Passively Mode-Locked Holmium-Doped Soliton Fiber Ring

Passively mode-locked holmium-doped soliton ﬁber ring oscillator

Masterabschlussarbeit

von Thomas Braatz

im Studiengang Optical Engineering/Photonics

an der HAWK Hochschule für angewandte Wissenschaft und Kunst

Hildesheim/Holzminden/Göttingen

Fakultät Naturwissenschaften und Technik in Göttingen

in Kooperation mit dem Deutschen Elektronen-Synchrotron

Erstprüfer: Frau Prof. Dr. Andrea Koch Zweitprüfer: Herr Prof. Dr. Franz X. Kärtner

May 2017

Acknowledgements

For the support and supervision while completing this thesis I would like to thank Prof. Dr. Andrea Koch, Professor at the University of Applied Sciences and Arts in Göttingen, as well as Prof. Dr. Franz X. Kärtner, group leader of the Ultrafast Optics and X-Rays Division of the Center for Free-Electron Laser Science. I also would like to express appreciation to Dr. Ingmar Hartl, head of the FS-LA group at DESY, as well as the FS-LA group in general for providing me with a warm and welcoming work environment. Special thanks go to Dr. Axel Rühl for helping me shape the ideas for this thesis and for his continuous support with theoretical input. Further appreciation goes to Chenchen Wan and Vinicius Silva de Oliveira for their guidance with the practical work in the laser laboratory as well as to Uwe Grosse-Wortmann for his instructions on the assembly of the mode-lock detector.

Abstract

Ultrashort laser pulses are used in physical analysis techniques as well as in materials processing and are generated in passively mode-locked oscillators. However, those oscillators produce low pulse energies, but can be used as seeding sources for regenerative amplifiers. Operating with 2 µm wavelength radiation, the amplified output is applicable for pumping optical parametric amplifiers. This allows for generating and amplifying intense light in the mid-infrared wavelength range. With usage of the high water absorption in this wavelength range, this technology can be used for remote sensing and in spectroscopy. This thesis describes the reconditioning of a preexisting, not working mode- locked holmium-doped fiber ring oscillator. The stability of this seed source has been optimized by shielding off external influences and setting up a mode- lock detector. Furthermore, the output power has been adjusted to match the working range of the regenerative amplifier at hand by changing the seed source to soliton operation. By extending the setup via additional fiber connectors a continuous monitoring and characterization of different laser parameters, i.e. the optical spectrum, the pulse duration, pulse energy and longterm stability are ensured. In future, this improvement will offer an efficient use of power while ensuring a reliable operation of the regenerative amplifier.

vii

Kurzfassung

Ultrakurze Laserpulse werden sowohl für physikalische Analyseverfahren als auch für die Materialbearbeitung verwendet und in passiv modengekoppelten Oszillatoren erzeugt. Diese Oszillatoren erzeugen Pulse mit geringen En- ergien, dennoch können sie als Seeding-Quellen für regenerative Verstärker verwendet werden. Bei der Verwendung von Strahlung mit einer Wellen- länge von 2 µm ist das verstärkte Ausgangssignal zum Pumpen von optisch parametrischen Verstärkern geeignet. Dabei wird intensives Licht im mittleren Infrarot-Wellenlängenbereich erzeugt und verstärkt. Die hohe Absorption von Wasser in diesem Wellenlängenbereich erlaubt es, diese Technologie für die Fernerkundung und in der Spektroskopie einzusetzen. Diese Arbeit beschreibt die Instandsetzung eines bereits vorhandenen, nicht funktionsfähigen, modengekoppelten Holmium-dotierten Faserringoszillators. Darüber hinaus wurde die Stabilität dieser Seeding-Quelle durch eine Ab- schirmung von externen Einﬂüssen verbessert und durch die Einrichtung eines Modenkopplungsdetektors optimiert. Weiterhin wurde die Leistung auf den Arbeitsbereich des vorhandenen regenerativen Verstärkers durch einen Wech- sel in den Soliton-Betrieb angepasst. Durch die Erweiterung des Aufbaus mit zusätzlichen Faseranschlüssen wird eine kontinuierliche Überwachung und Charakterisierung verschiedener Laser- parameter gewährleistet, d.h. das optische Spektrum, die Pulsdauer, die Pulsen- ergie und die Langzeitstabilität. Diese Verbesserung bietet künftig eine eﬃzientere Nutzung der Leistung und garantiert gleichzeitig einen zuverlässigen Betrieb des regenerativen Verstär- kers.

List of Abbreviations

ADC analog-to-digital conversion

AOM acousto-optic modulator

CW continuous-wave

DAQ data acquisition

DIAL diﬀerential absorption light detection and ranging

EOM electro-optical modulator

FC/APC Fiber-optic Connector with Angled Physical Contact

FFT fast Fourier transformation

FIR far-infrared

FWHM full width at half-maximum

GVD group-velocity dispersion

HDF holmium-doped ﬁber

HHG high-harmonic generation

Ho Holmium

HWP half-wave plate

KLM Kerr-lens mode-locking

LED light-emitting diode

LIDAR light detection and ranging

MFD mode-ﬁeld diameter

MIR mid-infrared

NA numerical aperture

xi NB narrow bandwidth

ND neutral density

NPE nonlinear polarization evolution

OPA optical parametric ampliﬁer

P-APM polarization-additive pulse mode-locking

PBS polarizing beam splitter

PCB printed circuit board

PSD power spectral density

QWP quarter-wave plate

RBW resolution bandwidth

RF radio frequency

RIN relative intensity noise

RMS root-mean-square

SMF single-mode ﬁber

SPM self-phase modulation

SSB single sideband

TEM transverse electromagnetic

TFP thin-ﬁlm polarizer

Tm Thulium

UV ultraviolet

WDM wavelength division multiplexer

xii List of Figures

2.1 Schematic of an optical fiber and its beam propagation inside the core due to total internal reflection on the left. On the right, the quadratic refractive-index n2 as a function of the fiber radius r in case of step-index fibers is shown...... 4 2.2 Losses in dB/km in silica glass fiber depending on the wavelength, figure adapted from [6]...... 6 2.3 Absorption spectrum of water, figure adapted from [1]...... 6 2.4 Absorption emission cross section spectra of Th and Ho-doped silica. Figure taken from [7]...... 7 2.5 Energy level of Ho-doped silica with two different pumping processes, both resulting in an emission of 2 µm radiation. Figure taken from [7]...... 8 2.6 Schematic drawing of an evanescent field coupler. Figure adapted from [8]...... 9 2.7 Gain bandwidth and cavity loss on the top and separated longitudinal modes supported by the cavity length (dashed) as well as the number of allowed modes (solid). Figure adapted from [10]...... 10 2.8 Schematic of Q-switching. Figure taken from [10]...... 12 2.9 Modes with no fixed phase relation (a) and phase-matched modes at one particular moment (b). The figure is adapted from [11]. . 13 2.10 Schematic of active mode-locking. Figure taken from [12]. . . . . 14 2.11 Schematic of (a) slow and (b) fast saturable absorber. Figures taken from [12]...... 15 2.12 Schematic of KLM. Figure taken from [12]...... 15 2.13 Schematic of P-APM. Figure taken from [14]...... 16

2.14 Refractive index n and the group refractive index ng as a function of the wavelength. Figure taken from [13]...... 19 2.15 Dispersion parameter D as a function of the wavelength λ. Fig- ure taken from [13]...... 19 2.16 Pulse broadening of a hyperbolic-secant pulse along the z-direction of a ﬁber. The ﬁgure is taken from [13]...... 20

xiii List of Figures

2.17 Time dependent intensity of a pulse on the top and its redistributed frequency components as a function of time. The figure is taken from [17]...... 22 2.18 Optical spectrum of an erbium-doped fiber laser. The figure is taken from [18]...... 23 2.19 Pulse train detected by a photodiode in (a) and the spectrum analyzer’s signal in (b). The figure is adapted from [22]...... 28

3.1 Photograph of the setup including pump, oscillator and characterization sections. PD: Photodiode; AC: Autocorrelator. . . . . 31 3.2 Schematic drawing of the pump section. HWP: half-wave plate; TFP: thin-film polarizer; QWP: quarter-wave plate; SMF: single- mode fiber; ND attenuator: neutral-density attenuator; PD: photodiode; MLDET: mode-lock detector...... 32 3.3 Photograph of the pump section...... 33 3.4 (a) Shows the beam profile after the telescope, (b) gives a top view of two fiber tips, i.e. one flat side for splicing and one angle-cleaved side used for coupling and (c) depicts the fiber characteristics of the angle-cleaved fiber tip measured by the splicer...... 34 3.5 Photograph of the fiber coupling...... 35 3.6 Schematic drawing of the oscillator...... 36 3.7 Photograph before (a) and after (b) the splicing process of the SMF from the WDM output (left fiber) to the HDF (right fiber). 37 3.8 Photograph of the oscillator...... 38 3.9 Schematic drawing of the characterization section...... 39 3.10 Photograph of the characterization section...... 40 3.11 Determination of the calibration factor by moving the corner mirror of the autocorrelator...... 42 3.12 Photograph of the mode-lock detector while the oscillator is working in the mode-locking operation indicated by the large carrier power and low noise power...... 43 3.13 Photograph of the stack of PCB with the photodiode board on the top. The photodiode (PD) is not yet soldered and the output not yet connected to the micro controller board. Bandpass filtered voltage signals corresponding to the carrier power can be measured using the test point...... 44

xiv List of Figures

4.1 Optical spectrum tuned to different center wavelengths by changing the wave plate combination...... 46 4.2 Optical spectrum with different bandpass filters...... 46 4.3 Autocorrelation without bandpass filters...... 48 4.4 Autocorrelation with 2050-12 bandpass filter...... 48 4.5 Autocorrelation with 2050-12 and 2085-10 bandpass filter. . . . 49 4.6 RF spectrum...... 49 4.7 Slope efficiency and output beam diameter...... 50 4.8 Relative intensity noise of the oscillator output with different narrow bandpass filters...... 53 4.9 Relative intensity noise of the pump at 35 % and the oscillator output...... 54 4.10 Relative intensity noise of the pump at 60 % and the oscillator output...... 55 4.11 Phase noise and RF spectrum...... 56 4.12 Integrated timing jitter...... 56 4.13 Long-term stability measured over 2 days using the mode-lock detector. The inset shows the transition from mode-locking to CW state followed by a disabling of the pump...... 57

List of Tables

3.1 List of the oscillator’s main components and their speciﬁcation. 34 3.2 List of the diagnostic tools used for characterizing the mode- locked laser...... 40

xvii

Table of Contents

Acknowledgementsv

Abstract vi

Kurzfassung viii

List of Figures xiii

List of Tables xv

1 Introduction1

2 Theoretical Background3 2.1 Fiber Lasers ...... 3 2.1.1 Optical Fibers and Fiber Components ...... 3 2.1.2 Operation Modes of Fiber Lasers ...... 10 2.2 Propagation of Ultrashort Pulses in Fibers ...... 18 2.2.1 Group Velocity Dispersion ...... 18 2.2.2 Self-phase Modulation ...... 21 2.2.3 Solitons ...... 23 2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses . 25 2.3.1 Pulse Characterization ...... 25 2.3.2 Output Power and Pulse Energy ...... 27 2.3.3 Noise ...... 27 2.3.4 Mode-locking Stability ...... 30

3 Experimental Setup 31 3.1 Available Components ...... 32 3.2 Oscillator ...... 36 3.3 Measurement Setup ...... 39 3.4 Mode-lock Detector ...... 43

xix 4 Results and Discussion 45 4.1 Pulse Characterization ...... 45 4.1.1 Optical Spectrum ...... 45 4.1.2 Autocorrelation ...... 47 4.1.3 Pulse Energy ...... 49 4.2 Noise ...... 52 4.2.1 Relative Intensity Noise ...... 52 4.2.2 Phase Noise ...... 55 4.3 Mode-locking Stability ...... 57

