, and the local symmetry is reduced to S4 from Td, as described in Section 4.3.1. However, any splitting and shifting in the absorption spectrum was not observed in the YAG and GGG.

The position of the absorption peaks, in both the visible and NIR region, of the Co2+:GGG (Sample C) was found to be slightly red-shifted compared to the Co2+:YAG (Sample A and B); however, the visible absorption of the Co2+:GGG (Sample C) was broadened in the shorter wavelength side compared to that of the Co2+:YAG

(Sample A and B). Thus, the Co2+:GGG was expected to exhibit a better saturation characteristics in the green wavelength region.

Pump-probe measurements were performed using Sample A and C. The normalized time-dependent PD signal

V (t)/V0, which is equivalent to the normalized transmission T (t)/T0, of Sample A and C at 632.8 nm when 4.4. Co2+-doped oxide crystals as saturable absorbers 91

1.0 Sample A: 1 wt. % Co, Si:YAG 0.8

0.6

0.4

0.2

0 Sample B: 1.5 wt. % Co, Si:YAG

2.0

1.0

0 Sample C: 0.1 wt. % Co, Si:GGG 4.0

Absorption coefficient (/cm) 3.0

2.0

1.0

0 400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 4.33: Absorption spectra of Co2+:YAG (Sample A and B) and Co2+:GGG (Sample C). The visible absorption centered at ∼600 nm and the NIR absorption spanning from 1.2 to 1.7 µm are attributed to Co2+ in tetrahedral site. The NIR absorption spanning from 0.9 to 1.3 µm are attributed to Co2+ in tetrahedral site. pumped at 607 nm is shown in Fig. 4.34. The pump energy was set to ∼3 mJ. The both samples clearly exhibited a saturable absorption. The normalized transmission of Co2+:YAG (Sample A) increased up to

∼1.06, which corresponded to the transmission change from 73.5% (initial transmission at 633 nm) to 77.9%.

The normalized transmission of Co2+:GGG (Sample C) increased up to ∼1.075, which corresponded to the transmission change from 83.2% (initial transmission at 633 nm) to 89.4%. Of course, the pump spot size on the samples were unknown, so the transmission change observed in the pump-probe measurements is much lower than the saturated transmission Tsat.

It was clearly seen that the bleaching of the Co2+:YAG (Sample A) immediately recovered despite of the strong bleaching characteristic. The very fast decay indicated that the recovery time was as fast as the pump pulse duration of ∼5 ns. The inset figures in Fig. 4.34 are calculated ln(ln(V (t)/V0)). Because of the comparable recovery time with the pump pulse duration, the recovery time could not be estimated from the inset figure.

Therefore, the recovery time of the Co2+:YAG (Sample A) was tentatively estimated to be ∼5 ns. It should be underlined that the transmission of the Co2+:YAG (Sample A) dropped to below the initial transmission after recovered, as seen in Fig.4.34(a). A similar effect was observed in the pump-probe measurements4+ ofCr :YAG as presented in Section 4.3.1. Again, the observation was attributed to the ESA to the conduction band of the crystalline host, and the subsequent color center formation. However, the recovery of the assumed color centers was much shorter than that in Cr4+:YAG. The color centers in the Co2+:YAG were perfectly remove in 100 ns, 4.4. Co2+-doped oxide crystals as saturable absorbers 92

1.06 1.08 -2.0 (a) (b) -2.0 -3.0 1.07 -3.0 1.05 -4.0 ) 0 ) -5.0 1.06 0 -4.0 -6.0 1.04 -5.0 -7.0 1.05 ln(ln( V ( t )/

ln(ln( V ( t )/ -6.0 0 0 1.03 -8.0 1.04 -9.0 -7.0

-10.0 1.02 -5 0 5 10 15 20 1.03 -8.0

V ( t )/ V ( t )/ -20 0 20 40 60 80 100 Time (ns) 1.02 Time (ns) 1.01 1.01 1.00 1.00 0.99 0.99 -20 -10 0 10 20 30 40 50 60 70 -20 0 20 40 60 80 100 Time (ns) Time (ns)

Figure 4.34: Time-dependent PD signal V (t)/V0, which is equivalent to normalized trans- 2+ 2+ mission T (t)/T0, of (a) Co :YAG (Sample A), and (b) Co :GGG (Sample B). The pump wavelength was 607 nm. while the lifetime of the color centers in Cr4+:YAG was estimated to be ∼7 ms. The observation was much significant when the sample was pumped by pulses of shorter wavelength.

The Co2+:GGG also showed a fast decay characteristic, as shown in Fig. 4.34(b). From the calculated curve of ln(ln(V (t)/V0)), the recovery time was estimated to be ∼12 ns, which was longer than the pump pulse duration, but still comparable. The onset of the parasitic absorption center observed in the Co2+:YAG (Sample A) was not evident in the Co2+:GGG (Sample C), even though the pump wavelength was tuned down to 523 nm.

2.5

1.5 2

2 Transmitted power (mW) 0 2 Y (mm) 0 -2 -2 X (mm) 1.5

Figure 4.35: Two-dimensional transmitted power of HeNe laser in Co2+:YAG crystal (Sample A). There is an area of higher doping concentration, which is typical in crystals grown by Czochralski method.

Z-scan measurements were conducted for Sample A and C. Sample B was not used since the non-uniform color of the sample clearly indicated that the doping concentration was not uniform. When Sample A was scanned around the focus of the pump laser, a transmission change was clearly observed; however, the obtained Z-scan curve had multiple peaks which could be explained only by a non-uniform transmission in the sample. To check the spatial distribution of the dopant in Sample A, the sample was transversally scanned in XY-plane with respect to the focused HeNe laser beam (632.8 nm, ∼4 mW). The spot diameter was measured at ∼450 µm.

The two-dimensional transmitted power distribution of the HeNe laser in the Co2+:YAG (Sample A) is shown 4.4. Co2+-doped oxide crystals as saturable absorbers 93 in Fig. 4.35.

Transmission as a function of incident pulse fluence at 545 nm, 607 nm, and 640 nm for2+ theCo :GGG (Sample

C) derived from the results of Z-scan measurements is shown in Fig. 4.36. At pump wavelength of 545 nm, the transmission monotonically decreased as the fluence increased, while a bleaching could be observed inthe pump-probe measurement at the same wavelength. This may be owing to the onset of strong nonlinear ESA, as seen in Co2+:MALO. Even though the recovery time was measured at ∼12 ns, the transmission reached

99% and 98% at 607 and 640 nm, respectively, when bleached. The small non-saturable loss indicates a very small ESA cross section of Co2+:GGG in the orange-red region. The transmission at 640 nm had its maximum around the fluence of ∼ 0.8 J/cm2, and the transmission decreased for even larger fluence level, which may be attributed to the strong nonlinear ESA assumed for the 545-nm results. It should be noted that this roll-over was also observed at 607 nm when the fluence was increased up to > 2 mJ/cm2, but it was less significant than at 640 nm.

(a) 1.00 (b) 1.00 (c) 1 0.90 0.95 0.95

T0 = 94.1% 0.80 0.90 0.9

0.70 0.85 0.85

Transmission Transmission Transmission T0 = 83.2% 0.60 0.80 0.8 T0 = 79.9%

0.50 0.75 0.75 0.0 0.2 0.4 0.6 0.8 0.0 0.5 1.0 1.5 0 0.5 1 1.5 2 2.5 Fluence (J/cm2) Fluence (J/cm2) Fluence (J/cm2)

Figure 4.36: Transmission of Co2+:GGG as a function of incident pulse fluence at (a) 545 nm, (b) 607 nm, and (c) 640 nm. The initial transmission measured by absorption spectroscopy was 94.1%, 79.9%, and 83.2% at 545, 607, and 640 nm, respectively.

Since the pulse duration was comparable with the estimated recovery time, the excitation can no longer considered to be instantaneous; therefore, the model described by Eq. (4.6) cannot be applied to the results of

Co2+:GGG. To determine the GSA and ESA cross sections, a rate equation model should be adopted. How- ever, a model considering both the temporal and spatial distribution of pump beam results in a huge computation cost. Therefore, a numerical fitting was not applied to the results2+ ofCo :GGG. Even though the GSA and

ESA cross sections were unknown, the figure of merit of saturable absorber fp, defined as the ratio of ESA cross section with respect to GSA cross section, can be estimated from the measured initial transmission T0 and saturated transmission Tsat. The figure of merit fp is given as follows:

σes σesntotlSA ln Tsat fp = = = . (4.11) σgs σgsntotlSA ln T0

The calculated fp was ∼0.045 and ∼0.11 at 607 and 640 nm, respectively. 4.4. Co2+-doped oxide crystals as saturable absorbers 94

2+ 4.4.4 Co :LiAlO2

γ γ 4 Lithium aluminate of -phase ( -LiAlO2) is categorized in the tetragonal space group of D4 in Schönflies notation, and contains four formula units in a single unit cell. The crystal structure is shown in Fig. 4.37.

O2- Tetrahedral Li+ site

Tetrahedral Al3+ site

γ + Figure 4.37: Crystal structure of -LiAlO2. Light-green, blue, and red spheres are Li , Al3+, and O2– , respectively. The crystal contains only tetrahedral sites.

A sample investigated in this work was a 0.5 wt. % Co, Si-doped LiAlO2 crystal. The thickness was measured at 3.70 mm. The crystal’s bluish color may indicate the formation of Co2+ in tetrahedral site. The Regarding the

+ 3+ + 3+ 2+ ionic radii of Li , Al , and Co ions (RCN=4(Li ) = 0.59 Å, RCN=4(Al ) = 0.39 Å, RCN=4(Co ) = 0.57 Å) [153], Co ions are likely to substitute for Li+ site rather than Al3+ site; however, formation of Co2+ in Li+ site may not be possible. Therefore, it was assumed that Co2+ was formed in Al3+ site despite of the difference in their ionic radii. This was the reason why Si4+ was co-doped for the charge compensation. The local symmetry of

3+ Al site is C2, so energy levels are expected to shift and split due to this reduced symmetry. It should be noted that, to the best of my knowledge, Co-doped LiAlO2 crystal has never been studied, so further investigations will be required to understand the substitution site and valence states of Co ions in LiAlO2 crystal.

Since LiAlO2 crystal was uniaxial and anisotropic, the absorption was polarization dependent. The measured polarization-resolved absorption spectrum is shown in Fig. 4.38. Since the crystal’s angle was unknown, the polarization angle which maximizes and minimizes the transmission at 650 nm were defined as polarization 1 and 2, respectively, for convenience. For taking into account the Fresnel reflections on the uncoated facets, the

Cauchy equation was fit to areas where absorption was absent for the both polarizations. The peak at650nm did not disappear even though the polarization was rotated by 90 degree. This fact indicated that the crystal was not cut perpendicular to crystal’s a-axis. It was straightforward to attribute the strong absorption in the visible region to Co2+ in tetrahedral site.

Pump-probe measurements were performed at various visible wavelength (from 500 to 700 nm) for two polarization angles. However, none of transmission was observed at the probe wavelength of 632.8 nm. Therefore, the recovery time could not be measured. Note that any emission could not be detected in the range of 500–1500 nm 4.4. Co2+-doped oxide crystals as saturable absorbers 95

4.0 polarization 1 polarization 2 3.0

2.0

1.0 Abs. coeff. (/cm) 0.0 400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 4.38: Polarization-resolved absorption spectrum of Co:LiAlO2 crystal. The sample’s thickness was 3.70 mm. when the sample was excited by intense visible pulses.

Subsequently, Z-scan measurements were performed at 523 and 607 nm for polarization 1, and 640 nm for polarization 2. The transmission versus crystal’s position with respect to the pump focus was plotted and shown in Fig. 4.39. At a wavelength of 523 nm, a small bleaching can be seen in Fig. 4.39(a), but a sharp drop in transmission was observed around the focus (Z = 0 mm), probably due to a nonlinear ESA as also seen in

Co2+:MALO and Co2+:GGG. At 607 nm, a saturable absorption may occur but the transmission change was as small as 1%, while the incident fluence was varied from 0.03 to 1.1 J/cm2. As seen at 523 nm, a roll-over in transmission was still observed. At 640 nm, a saturable absorption was clearly observed. The scanning range shown in Fig. 4.39(c) corresponded to an incident pulse fluence of 0.06 − 1.5 J/cm2. However, the transmission change was only ∼3%, while the initial transmission was 34%, indicating a large non-saturable loss.

(a) 0.61 (b) 0.8 (c) 0.38

0.37 0.60 0.79

0.36 0.59 0.78 0.35 Transmission Transmission Transmission 0.58 E = 2.7 mJ 0.77 0.34 E = 2.0 mJ E = 1.5 mJ

0.57 0.76 0.33 -10 0 10 20 30 40 50 60 70 80 90 -20 -10 0 10 20 30 40 50 60 70 80 90 -20 -10 0 10 20 30 40 50 60 70 80 Z (mm) Z (mm) Z (mm)

Figure 4.39: Transmission with respect to sample’s position with respect to beam waist measured at (a) 523 nm, (b) 607 nm, and (c) 640 nm. For 523 and 607 nm, the polarization was set to polarization 1, and for 640 nm, the polarization was set to polarization 2.

2+ It is concluded that the visible absorption in Co :LiAlO2 can bleach, but its saturation characteristics are not attractive due to its very limited modulation depth and large non-saturable loss. 4.4. Co2+-doped oxide crystals as saturable absorbers 96

2+ 4.4.5 Co :Ca2MgSi2O7 (åkermanite)

Calcium magnesium silicate Ca2MgSi2O7 is called åkermanite, and its crystal structure is categorized into the 1 tetragonal space group of D2d in Schönflies notation. The crystal structure of åkermanite is shown in Fig. 4.40.

Tetrahedral Si4+ site

O2- Tetrahedral Mg2+ site

Figure 4.40: Crystal structure of Ca2MgSi2O7 (åkermanite). Grey, orange, light-blue, and red spheres are respectively Ca2+, Mg2+, Si4+, and O2– . Åkermanite only consists of tetrahedral substitution sites for doped Co ions.

As seen in Fig. 4.40, åkermanite only consists of tetrahedral sites. Therefore, doped Co ions in åkermanite must

2+ 2+ 4+ 2+ be in the tetrahedral site. Regarding the ionic radii of Ca , Mg , Si , and Co ions (RCN=8(Ca ) = 1.12 Å,

2+ 4+ 2+ RCN=4(Mg ) = 0.57 Å, RCN=4(Si ) = 0.26 Å, and RCN=4(Co ) = 0.57 Å) [153], doped Co ions are likely to be substituted to Mg2+ site, and form Co2+ in tetrahedral site.

The sample investigated in this work was a 0.70-mm thick Co-doped åkermanite crystal cut perpendicular to the crystal’s c-axis. The conditions of crystal growth were unknown. The absorption spectrum shown in Fig. 4.41 is very similar to Co2+:MALO (Fig. 4.22), and clearly indicated the formation of Co2+ in the crystal.

3.0 2.5 2.0 1.5 1.0 0.5 Abs. coeff. (/cm) 0.0 400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 4.41: Absorption spectrum of c-cut Co2+:åkermanite. The sample’s thickness was 0.70 mm.

Pump-probe measurements of the sample were performed at 523, 545, 607, and 640 nm. For all the wavelengths, 4.5. Summary 97 the increase of the transmission for the probe beam was clearly observed. However, a decrease in transmission after the bleaching recovered was observed at 523, 545, and 607 nm, similar to Co2+:YAG (Fig. 4.34(a)).