5 Conclusion and Outlook 59

Bibliography 61 1 Introduction

Infrared laser systems are widely used for remote sensing, medical application and in spectroscopy. In particular, infrared lasers emitting at a wavelength of 2 µm are used due to the strong water absorption at this wavelength. Such radiation can be produced in active gain fibers doped with rare earth ions such as thulium or holmium. Examples for remote sensing techniques are light detection and ranging (LIDAR) used for aerosol density measurements and differential absorption LIDAR (DIAL), which allows for determination of the density of atmospheric components. Another advantage of laser systems emitting radiation at 2 µm wavelength is that they suit well as pump sources for optical parametric amplifiers (OPA). Those are used for generating and amplifying radiation with larger wavelengths, i.e. in the mid-infrared (MIR) wavelength range, which in turn can be used for remote sensing of other atmospheric compounds as well as chemical and biological hazards. [1] Additionally, the technique of high-harmonic generation (HHG) can be applied on the MIR light for producing radiation at wavelengths in the visible or ultraviolet (UV) region. MIR laser play also an important role in surgeries, where they function as an efficient tool for cutting by means of energy absorption. The resulting breaking of chemical bonds is especially used for cutting biological tissue, because it mainly consists of water. A major advantage of the usage of fiber is that it serves a compact delivery of the radiation to the target location during the surgery and thus allows an easy handling of the tool. In general, all those applications require high power, which is achieved in ultrashort pulses since they exhibit high peak power due to the specifically short pulse duration. Ultrashort pulses can be generated in passively mode-locked oscillators. Unfortunately, they provide low pulse energies. Nevertheless, such pulses can be amplified in regenerative amplifiers in which a pump source ensures an active laser medium to maintain a population inversion. The incoming seed pulse from the mode-locked oscillator is amplified due to stimulated emission. Placing the active laser medium inside a resonator allows for high amplification factors due to a multiple pass operation. [2] The holmium-doped yttrium lithium fluoride regenerative amplifier reported in [3] is recommended to be seeded with a laser source operating at a wave-

1 1 Introduction length of 2050 nm with pulse energies of 1-10 nJ at about 100 MHz repetition rate. In previous experiments the seed source exhibited a broad optical spectrum, which resulted in a reduction of the pulse energy from 1 nJ down to 60 pJ due to the limiting spectral width of chirped volume bragg gratings used for pulse stretching. Pulse stretching is necessary before seeding the regenerative amplifier to avoid damages of optical components inside the amplifier, which might be induced by a high peak power of the amplified pulses. [4] The aim of this thesis is to repair and modify the previous laser source used for seeding the regenerative amplifier at hand in order to guarantee an efficient usage of power by narrowing the emitted optical spectrum and a stable operation since additional amplification stages require a reliable operation of the seeding source. In this thesis the construction and characterization of a seeding source based on the concept of a passively mode-locked unidirectional holmium-doped fiber ring oscillator operating in the soliton regime as reported in [5] will be described. The thesis is organized as follows. Chapter 2 describes the fundamental theory concerning optical fibers, their specification and doping materials used for generating radiation at 2 µm wavelength. Furthermore, some fiber components acting as the equivalents to common free-space optics will be introduced as well as different configurations of pulsed lasers. The theory chapter will also discuss the effects of dispersion and self-phase modulation, two dominating mechanisms which are responsible for the formation and propagation of solitons. The last section of this chapter will show different techniques to characterize lasers with ultrashort pulse durations. In chapter 3 the available components will be presented, including the fiber coupling of the pump laser, the setup of the oscillator as well as the procedure for initiating mode-locking. Furthermore, the installation of several measurement devices will be discussed, which allow a simultaneous characterization of different parameters, e.g. the output power, the repetition rate, the optical spectrum and the pulse duration. Finally, the assembly and configuration of a mode-lock detector, a device developed by the FS-LA DESY group, will be explained. All the results will be shown and discussed in chapter 4. Chapter 5 will summarize the work and will give an outlook.

2 2 Theoretical Background

This chapter will provide an overview of optical fibers and pulse generation in lasers. Furthermore, the effects of group velocity dispersion and self-phase modulation will be introduced, which are the dominating effects for the formation of soliton pulses in optical fibers. Finally, techniques for characterizing ultrashort pulses from mode-locked lasers will be presented.

2.1 Fiber Lasers

This section will discuss the propagation of light in optical ﬁbers, doping materials for generating light at 2 µm wavelength and ﬁber equivalents to free-space optics. Furthermore, the continuous-wave, q-switching and mode-locking operation states of lasers will be discussed.

2.1.1 Optical Fibers and Fiber Components

Based on the concept of total internal reflection optical fibers are widely used for guiding light over long distances with low transmission losses. Common fields of application are, e.g. remote sensing, telecommunication engineering and laser development. In general, an optical fiber consists of an inner core and an outer cladding, where the core exhibits a slightly larger refractive index

(n1) than the cladding (n2) for allowing the propagation based on total internal reflection. The critical angle, i.e. the incident angle inside the fiber where total internal reflection still occurs, can be derived from Snell’s Law

n1 sin(θi) = n2 sin(θt), (2.1) where θi is the angle of the incident beam inside the core and θt is the angle of the transmitted beam in the cladding. For total internal reﬂection θt becomes ◦ 90 so that the angle of the reﬂected beam θr is equal to θi, which is according to (2.1) n2 θi = θr = arcsin . (2.2) n1

3 2 Theoretical Background

Figure 2.1: Schematic of an optical fiber and its beam propagation inside the core due to total internal reflection on the left. On the right, the quadratic refractive-index n2 as a function of the fiber radius r in case of step-index fibers is shown.

Hence, any beam with an angle larger than this critical angle θi will be guided through the fiber as shown in figure 2.1. Using Snell’s Law again, one can transfer the acceptance angle for coupling into the fiber and thus the numerical aperture ◦ NA = n0 sin(αc) = n1 sin (90 − θi) = n1 cos (θi), (2.3) where n0 represents the refractive index of the medium surrounding the fiber before coupling and αc is the maximal half-angle of the cone. With (2.2) and √ the relation cos(arcsin(x)) = 1 − x2 the NA can be calculated to q 2 2 NA = n1 − n2, (2.4) so that it is just dependent of the refractive indices of the core and the cladding.

The number of transverse modes propagating in a ﬁber depends on the V parameter q 2 2 V = k0a n1 − n2, (2.5) where k0 is the wave number and a is the core radius. For V < 2.405 the

fiber supports only the fundamental transversal mode LP01. These fibers are called single-mode fibers (SMF). Such fibers exhibit a small core diameter (8 to 12 µm) and a cladding diameter of about 125 µm. The NA and thus the difference in the refractive indices n1 and n2 is also small. Commonly, the core’s profile is a step-index, i.e. the refractive index of the core is constant, as shown in figure 2.1 on the right. In this work only single-mode fibers with a core and cladding composed of silica glass are used. In general, losses in fiber can be summarized as coupling/splicing, absorption/scattering and bending losses. For coupling the fundamental transverse

4 2.1 Fiber Lasers

electromagnetic modes of a free-space gaussian beam (TEM00) into a single- mode fiber it is straight forward to focus the beam in such a way that the beam diameter at the 1/e2 intensity matches the fiber’s mode-field diameter

(MFD). The resulting mode overlap of a gaussian TEM00 free-space beam and the fundamental mode LP01 coupled in a SMF in general is about 90 %. In order to reduce Fresnel reflections on both surfaces for coupling into and out of the fiber it is recommended to cleave, i.e. a precisely controlled breaking of the fiber, the surfaces with an angle of about 8◦. For splicing two different types of fibers, i.e. thermally fusing them together, both cleaved surfaces should be perpendicular and their MFDs should match, so that the light doesn’t leave the fiber through the cladding.

The transmitted optical power PT as a function of the ﬁber length L and can be calculated by

PT (z) = PI exp(−αL), (2.6) where PI is the instantaneous power in W and α is the attenuation coeﬃcient in units of km−1. Since it is more common to express the optical power in decibel units (dB) the attenuation coeﬃcient can be transferred to

10 PT αdB = − log (2.7) L PI with the units dB/km. The optical power P in W or mW can be converted to

PdB in the units of dB or dBm by

P PdB = 10 log , (2.8) Pref where Pref represents the reference power, e.g. 1 W or 1 mW. Besides the already discussed coupling and splicing losses, the attenuation of optical power in an optical ﬁber is caused by two wavelength dependent mechanisms, i.e. scattering and absorption.

Scattering in a fiber occurs due to impurities or particles in the core. Rayleigh scattering is the main scattering effect in fiber optics which results from inho- mogeneities with a size much smaller than the wavelength of the light. If the scattered light propagates in an angle which is not supported for guiding the light in the fiber it leaves the core and reduces the power. This type of scattering is λ−4 dependent so that with larger wavelength less Rayleigh scattering occurs. Other types of scattering that may arise are Mie scattering, Brillouin and Raman scattering. Mie scattering is less significant in optical fibers, because it results from particles with a size around the wavelength, variations of

5 2 Theoretical Background

Figure 2.2: Losses in dB/km in silica glass fiber depending on the wavelength, figure adapted from [6]. the refractive index of core and cladding or changes in the diameter, which had been reduced by modern optical fiber fabrication. Brillouin and Raman scattering are both intensity dependent effects that slightly change the wavelength and also the direction, i.e. even back scattering is possible, of the photons due to thermal influences and vibrations of the glass material, respectively. Material absorption is the power loss due to the energy conversion of the propagating lightwave into e.g. vibrations while interacting with certain fiber material components. In the ultraviolet region silica glass fibers have electronic resonances and vibrational resonances in the far-infrared (FIR) region. Wa-

Figure 2.3: Absorption spectrum of water, ﬁgure adapted from [1].

6 2.1 Fiber Lasers ter vapor deposits OH-ions in the material during the manufacturing process, which cause fundamental loss peaks at 1.24 and 1.38 µm as can be seen from figure 2.2. The combination of Rayleigh scattering and material absorption of silica glass shows a loss minimum around 1.55 µm. Light with this wavelength is produced in an erbium-doped active laser medium and is used in telecommunication, because it allows overcoming large distances with low transmission losses. Although the attenuation for 2 µm wavelength radiation becomes large due to IR vibrations it is still attractive for many applications such as remote sensing and medical methods. These applications mainly take advantage of the large water absorption peak at 2 µm (see figure 2.3), which also gives this wavelength range the name eye-safe region. For producing 2 µm wavelength radiation, silica glass fibers can be doped with optically active holmium (Ho) ions in order to create an active medium. The electronic states of the Ho ions in the holmium-doped fiber (HDF) can be excited by absorption of optical pump light. From figure 2.4 it can be seen that thulium (Tm) is an appropriate pump due to the intersection of the Tm emission cross section with the peak of the Ho absorption cross section around 1.95 µm. This allows a build-up of a population inversion between the lower 5 5 laser level I8 and the excited state I7. Pumping and emission occurs around similar wavelengths (see figure 2.5), which has on one hand the advantage that no parasitic energy transitions, e.g. rapid non-radiative decays, occur. On one

Figure 2.4: Absorption emission cross section spectra of Th and Ho-doped silica. Figure taken from [7].

7 2 Theoretical Background

Figure 2.5: Energy level of Ho-doped silica with two different pumping processes, both resulting in an emission of 2 µm radiation. Figure taken from [7]. hand an increase of the upper laser lifetime of the Ho ions is supported, all pump energy is stored in the excited state and can be extracted in a single, short pulse. On the other hand less heat arises from such energy transfers due to motion. In any case, the gain fiber as an active medium in comparison to doped crystals offer a large surface, so that no thermal management is necessary in case of fiber lasers. The amplification process is initiated by forming a laser cavity, thus stimulated emitted radiation propagates through the active medium for multiple times. This laser cavity can either be a conventional resonator, where the beam is reflected at the ends of the cavity and thus exhibits a bidirectional beam path. Otherwise the laser cavity can consist of a ring oscillator, where the end of the cavity is fed back to its beginning closing the ring, so that an unidirectional propagation can be accomplished. In fiber optics, the equivalents to free-space optics, such as partially re- flecting mirrors or beam splitters as well as dichroic mirrors are fiber couplers/splitters and wavelength division multiplexer (WDM) couplers, respectively. The most common fiber coupler/splitter consists of two single-mode fibers closely placed in parallel to each other. In total, it provides four ports, where

8 2.1 Fiber Lasers light with a certain power and wavelength is coupled into one of the two input ports and transfers its power in the interaction zone into the other fiber, resulting in a power splitting ratio between the two output ports. The concept of power distribution from one fiber to the other is dependent on the fabrication process. In evanescent field couplers two fibers are twisted in order to create a tight contact. The fibers cladding is then almost etched to the size of the fiber cores and becomes the common cladding. This allows the evanescent field, i.e. the part of the electromagnetic wave which enters the cladding during the total internal reflection, to transfer from the common cladding into the other fiber core. The length of the interaction zone in this type of coupler can be controlled by the number of fiber twists and defines the power splitting ratio of the coupler. [8] In fused couplers the cores of the two fibers are fused together and create a taper, i.e. a common core, where the light splits into the individual output fibers. During the fusion both fibers are pulled in order to reduce the fused core sizes precisely, which determines the splitting power ratio. [9] WDM couplers are similar passive fiber components, where different wavelengths can enter a common input port and the power gets split in the different wavelength portions. The insertion loss, i.e. the port-to-port loss, is wavelength dependent due to fabrication process. Especially, WDM couplers find application in fiber ring oscillators, where one WDM input port serves for coupling pump light into the laser cavity using the output port, which has a

Figure 2.6: Schematic drawing of an evanescent ﬁeld coupler. Figure adapted from [8].

9 2 Theoretical Background low insertion loss for the pump wavelength. Light with the laser wavelength is generated in a gain ﬁber, which is spliced to the second input port of the WDM coupler. This port of the WDM coupler has a high insertion loss for the pump wavelength with respect to the port spliced to the gain ﬁber and a low insertion loss for the laser wavelength. Hence, the WDM coupler transmits the laser wavelength and dumps most of the power of the residual pump light to the second output port.

2.1.2 Operation Modes of Fiber Lasers

Fiber lasers are realized in three different operation states, i.e. continuous-wave (CW), Q-switched and mode-locked. In CW laser light is generated without being interrupted and radiation is permanently emitted through the output coupler. This is achieved by con- tinuously pumping the active medium in the laser cavity. Hence, the gain of stimulated radiation emission γ0(ν) is always larger than the losses αr that occur inside the cavity, so that the laser operates consistently above its threshold and maintains an almost constantly stable output power. The wavelength of the emitted radiation depends on the kind of optically active medium, i.e. in case of fibers the dopants of the gain fiber segment. On one hand, it is possible that lasers emit a specific wavelength only, i.e. a narrow linewidth in the optical spectrum. These are called single-frequency or single-longitudinal-mode

Figure 2.7: Gain bandwidth and cavity loss on the top and separated longitudinal modes supported by the cavity length (dashed) as well as the number of allowed modes (solid). Figure adapted from [10].

10 2.1 Fiber Lasers lasers and provide almost monochromatic radiation. On the other hand the wavelength can spread over a deﬁned range, thus it contains multiple longitudinal modes. Rather than the wavelength λ the frequency ν is used in this context which can be obtained from the condition

c0 ν = , (2.9) λ where c0 is the speed of light in vacuum. In general, multiple longitudinal modes are supported by the cavity. If each experience a phase shift of a multiple of 2π during one roundtrip it allows them to oscillate as independent, free-running modes. In the frequency domain these modes are separated by c c ∆ν = = , (2.10) 2d L where d is the distance of a resonator with two mirrors, L is the length of a ﬁber ring oscillator, and c is the speed of light in the medium. The number of modes gaining ampliﬁcation in the laser cavity can be calculated from [10]

B M = , (2.11) ∆ν where B is the width of the spectral band for which the gain exceeds the losses. In conclusion, the amount of longitudinal modes depends on the atomic gain bandwidth of the active laser medium, the cavity losses and its length. Single- frequency lasers can be obtained by selecting only one longitudinal mode. For example this can be done by increasing the losses αr until only the fundamental mode ν0 oscillates. Of course, the mode itself suffers from the loss resulting in a weak output power. Another way would be to decrease the cavity length in order to increase the mode spacing ∆ν. However, a drawback is that this also reduces the active gain in length, i.e. pumping and thus amplification is less efficient. A more practical way is the use of an intracavity selective filter. In free-space optics this can be e.g. an etalon, which changes the optical path length of the cavity and thus the mode spacing. For fibers a fiber bragg grating could be used, where a special arrangement of alternating refractive indices reflects a specific wavelength and transmits the residual ones, similar as a dichroic mirror. CW lasers can be modified into pulsed lasers by placing an external optical switch, also called modulator, outside the cavity transmitting the radiation during a short time. This method is rather unsatisfactorily since power is lost, whenever the modulator absorbs the radiation and the pulse intensity never exceeds the CW power.

11 2 Theoretical Background

Figure 2.8: Schematic of Q-switching. Figure taken from [10].

Q-switching is a method for creating pulses with nanosecond pulse durations and much higher peak powers by means of a modulator inside the cavity. Figure 2.8 depicts a time dependent schematic of the process. In principle, permanent pumping ensures a build-up of the population inversion while the absorbing modulator prevents oscillation and thus the amplification. When- ever the population inversion is at its maximum the modulator reduces the cavity losses, the population inversion disintegrates due to stimulated emission and amplification takes place. Finally a short, intense laser pulse builds up and sustains during a couple of roundtrips. Active Q-switching is realized using, e.g. acousto-optic modulators (AOM) or electro-optical modulators (EOM) and passive Q-switching utilizing saturable absorbers. AOM and EOM make use of an electric field for producing the necessary losses. In an AOM the electric field generates a sound wave, which scatters the photons, whereas in an EOM the electric field changes the refraction index due to the electro-optic or Pockels effect, and thus deflects the photons on a voltage dependent path. The saturable absorber obtains an intensity dependent transmission, where the transmission increases with increasing intensity. In general, the Q-switching technique finds application in time-resolved experiments or ablation processes in materials processing. The duration of the pulse depends on a few parameters, for example the cavity length, the repetition rate and the pump power, as well as the type of gain medium determining the amount of storable energy. In contrast to the free-running modes that oscillate independently in a CW or Q-switched laser, these modes can be externally adjusted in their relative phase (see figure 2.9) and cause a coherent interference. An intracavity modulator, which is synchronized to the cavity roundtrip time, produces such an interference of these modes, thus a single pulse propagates inside the laser

12 2.1 Fiber Lasers

Figure 2.9: Modes with no ﬁxed phase relation (a) and phase-matched modes at one particular moment (b). The ﬁgure is adapted from [11]. cavity. The technique is called mode-locking and opens the sub-nanosecond pulse width regime. The output of a mode-locked laser is a train of pulses, where the period between two pulses depends on the cavity roundtrip time, calculated by the inverse of equation (2.10)

1 TR = . (2.12) ∆ν

The pulse width is inversely proportional to the number of modes supported by the cavity [10] TR 1 T0 = = . (2.13) M M∆ν Since the number of modes is quite large for media with a broad lasing bandwidth, they permit on one hand the evolution of short and intense laser pulses and on the other hand the tuning of the center wavelength over a large range. In principle, initiating mode-locking requires an event that causes the phases of the modes to match and allows a pulse to build up. Once this condition is fulﬁlled the modulator ensures the transmission of the overlapping modes for the short moment of passing it. Any other randomly arranged modes get blocked due to the high losses generated by the modulator. As in the case of Q-switching, mode-locked lasers are distinguished in active and passive modulators. In active mode-locking an amplitude modulator, e.g. an AOM oder EOM, creates a cosinusoidal loss modulation. Each roundtrip the single pulse arrives at the modulator, which ensures that gain exceeds losses for this particular

13 2 Theoretical Background

Figure 2.10: Schematic of active mode-locking. Figure taken from [12]. short moment. As shown in figure 2.10 the peak passes the gain window and experiences amplification. However, the wings get attenuated, because losses already ex- ceed the gain causing the pulse to shorten. This also means that the shorter the pulse gets the less losses appear and less changes of the pulse duration is achieved. Furthermore, electric signals can not be arbitrarily raised, thus active mode-locking can only be used to achieve sub-nanosecond pulses. For entering sub-picosecond pulse durations and thus the ultrashort pulse regime the method of passive mode-locking becomes necessary. In this case the modulator is a saturable absorber, which becomes more transparent for higher intensities or energies. In contrast to active mode-locking, no external source is required to manipulate the cavities transparence. Instead, the pulse itself causes the losses necessary for pulse shortening and thus determines the duration of the gain window. However, restriction is given by the recovery time of the saturable absorber, i.e. the time necessary for the saturable absorber to turn back from transparent to the absorbing, high loss state. Hence, one distinguishes fast and slow saturable absorber, where the latter provides a recovery time much larger than the pulse duration. However, under certain conditions slow saturable absorber still achieve significant pulse shortening. The schematic principle is shown in figure 2.11 (a). First, any parasitic light, e.g. background light or other long pulses potentially evolved in the cavity, get suppressed by high losses. Second, the leading edge of the pulse is shaped due to the losses, whereas the peak of the pulse causes the absorber to saturate and amplification occurs. Fast gain depletion, i.e. reduction of the population inversion of the active laser medium, allows again a quick predominance of the losses, thus the trailing wing is also shortened and parasitic light in the cavity is suppressed again. This becomes possible if the lifetime of the excited state is comparable to the cavity roundtrip time. [11]

14 2.1 Fiber Lasers

Figure 2.11: Schematic of (a) slow and (b) fast saturable absorber. Figures taken from [12].

Fast saturable absorbers don’t have such a dynamic gain behavior, but rather work in a regime where the active laser medium provides a constant gain during the process, as shown in figure 2.11 (b). In this case both sides of the pulse wings are formed by the loss modulation of the saturable absorber providing a response time similar to the pulse duration. However, pulses can’t be shortened down to pulse widths smaller than the response time of the saturable absorbers used, thus limitation is present due to the delay during the energy depletion. Such kind of saturable absorbers as discussed so far are called real saturable absorbers. Even shorter pulses can be achieved by using artificial saturable absorbers, where nonlinear effects cause the loss modulation rather than the absorption of the peak intensity. Examples for passive mode-locking techniques achieved with artificial fast saturable absorbers are Kerr-lens mode-locking (KLM) for free-space lasers and nonlinear-polarization evolution (NPE) for fiber lasers. KLM relies on the optical Kerr effect which gives an intensity dependent refractive index according to the equation [13]

n(λ, I) = nL(λ) + nNLI, (2.14) where nL is the linear part of the refractive index dominating at low intensities

Figure 2.12: Schematic of KLM. Figure taken from [12].

15 2 Theoretical Background

and nNL is the nonlinear part which starts to increase with high peak intensities and is expressed in the units m2/W. Since the response of nonlinearities is fast this effect is well suited for short pulses with high pulse energies, which thus exhibit high peak intensities. Such pulses cause the refractive index to increase having the effect of self-focussing, i.e. the more the refractive index increases the smaller gets the beam in the medium. Finally, an aperture inside the laser cavity, as shown in figure 2.12, produces high losses for non-focussed background light, whereas lower losses occur for focussed pulses, which pass the aperture and oscillate in the laser cavity. Passive mode-locking of fiber lasers can be achieved using the NPE technique, which is based on polarization-additive pulse mode-locking (P-APM). As shown in figure 2.13 an elliptically polarized pulse experiences an intensity dependent polarization rotation inside the fiber segment due to the Kerr effect. An analyzer transfers the elliptical to linear polarization, which is transmitted through a polarizer. Certain orientation of a waveplate turns the linear polarized light in such a way that it compensates for the nonlinear polarization evolved in the Kerr medium. Hence, this technique allows for high transmission of pulse peaks with high intensities, whereas the wings experience higher losses at the polarizer due to less rotation in the Kerr medium. NPE in fibers benefits from the high peak intensities due to a small fiber core diameter and from the simplicity of the setup. However, it is very sensitive for perturbation induced by the environment, e.g. changes in temperature or mechanical vibrations. [15] In conclusion, active mode-locking allows an efficient shortening of long pulses, but is restricted by the limitation of the velocity of electrical signals. In contrast, slow saturable absorbers provide a constant pulse shaping behavior, since the modulation by itself controls the amount of shortening, but it is

Figure 2.13: Schematic of P-APM. Figure taken from [14].