The time-dependent PD output signal V (t)/V0, which was equivalent to the normalized transmission T (t)/T0, of the Co2+:åkermanite pumped at 607 nm is shown in Fig. 4.42. The sample’s initial transmission at the probe wavelength was 87.2%. When the sample was excited by a ∼3-mJ pulse from the OPO, the normalized transmission instantaneously increased up to 1.018, corresponding to the modulation depth of ∼1.6%.

1.020 -3.0

-4.0

-5.0 1.015 )) 0 -6.0

-7.0 0 1.010 ln(ln( V ( t )/ -8.0

-9.0

-10.0 V(t)/V 1.005 -10 -5 0 5 10 15 20 25 30 35 40 Time (ns)

1.000

0.995 -20 0 20 40 60 80 100 120 140 Time (ns)

Figure 4.42: Time-dependent PD output signal V (t)/V0, which is equivalent to normalized 2+ transmission T (t)/T0, of Co :åkermanite pumped at 607 nm and probed at 632.8 nm. The inset figure is calculated ln(ln(V (t)/V0)) according to Eq. (4.5).

From the calculated ln(ln(V (t)/V0)) shown as the inset figure in Fig. 4.42, the recovery time was estimated to be ∼10 ns, which was comparable with that of Co2+:GGG. This very short recovery time results in a very high saturation intensity.

At the wavelength, a Z-scan measurement was performed, and a saturation characteristic was clearly seen in the calculated transmission versus incident fluence as shown in Fig. 4.43. The initial transmission T0 of the sample at 607 nm was 82.4% from the absorption spectroscopy. As Co2+:garnets, the estimated recovery time was comparable with the pump pulse duration, so a numerical model which enables to take into account not only spatial but also temporal distribution of the pump pulse is required to determine the GSA and ESA cross sections. The transmission converged to ∼86% as the fluence increased. The figure of merit of saturable absorbers fp was roughly calculated at ∼0.78 from Eq. (4.11), if the saturated transmission Tsat assumed to be 86%. Thus, the Co2+:åkermanite is expected to be a saturable absorber of high ESA cross section. For accurately determining the cross sections, numerical fitting with a more complicated model is necessary.

4.5 Summary

In this section, various Cr4+ and Co2+-doped oxide crystals were investigated as saturable absorbers in the visible region. Their parameters determining saturation properties, recovery time, and GSA and ESA cross 4.5. Summary 98

0.88

0.86

0.84

Transmission 0.82

0.80 0 0.2 0.4 0.6 0.8 Fluence (J/cm2)

Figure 4.43: Transmission of Co2+:åkermanite as a function of incident pulse fluence at 607 nm. sections, were measured by the pump-probe and Z-scan measurements.

Cr4+-doped YAG and forsterite were found to be good saturable absorbers in the visible region. Cr4+ in tetrahedral sites are thought to be responsible for bleaching. The saturation intensity of these Cr4+-based saturable absorbers were estimated to be several tens of kW/cm2, owing to their recovery times of a few microseconds.

The investigation of Cr4+:YAG turned out to be complicated due to the existence of several kinds of absorption centers in the visible region: Cr3+ and Cr4+ in octahedral site. Thus, the saturation characteristics, especially the effective ESA cross section, are expected to be strongly dependent on crystal growth conditions. Theapplied wavelength of this saturable absorber may be limited in the range of 600–680 nm. At even shorter wavelength, a formation of color centers was observed possibly due to the ESA to the conduction band of the crystalline host. In Chapter 5, passive Q-switching of Pr3+:YLF lasers at 640 nm is described. Cr4+:forsterite was found to be a broadband saturable absorber potentially cover the range of 500–750 nm, by using crystals of appropriate cut angle. The strong green absorption band for polarization parallel to the crystal’s a-axis showed a good bleaching, but the saturated transmission was limited to ∼84%. This non-saturable loss tells us the possibility of a parasitic absorption center, presumably Cr3+. Thus, the performance of Cr4+:forsterite may also depend on crystal growth conditions.

The two Cr4+-doped crystals were both expected to be crystal-growth-dependent, since they can comprise parasitic absorption centers due to several possible substitution sites and valence states. Therefore, it is concluded

4+ that crystalline hosts which have only tetrahedral sites to form Cr , such as LiAlO2, are attractive candidates.

All the Co-doped various oxide crystals, MALO, LGO, YAG, GGG, LiAlO2, and åkermanite, showed a strong visible absorption attributed to the tetrahedrally coordinated Co2+. Despite of similarity in their absorption spectra, their saturation characteristics strongly depend on the crystals. When the visible absorption band was excited, Co2+ in MALO and LGO only exhibited fluorescence in the visible and NIR regions. Moreover, the 4.5. Summary 99 recovery times of Co2+:MALO and LGO were mush longer than Co2+:garnets and åkermanite (a transmission

2+ 2+ change could not be detected for Co :LiAlO2). The saturation intensity of Co :MALO was roughly estimated to be 500 − 2000 kW/cm2, one or two order of magnitude larger than Cr4+-based saturable absorbers. Co2+- doped garnets and åkermanite exhibited very short recovery time of 5–10 ns, may be related to their non- radiative nature of relaxation. Such extremely short recovery time results in a very high saturation intensity.

Co2+:GGG was experimentally found to be good saturable absorber, despite of the very short recovery time.

From the experimental results of the Z-scan measurements, the transmission at 607 and 640 nm almost reached unity, indicating the limited ESA cross section. In Chapter 5, passive Q-switching of a 640-nm Pr3+:YLF laser with Co2+:GGG is presented.

The saturation characteristics of the investigated samples are summarized in Table 4.5. Other transition-metal- doped crystals, such as Ni2+-doped oxides, are also expected to be used as visible saturable absorbers. Ni2+- 3 3 →3 3 doped MALO spinel has an absorption in the range of 500–700 nm corresponding to transition A2( F) T1( P) [161, 162]. Regarding the presented ESA spectrum [162], this visible absorption is expected to be bleached, but not applied in the green region. In addition to the Cr4+- and Co2+-doped oxide crystals presented in this section, the saturation characteristics of Ni2+-doped åkermanite were investigated. Even though the crystal exhibited a strong absorption in the visible region for the both polarizations, a bleaching was not observed regardless the pump wavelength and polarization. The results tell us that host crystals of low crystal field strength, such as spinels, are favorable for Ni2+-based saturable absorbers. 4.5. Summary 100

Table 4.5: Summary of saturation characteristics of investigated Cr4+- and Co2+-doped oxide crystals at 523, 545, 607, and 640 nm. For Cr4+:forsterite, the bleaching was not observed at 607 nm for polarization parallel to the crystal’s a- and b-axes, but it may be obtained for polarization parallel to crystal’s c-axis (*1). For Co2+:GGG, the transmission only decreased as incident fluence increased owing to the too high peak intensity ofthe pump pulses. However, a strong bleaching was observed with ∼250-ns pump pulses at 527 nm (*2).

Sample Recovery time Saturable absorption

523 nm 545 nm 607 nm 640 nm

Cr4+:YAG ∼4 µs × △ ⃝ ⃝

4+ ∗1 Cr :forsterite ∼2.5 µs ⃝(E||a) ⃝(E||a) ⃝(E||c) ⃝(E||b,c)

Co2+:MALO 450–700 ns ⃝ ⃝ ⃝ ⃝

Co2+:LGO ∼200 ns ⃝ ⃝ ⃝ ⃝

Co2+:GGG ∼12 ns ⃝∗2 ⃝∗2 ⃝ ⃝

Co2+:YAG ∼5 ns △ △ △ △

2+ △ △ △ Co :LiAlO2 – –

Co2+:Åkermanite ∼10 ns – – △ △ Chapter 5

Passive Q-switching of Pr3+:YLF visible lasers

3+ 4+ In this chapter, passive Q-switching of visibly emitting Pr -doped LiYF4 (YLF) lasers by utilizing Cr - 2+ 4+ and Co -doped oxide saturable absorbers are presented. As saturable absorbers, Cr :Y3Al5O12 (YAG), 2+ 2+ Co :MgAl2O4 spinel, and Co :Gd3Ga5O12 (GGG) were adopted and examined.

4+ 5.1 Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber

In this section, passive Q-switching of diode-pumped Pr3+:YLF laser at 607 and 640 nm using Cr4+:YAG saturable absorbers is presented. In Section 5.1.1, the determination of saturation parameters of Cr4+:YAG crystals used for passive Q-switching is presented. Even though the Cr4+:YAG crystals were extensively investigated in Chapter 4, the effective cross sections are thought to depend on crystal growth conditions, owingto the existence of parasitic absorption centers including Cr3+. Then, the experimental results and rate equation analysis are described in the later sections.

5.1.1 Determination of saturation parameters of Cr4+:YAG saturable absorbers

We used 1.3- and 2.4-mm long (100)-cut Cr4+:YAG crystals (Scientific Materials), respectively named Sample

A and B, were used for laser experiments. The surfaces of these crystals were anti-reflection coated for 600–

650 nm. The initial transmission of these saturable absorbers were respectively 94.6% and 91.7% at 640 nm. As

101 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 102 presented in Section 4.3.1, the saturation parameters of Cr4+:YAG crystals vary from sample to sample due to the existence of the parasitic absorption centers. Therefore, their effective saturation parameters: ground state absorption (GSA) and excited state absorption (ESA) cross sections were determined by Z-scan measurements and numerical fitting, as described in Section 4.1. Since the size of these crystals were assmall ∼3 mm in diameter, an actively Q-switched Pr3+:YLF laser operated at 640 nm was used as the pump source instead of the wavelength tunable OPO used in Chapter 4. For modulating the intracavity loss, an acousto-optic modulator

(M200-4B/E-LD5, Gooch & Housego). The pump laser operated with a repetition rate of 5 kHz, and the pulse duration was measured to be 15 ns as full-width at half maximum (FWHM). The beam quality of the pump laser was measured to be M 2 = 1.02 × 1.00. Transmission of 1.3-mm and 2.4-mm Cr4+:YAG crystals as a function of position Z with respect to pump beam waist is shown in Figs. 5.1(a,b). The transmission versus input fluence is also shown in Figs. 5.1(c,d). The pump pulse energy was 6.0 µJ for Sample A, and5.6µJfor

Sample B. The solid lines in Fig. 5.1 are results of numerical fitting exhibiting the minimum fitting error given by Eq. 4.8. In the previous chapter, the GSA cross section was determined to be (4.6 − 4.8) × 10−18 cm2, the best numerical fit was attained with a larger GSA cross section of 7.5 × 10−18 cm2 for Sample A and B. This can be attributed to the large difference in doping concentration. The small signal absorption coefficient at

640 nm for the samples investigated in Chapter 4 were 16.60 and 24.87 /cm, respectively. The samples used for Q-switching (Sample A and B) have much lower doping concentration, since the small signal absorption coefficient at 640 nm was 0.427 and 0.361 /cm for Sample A and B, respectively. For Sample AandB,the best fit was obtained at fp = 0.67 and 0.62, respectively. Therefore, the amount of parasitic absorption centers was expected to be lower for Sample B. Even though the best fit was systematically obtained with the above mentioned parameters, good fitting could be still obtained for a wide range of parameter sets, due to thelimited number of the plots and the fluctuation in transmission.

−18 2 As shown as the dashed lines in Fig. 5.1, when GSA cross section σgs was assumed to be 4.7 × 10 cm , as determined in Chapter 4, the parameter fp was determined to be 0.60 and 0.51 for Sample A and B, respectively. However, the fitting error was 60% larger than the case of the best fit. The determined saturation parameters are further used for the rate equation analysis of passively Q-switched lasers. The determined parameters of the Cr4+:YAG crystals are summarized in Table 5.1.

Table 5.1: Determined parameters of Cr4+:YAG crystals.

Sample A Sample B Length (mm) 1.3 2.4 −18 2 GSA cross section σgs (10 cm ) 7.5 7.5 −18 2 ESA cross section σes (10 cm ) 5.0 4.6

fp (= σes/σgs) 0.67 0.61

Initial transmission T0 (%) 94.6 91.7

Saturated transmission Tsat (%) 96.3 94.8 Modulation depth ∆T (%) 1.7 3.1 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 103

0.965 0.950 experiment experiment -18 2 (a) σ = 7.5 x 10-18 cm2, f = 0.67 (b) σ = 7.5 x 10 cm , f = 0.62 gs p 0.945 gs p -18 2 σ -18 2 f σgs = 4.7 x 10 cm , fp = 0.60 gs = 4.7 x 10 cm , p = 0.51 0.960 0.940

0.935 0.955 0.930 Transmission Transmission 0.925 0.950 0.920

0.945 0.915 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Z (mm) Z (mm) (c) 0.960 (d) 0.945 0.940

0.955 0.935

0.930

0.950 0.925 Transmission Transmission experiment experiment σ = 7.5 x 10-18 cm 2, f = 0.67 0.920 -18 2 gs p σgs = 7.5 x 10 cm , fp = 0.62 σ = 4.7 x 10-18 cm 2, f = 0.60 -18 2 gs p σgs = 4.7 x 10 cm , fp = 0.51 0.945 0.915 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 Fluence (J/cm2) Fluence (J/cm2)

Figure 5.1: Transmission at 640 nm as a function of position Z respect to pump beam waist for (a) 1.3-mm long Cr4+:YAG (Sample A) and (b) 2.4-mm long Cr4+:YAG (Sample B). Calculated transmission versus fluence for Sample A (c) and Sample B (d). Black solid lines are results of numerical fitting which exhibited the minimum fitting error. The −18 2 best fit was attained with σgs = 7.5 × 10 cm and fp = 0.67 for Sample A, and −18 2 σgs = 7.5 × 10 cm and fp = 0.62 for Sample B. Dashed line are fitting results with GSA cross section of 4.7 × 10−18 cm2. 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 104

5.1.2 Passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorbers

The setup of the passively Q-switched Pr3+:YLF laser is depicted in Fig. 5.2. The V-fold laser cavity consists of three mirrors: a dichroic mirror (DM), a high-reflectivity (HR) concave mirror (CM) and a concave output coupler (OC) of 8.6%, with a curvature radius of 75 mm. The cavity length was approximately 22.5 cm. The angle of incidence on the CM was set to 11◦. The laser medium was a 0.5 at. % Pr3+-doped YLF rod (Unioriental

Optics) whose diameter and length were both 5 mm, and its end surfaces were both uncoated. The laser crystal was mounted on a water-cooled copper holder to reduce the thermal load, which tends to decrease the laser output.

Blue laser diode Cylindrical (442 nm) expander HWP (x 5) Aspherical lens (f = 3.1 mm)

a DM c Blue laser diode (444 nm) Cylindrical a expander Pr3+:YLF (x 5) PBS Lens (f = 75 mm)

4+ Cr :YAG HR (R = 75 mm) OC (R = 75 mm)

Figure 5.2: Experimental setup of an InGaN blue LD pumped Pr3+:YLF laser passively Q-switched by a Cr4+:YAG saturable absorber. PBS: polarizing beam splitter, HWP: half-wave plate, DM: dichroic mirror, HR: high reflectivity mirror, CM: concave mirror, OC: output coupler.