16 2.1 Fiber Lasers restricted to conditions of the gain medium. Finally, fast saturable absorbers increase the efficiency of shortening the pulses due to the instantaneously acting nonlinear processes. However they require already existing short pulses since the shortening of longer pulses using this method is less efficient. This may also cause problems for starting the mode-locking process without any external influences, such as abrupt changes in the cavity length. In general, pulses of passively mode-locked lasers utilizing fast saturable absorbers are the shortest produceable events ever induced by humankind and find application in, e.g. materials processing or pump-probe experiments. Rather than thermal processes the ablation or excitation relies on other physical phenomena, such as coulomb explosions or two-photon absorption.

17 2 Theoretical Background

2.2 Propagation of Ultrashort Pulses in Fibers

In this section group velocity dispersion and self-phase modulation will be presented, which are two dominating eﬀects that allow for a formation and propagation of soliton pulses in oscillators.

2.2.1 Group Velocity Dispersion

The propagation of an electromagnetic wave in a medium, e.g. air or an optical ﬁber, results in an interaction with its bound electrons. Absorption occurs when the optical frequency ω and thus the wavelength λ (with ω = 2πc0/λ) reaches the mediums characteristic resonance. In general, this eﬀect leads to a dependency of the refractive index n on the optical frequency ω and is called chromatic dispersion. The Sellmeier equation gives an approximation of the dependency on the refractive index by [13]

m 2 X Bjωj n2(ω) = 1 + , (2.15) ω2 − ω2 j=1 j j where Bj is the strength of the jth resonance at the corresponding resonance frequency ωj. Since a short pulse contains a broad optical spectrum dispersion has a crucial effect on the pulse propagation in a fiber. Each wavelength experiences a different refractive index and thus a different velocity c = c0/n(λ), which causes the pulse width to increase, i.e. the pulse broadens. In fiber optics the mode-propagation constant β can be expressed by [13]

ω 1 2 β(ω) = n(ω) = β0 + β1(ω − ω0) + β2(ω − ω0) + ..., (2.16) c 2 where β1 is the ratio of group refractive index ng and speed of light in vacuum c0 and thus determines the speed of the pulse envelope vg [13] 1 dn ng 1 β1 = n + ω = = . (2.17) c0 dω c0 vg

A dependency of the refractive index n and the group refractive index ng as a function of the wavelength λ is shown in ﬁgure 2.14. The parameter β2 contains information about the broadening of the pulse and is also called the group-velocity dispersion (GVD) parameter. It is calculated from [13]

1 dn d2n ω d2n λ3 d2n β2 = 2 + ω 2 ' 2 ' 2 2 (2.18) c0 dω dω c0 dω 2πc0 dλ

18 2.2 Propagation of Ultrashort Pulses in Fibers

Figure 2.14: Refractive index n and the group refractive index ng as a function of the wavelength. Figure taken from [13].

2 in ps /km. Rather than β2 the dispersion parameter is often expressed in [13]

2πc0 D = − β2, (2.19) λ2 with the units ps/(km · nm). A dependency of the GVD parameter D as a function of the wavelength λ is shown in ﬁgure 2.15. It is noticeable, that with increasing wavelength D changes from a negative to a positive value at around

1.3 µm. In cases where D is negative (β2 positive then according to (2.19)) the ﬁber acts in the normal dispersion regime, where larger wavelengths (lower frequencies) propagate faster than shorter wavelengths. Otherwise, for positive

Figure 2.15: Dispersion parameter D as a function of the wavelength λ. Fig- ure taken from [13].

19 2 Theoretical Background

D values the fiber obtains anomalous dispersion, i.e. shorter wavelengths travel faster than longer wavelengths. The effect of pulse broadening induced by GVD depends on the initial pulse width. For examination whether GVD has a relevant effect on the pulse propagation it is useful to know the actual propagation length, i.e. the physical

ﬁber length L, and to deﬁne the dispersion length LD [13]

2 T0 LD = , (2.20) |β2| where T0 is the initial pulse width. In cases where L << LD GVD has no remarkable inﬂuence and the pulse is not signiﬁcantly broadened. However, if

L >> LD GVD has an inﬂuence and broadens the pulse. The increased pulse width T (z) as a function of the propagation distance z can be calculated for a gaussian shaped pulse from [13]

2 1/2 T (z) = T0[1 + (z/LD) )] . (2.21)

On one hand from equation (2.20) and (2.21) it can be seen that the amount of pulse broadening depends on the initial pulse width T0 and the GVD parameter but does not rely on the sign of β2, thus normal and anomalous dispersion can lead to the same eﬀective broadening. Furthermore, pulse broadening depends on the shape of the pulse, where pulses with steep leading and trailing edges experience increased pulse broadening. Nevertheless, gaussian and hyperbolic- secant pulses show similar broadening. An example of the position dependent

Figure 2.16: Pulse broadening of a hyperbolic-secant pulse along the z- direction of a ﬁber. The ﬁgure is taken from [13].

20 2.2 Propagation of Ultrashort Pulses in Fibers pulse broadening and the resulting decrease in peak intensity is shown in ﬁgure 2.16.

2.2.2 Self-phase Modulation

As already discussed in section 2.1.2 and shown in equation (2.14) the refractive index of a medium is changeable through high intensities. In general, these intensities are produced in single-mode fibers using short pulses with high pulse energies. Especially in combination with the small core diameter and thus the small effective area Aeff high intensities are generated and are responsible for the appearance of nonlinear effects. Similar to the condition for GVD, a fiber behaves nonlinear if the physical fiber length L is larger than the nonlinear length LNL, which is given by [13]

−1 LNL = (γP0) , (2.22) where P0 is the peak power and γ is the nonlinear parameter [13]

nNLω0 2πnNL γ = = (2.23) c0Aeff λ0Aeff with units of rad/(Wm). The time dependent intensity and thus the variation of the refractive index n as a function of time results on one hand in a change in the nonlinear phase of the electromagnetic wave φNL(z, T ), which is induced by the pulse itself. This effect is called self-phase modulation (SPM) and the change in phase is determined by [13, 16]

ω0 2π φNL(z, T ) = γP0z = nNL Iz = nNLIz, (2.24) c0 λ where z is the propagation in a medium, which is assumed to be lossless. On the other hand the changing nonlinear phase φNL(z, T ) results in a symmetric generation of new frequency components, which is called SPM-induced spectral broadening. In general, the pulse energy is redistributed from the center frequency ω0 to the new generated frequencies and results in a time dependent frequency ω(t) = ω0 + δω(T ), where the time dependent change of the frequency is the time derivative of the nonlinear phase

dφNL 2π dI δω(T ) = = nNLz . (2.25) dT λ dT From ﬁgure 2.17 it can be seen that the optical spectrum with new frequencies obtains a time dependancy. Since the change of frequencies is negative for

21 2 Theoretical Background

Figure 2.17: Time dependent intensity of a pulse on the top and its redistributed frequency components as a function of time. The figure is taken from [17]. the leading edge of the pulse, the generated lower frequency components (larger wavelengths) travel in the front of the pulse, while the higher frequencies are shifted to the trailing part of the propagating pulse. As already discussed in section 2.2.1 this is a similar effect as in the case of normal dispersion. It should be pointed out that SPM results in a broadening of the optical spectrum caused by an intensity dependent nonlinear phase shift and remains constant in the temporal domain, whereas GVD broadens the pulse duration due to a wavelength dependent linear phase without any changes in the optical spectrum. Although normal dispersion and SPM rely on different phenomena their coex- istence can have a supporting effect and results in an increased broadening of the pulse duration due to the temporal separation of the spectral components. However, the pulse broadening induced by a medium with anomalous dispersion (short wavelengths travel fast) can be compensated in combination with exactly the counteracting SPM resulting in a constant temporal pulse profile over long distances, which is especially desired in optical fiber communication. A pulse propagating in a fiber, where the anomalous dispersion is balanced with the SPM is called an optical soliton.

22 2.2 Propagation of Ultrashort Pulses in Fibers

2.2.3 Solitons

In section 2.2.1 it was concluded that in general dispersion causes a pulse to broaden. In the case of anomalous dispersion pulse broadening occurs due to the fact that short wavelengths travel faster than long wavelengths. The exact opposite is shown in section 2.2.2, where SPM is responsible for shifting low frequencies and thus long wavelength to the front of the pulse (see figure 2.17 bottom), whereas the shorter wavelengths are moved to the trailing edge of the pulse. The superposition of these two effects results in a preservation of the pulse shape, i.e. the temporal intensity profile, as well as the optical spectrum of the pulse along the propagation distance. The condition for balancing GVD induced pulse broadening by means of the frequency variation due to SPM is that the dispersive length LD must be equal to the nonlinear length LNL. The propagating pulse is then called a fundamental soliton

LD N 2 = = 1, (2.26) LNL where the parameter N is referred to as the soliton order. Using equation

(2.20) and (2.22) the peak power P0 is determined by

|β2| P0 = 2 (2.27) T0 γ and thus a discrete pulse energy is given by a certain pulse width T0. The shape of a fundamental soliton is described by a hyperbolic secant function,

Figure 2.18: Optical spectrum of an erbium-doped ﬁber laser. The ﬁgure is taken from [18].

23 2 Theoretical Background which will be further discussed in section 2.3.1. Due to the stability of solitons the evolution and their propagation are not affected by small perturbation or deviations in peak power and thus in the soliton order N. [16] However, for small pulse durations, i.e. sub-picosecond pulse widths, spectral sidebands are generated. These sidebands, also called Kelly sidebands, are located in defined distances from the center wavelength. An example of the optical spectrum of an erbium-doped soliton laser including the characteristic Kelly sidebands is shown in figure 2.18. Kelly sidebands arise due to the fact that the soliton is influenced during one roundtrip by periodical perturbations in the cavity. These disturbances are represented on one hand by the amplification in the gain fiber and on the other hand in terms of losses arising, e.g. from the output coupler, free-space coupling sections and splices. After such a perturbation the soliton reshapes itself by depleting excessive energy into a dispersive wave co- propagating with the soliton. [19] In general, such a dispersive wave would not further affect the propagation of the soliton. But in cases where the relative phase per roundtrip between dispersive wave and soliton is an integer multiple of 2π both interfere constructively which results in a superposition visible in the optical spectrum. [18]

24 2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses

2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses

For characterizing mode-locked lasers and evaluating their operation state, it is necessary to measure various parameters with diﬀerent measurement equipment. The optical spectrum can be measured using an optical spectrometer and includes besides the wavelength also information about the pulse duration. The latter can be measured using an autocorrelator since the pulse durations of ultrashort pulses are beyond the response time of conventional photodiodes delivering electrically detectable power signals. Photodiodes in turn are used in combination with a spectrum analyzer for measuring the repetition rate of the pulse train in a radio frequency (RF) spectrum. Furthermore, a power meter can be used for determining the average output power with respect to the launched input power, which gives in combination with the repetition rate the corresponding pulse energies. Another important issue regarding the stability of the laser is its noise behavior, which in general is measured using a photodiode and additional analyzing equipment. Finally, long-term measurements regarding the mode-locking stability is also recommended, in order to ensure a reliable performance of the laser, which should resist environmental inﬂuences guaranteeing an operation without disturbances. The following four sections will explain these characterization methods in more detail.

2.3.1 Pulse Characterization

In section 2.1.2 it was already discussed and in equation (2.13) shown that mode-locked lasers with a broad optical spectrum, i.e. a large number of locked modes, produce very short pulses. An optical spectrometer is an instrument for measuring the intensity of incoming light with respect to the different wavelengths within the spectrum. Commonly, a movable grating diffracts the individual wavelengths on a detector. The light can be either coupled into the spectrometer using a free-space beam or directly via a fiber connector. From the recorded optical spectrum the center wavelength λ0 and the full width at half-maximum (FWHM) λFWHM, i.e. the wavelength range at half of the intensity, can be determined. Transfer- ring the wavelengths into frequencies using equation (2.9) the corresponding frequency value of the FWHM ∆νFWHM can be used in combination with the time-bandwidth product of a given pulse shape for identifying the lower limit

25 2 Theoretical Background

of the pulse duration T0. As already discussed in section 2.2.3 the shape of soliton pulses are well described by a hyperbolic secant function, so that the time-bandwidth product is given by [20]

∆νFWHM · T0 = 0.315. (2.28)

Hence, knowing the shape of the pulse and the FWHM of the optical spectrum results in a value for a pulse duration representing the lower limit. Such pulses are called transform limited pulses, i.e. they are unchirped. Unchirped pulses show no time dependency of the frequency or wavelength within the pulse duration. Such a time dependency can, as already discussed in section 2.2, be induced by SPM and dispersion. Due to the balancing of these two eﬀects solitons show the ability of producing almost transform limited pulses. However, it is necessary to measure the exact pulse duration to proof whether it is unchirped or how much chirp is present.

Photodiodes are not able to measure the duration of ultrashort pulses due to a slow response time compared to such a short event. One can overcome this restriction by using an autocorrelator in which the pulse itself works as a ruler for measuring its own duration. Such an instrument consists of a conventional Michelson interferometer, a nonlinear crystal and a photodetector. The Michelson interferometer splits the pulse train into two optical paths and recombines them again. The optical path in one arm is kept ﬁxed, whereas the other arm is equipped with a moving mirror. This allows a precise variation of the time in which the recombined pulses overlap and thus allows a time dependent scanning of one pulse over the other. A non-collinear focussing of the superimposing pulses on a nonlinear crystal, where the second harmonic is generated whenever the pulses overlap in time, allows a background-free measurement. The distance of the mirror movement can be transferred to a certain time delay τ, so that the intensity with respect to the time delay can be recorded. Finally, the FWHM of the intensity autocorrelation curve τFWHM, AC is directly correlated to the pulse duration T0. Again, the shape of the pulse plays an important role, so that a deconvolution factor is used for calculating the corresponding pulse duration from a certain intensity autocorrelation curve by [20]

τFWHM, AC = 1.542 · T0, (2.29) where the factor 1.542 is the deconvolution factor for a hyperbolic secant shaped pulse. The autocorrelator reported in [21] uses two parallel rotating mirrors rather than one moving mirror for inducing a continuous delay in order

26 2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses to display the autocorrelation trace on an oscilloscope. A corner mirror in the ﬁxed beam path of the Michelson interferometer is mounted on a translation stage. Tuning the position of this mirror results in a time variation of the autocorrelation trace. As in a conventional autocorrelator the displacement of the corner mirror can be transferred to a calibration factor which correlates the time delay of the pulse with the timescale on the oscilloscope. The detailed operation of this kind of autocorrelator will be further explained in section 3.3.

2.3.2 Output Power and Pulse Energy

The output power can be measured by a power meter, e.g. a thermopile. Such an instrument absorbs the incoming radiation and converts the resulting temperature diﬀerence to an electric signal. The internal wavelength depending calibration ﬁnally delivers the actual optical power Popt. The pulse energy Ep can thus be calculated by Popt Ep = , (2.30) frep where frep is the repetition rate. The repetition rate of a mode-locked laser can be measured by a photodiode, which detects each pulse of the pulse train, connected to an oscilloscope or a spectrum analyzer as shown in 2.19 (a). The oscilloscope gives the corresponding periodic signal in the time domain. In case of using a spectrum analyzer, which performs a fast Fourier transformation (FFT), the resulting signal is converted to the frequency domain. A perfect wave form in the time domain would correspond to a sharp peak in the frequency domain. However, due to noise the signal obtains sidebands, which cause a the frequency signal to broaden as shown in 2.19 (b).

2.3.3 Noise

Noise in mode-locked lasers is an undesired effect since it may influence the results of the particular application. In fact it can be reduced by various technical approaches but never vanishes completely. In general, noise arises from different sources, e.g. from instabilities of the pump source, acoustic vibrations, changes in ambient temperature and externally induced electrical influences as well as from amplification of spontaneous emission in the gain medium. For mode-locked lasers one distinguishes the amplitude noise and the phase noise. The amplitude noise represents random fluctuations of the pulse energy. Phase noise is represented by fluctuations of the phase of a wave resulting in a broad peak rather than a discrete line of the frequency

27 2 Theoretical Background

Figure 2.19: Pulse train detected by a photodiode in (a) and the spectrum analyzer’s signal in (b). The ﬁgure is adapted from [22]. spectrum as shown in ﬁgure 2.19. This section describes the measurement and characterization of these two types of noise.

Amplitude noise

Amplitude noise is measured in the frequency domain rather than an averaged power value for a defined duration. This offers the advantage of providing indi- cations for possible noise sources correlated with different frequencies. Hence, determining the predominating origin of the noise allows a systematic reduction by improving the setup. Examples for such frequency depending noise sources are relaxation oscillations, power supplies, vibrations or electromagnetic influences. Relaxation oscillations are correlated with the lifetime of the excited state in the gain medium and appear as a broad peak. Noise from power supplies is located at multiples of 60 Hz or several tens or hundreds of kilohertz and is visible as discrete spectral lines. Finally, vibrations or electromagnetic influences appear as spurious lines. [22] Furthermore, amplitude noise is defined in a relative expression in order to be able to easily compare different measurements, taken with different equipment and laser systems at different power levels. Hence, the relative intensity noise (RIN) is defined as [22] 2 Popt(f) RIN(f) = , (2.31) Popt, c where Popt(f) is the optical power spectrum per 1 Hz bandwidth with the unit dB/Hz and Popt, c is the average output power. Thus, the signal is normalized to the carrier power and is expressed by the unit dBc/Hz. Since the squared

28 2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses optical power is proportional to the electrically detected power [22] equation (2.31) can be written as P (f) RIN(f) = , (2.32) Pc where P (f) is the power spectral density (PSD), i.e. the frequency depending electrical power in 1 Hz bandwidth with units dB/Hz and Pc is the electrical DC power of the carrier in unit dB. While P (f) can be measured by a vector signal analyzer in combination with an irradiated photodiode, the carrier power can easily be determined by connecting the photodiode output to a voltmeter. The electrical carrier power is calculated from

V 2 Pc = , (2.33) Ri where V is the measured voltage and Ri represents the input resistance which is typically 50 Ω. It should be pointed out that it is necessary to transfer PDC to dB units using equation (2.8) before calculating the RIN with equation (2.32). Finally, the RIN in dBc/Hz as a function of the frequency can be plotted using a logarithmic scale. Solving equation (2.8) to P in W the equation can be used to transfer the RIN(f) from dBc/Hz to 1/Hz units, so that the RIN curve can be integrated over a deﬁned frequency range. Applying the square root and multiplying the value with 100 result in a ﬁnal root-mean-square (RMS) amplitude noise value in % RMS s Z fmax RIN%RMS = 100 · RIN(f). (2.34) fmin

Phase Noise

Random phase variations create sidebands in the frequency domain due to ﬂuctuations in the time domain, i.e. instead of a single spectral line the bandwidth of the frequency signal is broadened. A varying pulse period TR in mode-locked lasers, e.g. due to temporally induced variations of the cavity length, thus introduces a phase noise which is related to a timing jitter. For phase noise measurements it is necessary to isolate the phase noise from the random amplitude ﬂuctuation of a periodic signal. In a phase noise analyzer this separation is achieved by mixing the signal from the device under test, i.e. the periodic signal on an irradiated photodiode by a mode-locked laser, with that of a tunable and highly stable reference oscillator. The latter is tuned in such a way that both oscillators provide identical frequencies. A balanced mixer performs a multiplication of the two wave signals and introduces a 90◦

29 2 Theoretical Background phase shift. The resulting signal is directly correlated with a phase difference, where a perfect match of the two oscillator signals would correspond to 0 V. Hence, phase variation can be directly detected with a spectrum analyzer, which provides in practice a phase noise measured at different offset frequencies of the carrier frequency. This measured phase noise is represented as the single sideband (SSB) power spectrum in 1 Hz bandwidth relative to the carrier with units dBc/Hz and is denoted as L(f). For proper phase noise measurements the signal of the photodiode needs to be amplified to a value within the detection range of the phase noise analyzer. Furthermore, the frequency of the signal needs to be bandpass filtered to the fundamental repetition rate of the laser or any of its harmonics. Finally, L(f) can be transferred to an integrated

RMS timing jitter ∆tRMS in a deﬁned range of frequencies by [22] s 1 Z f2 ∆tRMS = 2 L(f)df, (2.35) N2πfrep f1 where N is the number of the harmonic of the fundamental repetition rate frep. The frequency range for integrating the RMS timing jitter of mode-locked lasers is commonly f1 = 10 kHz to f2 = 10 MHz.

2.3.4 Mode-locking Stability

During the operation of regenerative amplifiers it is crucial to ensure a stable operation state of the seed oscillator. Especially during the transition from CW to mode-locking operation spikes with high peak power may appear, which experience amplification and could damage sensitive components of the regenerative amplifier. The mode-lock detector is a device providing a monitor for the mode-locking state, for various power values, e.g. the oscillator output and the pump power, and offers a relay for switching off the pump if the seed’s mode-locking operation is interrupted. In principle, the mode-lock detector consists of a photodiode detecting the periodic pulse train of the oscillator. This power signal is filtered in the frequency domain by two bandpass filters separating the signal into two parts, the noise and the carrier power. The noise signal obtains the power in the lower frequencies around 10 Hz to 100 kHz, while the carrier power is measured at the repetition rate of the oscillator. In cases where the oscillator works in the mode-locking regime the carrier power is high compared to the power of the noise signal. Whenever the mode-locking state is lost the carrier power drops and the noise power dominates.

30 3 Experimental Setup

The experimental setup of the passively mode-locked holmium-doped soliton fiber ring oscillator and its characterization can be divided in three sections. It consists of two closed boxes, i.e. one for coupling the pump laser into fiber and the other for the oscillator itself. The third section represents a setup of different measuring devices. A photograph of the setup including the pump, oscillator and characterization section as well as the mode-locked detector is shown in figure 3.1. This chapter will present the construction of those three sections as well as the assembly of the mode-lock detector.

Figure 3.1: Photograph of the setup including pump, oscillator and characterization sections. PD: Photodiode; AC: Autocorrelator.

31 3 Experimental Setup

3.1 Available Components

The main components used for the construction of the passively mode-locked holmium-doped soliton fiber ring oscillator are listed in table 3.1. Since the pump laser is equipped with a fixed output collimator it is necessary to couple the free-space beam into the fiber, rather than splicing a bare fiber tip directly to the input of the oscillator. Hence, all mechanical and optical components used for coupling the pump light into the oscillator are located on a separated breadboard and are isolated by a box. In the following this is referred to as the pump section. A schematic drawing is given in figure 3.2 and a photograph of the opened housing is depicted in figure 3.3. The linear polarized output of the pump laser passes a half-wave plate and meets a thin-film polarizer (TFP) in a 65◦ angle. Rotating the half-wave plate (HWP) allows for precise power adjustments due to the polarization depending reflectivity or transmission of the polarizer. Vertically polarized (i.e. s-polarized) light is completely reflected, whereas horizontally polarized (i.e. p-polarized) light passes the TFP. The transmitted beam is absorbed by a beam block and the reflected beam travels through a telescope. It consists of a combination of plano-convex lenses with focal lengths of 100 mm and 50 mm for reducing the beam diameter to the half of its initial size from 5 to about 2.6 mm. The alignment is carried out using a camera for observing

Figure 3.2: Schematic drawing of the pump section. HWP: half-wave plate; TFP: thin-ﬁlm polarizer; QWP: quarter-wave plate; SMF: single- mode ﬁber; ND attenuator: neutral-density attenuator; PD: photodiode; MLDET: mode-lock detector.