(a) 250 200 Pr3+:YLF Cr4+:YAG 150 100 sagittal 50 tangential

Beam radius ( µ m) 0 0 50 100 150 200 Position along the cavity (mm)

(b) 250 200 Pr3+:YLF Cr4+:YAG 150 100 sagittal 50 tangential 0 Beam radius ( µ m) 0 50 100 150 200 Position along the cavity (mm)

Figure 5.3: Calculated cavity mode radius of V-shaped cavity with (a) 1.3-mm and (b) 2.4-mm long Cr4+:YAG crystal as saturable absorber. 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 105

The laser rod was pumped by polarization-combined InGaN blue LDs (Nichia Corp.). Each LD was mounted on a Peltier-cooled aluminum plate. The maximum output power of each LD was 3.5 W. The Pr3+:YLF crystal has its absorption peaks at 444 nm and 442 nm for polarization parallel to the crystal’s c-axis and a-axis, respectively. Therefore, the temperatures of LD mounts were controlled to maximize the absorption in the Pr3+:YLF crystal. Both pump beams were collimated by an aspherical lens of 3.1-mm focal length, and expanded along the slow axis of the LD by a pair of cylindrical lenses by a factor of five. Then, these beams were combined at the polarization beam splitter, and focused into the laser rod by a lens of 75-mm focal length.

The pump spot size within the gain medium was calculated to be 5.6 × 33 µm2. The saturable absorbers were inserted into the focal spot between CM and OC for passive Q-switching. The beam width inside the cavity was calculated by means of the ABCD matrix method, and the maximum mode-matching efficiency was calculated to be 78%. The calculated beam radius along the cavity position with the 1.3-mm and 2.4-mm Cr4+:YAG crystals are shown in Fig. 5.3. The beam radius at the gain medium and saturable absorber were calculated at

65 × 69 and 60 × 65 µm2, respectively. Before the Q-switching experiments, a CW operation was performed by simply removing the Cr4+:YAG from the cavity. Its maximum output power reached 1.52 W with a maximum absorbed pump power of 4.3 W, and the slope efficiency was 43.7%. The threshold pump power was 770mW.

With the maximum output, the beam quality factor was measured to be M 2 = 1.1 × 1.7 along the fast and slow axes, respectively. Subsequently, passive Q-switching experiment using the Cr4+:YAG saturable absorbers of

1.3-mm (Sample A) and 2.4-mm long (Sample B) was carried out. The measured averaged output power, pulse width (FWHM), and repetition with respect to absorbed pump power plotted as red symbols in Figs. 5.4, 5.5, and 5.6, respectively. When the 1.3-mm long crystal (Sample A) was used, the lasing threshold increased up to

1 W, and the maximum average output power was 650 mW at the highest absorbed pump power of 4.2 W. The shortest Q-switch pulse duration was 116 ns was obtained at a repetition rate of 105 kHz. The pulse energy and peak power were calculated to be 6.2 µJ and 53.2 W, respectively. When the 2.4-mm long crystal (Sample

B) was used as saturable absorber, the lasing threshold was 1.4 W, slightly increased as compared to that with

Sample A, due to its lower initial transmission. The highest averaged output power of 408 mW was obtained with the shortest pulse duration of 95 ns, and the highest pulse repetition frequency of 67 kHz. The highest pulse energy and peak power were calculated to be 6.1 µJ and 64 W, respectively.

The pulse repetition frequency increased linearly with the absorbed pump power, as shown in Fig. 5.6, because the pulse energy becomes constant once the laser is Q-switched. From Fig. 5.5, the pulse duration converged to ∼90 ns and ∼115 ns for Sample A and B, respectively. In general, the pulse duration of Q-switched pulses is mainly determined by the cavity length. In fact, the Q-switch pulse width is theoretically proportional to the photon lifetime (or cavity lifetime). However, practically, the duration of Q-switch pulses depends on properties of saturable absorbers. The shorter pulse could be obtained with Sample B, because of its larger modulation depth. In general, saturable absorbers of lower initial transmission exhibit larger modulation depth; therefore, a Cr4+:YAG crystal of lower initial transmission enables to generate shorter Q-switched pulses. 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 106

0.7 0.5 (a) experiment (b) experiment -18 2 -18 2 simulation (σes = 4.6 x 10 cm ) simulation ( σes = 5.0 x 10 cm ) 0.6 simulation (σ = 5.3 x 10-18 cm2) 0.4 es 0.5

0.4 0.3

0.3 0.2 0.2 0.1 0.1 Averaged output power (W) Averaged output power (W) 0.0 0.0 0 1 2 3 4 0 1 2 3 4 Absorbed pump power (W) Absorbed pump power (W)

Figure 5.4: Averaged output power of passively Q-switched Pr3+:YLF laser oscillating at 640 nm with (a) 1.3-mm and (b) 2.4-mm long Cr4+:YAG saturable absorber. Black dashed lines are numerically obtained results from rate equations presented in the following section.

220 150 (a) experiment (b) experiment -18 2 -18 2 σ simulation (σ = 5.0 x 10 cm ) simulation ( es = 4.6 x 10 cm ) es 140 σ -18 2 200 simulation ( es = 5.3 x 10 cm ) 130 180 120

160 110

100 140 Pulse width (ns) Pulse width (ns) 90 120 80

100 70 1 2 3 4 1 2 3 4 Absorbed pump power (W) Absorbed pump power (W)

Figure 5.5: Q-switched pulse width (FWHM, Full-width at half maximum) of passively Q-switched Pr3+:YLF laser oscillating at 640 nm with a (a) 1.3-mm- and (b) 2.4-mm long Cr4+:YAG saturable absorber. Black dashed lines are numerically obtained results from rate equations presented in the following section.

(a) 150 (b) 80 70

60 100 50

30 50 20

Repetition rate (kHz) Repetition rate (kHz) experiment -18 2 experiment 10 simulation (σe s = 4.6 x 10 cm ) -18 2 σ -18 2 simulation (σes = 5.0 x 10 cm ) simulation ( e s = 5.3 x 10 cm ) 0 0 1 2 3 4 1 2 3 4 Absorbed pump power (W) Absorbed pump power (W)

Figure 5.6: Pulse repetition rate of passively Q-switched Pr3+:YLF laser oscillating at 640 nm with a (a) 1.3-mm- and (b) 2.4-mm long Cr4+:YAG saturable absorber. Black dashed lines are numerically obtained results from rate equations presented in the following section. 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 107

The beam quality of the passively Q-switched laser was measured to be M 2 < 1.1, and this was better than the laser operated in CW mode. This is because the saturable absorbers can acts as spatial mode filter to suppress higher order modes. The intracavity beam has Gaussian distribution, the intensity is the highest at the center of optical axis, and the central part is dominated by the fundamental transverse mode (TEM00). At the saturable absorber, the non-intense higher order modes undergo lower transmission as compared to TEM00 mode.

5.1.3 Rate equation analysis

In this section, rate equation analysis of the passively Q-switched Pr3+:YLF laser with Cr4+:YAG saturable absorbers is presented. This numerical analysis enabled to check the accuracy of the estimated parameters of Cr4+:YAG saturable absorbers. Rate equations for passively Q-switched lasers were established for

Nd3+:YAG/Cr4+:YAG Q-switched lasers [90]. Saturable absorbers are modeled by four-level system presented in Fig. 4.1. A passively Q-switched laser is represented by the following rate equations:

dϕ cϕ ϕ = {σst∆Nlg − σgsngslSA − σes(ntot − ngs)lSA} − + S, (5.1) dt lc τc

d∆N ∆N Ntot − ∆N ηQηStokesηmPabs = −cϕσst∆N − + · , (5.2) dt τf Ntot hνLV

dngs Ag ntot − ngs = −σgscϕngs + . (5.3) dt ASA τSA

This is a simplified single-element model under plane-wave approximation [163]. The model consider thelaser cavity as a volume with the cross section Ag, the beam cross section at the gain medium, and length of lc, and the gain medium and saturable absorber are diluted and uniformly distributed through out the volume. This is reason why the factors lg/lc and lSA/lc in Eq. 5.1 and Ag/ASA in Eq. 5.3 appear. Therefore, the photon number density Since the population of the excited state in saturable absorber can be directly obtained as ntot − ngs, the number of the rate equations are reduced to three. The symbols and values of parameters used for calculations are listed in Table 5.2. The rate equations were numerically solved by the Runge-Kutta algorithm. The calculated averaged output power, pulse width (FWHM), and repetition frequency as a function of absorbed pump power are shown as dashed lines in Figs. 5.4, 5.5, and 5.6. The cavity round-trip loss Li was adjusted to get a good agreement with the experimental results in the averaged output power. Other parameters were not varied to fit the numerical results to the experimental results. As seen in Figs. 5.4,5.5, and 5.6, the numerical results exhibited roughly a good agreement with the experimental results. Although the calculated pulse width with the 1.3-mm long Cr4+:YAG crystal (Sample A) exhibited very good agreement with the experimental results (Fig. 5.5(a)), for the results with the 2.4-mm long Cr4+:YAG crystal (Sample B), the calculated pulse widths were somehow shorter than that in the experiments (Fig. 5.5(b)). The best fit in pulse width could be obtained with a larger ESA cross section of 5.3×10−18 cm2, as shown in Figs. 5.4(b), 5.5(b), and 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 108

5.6(b). This discrepancy can be attributed to the underestimated ESA cross sections in the characterization. In fact, good fitting could be obtained in wide range of the parameter space. As shown in Fig. 5.6, the experimental slope in the pulse repetition rate is lower than that of the model calculation. Presumably, this may indicate that the mode-matching efficiency and calculated effective mode area in the gain medium does not agreewith the actual values. Note that these parameters were not varied for further adjustment.

The rate equations were solved also with the GSA and ESA cross sections of 4.7 and 2.8 × 10−18 cm2, values estimated in Chapter 4. It turned out that the numerical results do not dramatically change for the cross sections exhibiting a similar saturation characteristics. As shown in Fig. 5.1, the saturation curves could be reproduced with a wide range of parameter sets. It was further confirmed that the results were mainly determined by the parameter fp, the ratio of ESA cross section with respect to GSA cross section. Thus, the parameter sets resulting the same amount of modulation depth are expected to provide the same numerical results. However, the Q-switching threshold strongly depends on the saturation intensity, which is given by GSA cross section.

Therefore, the performance in the vicinity of lasing threshold may sensitively change with GSA cross section in addition to the parameter fp.

5.1.4 Design of Pr3+:YLF/Cr4+:YAG microchip Q-switched laser

The duration of pulses generated by Q-switching strongly depends on the cavity length, and the shortening of the laser cavity is an effective way to make Q-switch pulse duration shorter. The shortening of the pulse enables to achieve a higher peak power. In this section, the numerical design of a Pr3+:YLF microchip laser Q-switched laser Q-switched by a Cr4+:YAG saturable absorber oscillating at 640 nm, and its performance predicted by the rate equation model, presented in the previous section. The determined parameters of the saturable absorber enable to simulate the microchip laser before an experimental demonstration.

Although Nd3+:YAG/Cr4+:YAG microchip lasers adopted a plane-plane cavity stabilized by a positive thermal lens appearing in the laser rod, a conventional plane-concave cavity was adopted for the designed microchip laser, since the YLF crystal exhibits an anisotropic thermal lensing owing to its anisotropy in thermo-optic coefficient (dn/dT ) [132], as shown in Fig. 3.21. A 15-mm long plane-concave cavity, consisting of an HR concave mirror of 20-mm curvature radius and a plane output coupler of 10% transmission, was assumed. We set maximum pump power of 10 W, which can be simply achieved by the polarization-combined two 5-W blue

LDs. As a gain medium, a 3-mm long Pr3+:YLF crystal of 1 at. % doping concentration was assumed. Richter et al. investigated the fluorescence quenching effect3+ inPr :YLF crystal [133], and the fluorescence lifetime of a 1 at. % crystal was measured to be ∼28 µs. As discussed in the previous section, the modulation depth of saturable absorber affects on Q-switch pulse duration and pulse energy. The pulse energy and pulse duration can be improved as the modulation depth increases. However, the large modulation depth simultaneously brings 4+ 5.1. Passive Q-switching with Cr :Y3Al5O12 (YAG) saturable absorber 109

Table 5.2: Parameters and their values used in numerical simulation of passively Q- switched Pr3+:YLF laser with Cr4+:YAG saturable absorber.

Symbol Parameter Value (or definition) Unit

−7 λL Laser wavelength 640 × 10 cm

νL Laser frequency c/λL Hz

ϕ Intracavity photon number density Variable cm−3

∆N Population inversion density Variable cm−3

−3 ngs Population density in ground state of saturable absorber Variable cm

−19 2 σst Stimulated emission cross section of gain medium 2.2 × 10 cm

−18 2 σgs Ground-state absorption cross section of saturable absorber 7.5 × 10 cm

−18 2 σes Excited-state absorption cross section of saturable absorber 5.0/4.6 × 10 cm

lg Length of gain medium 0.5 cm

lSA Length of saturable absorber 0.13 / 0.24 cm

lc Cavity length 21.5 cm

19 −3 Ntot Total population density of active ions in gain medium 7.0 × 10 cm

16 −3 ntot Total population density of absorption centers in saturable absorber 9.08/7.68 × 10 cm

τc Cavity lifetime (or photon lifetime) 2lc/{c(Li − ln R)} s

τf Fluorescence lifetime of gain medium 38 µ s

τSA Recovery time of saturable absorber 4.2 µ s

Li Cavity round-trip loss 0.03 / 0.07 –

R Reflectivity of output coupler 0.925 –

−4 2 Ag Effective mode area in gain medium 1.7 × 10 cm

−4 2 ASA Effective mode area in saturable absorber 1.2 × 10 cm

S Contribution of spontaneous emission Arbitral (small value) –

ηQ Quantum efficiency 1 –

ηStokes Stokes efficiency 0.693 –

ηm Mode-matching efficiency 0.78 –

Pabs Absorbed pump power Variable W 2+ 5.2. Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber 110 a large non-saturable loss. Here, the initial transmission of the Cr4+:YAG saturable absorber was set to 70%, which is expected to be bleached up to ∼80% from the determined GSA and ESA cross sections.

The rate equations were solved with the above mentioned conditions. At the absorbed pump power of 10 W, the predicted averaged output power was 440 mW, pulse duration was 1.5 ns, and repetition frequency was

50 kHz. The pulse energy and peak power were then calculated to be 8.8 µJ and 5 kW, respectively. The pulse energy and peak power can be further scaled up by adopting Cr4+:YAG saturable absorbers of even lower initial transmission. From the numerical simulation, it was predicted that kW-peak power red solid-state laser can be obtained from Pr3+:YLF/Cr4+:YAG microchip.

2+ 5.2 Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber

As presented in Section 4.4.1, Co2+-doped MALO was found to be a broadband saturable absorber which covers from the green to red region. Demesh et al. have already demonstrated passive Q-switching of a 2ω-OPSL- pumped Pr3+:YLF laser with a Co2+:MALO saturable absorber [71]. In this section, passive Q-switching of a diode-pumped Pr3+:YLF laser with a Co2+:MALO at 523, 607, and 640 nm is presented.

5.2.1 Co2+:MALO crystal for passive Q-switching

For passive Q-switching, a Co2+:MALO crystal (EKSMA Optics) of 0.35-mm length was used. The crystal’s surfaces were coated for anti-reflection (AR) from 500 to 650 nm. Its transmission spectrum recorded bya double-beam spectrometer (LAMBDA1050, Perkin Elmer) is shown as the red solid line in Fig. 5.7. The crystal’s initial transmission was measured to be 97.4%, 93.9%, and 94.2% at 523, 607, and 640 nm, respectively. Because the absorption spectrum of an uncoated Co2+:MALO is known (Fig. 4.22), the transmission spectrum of the applied coating was estimated as shown as the black dashed line in Fig. 5.7. Note that the estimated transmission spectrum was derived with the assumption that the AR coating at a wavelength is perfect (∼600 nm in Fig. 5.7).