32 3.1 Available Components the beam diameter in various distances for collimating the beam. The beam diameter after the telescope is shown in figure 3.4 (a). Two mirrors fixed in mountings with adjustable screws allow a precise manipulation of the beam for coupling into the fiber. Before, the beam passes a quarter-wave plate (QWP) for changing the polarization state from linear to elliptical polarization. The SMF is fixed using copper tape and a magnetic stripe in a V-groove, which is screwed on an XYZ translation stage. The beam is coupled into the fiber using a coated aspheric lens with a focal length of 11 mm. A more detailed explanation of the procedure for efficient fiber coupling is given later. The SMF is spliced to a series of fiber couplers with different splitting ratios. 80 % of the coupled power is directly delivered to the oscillator. The resulting 20 % power is divided again, where 90 % of the power is used for observing the coupled power with a power meter and the output of the 10 % port is attenuated by a neutral density (ND) attenuator before it is focussed on a photodiode. In the final setup the ND attenuator is replaced by bending and glueing the fiber on a post to introduce a certain amount of bending loss, which prevents the photodiode from saturation. Finally, the fiber tip is spliced to an FC/APC (Fiber-optic Connector with Angled Physical Contact) fiber connector, which is directly attached to the photodiode of the mode-lock detector. For reducing Fresnel reflections on the surface of the fiber tip is cleaved with a 7.6◦ angle. A photograph of the fiber tip placed inside the splicer and the resulting measurements of the angle are given in figure 3.4 (b)

Figure 3.3: Photograph of the pump section.

33 3 Experimental Setup

Component Company Main parameters Pump laser IPG λc=1938 nm, Pmax=10 W, øbeam=5 mm ◦ TFP Layertec θi=65 SMF Thorlabs NA=0.11, øcore=11 µm, øclad=125 µm 80/20 coupler AFR Pthreshold=10 W Other couplers AFR Pthreshold=400 mW WDM Gooch & Housego α1940 nm=23 dB, α2050 nm=0.4 dB HDF Nufern NA=0.15, øcore=10 µm, øclad=130 µm Faraday isolator EOT øaperture=4 mm, T=89%, αiso=30 dB Isolator Thorlabs øaperture=3.6 mm, T=88%, αiso=33 dB NB ﬁlters Spectrogon λc=2050 nm and λc=2080 nm

Table 3.1: List of the oscillator’s main components and their specification. and (c), respectively. In figure 3.5 the procedure of coupling the pump laser beam into the fiber is illustrated. As a first step the XYZ translation stage is roughly adjusted using the three provided micrometer screws. This is done in such a way that an FC/APC fiber holder can easily be moved through the profile. The fiber holder functions as an aperture and is moved several times from the front to the back during the beam adjustments. While mirror 1 is used for guiding the beam through the aperture when it’s located in the front position, mirror 2 is adjusted for the case the fiber holder is in the back position. The power meter behind the translation stage is used for observing the power until it shows similar maximum values for both positions of the aperture. Hence, the beam

Figure 3.4: (a) Shows the beam profile after the telescope, (b) gives a top view of two fiber tips, i.e. one flat side for splicing and one angle- cleaved side used for coupling and (c) depicts the fiber characteristics of the angle-cleaved fiber tip measured by the splicer.

34 3.1 Available Components is centered and horizontally aligned with respect to the XYZ translation stage. As a next step the fiber holder is removed and replaced by the V-groove as can be seen from figure 3.3 including the fixed fiber. Furthermore, the focussing lens with 11 mm focal length is screwed on the fixed part of the translation stage. Since the power meter doesn’t provide a fast and sensitive response it is replaced by a photodiode connected to an oscilloscope and the X Y and Z position is tuned for optimizing the signal. By measuring the power before focussing and at the end of a short fiber segment the coupling efficiency is maximized to about 72 %. Finally, the remaining fiber components are spliced to the fiber. The breadboard is put on a foam with lead inside for reducing acoustical and mechanical vibrations. Furthermore, a housing is constructed around the pump section. It consists of a framework of rails fixed on the breadboard with foam tape in between. Acrylic glass with a layer of dense rubber tape for blocking acoustical vibrations from outside and preventing scattering light from inside to exit is fixed to the rails using wing nuts and washers screwed to threaded bolts, which are inserted into the rails. The bare fiber terminations leave the housing at two locations. On one hand the output fiber is fixed between two washers and is guided in between the foam tape and the breadboard (see figure 3.3 on the left) towards the oscillator. On the other hand the two monitoring ports, i.e. the 90 % and 10 % outputs from the coupler, share the slit in the front of the housing for leaving the box, which initially serves as the input of the yellow pump fiber as shown in figure 3.1.

Figure 3.5: Photograph of the ﬁber coupling.

35 3 Experimental Setup

3.2 Oscillator

The oscillator consists of different fiber segments and fiber components as well as optical free-space paths as illustrated in the schematic drawing in figure 3.6. The fiber from the pump section is guided into the oscillator section and is directly spliced to the input port of the WDM which provides low losses for the pump wavelength, i.e. 1940 nm. Hence, the output port of the WDM is spliced to an 88 cm fiber segment, which is doped with holmium ions and thus represents the active gain in the oscillator. Although the SMF output of the WDM and the HDF vary slightly in their cladding and core diameters (see table 3.1) the splicing results in a proper fusion of the fiber segments as can be seen from figure 3.7. The end of the HDF is angle-cleaved and fixed in a V-groove on an XYZ translation stage. Furthermore, the output beam is collimated by a coated aspheric lens with a focal length of 4 mm. The beam is coupled back into a 214 cm SMF segment provided with an FC/APC connector using another XYZ translation stage which is equipped with the same type of lens and a fiber holder. In between this free-space path the artificial saturable absorber, i.e. a combination of QWP, HWP, Faraday isolator and a second QWP, is positioned, where the first polarizing beam splitter (PBS) of the Faraday isolator serves as the output coupler of the mode-locked laser. The SMF is spliced to a fiber coupler with 99:1 splitting ratio, where the 99 % port is spliced to the remaining input port of the WDM providing low losses for the lasing wavelength, i.e. 0.4 dB for 2050 nm, and high losses for the pump light,

Figure 3.6: Schematic drawing of the oscillator.

36 3.2 Oscillator

Figure 3.7: Photograph before (a) and after (b) the splicing process of the SMF from the WDM output (left fiber) to the HDF (right fiber). i.e. 23 dB for 1940 nm. Eventually, the ring of the oscillator is closed and the remaining pump light is removed from the cavity. The 1 % port is spliced to another fiber coupler with a 50:50 splitting ratio providing two monitoring ports for observing the optical spectrum and power level inside the ring oscillator. In order to prevent back reflections into the oscillator a second isolator is placed behind the output coupler followed by a combination of narrow bandpass (NB) filters used for removing the Kelly sidebands of the soliton spectrum. The NB filters provide different central wavelengths and transmitting bandwidths, i.e. 2050 nm and 2085 with 12 nm and 10 nm, respectively. Since the second bandpass filter is optimized for a larger center wavelength compared to the laser’s operation wavelength at 2050 nm it is arranged in an angled position, which allows for the transmission of lower wavelengths. Finally, the output beam is coupled into fiber using a mirror and a third translation stage equipped with a coated aspheric lens with 11 mm focal length and an FC/APC fiber holder. From figure 3.8 it can be seen that in order to characterize the parameters of the mode-locked oscillator the free-space beam is temporarily guided directly through a hole in the oscillator housing rather than coupled into fiber. The conditions for initiating mode-locking are on the one hand that the pump power inside the cavity has to be high enough to overcome the lasing threshold and provides enough power for starting the evolution of a dominating polarization direction inside the fiber caused by the Kerr effect. On the other hand the three waveplates of the artificial saturable absorber have to be orientated in such a way that the preferred polarization is transmitted through the output coupler, i.e. the first polarizer of the Faraday isolator, and thus maintains inside the cavity, whereas other polarization states are reflected and removed from the cavity. It should be pointed out that there is not only one perfect combination of waveplate orientations leading to the evolution of ultrashort lasers pulses thus there are multiple combination possibilities for initiating mode-locking. For starting mode-locking a random fluctuation is

37 3 Experimental Setup required which causes longitudinal modes to match in phase what allows them to interfere coherently. However, simple increasing of the pump power doesn’t result in self-starting of the oscillator. In fact, mode-locking is achieved by fast changes in the optical path length of the cavity due to induced birefringence in the gain fiber. This is achieved by carefully touching or bending the gain fiber in a case where the waveplates are properly orientated and a certain pump power is provided to allow a soliton pulse to evolve. Just like the enclosing box of the pump section, the housing of the oscillator is provided with foam tape between breadboard and rails. This allows for decoupling possible mechanical vibrations induced on the wall and guided to the breadboard thus also directly to the fiber since it is directly fixed on the breadboard using kapton tape. Since the delivery fiber from the pump section is guided underneath a rail and is fixed between two washers (see figure 3.8 on the right) the foam tape also provides a smooth and safe environment between breadboard and rail. As can be seen in the top right corner of figure 3.8 the housing is screwed to the breadboard with compact table clamps inserted in the profile of the rails. For the output and the monitoring ports holes are drilled into the wall of the box into which FC/APC fiber connectors are mounted.

Figure 3.8: Photograph of the oscillator.

38 3.3 Measurement Setup

3.3 Measurement Setup

To characterize the constructed mode-locked laser different kinds of measuring equipment are set up that allow for simultaneous measurements of various laser parameters, e.g. the output power, the repetition rate, the optical spectrum and the pulse duration. A schematic drawing of the setup is illustrated in figure 3.9 and an overview of the diagnostic tools used including their specifications is given in table 3.2. The free-space beam leaving the oscillator passes a HWP and is split by a PBS into two beams, where the power of each path is adjustable through the HWP. The power of the reflected beam is reduced by an ND attenuator and focussed by a lens with a 50 mm focal length on a photodiode. Two types of photodiodes, i.e. either a fast or a slow one, are used for the measurements depending on the device connected. On one hand for measuring the repetition rate with a spectrum analyzer the fast photodiode is used offering a cutoff frequency of more than 12.5 GHz. On the other hand in case of amplitude noise measurements the slow photodiode with a cutoff frequency of 140 MHz in combination with a transimpedance amplifier delivers low noise and a high sensitivity in combination with a vector signal analyzer. Phase noise measurements are carried out using the fast photodiode connected to a series of bandpass filters and an amplifier for filtering the fundamental harmonic and amplifying the power signal to the operation range of the phase noise analyzer, respectively. The beam that is transmitted through the PBS is adjusted to the height

Figure 3.9: Schematic drawing of the characterization section.

39 3 Experimental Setup

Device Company Main parameters Power meter Gentec Thermopile, Pmax = 30 W Photodiode Newport InGaAs, fcutoﬀ > 12.5 GHz Photodiode Hamamatsu InGaAs, fcutoﬀ = 140 MHz Spectrometer Ocean Optics NIRQuest, λrange: 1890 - 2140 nm Oscilloscope R&S fmax = 100 MHz Spectrum analyzer Rigol frange: 9 kHz - 1.5 GHz Vector signal anaylzer Agilent/HP frange: DC - 10 MHz Phase noise analyzer Holzworth 0 < Pinput < 20 dBm Autocorrelator Femtochrome LiIO3 crystal, Si Photodiode

Table 3.2: List of the diagnostic tools used for characterizing the mode- locked laser. of the autocorrelator’s input and is brought to a horizontal propagation with respect to the optical table by means of two mirrors. Before entering the autocorrelator a small fraction of the beam power is reflected by a wedge and propagates into the spectrometer. For observing the optical spectrum inside the oscillator cavity rather than the bandpass filtered output spectrum a patch cable can be connected between one of the monitoring ports and the spectrometer. The second monitoring port is connected via fiber to the photodiode of the mode-lock detector. The remaining power transmitted by the wedge passes

Figure 3.10: Photograph of the characterization section.

40 3.3 Measurement Setup a HWP, which rotates the linear polarization to s-polarization, and is guided into the autocorrelator. Since the beam is split, recombined and focussed into a nonlinear crystal the alignment of the autocorrelator with respect to the incoming beam requires careful handling and patience.

As a first step the autocorrelator is aligned horizontally setting three foot screws while measuring the alignment with a bull’s eye spirit level. Further- more, the orientation of the autocorrelator is adjusted so that the beam passes the center of the input aperture. Aligning the autocorrelator is carried out first regarding the reference path, which is transmitted by the beamsplitter and should hit the left side of the first mirror. This allows the returning beam from the corner mirror to come back on the right side of the first mirror as depicted in figure 3.9. At this point the autocorrelator’s orientation is well aligned and is clamped to the optical table. The returning reference path is reflected by the beamsplitter and is focussed downwards by a concave mirror into a nonlinear crystal thus the fundamental beam appears on the right side next to the aperture of the photodiode. The delayed beam, which is initially reflected by the beamsplitter, travels through the combination of rotating parallel mirrors representing the continuous path length variation and hits a long horizontally aligned mirror. Due to the rotation of the two parallel mirrors the beam is horizontally scanned over this mirror. Its orientation is adjusted using two set screws for manipulating the reflected beam in such a way that after passing the rotating mirrors again it transmits through the beamsplitter and is focussed by the concave mirror into the nonlinear crystal. In this case the fundamental harmonic of the delayed beam appears on the left side next to the photodiode. This non-collinear superposition allows for background-free measurements since the generated second harmonic (shown as a green beam in figure 3.9) travels in the center of both fundamental beams directly pointing on the photodiode.

Measurements are carried out by detecting two types of signals from the autocorrelator with an oscilloscope. While one channel is fed with a trigger signal with a duration corresponding to the rotation frequency of the parallel mirrors, the second signal corresponds to the power of the second harmonic detected by the photodiode. This signal will only appear if the two beams are well aligned and the phase matching angle of the crystal is correct. The latter can be tuned with a micrometer screw which causes a rotation of the nonlinear crystal. In this application a maximum signal on the oscilloscope is achieved by setting the screw to 2.81 mm. Finally, the symmetric autocorrelation curve on the oscillator contains information about the pulse duration. For calculating

41 3 Experimental Setup the pulse width a calibration factor needs to be determined used for converting the ms timescale on the oscilloscope, which shows multiple pulses scanned over the reference pulses, into the actual timescale determining the pulse duration during which a superposition of reference and delayed pulses generate the second harmonic. The calibration factor is determined by moving the corner mirror over a certain distance what causes a shift of the autocorrelation curve on the oscilloscope. As shown in ﬁgure 3.11 a mirror displacement of s = 6.6 mm results in a time shift of t = 1.464 ms on the oscilloscope. Since the beam in the reference path moves twice the increased distance the induced delay in the time domain corresponds to

2s τ = = 44.03 ps. (3.1) c

Finally, the calibration factor is determined to be

τ 44.03 ps = = 30.075 ps/ms, (3.2) t 1.464 ms which can be used for transferring the timescale of the oscilloscope and thus allows for determining the FWHM of the autocorrelation curve τFWHM, AC con- taining the actual pulse duration according to equation (2.29). In conclusion, the setup depicted in ﬁgure 3.10 allows for simultaneous measurements for characterizing the mode-locked laser pulses.

Figure 3.11: Determination of the calibration factor by moving the corner mirror of the autocorrelator.

42 3.4 Mode-lock Detector

3.4 Mode-lock Detector

In general, the mode-lock detector consists of four stacked printed circuit boards (PCB) and offers two input photodiodes for detecting the oscillator and pump power. Functioning as the fundamental PCB the photodiode board is located at the bottom of the stack collecting the oscillator’s power on a photodiode. The detected signal is amplified and split, where one of the signals is bandpass filtered by an LC circuit particularly working at the oscillator’s repetition rate. This signal is referred to as the carrier power. The second portion of the split power signal is directed to the second PCB, i.e. the noise board. It filters the signals in the lower frequency range which represent the noise power. Furthermore, the noise board provides an additional photodiode for detecting the pump light. Analog signals from the first and second PCB are transferred to the third, i.e. the micro controller board. It contains several analog-to- digital converters (ADC), which deliver the digital data to a micro controller. It transfers the raw ADC values into power values in dBm units according to a programmable calibration and visualizes both of them on the display of the top PCB as shown in figure 3.12. Furthermore, the micro controller board detects the actual operation, e.g. high (low) carrier power for mode-locking (CW), and switches a relay in case of changing states.

Figure 3.12: Photograph of the mode-lock detector while the oscillator is working in the mode-locking operation indicated by the large carrier power and low noise power.

43 3 Experimental Setup

Soldering the surface-mount components, i.e. resistors, capacitors, inductors and light-emitting diodes (LED), on the PCB is carried out by diluting tin-solder on the solder pads with an electrically driven syringe, placing the components on the corresponding positions and carefully laying the prepared PCB into a soldering bath. After the soldering process additional components that obtain a larger size, i.e. capacitors and inductors as well as photodiodes, test points, wire, the power supply connector, coaxial RF and other connectors used for transferring signals to the different PCB, are soldered using a conventional soldering machine. Finally, the four PCB are connected and screwed together as shown in figure 3.13. The transformation of raw ADC to dBm power values relies on calibration factors stored in the micro controller, which can be set via serial connection to a computer and sending defined commands to the micro controller. The adjustment is carried out by measuring the oscillators output power and the input power before coupling into the fiber with a power meter and combine the measured values with the corresponding raw ADC values so that finally the values on the display correspond to the power measurements.

Figure 3.13: Photograph of the stack of PCB with the photodiode board on the top. The photodiode (PD) is not yet soldered and the output not yet connected to the micro controller board. Bandpass ﬁltered voltage signals corresponding to the carrier power can be measured using the test point.

44 4 Results and Discussion

This chapter will present and discuss the characterization of the pulse, the noise measurements and the long-term stability of the mode-locking state. For the pulse characterization the optical spectrum, the pulse duration, the repetition rate and the output power are measured. Noise measurements are carried out in terms of relative intensity noise and phase noise.

4.1 Pulse Characterization

In this section the results for the measured optical spectrum, the pulse duration and the pulse energy will be presented and discussed.

4.1.1 Optical Spectrum

During the attempts of initiating mode-locking with random adjustments of the three waveplates of the artificial saturable absorber the CW peak in the optical spectrum changes its center wavelength depending on the orientation of the waveplates. With the waveplates in an appropriate orientation with respect to each other as well as to the incoming polarization the laser starts mode-locking at a pump power of about 2 W and by carefully penetrating the gain fiber. 2 W pump power corresponds to about 1.1 W in the cavity assuming a coupling efficiency of 72 % and 20 % power coupled to the monitoring ports. Mode-locking is indicated by a rapid broadening of the CW peak around its initial center frequency and an appearance of Kelly sidebands. As the position of the CW peak in the optical spectrum is tunable, so is the center wavelength of the mode-locking operation. Figure 4.1 shows five soliton spectra at different center wavelengths (the blue spectrum for the shorter and red for the longer wavelengths) with a normalization with respect to the intensity at 2060 nm. The center wavelength of the mode-locked oscillator is tuned over a 20 nm range from 2045 up to 2065 nm. Each of the spectra is recorded by interrupting the mode-locking state, tuning the waveplates roughly thus the CW peak changes followed by gentle tuning while touching the gain fiber until the oscillator starts mode-locking. Tuning the center wavelength without

45 4 Results and Discussion

Figure 4.1: Optical spectrum tuned to different center wavelengths by changing the wave plate combination. losing mode-locking is also achieved in a range of approximately 5 nm by gently changing the HWP and adjusting the other two QWP simultaneously. Since the regenerative amplifier operates at a center wavelength of 2050 nm further pulse characterization is carried out for soliton pulses tuned to this particular center wavelength. The final values for the angles read from the ◦ ◦ mounting of the different waveplates are QWP1 = 54 , HWP = 194 and

Figure 4.2: Optical spectrum with diﬀerent bandpass ﬁlters.

46 4.1 Pulse Characterization

◦ QWP2 = 191 where the subscript numbering corresponds to the direction of the beam propagation. The evolved polarization inside the fiber depends on the placing and fixation of the fibers on the breadboard. Any change of the orientation of the fiber will change the birefringence and thus those values may change if the fiber was rearranged. Furthermore, the Kelly sidebands are removed using different bandpass filters as shown in figure 4.2. For each recorded spectrum the total output power and the FWHM of the optical spectrum are measured. The spectra are normalized to the intensity of the unfiltered spectrum at 2050 nm. With a pump power of 2 W and without any bandpass filters used the output power is 440 mW and the FWHM is 7.3 nm. Not shown in figure 4.2 is that this spectrum also contains pump light. Placing one bandpass filter removes the pump light completely and causes a significant reduction of the Kelly sidebands with resulting 59 mW output power and 6.2 nm FWHM. Finally, the Kelly sidebands vanish by placing a second bandpass filter in an angled position with an output power of 37 mW and 5.2 nm FWHM. In the following measurements of the autocorrelation, the power and the amplitude noise the color definition from figure 4.2 is preserved regarding the different bandpass filtered pulses.

4.1.2 Autocorrelation

Pulse width measurements are carried out saving the autocorrelation curve on the oscilloscope with a time resolution of 100 µs/div. The time domain is transferred by multiplying the data with the calibration factor derived in equation (3.2). Furthermore, the intensity of the peak of the autocorrelation curve is normalized and shifted to 0 s. Finally, the FWHM of the autocorrelation curve is measured and used for calculating the duration of the soliton pulse according to equation (2.29). In addition, the transform limit is calculated using equation (2.28) based on the FWHM of the optical spectrum in figure 4.2 and is plotted with dashed lines. The autocorrelation curve of the soliton with an unfiltered optical spectrum is depicted in figure 4.3 with a pulse duration of 860 fs and a transform limit of 605 fs. Clearly visible is a ringing background arising from the Kelly sidebands with longer pulse durations. The autocorrelation curve is slightly asymmetric due to imperfections in the alignment of the autocorrelator. Output pulses transmitted through one bandpass filter produce the autocorrelation curve shown in figure 4.4. The decrease in FWHM of the optical spectrum increases the pulse duration to 1020 fs with a transform limit of 710 fs.

47 4 Results and Discussion

Figure 4.3: Autocorrelation without bandpass ﬁlters.

Finally, in ﬁgure 4.5 the autocorrelation curve of the soliton pulses with completely removed Kelly sidebands using two bandpass ﬁlters is illustrated. The pulse duration is increased to 1225 fs with a transform limit of 850 fs. In general, the measured pulse durations are larger than the transform limits thus the pulses are chirped. Comparing the pulse duration measurements to the corresponding transform limits by dividing transform limit through measured pulse duration give a percentage value of about 70 %.

Figure 4.4: Autocorrelation with 2050-12 bandpass ﬁlter.

48 4.1 Pulse Characterization

Figure 4.5: Autocorrelation with 2050-12 and 2085-10 bandpass ﬁlter.