Even though the best coating was assumed, the single pass loss owing to the coating was estimated to be ∼1.1% at 523 nm, resulting ∼2.2% loss when inserted in a cavity. Because parasitic absorption centers are thought to be absent in Co2+:MALO, the parameters of the saturable absorber determined in Section 4.4.1 were directly adopted. The crystal’s saturated transmission and modulation depth were calculated and listed in Table 5.3. 2+ 5.2. Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber 111

1.00

0.98

0.96

0.94

Transmission 0.92 AR coat Co2+:MALO (0.35 mm) Coating 0.90 450 500 550 600 650 700 Wavelength (nm)

Figure 5.7: Transmission spectrum of AR-coated Co2+:MALO crystal of 0.35 mm. Black dashed line is estimated transmission spectrum of the coating (both surfaces) from the spectrum of uncoated Co2+:MALO crystal.

Table 5.3: Parameters of Co2+:MALO used for passive Q-switching.

Wavelength (nm) 523 607 640 −19 2 GSA cross section σgs (10 cm ) 3.2 14.0 11.0 −19 2 ESA cross section σes (10 cm ) – 2.0 6.0

fp (= σes/σgs) – 0.14 0.54 Measured transmission T (%) 97.4 93.9 94.2

Highest transmission of AR coating TAR (%) 99.42 99.97 99.56

Effective initial transmission T0 (%) 98.5 94.0 95.0

Effective saturated transmission Tsat (%) – 99.1 97.3 Modulation depth ∆T (%) – 5.1 2.3 2+ 5.2. Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber 112

5.2.2 Passively Q-switched Pr3+:YLF laser with Co2+:MALO saturable absorber

The experimental setup of a passively Q-switched diode-pumped Pr3+:YLF laser with a Co2+:MALO saturable absorber is depicted in Fig. 5.8.

Blue laser diode Cylindrical (442 nm) expander Isolator (x 5) HWP Aspherical lens (f = 3.1 mm)

Cylindrical HWP DM expander a Blue laser diode (plane) c (x 5) (444 nm) DM Blue laser diode Cylindrical a Pr3+:YLF (R = 75 mm) Isolator (442 nm) expander (x 5) PBS Lens (f = 120 mm)

Aspherical lens OC Lens PBS (plane) Co2+:MALO (f = 3.1 mm) (f = 150 mm) Cylindrical Blue laser diode expander (444 nm) (x 5)

Figure 5.8: Experimental setup of an InGaN blue LD pumped Pr3+:YLF laser passively Q-switched by a Co2+:MALO saturable absorber. PBS: polarizing beam splitter, HWP: half-wave plate, DM: dichroic mirror, HR: high reflectivity mirror, CM: concave mirror, OC: output coupler.

The pump configuration was same as the continuous-wave operation (Section 3.4.1). The V-shaped cavity consisted of three mirrors: a plane dichroic mirror (DM), a concave dichroic mirror (DM) with a curvature radius of 75 mm, and a plane output coupler (OC). A 12-mm long, 0.3 at. % Pr3+:YLF crystal (Unioriental

Optics) was placed in the vicinity of the plane DM. The crystal was mounted on a water-cooled copper heat sink with an indium foil for filling the air-gap. The2+ Co :MALO saturable absorber was placed in the vicinity of

OC. Since the saturation intensity of Co2+:MALO is expected to be larger than that of Pr3+:YLF, it is essential to focus in the saturable absorber more strongly than in the gain medium for 607- and 640-nm operation. It is noteworthy that the saturation intensity at 523 nm of Pr3+:YLF may be comparable with that of Co2+:MALO.

For 523-nm, 607-nm, and 640-nm, output couplers 2.8%, 11.4%, and 9.1% transmission were used, respectively.

The angle of incidence on the concave DM was ∼ 20◦. By means of ABCD matrices, the cavity mode radius in the gain medium and saturable absorber was calculated for each operation wavelength. For 607- and 640-nm operations, the cavity length was set to ∼130 mm. The mode radius in the gain medium was calculated at

114×92 and 117×97 µm2 (vertical × horizontal), and the mode radius in the saturable absorber was calculated at 68 × 65 and 70 × 67 µm2 for 607 and 640 nm, respectively. For operating at 523 nm, the cavity length was set to ∼150 mm so that the mode radius in the gain medium became smaller to suppress the thermal aberration, since the 523-nm light undergoes a strong negative thermal lensing (discussed in Chapter 3). The resulting mode radius in the gain medium and saturable absorber was calculated at 60 × 55 and 76 × 60 µm2.

Passive Q-switching was successfully obtained at all the operated wavelengths. Averaged output power, pulse width (FWHM), and repetition rate with respect to absorbed pump power are plotted in Figs. 5.9, 5.10, and

5.11 for 523 nm (a), 607 nm (b), and 640 nm (c). Note that a concave DM with a relatively low transmission at the pump wavelength was used for the 607-nm operation. This is reason why the maximum absorbed pump 2+ 5.2. Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber 113 power in 607-nm results was limited at ∼10 W.

Due to the large insertion loss of the saturable absorber, such as the imperfect coating, the averaged output power significantly decreased from the output power in CW operation. The deterioration in output powerat

523 nm was significant because the small emission cross section at 523 nm makes the laser sensitive tointracavity loss. The slope efficiency with respect to absorbed pump power was measured tobe ∼5%, ∼17%, and ∼23% at

523, 607, and 640 nm, respectively.

The shortest duration of Q-switch pulses at 523 nm was ∼300 ns, which was much longer than at 607 and

640 nm, despite of the shorter cavity length. This may be due to the limited modulation depth in the saturable absorber in the green region. Regarding the values in Table 5.3, the largest possible modulation depth is 1.5% even when the ESA cross section was assumed to be zero. Thus, the actual modulation depth is expected to be less than 1%, and such small modulation depth generally results in long Q-switch pulses.

0.5 1.2 2.5 experiment experiment -19 2 simulation (σes = 2.0 x 10 cm ) simulation -19 2 (a) 1 simulation (σes = 7.0 x 10 cm ) 0.4 2 0.8 (b) (c) 0.3 1.5 0.6 0.2 1 0.4

0.1 0.5 0.2 Averaged output power (W) Averaged output power (W) Averaged output power (W) 0 0 0 0 2 4 6 8 10 12 0 2 4 6 8 10 0 2 4 6 8 10 12 Absorbed pump power (W) Absorbed pump power (W) Absorbed pump power (W)

Figure 5.9: Averaged output power of passive Q-switched diode-pumped Pr3+:YLF laser at (a) 523 nm, (b) 607 nm, and (c) 640 nm. Black dashed lines are results of numerical simulation.

250 experiment 1400 experiment -19 2 200 simulation simulation (σes = 2.0 x 10 cm ) simulation (σ = 7.0 x 10-19 cm2) 1200 200 es

1000 150 150 800

600 100 100 Pulse width (ns) Pulse width (ns) Pulse width (ns)

400 50 (a) (b) 50 (c) 200 0 2 4 6 8 10 12 2 4 6 8 10 0 2 4 6 8 10 12 Absorbed pump power (W) Absorbed pump power (W) Absorbed pump power (W)

Figure 5.10: Pulse width of passive Q-switched diode-pumped Pr3+:YLF laser at (a) 523 nm, (b) 607 nm, and (c) 640 nm. Black dashed lines are results of numerical simulation.

5.2.3 Rate equation analysis

A rate equation model was established to evaluate the passively Q-switched Pr3+:YLF laser with the Co2+:MALO saturable absorber. This numerical modeling enabled to evaluate the accuracy of the determined saturation parameters of Co2+:MALO saturable absorber. As presented in Chapter 4, the relaxation of Co2+ in MALO 2+ 5.2. Passive Q-switching with Co :MgAl2O4 (MALO) spinel saturable absorber 114

90 100 200 180 80 (a) (b) (c) 80 160 70 140 60 120 60 100 40 50 80 60 Repetition rate (kHz) Repetition rate (kHz) 20 Repetition rate (kHz) 40 experiment simulation (σ = 2.0 x 10-19 cm2) es 40 experiment -19 2 simulation (σes = 7.0 x 10 cm ) simulation 30 0 20 0 2 4 6 8 10 12 2 4 6 8 10 0 2 4 6 8 10 12 Absorbed pump power (W) Absorbed pump power (W) Absorbed pump power (W)

Figure 5.11: Pulse repetition rate of passive Q-switched diode-pumped Pr3+:YLF laser at (a) 523 nm, (b) 607 nm, and (c) 640 nm. Black dashed lines are results of numerical simulation. is complicated due to the existence of multiple relaxation paths. However, the conventional four-level model

(Fig. 4.1) was adopted for the rate equation analysis. In fact, the recovery time is an important parameter which determine the saturation intensity, and this parameter strongly affects to the condition to obtain Q-switching.

However, in the numerical calculation, it was found out that the performances of passively Q-switched lasers are insensitive to the recovery time. It was confirmed that the Q-switching threshold changed with the recovery time, but averaged output power, pulse duration, and repetition rates did not change once Q-switching was obtained. In the numerical model, the recovery time was tentatively assumed to be 500 ns, which was roughly estimated from the pump-probe measurement described in Section 4.4.1. Parameters to solve the rate equations

Eqs. (5.1–5.3) are listed in Table 5.4. The intracavity loss Li and effective mode area in the gain medium Ag were only treated as a fitting parameter. These parameters were optimized for each operation wavelength so that a good agreement was obtained in the averaged output power.

Dashed lines in Figs. 5.9–5.11 show numerically calculated results were shown as dashed lines in Figs. 5.9–5.11.

For 523 nm, the experimental results could not be reproduced even though the intracavity loss was varied for fitting. In the numerical model, Q-switching threshold at 523 nm was ∼9 W of absorbed pump power, while

Q-switching could be experimentally obtained from an absorbed pump power of ∼2 W. This discrepancy in the

Q-switching threshold was only seen in the 523-nm operation, presumably because the emission cross section at 523 nm was smaller for an order of magnitude than that at 607 and 640 nm. This may caused the imperfect modeling of relaxation in Co2+:MALO. The recovery time is an important parameter which determines the

Q-switching threshold. Therefore, a rigorous model in which intermediate levels of different lifetimes are taken into account may be required to model for the Q-switched laser at 523 nm.

For 607 nm, the intracavity loss was set to 12% to fit in output characteristic. Such large loss is understood by the existence of the GSA in the orange region. The calculated results with the determined ESA cross section (2.0 × 10−19 cm2) exhibited much shorter pulse as compared to the experimental results. In the model calculation, it was confirmed that the pulse width was mainly determined by the modulation depth ofthe saturable absorber when the cavity length was fixed. In theory, Q-switch pulse width is proportional to cavity 5.3. Passive Q-switching with Co2+-doped garnet saturable absorber 115 lifetime, and cavity lifetime is affected by transmission of output coupler and intracavity loss; however, these parameters only slightly changed the pulse width in the model calculation. Moreover, the calculated pulse width was independent from other parameters of the saturable absorber. Thus, the determined ESA cross section at

607 nm might be underestimated. The value of ESA cross section was further varied to obtain a good fitting in pulse width, and a good agreement with the experimental results was achieved with an ESA cross section of

∼ 10 × 10−19 cm2 as shown in Figs. 5.9–5.11(b).

For the results at 640 nm, a good agreement in pulse width was obtained using the ESA cross section determined by the Z-scan measurement (as presented in Chapter 4). However, the calculated repetition rate was largely different from the experimental results. It should be noted that the saturating nature of repetition ratecan be never simulated in the model calculation. The calculated repetition rate always shows a linear increase with respect to the absorbed pump power. In experiments, the pulse jitter in energy, width, and repetition rate became very large when the saturating nature of repetition rate was seen. Such characteristic was always observed when a saturable absorber of high initial transmission was used. This jitter may be caused by the competition between Q-switching and CW operations. The CW component may try to build up in the pulse intervals. Further investigations are required to fully understand the observation.

5.3 Passive Q-switching with Co2+-doped garnet saturable absorber

3+ 2+ Experiments on passive Q-switching of a Pr :YLF laser were performed by utilizing Co -doped Gd3Ga5O12 (GGG) saturable absorber. To the best of knowledge, passive Q-switching in the visible with Co2+-doped garnets has never been reported.

The laser setup is depicted in Fig. 5.12. Only for this experiment, a frequency-doubled optically-pumped semiconductor laser (2ω-OPSL) at a wavelength of 479 nm (Coherent) delivering 5 W of output power was used. The laser crystal was a 12 mm long, Pr3+ (0.5 at. %):YLF crystal. The Z-shaped cavity enabled a variable beam diameter inside the Co2+-doped garnets as well as a focus in the laser crystal, both being placed close to the end mirrors of the cavity (see Fig. 5.12). The cavity mode radius in the gain medium and saturable absorber was calculated at 100 µm and 40 µm, respectively.

As presented in the previous section, the recovery times of the Co2+-doped garnets are two orders of magnitude shorter than that in spinels, resulting in much higher saturation intensities. To achieve the required intracavity intensity, an output coupler (OC) of only 2% transmission was used. Note that the Co2+:garnets used in this experiment were uncoated, and their facets were not perfectly parallel, both causing comparably large insertion losses when placed in the cavity. Due to these high losses in theses initial experiments we aimed laser oscillation at 640 nm, where the gain is largest. Before inserting the saturable absorbers, the maximum continuous wave 5.3. Passive Q-switching with Co2+-doped garnet saturable absorber 116

Table 5.4: Parameters and their values used in numerical simulation of passively Q- switched Pr3+:YLF laser with Co2+:MALO saturable absorber.

Symbol Parameter Value (or definition) Unit −7 λL Laser wavelength 523 × 10 cm 607 × 10−7 640 × 10−7

νL Laser frequency c/λL Hz ϕ Intracavity photon number density Variable cm−3 ∆N Population inversion density Variable cm−3 −3 ngs Population density in ground state of saturable absorber Variable cm −19 2 σst Stimulated emission cross section of gain medium 0.3 × 10 (523 nm) cm 1.4 × 10−19 (607 nm) 2.2 × 10−19 (640 nm) −19 2 σgs Ground-state absorption cross section of saturable absorber 3.2 × 10 (523 nm) cm 14.0 × 10−19 (607 nm) 11.0 × 10−19 (640 nm) 2 σes Excited-state absorption cross section of saturable absorber Not Available (523 nm) cm 2.0 × 10−19 (607 nm) 6.0 × 10−19 (640 nm)

lg Length of gain medium 1.2 cm

lSA Length of saturable absorber 15.0 (523 nm) cm 17.0 (607 nm) 17.0 (640 nm)

lc Cavity length 21.5 cm 19 −3 Ntot Total population density of active ions in gain medium 7.0 × 10 cm 18 −3 ntot Total population density of absorption centers in saturable absorber 1.3 × 10 cm

τc Cavity lifetime (or photon lifetime) 2lc/{c(Li − ln R)} s

τf Fluorescence lifetime of gain medium 38 µ s

τSA Recovery time of saturable absorber 500 n s

Li Cavity round-trip loss Not Available (523 nm) – 0.12 (607 nm) 0.03 (640 nm) R Reflectivity of output coupler 0.985 (523 nm) – 0.886 (607 nm) 0.909 (640 nm) −4 2 Ag Effective mode area in gain medium 1.9 × 10 (523 nm) cm 2.0 × 10−4 (607 nm) 2.3 × 10−4 (640 nm) −4 2 ASA Effective mode area in saturable absorber 1.4 × 10 cm S Contribution of spontaneous emission Arbitrary (small value) –

ηQ Quantum efficiency 1 –

ηStokes Stokes efficiency λP/λL –

ηm Mode-matching efficiency 0.45 (523 nm) – 0.70 (607 nm) 0.72 (640 nm)

Pabs Absorbed pump power Variable W 5.3. Passive Q-switching with Co2+-doped garnet saturable absorber 117

Dumper HWP PBS Dichroic mirror (plane) Pr3+:YLF (0.3 at.%, 12 mm)

Lens (f = 200 mm)

HR HR (R = 200 mm) (R = 100 mm) Co2+:GGG OC (plane, T = 2%)

Figure 5.12: Schematic view of 2ω-OPSL-pumped Pr3+:YLF laser Q-switched by Co2+:GGG saturable absorber.