4.1.3 Pulse Energy

The pulse energy of the soliton without Kelly sidebands (black curve in ﬁgure 4.2) is determined with respect to the input power using a power meter. Each measured power value can be transferred to a pulse energy in combination with the repetition rate of the oscillator according to equation (2.30). First of all the repetition rate is measured with the fast photodiode attached to the spectrum analyzer. The repetition rate is measured to be f0 = 55 MHz with a resolution bandwidth (RBW) set to 100 kHz. With an output power of 37 mW the electrical power in the spectrum analyzer is −22 dBm. As can be seen from ﬁgure 4.6 the harmonics appear over the full span width without peaks in between and an almost constant electrical power indicating proper mode-locking. Next the mode-locking threshold is determined by reducing the input power using the HWP and TFP combination in the pump section, i.e.

Figure 4.6: RF spectrum.

49 4 Results and Discussion rotating the HWP until mode-locking drops into CW mode. The corresponding threshold power represents the starting point of the slope efficiency curve in figure 4.7. It shows the measured output power on the left axis and the calculated pulse energy on the right axis with respect to the input power. The input power is measured with a power meter before the fiber coupling lens in the pump section, the output power is measured behind the two bandpass filters in the oscillator section. All these measured values have been verified with those shown on the display of the mode-lock detector. Since the output beam is blocked by the power meter the optical spectrum is observed using the fiber coupled monitor port. With an increase of the pump power the pulse propagating in the oscillator increases in terms of energy. Due to Kerr non- linearity this results in a change of the evolved polarization state thus the waveplates of the artificial saturable absorber require an adjustment for reach- ing the maximum possible pulse energy. Furthermore, an increase of pump power causes a shift of the center wavelength to larger values. Rotating the HWP of the artificial saturable absorber clockwise (with respect to the beam propagation direction) brings the center wavelength back to its initial value of 2050 nm. Tuning the second QWP also clockwise reduces the Kelly sidebands of the soliton pulse oscillating in the cavity without changing the center wavelength and results in a maximized output power. As shown in figure 4.7 the output power increases linearly from about 1 to 2 W pump power with a slope of 2.38 % to almost 40 mW corresponding to approximately 700 pJ. Within this power regime the mode-locking is quite stable against externally

Figure 4.7: Slope eﬃciency and output beam diameter.

50 4.1 Pulse Characterization induced influences, such as bumping the optical table, clapping hands and slight knocking the oscillator’s housing. Further increase of the pump power up to more than 3 W increases with a lower slope. However, in this pump regime the mode-locking operation becomes much more sensitive to external influences thus mode-locking easily drops to CW operation. Also reinitiating mode-locking becomes more difficult thus it is more easy to tune the center wavelength to about 2060 nm in CW mode using the HWP and reduce the center wavelength again after mode-locking is initiated. Furthermore, the absolute limit is reached for pump powers of 3.2 W and leads to a maximum output power of 50 mW corresponding to 900 pJ. Further increase of the pump power either doesn’t even support mode-locking at 2050 nm or ends up in multi pulsing, i.e. more than one pulse is oscillating in the cavity. This is clearly visible in the RF spectrum as additional spikes in between the harmonics appear or in the optical spectrum as a superposition of two soliton spectra, where one is slightly shifted in the center wavelength.

51 4 Results and Discussion

4.2 Noise

This section will show and discuss the results for amplitude noise measurements regarding different bandpass filtering arrangements and different power regimes of the pump laser as well as phase noise measurements.

4.2.1 Relative Intensity Noise

The relative intensity noise measurements are carried out first by measuring the DC voltage with a voltmeter connected to the output of the slow photodiode and transimpedance amplifier combination. Next the voltmeter is removed and the output is connected to the input of the vector signal analyzer, which measures the PSD in dBm/Hz. Measurements are carried out in multiple steps over defined frequency ranges with increasing RBW settings in order to plot the results over a logarithmic frequency range. The resulting PSD measurements are stitched together and transferred to RIN values according to equations (2.32) and (2.33) thus the results are plotted over the full frequency range from 1 Hz to 10 MHz in a logarithmic scale. In general, all RIN plots include the noise floor which results from measurements with a blocked photodiode. The RIN of differently bandpass filtered output pulses, i.e. with and without Kelly sidebands as shown in figure 4.2 are measured. Furthermore, RIN measurements are carried out to compare the completely filtered output soliton with the pump running in low and high power operation. In both cases the input power of the oscillator is maintained equal thus in case of the high power operation of the residual power is dumped to the beam block using the HWP and TFP combination in the pump section.

Inﬂuence of sideband ﬁltering on the RIN

The top of figure 4.8 shows the three measured RIN curves measured at the oscillator output with different bandpass filter configurations for suppressing the Kelly sidebands. In general, for all curves noise is dominated in the frequency range from 1 to 10 Hz due to mirror vibrations and acoustical noise. Discrete spectral lines appear in the range from 30 Hz to 20 kHz induced by the power supply. Especially, the spike at 60 Hz is clearly visible. Furthermore, the broad peak between 100 an 200 kHz, i.e. the relaxation oscillation, is the main source of amplitude noise. At higher frequencies the noise drops to less than −130 dBc/Hz but doesn’t reach the noise floor at −145 dBc/Hz. Com- plete bandpass filtering results in a −10 dB offset with respect to the unfiltered curve. Finally, the relaxation oscillation peak is reduced by 20 dB.

52 4.2 Noise

Figure 4.8: Relative intensity noise of the oscillator output with diﬀerent narrow bandpass ﬁlters.

Using equation (2.34) the integrated RIN in %RMS is plotted from high to low frequencies with respect to the right axis in the bottom of figure 4.8. Filtering the Kelly sidebands results in a reduction from 0.95 %RMS down to 0.13 %RMS, which is sufficiently low for seeding regenerative amplifiers.

Inﬂuence of the pump operation

For comparing the inﬂuence of the pump operation, measurements at the 10 % monitoring output in the pump section as well as at the oscillator output are carried out. In the measurements the pump runs at 35 % and 60 % of the pump current. The power inside the cavity is kept in both cases at the same value by dumping the residual power to the beam block behind the TFP in the pump section. In the following RIN plots the pump is shown in black and

53 4 Results and Discussion

Figure 4.9: Relative intensity noise of the pump at 35 % and the oscillator output. the oscillator in blue. Comparing figure 4.9 and 4.10 it is noticeable that increasing the pump operation state on one hand reduces the spurs in the region from 30 Hz to 20 kHz for both, the pump and the oscillator RIN curve. On the other hand the relaxation oscillation of the pump is slightly reduced by about 4 dB. Still, this causes the relaxation oscillation coupled to the oscillator to significantly decrease by about 10 dB. In contrast to the oscillator the RIN of the pump approaches the noise floor at about 1 MHz. In case of low pump power operation the integrated RIN is calculated to 1.08 %RMS for the pump and 0.13 %RMS for the oscillator. For high pump power operation in turn the integrated RIN is calculated to 0.84 %RMS for the pump and 0.07 %RMS for the oscillator. Nevertheless, significant longterm fluctuations of the pump power appear

54 4.2 Noise

Figure 4.10: Relative intensity noise of the pump at 60 % and the oscillator output. at higher pump currents, which even cause the oscillator to lose mode-locking if the waveplates of the artiﬁcial saturable absorber in the oscillator section (as explained in section 4.1.3) or the HWP in the pump section were not readjusted. Hence, although the integrated RIN is lower it is not recommended to operate at high pump power.

4.2.2 Phase Noise

As explained in section 2.3.3 phase noise measurements require bandpass filtering of one harmonic in the RF spectrum and amplifying the signal to the detection range of the phase noise analyzer. As can be seen from the inset of figure 4.11 the RF spectrum is filtered to the fundamental harmonic. The second harmonic is suppressed of more than 30 dB, whereas the third doesn’t

55 4 Results and Discussion

Figure 4.11: Phase noise and RF spectrum. appear at all. Compared to figure 4.6 the signal is amplified from −22 dBm to 10 dBm, which matches the phase noise analyzer’s detection range, as can be seen from table 3.2. The resulting measurements for the SSB phase noise is shown in figure 4.11. It can been seen that the SSB phase noise decreases with about 40 dB per decade and the relaxation oscillation arises again.

Figure 4.12: Integrated timing jitter.

Using equation (2.35) an integrated timing jitter from 1 kHz to 10 MHz is calculated to 2.5 ps. As shown in ﬁgure 4.12 the relaxation oscillation at about 150 kHz mainly generates the timing jitter, i.e. the timing jitter is limited due to amplitude noise that couples to the phase noise. This might be reduced by replacing the pump laser with another which has less amplitude noise.

56 4.3 Mode-locking Stability

4.3 Mode-locking Stability

To prove a satisfying long-term stability of the oscillator its mode-locking state is monitored with the mode-lock detector and a data acquisition (DAQ) device. The carrier power and the noise power can be observed by measuring voltage signals at test points located on the photodiode board (see figure 3.13) and noise board, respectively. Since the carrier power is high and the noise power is low in case of mode-locking and vice versa for CW operation the long-term stability can be observed by connecting both analog outputs, i.e. the test points on the PCB, to a DAQ device. In case of a mode-locked oscillator with 1.5 W input power and resulting 30 mW output power the carrier signal corresponds to 2 V and the noise signal to 1 V. As shown in figure 4.13 this operation state is maintained for more than two days. The transition is shown in detail in the inset, where the noise signal increases to 1.5 V and the carrier signal decreases turning into fluctuations between 1 and 1.5 V. Finally, the pump power is switched off resulting in a carrier signal and noise signal of 0.5 and 0.25 V, respectively. The denoted power values in dBm are read from the mode-lock detector’s display. The termination of mode-locking happened when the observation period was ended intentionally.

Figure 4.13: Long-term stability measured over 2 days using the mode-lock detector. The inset shows the transition from mode-locking to CW state followed by a disabling of the pump.

5 Conclusion and Outlook

A holmium-doped fiber ring oscillator used for seeding a holmium-doped yttrium lithium fluoride regenerative amplifier has been repaired and modified. The change to soliton operation will allow full usage of the seeding power due to a narrower optical spectrum. The preexisting setup has been completely disassembled to check the functioning of all fiber components and to ensure that all splice connections produce low losses. Furthermore, a modular design of a box has been set up around the pump section, which on one hand allows for an easy removal of the walls if adjustments become necessary and on the other hand reduces external influences. In order to monitor different parameters various fiber couplers have been added to the pump and the oscillator section. The latter’s housing has been also im- proved by decoupling vibrations and providing fiber connectors that allow an easy and versatile attachment of monitoring equipment. A mode-lock detector has been assembled and configured, which allows a permanent observation of different power values. Furthermore, the device ensures a reliable and safe operation of the regenerative amplifier and prevents it from damages caused by possible interruptions of the mode-locking state of the seeding source. Finally, an extensive characterization has been performed, where the setup of different measuring equipment allowed for simultaneous measurements of important parameters. In the optical spectrum the center wavelength has been shown to be tunable from 2045 to 2065 nm. The generated sidebands have been completely removed using bandpass filters with a fixed center wavelength at 2050 nm. Differently filtered spectra have been analyzed in their pulse duration, pulse energy and amplitude noise. Without bandpass filters the lowest pulse duration achieved was 860 fs. The bandpass filtered soliton has a maximum pulse energy of 900 pJ, which is more than an order of magnitude larger than the pulse energy provided for seeding the regenerative amplifier in the previous setup. The amplitude noise of the oscillator has been minimized to 0.07 %RMS and the integrated timing jitter of 2.5 ps has been measured. However, the pump laser has been found to be working unstable at high power on the longterm time scale and seemed to be the main source of noise. Fur- thermore, the oscillator has been shown to be mode-locked for more than two

59 5 Conclusion and Outlook days without interruption. In conclusion, the seed source has been repaired, modified and optimized allowing for a reliable functionality as the front-end of an amplifier chain. The amplified 2050 nm wavelength radiation can finally be used for example for pumping optical parametric amplifiers for generating intense light in the mid-infrared wavelength range, e.g. used for spectroscopic experiments.

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