2+ output power was 2.1 W at an absorbed pump power of 4.2 W. Once the Co :GGG (T0 = 83%) was inserted in the cavity, stable Q-switching was observed, but the output power was strongly reduced to 12 mW. We attribute this to the large additional cavity losses due to the Fresnel reflection from the not-parallel facets. The recorded

Q-switched pulse train and single pulse waveform are shown in Fig. 5.13. The pulse duration was ∼300 ns, at

2+ a pulse repetition rate of ∼140 kHz. We also inserted the Co :YAG sample (T0 = 78%), but Q-switching was not observed. This may be due to an even higher saturation intensity which can be concluded from the three times shorter recovery time compared to Co2+:GGG. We thus conclude that also Co2+:YAG can be utilized as a saturable absorber if the intracavity intensity is increased by lower cavity losses and/or a stronger focus in the saturable absorber.

(a) 1 (b) 1

0.8 0.8

0.6 0.6

307 ns 0.4 0.4

0.2 Intensity (arb. units) 0.2 Intensity (arb. units)

0 0 0 20 40 60 80 100 -1000 -500 0 500 1000 Time (µs) Time (ns)

Figure 5.13: (a) Q-switched pulse train and (b) single pulse waveform obtained with Co2+:GGG saturable absorber. 5.4. Summary 118

5.4 Summary

In this chapter, passive Q-switching of visibly emitting Pr3+:YLF laser with three different solid-state saturable absorbers are presented. Even though Cr4+-doped YAG crystals were extensively investigated as presented in Chapter 4, the samples used for Q-switching experiments were characterized since Cr4+:YAG inevitably contains parasitic absorption centers in the visible region, such as Cr3+ and Cr4+ ions in octahedral site. Using an actively Q-switched Pr3+:YLF laser as the pump source, two AR-coated Cr4+:YAG crystals prepared for passive Q-switching were investigated by means of Z-scan measurements. The determined GSA cross section at

640 nm was larger than that determined in Chapter 4. Moreover, the parameter fp, defined as the ratio of ESA cross section to GSA cross section, was estimated to be slightly larger than the previous characterization, since the absorption due to all the parasitic absorption centers are treated as the non-saturable loss. By utilizing

Cr4+:YAG saturable absorbers of 94.6% and 91.7% initial transmission at 640 nm, Q-switched pulses of ∼115 and ∼90 ns width were obtained at a repetition rate of ∼100 kHz and ∼65 kHz, respectively. The pulse duration was mainly determined by the cavity length. In the hypothetical model calculation, <2 ns pulses with kilowatt peak power can be generated from Pr3+:YLF/Cr4+:YAG microchip with 1.5-cm short cavity.

Since the visible absorption in Co2+:MALO is expected to be purely due to Co2+ in tetrahedral site, the sample used for Q-switching experiments was not investigated. The initial transmission of the AR-coated Co2+:MALO was 97.4, 93.9, and 94.2% at 523, 607, and 640 nm. Passive Q-switching was successfully obtained at the operated wavelengths. Since the emission cross section of Pr3+:YLF at 523 nm was smaller for an order of magnitude than these at 607 and 640 nm, the output power dramatically decreased with the saturable absorber. The

Q-switch pulse width at the highest absorbed pump power was ∼300 ns, ∼70 ns, and ∼50 ns for 523-, 607-, and

640-nm operation, respectively. Even though the cavity length was shorter for 523-nm experiment than for 607- and 640-nm operations, the pulse duration was much longer, because the modulation depth of the Co2+:MALO was limited below 1.5% due to its high initial transmission. For obtaining even shorter Q-switch pulses at

523 nm, a saturable absorber of lower initial transmission is required; however, such saturable absorber always brings larger non-saturable loss which easily deteriorate the output performance at 523 nm. Therefore, visible saturable absorbers of very small non-saturable loss is necessary.

For the passively Q-switched Pr3+:YLF laser with the Cr4+:YAG and Co2+:MALO, rate equation analyses were performed to understand the laser dynamics. From the model simulations, it was found out that fp is one of the most important parameters determining performance of passively Q-switched laser. When the cavity length is given, the pulse duration and accordingly the peak power was mainly affected by the amount ESA cross section which gives the saturated transmission and modulation depth. In general, GSA cross section is considered as an important parameter to evaluate saturable absorbers, because this parameter determines saturation fluence and intensity. However, the model calculations told us that GSA cross section only affects to the threshold of 5.4. Summary 119

Q-switching, and it no longer gives a strong influence on laser performances.

In the characterization presented in Chapter 4, Co2+-doped garnets exhibited very short recovery times, resulting in very high saturation intensity. Despite high saturation intensities were expected, passive Q-switching was successfully demonstrated using a Co2+:GGG saturable absorber. The Q-switching experiment was only to check whether the saturable absorber is practically useful for Q-switching visible lasers, so the used crystal was not optimized for laser experiments. While the unoptimized saturable absorber induced a huge intracavity loss, stable Q-switching was observed at 640 nm. The pulse duration was measured to be ∼300 ns, and the repetition rate was ∼140 kHz. By optimizing initial transmission and applying an AR-coating on the crystal, much greater laser performances should be obtained. Regarding the characterization, Co2+:GGG can be used as a broadband visible saturable absorber of very small non-saturable loss. Thus, Co2+:GGG saturable absorber may enable to generate high-peak power Q-switch pulses. Chapter 6

Frequency conversion of Pr3+:YLF lasers for ultraviolet generation

In this chapter, we present the experimental demonstration of 320-nm ultraviolet (UV) lasers by applying intracavity second harmonic generation (SHG) to a diode-pumped Pr3+:YLF laser oscillating at 640 nm. First, the experiment in continuous-wave (CW) operation is described. In the later section, 320-nm UV pulse generation from frequency-doubled Pr3+:YLF laser passively Q-switched by Cr4+:YAG saturable absorber is presented.

Deep ultraviolet (DUV) coherent light is, in general, generated by means of successive frequency conversion of high-power near infrared (NIR) lasers. Using a Q-switched Nd3+-doped solid-state laser oscillating at 1064 nm, the deep-UV (DUV) region is accessible as forth-harmonic (266 nm) and fifth-harmonic (213 nm). In this chapter, the demonstration of 213-nm DUV pulses by means of second harmonic generation (SHG) and sum-

3+ frequency generation (SFG) of visible pulses is described. The use of an actively Q-switched Pr :YLF (LiYF4) laser operated at 640 nm enabled to simplify the frequency conversion processes as compared to the fifth harmonic generation of Nd3+ lasers.

6.1 Continuous-wave ultraviolet Pr3+:YLF laser at 320 nm

6.1.1 Experiment

In this section, an intracavity frequency doubled Pr3+:YLF laser emitting at 320 nm is described. Figure 6.1 depicts the laser setup. A pair of 5-W output blue LDs were employed as pump sources. As the gain medium, a 0.5 at. % 5-mm long Pr3+:YLF crystal (Unioriental Optics) cut perpendicular to the crystal’s a-axis was adopted. The crystal’s surfaces were uncoated. As described in Chapters 3 and 5, the gain medium was

120 6.1. Continuous-wave ultraviolet Pr3+:YLF laser at 320 nm 121 mounted on a copper heat sink in which cooling water was circulating. The temperature of the cooling water was fixed at 16◦C. The air-gap between the crystal and copper holder was filled by a 0.1-mm thick indium foil for better thermal contact. The laser cavity consisted of three mirrors: a plane dichroic mirror (DM), which was highly reflecting at 640 nm and highly transmissive at the pump wavelength∼ ( 444 nm), and two concave mirrors. The folding concave mirror of 150-mm radius of curvature acted as the output coupler to extract

320-nm second harmonic (SH) light. The end concave mirror of 50-mm focal length was highly reflecting at both the fundamental and SH wavelengths. For frequency doubling, a 8-mm long Type–I lithium triborate

◦ ◦ (LiB3O5 (LBO)) (CASTECH) was adopted. The cut angles were θ = 90 , φ = 53.5 . The both surfaces of the LBO was coated for anti-reflection at both fundamental and SH wavelengths. The LBO was placed between the two concave mirrors. The angle of incidence on the folding concave mirror was measured to be 20◦. Due to the difference in the focal length for vertical and horizontal planes of the concave mirror with angled incidence, the calculated cavity mode size was astigmatic as shown in Fig. 6.2. In the vicinity of the plane dichroic mirror, where the gain medium located, the cavity astigmatism was compensated; however, at the position of the LBO, the cavity mode was elliptical. The spot radius at the LBO’s position was calculated at 50 × 130 µm2. Each pump beams from pump LD was collimated by an aspherical lens of 3.1-mm focal length and expanded along the slow axis by a factor of five. The two beams were then combined at a polarizing beam splitter (PBS),and focused into the Pr3+:YLF crystal by a 100-mm spherical lens. The mode-matching efficiency between the pump and cavity modes was calculated at 74% when the pump profile was considered to be Gaussian. The calculated mode-matching was reduced to 70% when a top-hat pump profile was assumed. Since the actual pump profile was between Gaussian and top-hap shapes, the mode-matching efficiency was expected to be between the two values.

Blue laser diode Cylindrical (442 nm) expander HWP (x 5) Aspherical lens (f = 3.1 mm)

DM (plane) a Pr3+:YLF Blue laser diode c (444 nm) Cylindrical a expander (x 5) PBS Lens (f = 100 mm)

Concave OC LBO (HR@640 nm, Concave HR HT@320 nm, (640+320 nm R = 150 mm) R = 50 mm)

Figure 6.1: Experimental setup of intracavity frequency-doubled Pr3+:YLF laser in continuous-wave operation.

The output characteristic of the frequency-doubled Pr3+:YLF laser is shown in Fig. 6.3. The highest incident pump power was measured to be 8.68 W, and the highest absorbed pump power was 5.9 W, corresponding to the absorption efficiency of 68%. The maximum output SHG power was measured to be 880 mW at the highest 6.1. Continuous-wave ultraviolet Pr3+:YLF laser at 320 nm 122

600 500 400 300 200 vertical plane 100

Beam radius ( µ m) horizontal plane 0 0 50 100 150 200 250 300 Distance from DM (mm)

Figure 6.2: Calculated beam radius of V-shaped cavity for intracavity frequency-doubled Pr3+:YLF laser. absorbed pump power. The optical-to-optical efficiency of the laser was calculated at ∼15%. Even though all the cavity mirrors highly reflective at the fundamental wavelength (640 nm) for high-Q cavity, the leakage from the mirrors were not negligible. From the concave end mirror, a fundamental power of 350 mW at 640 nm was leaked. Laser cavities for intracavity frequency conversion are very sensitive to the intracavity loss.

1 Experiment Simulation 0.8

0.6

0.4

Output power (W) 0.2

0 0 1 2 3 4 5 6 7 Absorbed pump power (W)

Figure 6.3: Calculated beam radius of V-shaped cavity for intracavity frequency-doubled continuous-wave Pr3+:YLF laser. Dashed black line is numerically calculated result.

6.1.2 Rate equation analysis

The intracavity frequency-doubled continuous-wave Pr3+:YLF laser was then simulated by rate equations to interpret the experimental result. The rate equations for intracavity SHG are described by the following equations: 2 dϕ lg ϕ c 2 = cσstϕ∆N − − γSHGhν2ωANLϕ − S, (6.1) dt lc τc 2lc

d∆N ∆N Ntot − ∆N ηPabs = −cϕσst∆N − + · , (6.2) dt τf Ntot hνωV 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 123

where γSHG is the nonlinear conversion coefficient, and ANL the effective mode area in the nonlinear crystal. Other symbols are same as Eqs. 5.1 and 5.2 in Chapter 5. The third term on the right hand side of Eq. (6.1) represents frequency conversion from fundamental wave at 640 nm to SH wave at 320 nm. Assuming perfect phase matching, nonlinear conversion coefficient γSHG is given as follows:

2 2 2ω deﬀ lNLk ′ ′ γSHG = 3 3 h (B , ξ), (6.3) πnNLc ϵ0 where h′(B′, ξ) is Boyd-Kleinman factor [164]. Since we assumed a loose focusing condition in the nonlinear crystal, the Boyd-Kleinman factor is approximately given as

h′(B′, ξ) ≈ ξ(1 − t′2/12 + t′4/120 − t′6/1344 + ... ), (6.4)

√ where t′ = 2B′ 2ξ, and B′ and ξ are the walk-off and focusing parameters, respectively. Using the parameters in the experiment, the nonlinear conversion coefficient was calculated at 2.14×10−5 /W. The dashed line shown in

Fig. 6.3 was obtained by solving the rate equations, Eqs. 6.1 and 6.2. Since the actual cavity loss was unknown, the parameter of intracavity loss Li was treated as a fitting parameter. Moreover, the intracavity fundamental power could be estimated from the leaked fundamental wave from the end mirror, the relevance of the numerical simulation could be checked. The dashed line in Fig. 6.3 was obtained when the cavity loss was set to 5.5% per round-trip. The calculated leaked fundamental power from the end mirror was ∼330 mW, exhibiting good agreement with the experiment. The relatively large cavity loss was attributed to the uncoated gain crystal and non-negligible transmission of the concave output coupler at 640 nm. A gain crystal of anti-reflection coating and mirrors of better reflectivity are expected to significantly improve the performance of the continuous-wave intracavity SHG laser.

6.2 Intracavity frequency-doubling of passively Q-switched Pr3+:YLF

ultraviolet laser

6.2.1 Experiment

The experimental setup of a Q-switched UV laser is depicted in Fig. 6.4. The V-fold cavity consists of three mirrors, two plane mirrors (PM1 and PM2), and a concave output coupler (OC) whose radius of curvature

(RoC) was 75 mm. We employed a 5.0-mm long Pr3+:YLF crystal (AC Materials) as the gain medium. The crystal’s doping concentration was 0.5 at. %, and it was cut perpendicular to the crystal’s a-axis. Its end facets were polished and uncoated. As described in the previous section, the crystal was mounted on a water-cooled copper holder, and the temperature of the circulating water was fixed to◦ 16 C. As a saturable absorber, a 2.4- 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 124 mm long Cr4+:YAG crystal (Sample B in Section 5.1.1) was placed in the vicinity of the PM1. The crystal was anti-reflection (AR)-coated at the fundamental wavelength (640 nm), and its orientation was (100). The initial transmission was measured to be 91.7% at 640 nm. To convert the 640-nm fundamental wave into a 320-nm second-harmonic wave, an AR-coated 8-mm long LBO crystal (same as in the previous section) was again used.

Since the plane end mirror PM2 had high reflectivity both at 640 and 320 nm, the second harmonic was extracted from the dichroic output coupler, which was highly reflective at 640 nm but highly transmissive at 320 nm.The transmission of the OC at 320 nm was 80%. Any cooling was not applied to the Cr4+:YAG and LBO crystals.

Figure 6.5 shows the change in the beam size along the cavity calculated by the ABCD matrix method, assuming the lowest order mode. The distances between PM1 and OC, and OC and PM2 were measured to be 73 and

67 mm, respectively. In the cavity mode calculation, the experimental cavity configuration was assumed. The beam radius within the gain medium (Pr3+:YLF), the saturable absorber (Cr4+:YAG), and the nonlinear crystal

(LBO) were approximately calculated to be 98 × 100 µm2, 68 × 86 µm2, and 60 × 75 µm2 in horizontal and vertical planes, respectively. In this calculation, no thermal lens in the gain medium was considered because the thermal lens at the pump level for σ-polarization was sufficiently small (see Section 3.4.3).

Blue laser diode Cylindrical (442 nm) expander HWP (x 5) Aspherical lens (f = 4.6 mm)

3+ a Pr :YLF Blue laser diode c (444 nm) Cylindrical Cr4+:YAG expander a (x 5) PBS Lens PM1 OC (HR@640 nm) (f = 75 mm) (R = 75 mm, HR@640 nm, LBO HT@440-450 nm, HT@320 nm) PM2 (HR@640+320 nm)

Figure 6.4: Experimental setup of 320-nm Q-switched SHG Pr3+:YLF laser pumped by blue LDs. PBS: polarizing beam splitter, HWP: half-wave plate, PM: plane mirror, OC: output coupler.

250

200

150 :YLF 3+ Pr :YAG 4+ Cr 100 LBO vertical Beam radius ( µ m) horizontal 50 0 20 40 60 80 100 120 140 Distance from PM1 (mm)

Figure 6.5: Beam radius along cavity in horizontal and vertical planes calculated by ABCD matrix method. 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 125

The laser was pumped by polarization-combined 3.5-W output blue LDs. The beam quality M 2 at a forward current of 2.3 A (nominal current to provide an output power of 3.5 W) was measured to be <2×15 in vertical and horizontal planes, respectively. The diode outputs were collimated by an aspherical lens (f = 4.6 mm) and expanded along the slow axis by the cylindrical lens pair (f = −20 mm and 100 mm) to shape a symmetrical focal spot. The pump beams were combined at a polarizing beam splitter (PBS) and focused into the Pr3+:YLF crystal through a spherical lens (f = 75 mm). The focal spot radius was calculated to be ∼ 32 × 48 µm2. The mode matching efficiency between the cavity and pump modes was calculated at ∼80% and ∼85%, when top-hat and Gaussian shaped pump profile were respectively assumed.

The temperature of pump LDs were optimized to obtain the highest possible absorbed power. The resulting effective absorption coefficient was measured to be 3.5 and 1.6 /cm for the LDs emitting at 444 nmand442nm, respectively. The total absorbed pump power was 3.84 W, which corresponded to 70% of the total incident pump power.

Before Q-switching experiments, the laser was operated in CW mode without the Cr4+:YAG crystal. The output CW UV power with respect to the absorbed pump power is shown as open circles in Fig. 6.6. The lasing threshold was 450 mW, and the output power increased up to 320 mW with a quadratic function of the absorbed pump power.

350 Continuous-wave 300 Q-switched γ -5 Simulation ( SHG = 1.85 x 10 /W) γ -5 250 Simulation ( SHG = 1.20 x 10 /W)

200

150

100

Averaged output power (mW) 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Absorbed pump power (W)

Figure 6.6: UV output power with respect to absorbed pump power.

Once the Cr4+:YAG saturable absorber was inserted, a stable Q-switched operation was observed. The averaged output power is shown as filled circles in Fig. 6.6. The threshold power increased upto ∼2.3 W, and the maximum output power was measured to be 76 mW. The averaged power showed a linear function with the absorbed power. The peak power of a passively Q-switched laser is constant once stable Q-switching is achieved, and consequently, the SHG conversion efficiency remains constant. Slope efficiency with respect to the absorbed pump power was ∼3.2%.

The measured Q-switched UV pulse width (FWHM: full-width at half-maximum) and the pulse repetition 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 126

100 60 Pulse width (experiment) Rep. rate (experiment) Pulse width (simulation, γ = 1.85 x 10-5 /W) 90 γSHG -5 Pulse width (simulation, SHG = 1.20 x 10 /W) Rep. rate (simulation γ = 1.85 x 10-5 /W) 50 γSHG -5 Rep. rate (simulation SHG = 1.20 x 10 /W) 80

40 70

60 30

50 20

40 Repetition rate (kHz) Q-switch pulse width (ns) 30 10 2.0 2.5 3.0 3.5 4.0 Absorbed pump power (W)

Figure 6.7: Q-switched pulse width (FWHM) and pulse repetition rate with respect to absorbed pump power. Dashed lines are simulation results calculated with γSHG = 1.85 × 10−5 and 1.20 × 10−5 W−1. rate are shown in Fig. 6.7. Just above the lasing threshold, since the Q-switching was not stable, the pulse width and the repetition rate could not properly be estimated. Stable Q-switched pulses were observed beyond an absorbed pump power of 2.5 W. Once stable Q-switching was obtained, the pulse width no longer varied significantly. The shortest pulse width was measured to be 50 ns at a maximum absorbed pump powerof3.8W.

The pulse repetition rate linearly increased up to 52 kHz as the absorbed pump power increased. Consequently, the maximum pulse energy was calculated to be 1.54 µJ, and by considering the asymmetric pulse shape

(Fig. 6.8(b)), the peak power was estimated to be ∼ 28.2 W.

The recorded Q-switched pulse train at maximum pump power is shown in Fig. 6.8(a). A 40-GHz photodetector

(Fiber-Optic Detector model:1004, New Focus) and a 600-MHz oscilloscope were employed and the rise/fall time of the recording system was approximately estimated to be ∼0.6 ns. A pulse waveform of the Q-switched pulse whose half-width was 50 ns is shown in Fig. 6.8(b). The timing jitter was evaluated to be 6% from the recorded waveform. The fluctuation in the peak power was estimated tobe ∼10%.

(a) (b) 1 1

0.5 0.5 Intensity (arb. units) Intensity (arb. units) 0 0 0 50 100 150 -150 -100 -50 0 50 100 150 Time (µs) Time (ns)

Figure 6.8: (a) Q-switched UV pulses recorded over 150 µs with maximum pump power and (b) waveform of a single pulse

The beam quality of the Q-switched UV laser was also evaluated. The beam size variation around a focal spot was measured, and plotted in Fig. 6.9. These plots show a slight ellipticity and an absence of astigmatism. 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 127

The beam quality factor M 2 in each planes was determined by fitting the theoretical curve of Gauss beam propagation to the experimental results. The best fit was obtained with M 2 = 1.22 × 1.64 in vertical and horizontal planes, respectively.

The M 2 factor in horizontal plane was relatively large compared with the diffraction limit. Note that the beam quality of the fundamental wave was nearly diffraction limitedM ( 2 < 1.1), owing to the saturable absorber. As shown in Fig. 6.5, the beam was focused in the saturable absorber, and it acted as an aperture for the higher- order modes which have lower intensity than the lowest order mode. Therefore, the slight deterioration of the second harmonic (SH) beam quality was attributed to the walk-off effect in the nonlinear crystal. Compared with the previous demonstration of a CW frequency-doubled Pr3+:YLF laser at 261.3 nm with a BBO as the nonlinear crystal [69], the obtained beam quality significantly improved while a relatively long LBOwas employed. This is owing to the smaller walk-off angle of LBO compared to that ofBBO.

500 horizontal fit (M2 = 1.64) 2

µ m) 400 vertical fit (M = 1.22)

300

200

100 Beam radius ( 0 -30 -20 -10 0 10 20 30 Position (mm)

Figure 6.9: Beam radius in horizontal and vertical planes around focal spot. The inset shows the profile of the output captured by a CMOS camera. The size of theimageis 2×2 mm2.

6.2.2 Rate equation analysis

A numerical simulation was performed based on rate equations to analyze the experimental results. The passively Q-switched SHG laser was modeled by the following three equations:

2 dϕ cϕ ϕ c 2 = (σst∆Nlg − σgsngslSA − σes(ntot − ngs)lSA) − − γSHGhνωANLϕ − S, (6.5) dt lc τc 2lc

dN ∆N Ntot − ∆N ηPabs = −cϕσst∆N − + · , (6.6) dt τf Ntot hνωV

dngs Ag ntot − ngs = −σgscϕngs · + . (6.7) dt ASA τSA

These are the rate equations of three parameters: intracavity photon number density ϕ, the population inversion in gain medium N, and ground-state density in the saturable absorber ngs. Effective mode cross sections Ag, 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 128

ASA, and ANL were estimated from the cavity mode calculation shown in Fig. 6.5. Assuming a perfect phase matching, the nonlinear conversion coefficient was calculated using Eq. (6.3). Equation (6.4) was again usedto calculate the Boyd-Kleinman factor.

The parameters and their values used in the simulation are summarized in Table 6.1. The saturable parameters of the Cr4+:YAG crystal was directly adopted from the results of characterization (see Section 5.1.1). The rate equations were numerically solved by the Runge–Kutta algorithm, and the results are shown in Figs. 6.6 and

6.7. In the model, since the intracavity loss for the fundamental wave was unknown, the equations were solved for several values of intracavity loss Li. Consequently, the best fit of the output power with the experimental results was obtained when an intracavity loss of 5.8% was assumed. With a nonlinear conversion coefficient of 1.85 × 10−5 W−1, the calculated averaged output power, pulse width, and repetition rate are displayed in

Figs. 6.6 and 6.7. The calculated repetition rate was consistent with the experimental result. However, the calculated pulse width was slightly longer than that in the experiment. This deviation can be attributed to an overestimation of the nonlinear conversion coefficient. We calculated the rate equations with a decreased nonlinear conversion coefficient and obtained good agreement ofthe Q-switched pulse width with a coefficient of

1.2×10−5 W−1 while the other parameters were fixed. The numerical simulation also showed that the averaged output power and repetition rate were not so sensitive to the nonlinear conversion coefficient; they slightly decreased by reducing the coefficient, as shown in Figs. 6.6 and 6.7. The other parameters were no longervaried to fit the numerical results to the experimental results.

The dependence of pulse duration on the SHG conversion coefficient was further studied in the numerical model, and revealed that the pulse width increased linearly as the SHG conversion coefficient increased. The calculated pulse width with varied SHG conversion coefficient is shown in Fig. 6.10. The pulse energy and peak power with respect to the SHG conversion coefficient were also numerically calculated (Fig. 6.11). According tothe

−5 −1 numerically obtained results, the peak power becomes maximum with γSHG = 1.0 × 10 W .

In the experiment, the laser was optimized so that the highest averaged output power was obtained. The numerical simulation told that even shorter pulses are obtainable by slightly tilting the nonlinear crystal to decrease the effective nonlinear conversion coefficient. 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 129

Table 6.1: Parameters for simulating passively Q-switched SHG Pr3+:YLF laser with Cr4+:YAG saturable absorber.

Symbol Parameter Value (or definition) Unit

−7 λω Wavelength of fundamental wave 640 × 10 cm

−7 λ2ω Wavelength of second harmonic wave 320 × 10 cm

νω Frequency of fundamental wave c/λω Hz

ν2ω Frequency of second harmonic wave c/λ2ω Hz

ϕ Intracavity photon flux density Variable cm−3

∆N Population inversion density Variable cm−3

−3 ngs Population density in ground state of saturable absorber Variable cm

−19 2 σst Stimulated emission cross section of gain medium 2.2 × 10 cm

−18 2 σgs Ground-state absorption cross section of saturable absorber 7.5 × 10 cm

−18 2 σes Excited-state absorption cross section of saturable absorber 4.6 × 10 cm

lg Length of gain medium 0.5 cm

lSA Length of saturable absorber 0.24 cm

lNL Length of nonlinear crystal (two passes) 1.6 cm

lc Cavity length 14.0 cm

19 −3 Ntot Total population density of active ions in gain medium 7.0 × 10 cm

16 −3 ntot Total population density of absorption centers in saturable absorber 4.8 × 10 cm

τc Cavity lifetime (or photon lifetime) 2lc/{c(Li − ln R)} s

τf Fluorescence lifetime of gain medium 38 µ s

τSA Recovery time of saturable absorber 4.2 µ s

Li Cavity round-trip loss 0.06 –

R Total reflectivity of cavity mirrors for fundamental wave 0.998 –

−5 −1 γSHG Nonlinear conversion coefficient 1.85 × 10 W

nNL Refractive index of LBO 1.60 –

K Wavenumber of fundamental wave 9.82 × 104 cm−1

−13 deﬀ Effective nonlinear coefficient of LBO at 640nm 6.82 × 10 pm/V

h′(B′, ξ) Boyd-Kleinman factor 0.93 –

−4 2 Ag Effective mode area in gain medium 3.0 × 10 cm

−4 2 ASA Effective mode area in saturable absorber 1.8 × 10 cm

−4 2 ANL Effective mode area in nonlinear crystal 1.4 × 10 cm

S Contribution of spontaneous emission Arbitrary (small value) –

η Total laser efficiency 0.53 –

Pabs Absorbed pump power Variable W 6.2. Intracavity frequency-doubling of passively Q-switched Pr3+:YLF ultraviolet laser 130

Q-switched pulse width (ns) 40 0.5 1.0 1.5 2.0 SHG conversion coefficient (x 10-5 W-1)

Figure 6.10: Simulated Q-switched pulse width with varied SHG conversion coefficient.

30 2

29 1.8

28 1.6

27 1.4

Peak power (W) 26 1.2 Peak power Pulse energy ( µ J) Pulse energy 25 1 0.5 1.0 1.5 2.0 SHG conversion coefficient (x 10-5 W-1)

Figure 6.11: Simulated peak power and pulse energy with varied SHG conversion coefficient. 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 131

6.3 213-nm deep ultraviolet pulse generation from actively Q-switched

Pr3+:YLF laser

6.3.1 Diode-pumped 640-nm Pr3+:YLF laser actively Q-switched by acousto-optic modulator

As the pump source for frequency conversion to generate UV light, an actively Q-switched Pr3+:YLF laser at

640 nm was built. The laser setup is depicted in Fig. 6.12. The pump sources were polarization-combined two blue LDs of 3.5-W output power. The gain medium was a 0.5 at. % Pr3+-doped YLF crystal (Unioriental

Optics). The crystal was cut perpendicular to the crystal’s a-axis, and its surfaces were uncoated. The short linear cavity consisted of a plane dichroic mirror (DM), which had a high transmission for the pump wavelength and a high reflectivity at the laser wavelength, and a concave output coupler of 75-mm curvature radius. The transmission of the output coupler was 8.6%. The output of each pump LD was first collimated by an aspherical lens of 3.1-mm focal length, and expanded along the slow-axis (in horizontal plane) by a factor of five. Then the beams were combined by the polarizing beam splitter (PBS) and focused into the gain medium through DM by a spherical lens of 75-mm focal length. For Q-switching, an acousto-optic modulator (AOM) (M200-4B/E-LD5,

Gooch & Housego) was inserted in the cavity. The AOM was operated by a 5-W RF driver (A35200-S-1, Gooch

& Housego) supplying 200-MHz RF power. An anti-reflection coating was applied to the diffracting opticsin the AOM. The diffraction efficiency was measured at >70% at 632.8 nm at the maximum RF power. A5-kHz trigger signal to the RF driver was supplied by a function generator.

Blue laser diode Cylindrical (442 nm) expander HWP (x 5) Aspherical lens (f = 3.1 mm)

Acousto-optic DM a Blue laser diode c modulator (444 nm) Cylindrical a expander (x 5) PBS Lens Pr3+:YLF (f = 75 mm) OC (R = 75 mm)

Figure 6.12: Schematic of actively Q-switching diode-pumped Pr3+:YLF laser at 640 nm. HWP: half-wave plate, PBS: polarizing beam splitter, DM: dichroic mirror, OC: output coupler.

At the maximum absorbed pump power of 4.45 W, the averaged output power from the Q-switched laser was measured to be 280 mW. The pulse energy was therefore calculated to be 56 µJ. The temporal shape of the pulse train and single Q-switched pulse are shown in Fig. 6.13. The full width at half-maximum (FWHM) of 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 132 the pulse was measured at 9.9 0.1 ns. The peak power was estimated to be 4.5 kW by taking into account the non-symmetric pulse shape. It was confirmed that any parasitic lasing at other wavelengths did not occur as seen in the output spectrum (Fig. 6.14) captured by a spectrometer (HR4000, Ocean Optics).

5 (a) 200 µs (b)

3 9.9 ± 0.1 ns 2

1 Instantaneous power (kW)

0 -30 -20 -10 0 10 20 30 40 50 Time (ns)

Figure 6.13: (a) Screenshot of Q-switch pulse train monitored in oscilloscope. (b) Single Q-switch pulse shape.

0.8

0.6

0.4

Intensity (arb. units) 0.2

0 630 635 640 645 650 Wavelength (nm)

Figure 6.14: Output spectrum of actively Q-switched laser at 640 nm.

The beam quality M 2 was measured to be <1.2 and <1.3 in vertical and horizontal planes, respectively, as shown in Fig. 6.15. The beam was slightly elliptic but the astigmatism was negligibly small.

6.3.2 Frequency tripling using optically active quartz for successive Type-I phase matching

The optical layout of successive SHG and SFG using the actively Q-switched Pr3+:YLF laser at 640 nm is depicted in Fig. 6.16.

There were basically three candidates of nonlinear crystals for SHG: Type–I and Type–II β-barium borate

(BaB2O4, BBO) and Type–I lithium triborate (LiB3O5, LBO). Their phase matching angle for SHG of 640-nm light, effective nonlinear coefficient, and walk-off angles are listed in Table6.2.

Although the effective nonlinear coefficient of Type–I LBO is smaller than BBO, a Type–I LBO crystalwas 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 133

400 measurement (sagittal plane) measurement (tangential plane) 350 Gauss beam fit (M2 = 1.12) Gauss beam fit (M² = 1.25) 300 250 200 150

Beam radius ( µ m) 100 50 0 -30 -20 -10 0 10 20 Position (mm)

Figure 6.15: Beam radius around beam waist with respect to position. Beam profiles at Z = −30, 0, and 20 mm are shown as inset figures.

Optically active quartz crystal Lens (Fused silica)

Type-I Lens LBO (f = 60 mm) Type-I Lens BBO (Fused silica, f = 75 mm) Prism 640 nm

320 nm 213 nm

Figure 6.16: Experimental setup for 213-nm DUV generation by SHG and SFG of 640-nm pulses from actively Q-switched Pr3+:YLF laser.

Table 6.2: Parameters of Type–I BBO, Type–II BBO, and Type–I LBO as candidates for SHG at 640 nm.

Type–I BBO Type–II BBO Type–I LBO

Phase matching angle for SHG at 640 nm (deg.) 52.6 55.7 θ = 90, φ = 53.5

Effective nonlinear coefficient deﬀ (pm/V) 1.92 0.63 0.54

Walk-off angle (mrad) 79.4 72.8 18.4 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 134 adopted for SHG in this experiment, because the small walk-off angle of Type–I LBO enables to use a relatively long crystal. The interaction length is limited in BBO crystal due to its large walk-off. It should be noted that Type–II nonlinear crystals are advantageous because they do not require any polarization control for the following SFG; however, the conversion efficiency decreased.

The 640-nm pulses were focused into a type–I LBO for SHG. The crystal’s length was 8 mm, and it surfaces were coated for anti-reflection (AR) at both the fundamental (640 nm) and second harmonic (SH) wavelengths

(320 nm). The focusing condition was optimized by using a variety of lenses of different focal length, and the highest pulse energy of SH was obtained with a lens of 75-mm focal length. The spot diameter of the fundamental wave was measured at 90 µm. The peak intensity was then calculated to be 1.8 GW/cm2. The averaged power of the generated SH was measured to be 37 mW by a photodiode-type power meter (PowerMax USB UV/VIS

Quantum Sensor, Coherent), corresponded to a pulse energy of 7.4 µJ. The SHG conversion efficiency was calculated to be 13%. The generated SH pulses were detected by a Si-photodiode (S3883, Hamamatsu) and monitored by an oscilloscope. The single SH pulse shape and spectrum are shown in Fig. 6.13. The FWHM in pulse duration was 6.500.08 ns, which is good agreement with the estimated pulse width from the fundamental pulse shape of 6.2 ns. By taking into account the non-symmetric pulse shape, the peak power was estimated to be 800 W.

1 (a) (b) 1

0.8 0.8

0.6 6.50 ± 0.08 ns 0.6

0.4 0.4 Intensity (arb. units) Intensity (arb. units) 0.2 0.2

0 0 -20 -10 0 10 20 30 40 310 315 320 325 330 Time (ns) Wavelength (nm) Figure 6.17: (a) Single SH pulse shape detected by Si-photodiode. (b) Spectrum of SH pulses.

For the following SFG, the phase matching to generate 213.3 nm can be realized only by Type–I BBO or

CsLiB6O10 (CLBO). Therefore, it was required to align the polarization of the fundamental and SH waves. This task was accomplished by use of an optically active quartz plate. Gaponentsev et al. demonstrated the

355-nm third harmonic generation (THG) based on the use of a Type–I phase-matched LBO crystal and an optically active quartz crystal, and experimentally obtained 1.6-times higher conversion efficiency with Type–I phase matching than with the conventional Type-II phase matching in SFG [165]. The values of polarization rotating angles per unit length of quartz crystal were 20.9 and 86.1◦/mm, respectively [166]. The optimum 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 135 thickness of quartz crystal L to align the polarizations of fundamental and SH waves is given as follows:

π/2 L = , (6.8) θ2ω − θω

where θω and θ2ω are polarization rotating angles per unit length for fundamental and SH waves, respectively. The optimum thickness of quartz plate to align the polarization was then calculated at 1.38 mm. The surfaces of the used quartz crystal were coated for anti-reflection at both fundamental and SH wavelengths. The polarization of the fundamental and SH waves were checked by the following procedure:

• Remove the SHG crystal and insert a half-wave plate before the quartz crystal so that the transmitted

fundamental wave was polarized parallel to the optical table (this was simply checked by use of a polarizing

beam splitter).

• Place again the SHG crystal at the beam waist and rotate it to maximize SHG conversion.

• A fused silica glass plate was placed after the quartz crystal, and the SH reflectivity from the silica glass

was plotted as a function of incident angle as shown in Fig. 6.18.

20 Measurement Theory

Reflectivity (%) 5

0 20 30 40 50 60 70 80 Incident angle (deg.)

Figure 6.18: Reflectivity of 320-nm second harmonic from silica glass as a function of incident angle. Red symbols were measured results, and black solid line is theoretical Fresnel reflection curve. The Brewster angle at 320 nm◦ was56 .

As seen in Fig. 6.18, the experimentally obtained reflectivity from the fused silica glass plate showed agood agreement with the theoretical curve of Fresnel reflection. Thus, the polarizations of fundamental and SH waves could be aligned by the optical activity of the quartz plate.

Finally, the fundamental and SH beams of aligned polarization were focused into a Type–I BBO crystal. The cut angle was 64.0◦ to satisfy the Type–I phase matching for the SFG 640(o) + 320(o) → 213.3(e). The focal length of the focusing lens was 60 mm. The transmitted beam was then collected by a lens of 75-mm focal length. It should be noted that optics used after the SFG were fused silica rather than BK7 since 213.3-nm DUV undergoes a strong absorption in BK7 glass. The collected beam was spatially dispersed by a fused silica prism. 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 136

The apex angle was 60◦. The generated 213.3-nm DUV could be confirmed by a fluorescence of a conventional copy paper, as shown in Fig. 6.20. To detect the 213.3-nm DUV, a biplanar phototube (R1328U, Hamamatsu) was used. Even though the rise time of the detector was nominally 60 ps, the recorded pulse duration for

320-nm SH pulses were longer than that detected by the Si-photodiode. This may be owing to the insufficient applied bias voltage. The detector nominally needed a bias voltage of 2 kV, but the employed power supplied could provide up to 1.5 kV. The recorded pulse shape of a 320-nm SH and a 213.3-nm third-harmonic (TH) pulses were shown in Fig. 6.19. The FWHM of the SH pulse was measured at 8.10 0.16 ns, and 7.00 0.20 ns, respectively.

1 320 nm 213.3 nm 0.8

0.6

0.4

Intensity (arb. units) 0.2

0 -20 -10 0 10 20 30 40 Time (ns)

Figure 6.19: Pulse shape of second harmoinic and third harmonic detected by biplanar phototube.

Because a power meter for the DUV region was not available, a GaP-photodiode (G1962, Hamamatsu) was used to estimate the energy of the 213-nm pulses. Since the photodiode had a sensitivity up to 550 nm, the relation between the pulse energy and integrated signal from the photodiode was calibrated for the SH pulses. The relation for the 213.3-nm pulses was simply obtained by taking into account the sensitivity curve. The linearity between pulse energy and integrated photodiode signal was confirmed up to the output integrated signal of

25 nVs, as shown in Fig. 6.21. The energy of the TH pulses were estimated to be ∼15 nJ, corresponding to an averaged output power of 75 µJ. It should be noted that >30% of the energy of TH pulses were disappeared by the reflections at the uncoated lens and prism. Therefore, the averaged output power just after the SFGcrystal was expected to be >100 µJ. Thus, the total conversion efficiency of the THG was only ∼0.03%. This was of course due to the limited pump pulse energy from the Pr3+:YLF laser at 640 nm. Regarding the nonlinear nature of frequency conversion, the conversion efficiency is expected to increase dramatically by energy scaling of the visible pump pulse. 6.3. 213-nm deep ultraviolet pulse generation from actively Q-switched Pr3+:YLF laser 137

640 nm 320 nm 213.3 nm (Fundamental) (Second harmonic) (Third harmonic)

Figure 6.20: Photograph of conventional copy paper irradiated by spatially dispersed fundamental wave (640 nm), second harmonic (320 nm), and third harmonic (213.3 nm). Second and third harmonics are recognized by bluish white fluorescence.

Pulse energy (nJ) 5 Measurement Linear fit Expected sensitivity at 213 nm 0 0 10 20 30 40 Integrated PD signal (nVs)

Figure 6.21: Relation between pulse energy and integrated signal of GaP-photodiode (red symbols). Black dashed line is linear fitting for SH pulses. Blue dashed line is estimated relation for 213.3 nm TH pulses. 6.4. Summary 138

6.4 Summary

Frequency doubling and tripling of diode-pumped Pr3+:YLF lasers operated at 640 nm were demonstrated.

The visibly emitting front ends opened the way to access the UV region with much simpler scheme compared to systems adopting NIR lasers.

Continuous-wave UV coherent sources are difficult to realize with lasers emitting in the near-infrared (NIR) region, because high peak power lasers are in general required to obtain high efficiency in two-step conversion stages. Therefore, continuous-wave UV lasers have been only achieved with external enhancement cavities which require the resonator locking. High conversion efficiency of continuous-wave lasers are possible by utilizing periodically-poled nonlinear crystals based on quasi phase matching (QPM); however, due to the short period of QPM devices to realized conversion from the visible to UV, it is very challenging to fabricate a QPM device of good quality. Intracavity frequency doubling of visibly emitting Pr3+ lasers is therefore one of the most simple and powerful approaches. The technique of intracavity frequency doubling theoretically allows us to generate the same order of output as the fundamental wave output extracted by the output coupling mirror, since the nonlinear crystal can be considered as the effective output coupler. In the experimental demonstration presented in Section 6.1, an output power of 880 mW was obtained at an absorbed pump power of 5.9 W. The rate equation analysis showed that the laser output could be improved up to multi-watt output power by reducing the cavity losses, mainly insufficient reflectivity of the cavity mirrors. Because lasers of intracavity frequency doubling show a quadratic increase with pump power, the conversion efficiency is dramatically improved by scaling the pump power, as far as thermal lensing does not induce a detrimental amount of diffraction losses.

By applying frequency doubling to a blue diode-pumped Q-switched Pr3+:YLF laser, 50-ns UV pulses at 320 nm were generated at a repetition rate of 52 kHz. The Q-switching of the 640-nm laser was accomplished with a

Cr4+:YAG crystal. By employing two blue diode lasers of 3.5-W output power, an averaged output power of

76 mW was achieved. The maximum pulse energy and peak power were calculated to be 1.54 µJ and 28.2 W, respectively. The laser can be further power-scaled by simply increasing the pump power until the onset of a thermal lensing effect in the3+ Pr :YLF crystal. We conducted a numerical simulation based on the rate equation analysis and confirmed good agreement with the experimental results by just controlling one fitting parameter.

The frequency doubled Pr3+ lasers enable to reach the UV region in much simpler scheme compared to the conventional frequency-tripled near-infrared lasers.

The generation of 213.3-nm DUV pulses as third harmonic of a visibly emitting laser was experimentally demonstrated for the first time, to the best of the author’s knowledge. The use of visibly-emitting solid-state lasers as pump sources enables to simplify the frequency conversion processes to achieve the DUV region. The wavelength of 213 nm corresponds to fifth-harmonic of 1-µm3+ Nd or Yb3+ solid-state lasers, and three conversion steps are conventionally required since the 213-nm light is generated as a sum-frequency of fundamental wave 6.4. Summary 139 at 1064 nm and third-harmonic at 355 nm. On the other hand, the 213-nm DUV is obtained as third-harmonic of 640-nm fundamental wave from Pr3+:YLF laser which required only two frequency conversion steps. In the demonstration, the total conversion efficiency was as low as ∼0.03% due to the limited pump energy from the

640-nm Pr3+:YLF laser. Pr3+-based solid-state lasers are not capable to generate MW-peak pulses because the fluorescence lifetime of3+ Pr is much shorter than that of Nd3+. Instead of a Q-switched Pr3+ solid-state laser, an ultrafast visible master oscillator pulse amplifier (MOPA) system providing picoseconds or sub-picosecond pulses of >100 µJ is adequate for future pump source. Such high-peak power laser system enables to obtain much higher conversion efficiency to generate third-harmonic DUV pulses. Moreover, the use of CLBO forthe

SFG stage is attractive for energy scaling, since the interaction length is expected to be much longer than that of BBO crystal. Chapter 7

Conclusion

Continuous-wave operation of Pr3+:YLF visible lasers

3+ The highest continuous-wave output power of direct-diode-pumped Pr :LiYF4 (YLF) lasers at 640 and 607 nm were achieved, using four 5-W output single emitter blue laser diodes (LDs). Even though the crystalline host of YLF exhibited a small thermal lensing for σ-polarization, an appropriate cavity design is essential for power scaling to suppress thermal lens aberration. Due to the strong negative thermal lensing for π-polarization, the power scaling at 523 nm was inhibited. The small emission cross section at the wavelength made the laser very sensitive to diffraction losses due to the thermal lens. While the pump powerof ∼20 W was available, the highest output power was obtained at the absorbed pump power of 5.4 W. To suppress the strong thermal lens aberration to achieve a stable laser demonstration, a short gain crystal with higher doping concentration may be advantageous. However, Pr3+:YLF crystal is known to show a fluorescence quenching at high doping level.

Moreover, higher doping concentration results in higher tensile stress in the vicinity of the front facet, which tends to induce a fracture of laser crystals. Thus, the power scaling of Pr3+:YLF lasers for π-polarization, including at 523 nm, are challenging in end-pumping scheme. Sophisticated cooling and pump configurations need to be considered to overcome the above mentioned problem. Although the use of oxide crystalline hosts is advantageous to improve the thermal lensing properties, none of Pr3+-doped crystals exhibit better laser

3+ 3+ performance in the green region. Pr hexaaluminate lasers, such as Pr :SrAl12O19 (SRA) laser, potentially enables the high power green operation, since it has good thermal and mechanical properties, and comparable emission cross section with Pr3+:YLF. However, up to now, the power scaling of Pr3+:SRA green lasers have been limited may be owing to the insufficient crystal quality. Thus, the improvement of crystal growth is important to realize high power green Pr3+:SRA lasers.

A state-of-the-art fiber-couple blue LD module was also used for exciting3+ Pr :YLF laser. Since the tensile

140 141 stress induced in the laser crystal was expected to be large, a gain crystal of 0.3 at. % doping concentration was adopted. Despite of the effort to evacuate the generated heat, a 0.5 at. % crystal was fracture at the pumppower of ∼20 W. It should be noted that shorter gain media are suitable for improving mode-matching efficiency in the end-pumping configuration with low brightness sources. However, the relatively low fracture 3+limit ofPr :YLF laser inhibited this approach. When a Pr3+:YLF crystal was pumped by the fiber-coupled pump source, a strong thermal lensing was observed. The power scaling of 640-nm Pr3+:YLF laser was successfully demonstrated by optimizing the cavity mode size and pump beam size in the laser crystal for suppressing thermal aberration.

However, the highest output power was attained with an output coupler of low transmission (T = 1.1%). The slope efficiency dropped when output couplers of higher transmission were used. A part of the degradation could be reduced by operating the pump source in quasi-continuous-wave (CW) mode, but the slope efficiency was still higher when output couplers of lower transmission were used. This dependence was observed also by other groups [44, 46]. Presumably, an inversion dependent loss mechanism takes place, so it is significantly important to suppress the cavity losses so that the optimum output coupling is attained with output couplers of low transmission. Further detailed investigations are required to fully understand the mechanism. Moreover, it is worthwhile to examined whether this mechanism is originated from the active ions or host crystal. If this effect is intrinsic for all Pr3+-doped lasers, this can be a major limitation for further power scaling of visible

Pr3+ lasers.

Transition-metal-doped saturable absorbers in the visible region

A variety of transition-metal-doped oxide crystals were investigated in detail to identify saturable absorbers working in the visible spectral region. Their recovery time, ground-state absorption (GSA) and excited-state absorption (ESA) cross sections were determined for the first time. Tetravalent chromium4+ (Cr ) and divalent cobalt (Co2+)-doped crystals were mainly focused on.

4+ As the result, Cr -doped crystals are identified as visible saturable absorbers of long recovery3 time.InY Al5O12 4+ 4+ (YAG) and Mg2SiO4 (forsterite), Cr exhibited a recovery time of a few microseconds. Cr :YAG can be used for passive Q-switching of lasers operated in the range 600–680 nm. The visible absorption of Cr4+:forsterite is anisotropic, and it can be used as a saturable absorber in the green region when the incident light is polarized parallel to the crystal’s a-axis. It is possible to demonstrate a passively Q-switched green Pr3+:YLF laser at 523 nm. However, the absorption peak locates at 570 nm, and the absorption cross section at 523 nm is relatively small, resulting lower figure of merit of saturable absorber (defined as the ratio of ESA cross section to GSA cross section). For the both crystalline hosts, Cr4+ in tetrahedrally coordinated sites are responsible for saturable absorber action. However, due to the existence of several kinds of symmetries and valence, parasitic absorption centers were found in these crystals. It should be noted that the crystal growth conditions strongly 142 affect the density of different site and valence. The optimum crystal growth conditions need to be foundout for better Q-switching performance.

Co2+-doped crystals have a broad absorption centered around 600 nm, regardless the crystal field strength of crystalline host. However, the properties of saturable absorption was strongly affected by host crystals. The recovery time of Co2+ in oxide crystals of low crystal field, such as spinels, were measured at a few hundreds of nanoseconds, and the fluorescence in the visible and near-infrared regions was observed. On the otherhand,

Co2+ in high field crystals, such as garnets, did not exhibit fluorescence when excited by visible light,andthe recovery time was as short as <10 ns. Such short recovery time results in high saturation intensity. However,

2+ Co -doped Gd3Ga5O12 (GGG) exceptionally exhibited an attractive saturation properties.

The work on the characterization of transition-metal-doped saturable absorbers is effective for developing Q- switched visible lasers in the future. Especially, there are many rare earth ions suitable for passive Q-switching due to their fluorescence lifetime of a few milliseconds, such as terbium and europium. The parameters presented in this work enables to predict the performances of new passive Q-switching visible lasers.

Passive Q-switching of Pr3+:YLF visible lasers

4+ 2+ 3+ Using Cr :YAG and Co :MgAl2O4 (MALO), passive Q-switching of diode-pumped visible Pr :YLF lasers were demonstrated for the first time. The low saturation intensity4+ ofCr :YAG saturable absorber relaxed the restriction in cavity design, since it is not necessary to place the saturable absorber at a focus. Since the saturation intensity of Co2+:MALO is higher than that of Pr3+:YLF, Co2+:MALO needs to be placed at a focus of cavity. Instead, Co2+:MALO’s visible absorption covers the wider spectral range than Cr4:YAG. It is significantly important that Cr4+:YAG does not work as a green saturable absorber. Rate equation models for the both saturable absorbers were established for the first time, based on the results of characterization presented in Chapter 4. The numerical models are useful for analyzing the conditions to obtain passive Q-switching, and for predicting performances. The models can be of course applied to other visible lasers. Regarding the results of characterization, Co2+:GGG is expected to be useful for passive Q-switching because of its limited non-saturable loss. The passively Q-switched Pr3+:YLF laser at 640 nm with Co2+:GGG saturable absorber was realized for the first time. In this work, a sample not suitable for laser experiments was used for the proof-of-concept experiment. Much better performances are expected to be obtained using well-prepared samples. 143

Frequency conversion for ultraviolet lasers

Visibly emitting Pr3+:YLF lasers in continuous-wave and passive Q-switching operations were extended to ultraviolet (UV) generation by means of intracavity second harmonic generation (SHG). Using two 5-W output single-emitter blue LDs, at an absorbed pump power of 5.9 W, a continuous-wave UV output power of 880 mW was obtained at 320 nm. The performance of intracavity frequency doubled lasers are sensitively degraded by slight increase of cavity losses. Since the cavity mirrors used in the experiments were not perfectly optimized for the intracavity frequency doubling, the non-ideal reflectivity of cavity mirrors resulted a significantly large cavity loss. However, the continuous-wave UV output power obtained in this work is the highest to the best of author’s knowledge. The rate equation analysis indicated that more than 2 W UV output power can be obtained by reducing the cavity losses. Regarding the observation in the power scaling experiment, that the optimum output coupling was achieved with a low output coupling, the scheme of intracavity frequency doubling may be suitable since the intracavity power is kept high during operation, which may result in the suppression of the inversion dependent loss.

The frequency doubling Pr3+:YLF laser Q-switched by Cr4+YAG saturable absorber generated 50-ns UV pulses at a repetition rate of 50-kHz. The pulse energy and peak power was respectively measured at 1.5 µJ and 28 W.

The models of rate equations and saturable absorber was combined and a new numerical model representing frequency doubled passive Q-switching lasers were established. It should be noted that the laser consisted of two nonlinear components: saturable absorber and nonlinear crystal. Consequently, the laser performance was complex. The dependence of performances on parameters could not be understood by the laser theory. Thus, such numerical model only enables to interpret experimentally obtained results of frequency doubled passive

Q-switching lasers.

A proof-of-concept experiment for generating 213-nm deep UV third harmonic was demonstrated using an actively Q-switched Pr3+:YLF laser delivering ∼10 ns pulses. Because of the limited choice of nonlinear crystals for the frequency conversion, successive Type–I phase matching was demonstrated using an optically active quartz for polarization rotation. The total conversion efficiency was as low as ∼ 0.03%. However, this proof- of-concept experiment is useful for predicting further power scaling. Instead of a Q-switched laser, an ultrafast visible master oscillator power amplifier (MOPA) system providing picoseconds or sub-picosecond pulses of

>100 µJ is suitable for the pump source. A significantly high conversion efficiency is expected to be attained with such high peak power laser system. 144

Future prospect

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LDs may dramatically reduce by the mass production. Thus, blue-diode-pumped praseodymium lasers are also expected to be cost effective light sources. This work will support the further development of diode-pumped visible Pr3+-doped visible solid-state lasers. Bibliography

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Journal papers (related to this thesis)

1. H. Tanaka, R. Kariyama, K. Iijima, K. Hirosawa, and F. Kannari, “Saturation of 640-nm absorption in

Cr4+:YAG for an InGaN laser diode pumped passively Q-switched Pr3+:YLF laser,” Opt. Express 23(15),

19382–19395 (2015).

2. H. Tanaka, R. Kariyama, K. Iijima, and F. Kannari, “50-kHz, 50-ns UV pulse generation by diode-pumped

frequency doubling Pr3+:YLF Q-switch laser with a Cr4+:YAG saturable absorber,” Appl. Opt. 55(23),

6193–6198 (2016).

3. H. Tanaka, S. Fujita, and F. Kannari, “High-power visibly emitting Pr3+:YLF laser end pumped by

single-emitter or fiber-coupled GaN blue laser diodes,” Appl. Opt. 57(21), 5923–5928 (2018).

Other journal papers

1. J. Kojou, R. Abe, R. Kariyama, H. Tanaka, A. Sakurai, and F. Kannari, “InGaN diode pumped actively

Q-switched intracavity frequency doubling Pr:LiYF4 261 nm laser,” Appl. Opt. 53(10), 2030–2036 (2014).

2. K. Iijima, R. Kariyama, H. Tanaka, and F. Kannari, “Pr3+:YLF mode-locked laser at 640 nm directly

pumped by InGaN-diode lasers,” Appl. Opt. 55(28), 7782–7787 (2016).

3. R. Sawada, H. Tanaka, N. Sugiyama, and F. Kannari, “Wavelength-multiplexed pumping with 478- and

520-nm indium gallium nitride laser diodes for Ti:sapphire laser,” Appl. Opt. 56(6), 1654–1661 (2017).

4. N. Sugiyama, H. Tanaka, and F. Kannari, “Mode-locked Ti:sapphire laser oscillators pumped by wavelength-

multiplexed laser diodes,” Jpn. J. Appl. Phys. 57(5), 052701 (2018).

158 Proceedings

1. H. Tanaka, R. Kariyama, K. Iijima, R. Sawada, and F. Kannari, “Solid-state lasers directly pumped by

3+ InGaN diode lasers: Ti:sapphire and Pr :LiYF4 lasers,” Proc. of SPIE 9726, Solid State Lasers XXV: Technology and Devices 9726, 97261X (2016).

International conferences

1. H. Tanaka, R. Kariyama, J. Kojou, F. Kannari, “Passively Q-switched Pr3+:YLF Laser with Cr4+:YAG

Saturable Absorber and Intracavity Frequency Doubling,” The 3rd Advanced Lasers and Photon Sources

(ALPS’14), paper ALPS-p12, Yokohama, Japan (2014).

2. H. Tanaka, R. Kariyama, J. Kojou, F. Kannari, “Intracavity Second Harmonic Generation of Passively Q-

switch Mode Locked Pr3+-doped Fluoride Lasers and using Cr4+:YAG Saturable Absorber,” Conference

on Lasers and Electro-Optics 2014 (CLEO:2014), paper SM3F.7, San Jose, USA (2014).

3. H. Tanaka, R. Kariyama, K. Iijima, K. Hirosawa, F. Kannari, “Rate Equation Analysis of a Passively

Q-switched Pr3+:YLF Laser with a Cr4+:YAG Saturable Absorber in Visible Region,” The 4th Advanced

Lasers and Photon Sources (ALPS’15), paper ALPSp14-12, Yokohama, Japan (2015).

4. H. Tanaka, R. Sawada, R. Kariyama, A. Hosaka, K. Hirosawa, F. Kannari, “Power Scaling of Modelocked

Ti:sapphire Laser Pumped by High Power InGaN Green Laser Diode,” 2015 Conference on Lasers and

Electro-Optics and the European Quantum Electronics Conference (CLEO/Europe-EQEC 2015), paper

CA-6.2 MON, Munich, Germany (2015).

5. H. Tanaka, K. Hirosawa, and F. Kannari, “Repetition-rate-tunable Yb-doped Fiber Chirped Pulse Ampli-

fier Toward Waveguide Direct Writing in Transparent Materials,” The 5th Advanced Lasers and Photon

Sources (ALPS’16), paper ALPSp14-26, Yokohama, Japan (2016).

6. H. Tanaka, K. Hirosawa, and F. Kannari, “Repetition-rate-variable ytterbium-doped fiber MOPA for

waveguide direct writing in transparent materials,” Advanced Solid State Lasers (ASSL 2016), paper

AM5A.16, Boston, USA (2016).

7. H. Tanaka, K. Iijima, Y. Kiyota, F. Kannari, “Pr3+:YLF laser directly pumped by high power blue diode

laser,” The 6th Advanced Lasers and Photon Sources (ALPS’17), paper ALPS6-2, Yokohama, Japan

(2017).

8. H. Tanaka, K. Iijima, Y. Kiyota, F. Kannari, “Power scaling, Q-switching and frequency conversion of

Pr3+:YLF laser directly pumped by InGaN blue diode lasers,” Conference on Lasers and Electro-Optics

159 and the European Quantum Electronics Conference (CLEO/Europe-EQEC 2017), paper CA-1.5, Munich,

Germany (2017).

9. H. Tanaka, K. Iijima, R. Sawada, N. Sugiyama, Y. Kiyota, F. Kannari, “Solid-state lasers directly pumped

by InGaN-based green and blue laser diodes,” The 12th Conference on Lasers and Electro-Optics Pacific

Rim (CLEO-PR 2017), paper Oral 3-2M-5, Singapore, Singapore (2017).

10. H. Tanaka, K. Iijima, Y. Kiyota, F. Kannari, “Visible and Ultraviolet Praseodymium Lasers Directly

Pumped by High-power Blue Laser Diodes,” The 24th Congress of the International Commission for

Optics, paper Th1D-08, Tokyo, Japan (2017).

11. H. Tanaka, F. Kannari, “Power scaling of continuous-wave visible Pr3+:YLF laser end-pumped by high

power blue laser diodes,” Advanced Solid State Lasers (ASSL 2017), paper ATu1A, Nagoya, Japan (2017).

12. H. Tanaka, E. Castellano-Hernández, C. Kränkel, F. Kannari, “Characterization of Transition- Metal-

Doped Saturable Absorbers for Passive Q-switching of Visible Lasers,” The 7th Advanced Lasers and

Photon Sources (ALPS’18), paper ALPS13-D2-2, Yokohama, Japan (2018).

13. H. Tanaka, E. Castellano-Hernández, C. Kränkel, F. Kannari, “Transition-metal-doped saturable ab-

sorbers for passively Q-switched visible Pr:YLF lasers,” Conference on Lasers and Electro-Optics 2018

(CLEO:2018), paper SM1N.6, San Jose, USA (2018).

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