High Power Ultrafast Yb:Fiber Laser a Thesis Presented by Xinlong Li To

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High Power Ultrafast Yb:ﬁber Laser

A Thesis presented

Xinlong Li

The Graduate School

in Partial Fulﬁllment of the

Requirements

for the Degree of

Master of Science

Instrumentation

(Physics)

Stony Brook University

August 2015 Stony Brook University

The Graduate School

Xinlong Li

We, the thesis committe for the above candidate for the

Master of Science degree, hereby recommend

acceptance of this thesis

Thomas K.Allison - Thesis Advisor Assistant Professor, Department of Physics and Astronomy, Department of Chemistry

Eden Figueroa - Committee Member Assistant Professor, Department of Physics and Astronomy

Matthew Dawber - Committee Member Associate Professor, Department of Physics and Astronomy

Meigan C. Aronson - Committee Member Professor, Department of Physics and Astronomy

This thesis is accepted by the Graduate School

Charles Taber Dean of the Graduate School

ii Abstract of the Thesis

High Power Ultrafast Yb:ﬁber Laser

Xinlong Li

Master of Science

Instrumentation

(Physics)

Stony Brook University

2015

High power ultrafast laser pulses have broad applications in many fields such as micromachining, real time imaging of ultrafast process, and frequency-comb-based precision spectroscopy, enabling large numbers of breakthroughs in science and technology. They even open the door to the attosecond (10−18 s) world via high harmonic generation thus gaining the insight into a wide range of electron dynamics. In this thesis, I present a linearly amplified Yb:fiber laser with 55 W average output power and 150 fs pulse duration. This laser is used for cavity-enhanced high harmonic generation to produce high-repetition-rate (78 MHz) extreme ultraviolet (XUV) femtosecond pulses.

iii Contents

List of Figures v

List of Tables viii

Acknowledgement ix

1 Introduction 1 1.1 Mode-Locking ...... 1 1.2 Frequency Comb ...... 3 1.3 Pulse Propagation ...... 4 1.4 High Harmonic Generation ...... 6 1.5 Fiber Laser ...... 9 1.6 Nonlinear Eﬀect ...... 11

2 High Power Yb:Fiber Comb 16 2.1 Oscillator ...... 16 2.2 Comb Tooth Linewidth ...... 18 2.3 Stretcher ...... 21 2.4 Optical Ampliﬁer ...... 22 2.5 Compressor ...... 25 2.6 FROG Measurement and Pulse Duration ...... 25 2.7 Beam Mode ...... 28 2.8 Relative Intensity Noise ...... 29 2.9 Interlock ...... 30 2.10 LabVIEW Control ...... 32 2.11 Mechanical Design and Cooling system ...... 32

3 Conclusion 35

Bibliography 38

Appendix 43 A. LabView code ...... 43

iv List of Figures

1.1 Spectrum consists of discrete lines with equal spacing...... 1 1.2 (a) 10 frequency modes without model-locking. (b) Mode-locking with 2, 5, 10 frequency modes, respectively...... 2 1.3 Schematic of a conventional pulse laser...... 2 1.4 (a) The spectrum of frequency comb. Each comb tooth is equally spaced and has a very narrow bandwidth of usually kHz level.. (b) Pulse train in the time domain. Pulses are equally spaced by the time T = 1/f. The phase difference between carrier and envelope is shifted by ∆Φ between adjacent pulses. . . . 4 1.5 Schematic of compressor (top view). Light with longer wavelength will travel longer distance than shorter wavelength. G1 and G2 are gratings. G: normal distance between gratings. Roof reflector changes the beam hight so we can sort out the output beam of the compressor. Detailed information of parts is in table 3...... 5 1.6 Refractive index distribution of dressed cladding fiber [1] ...... 6 1.7 Three step model for HHG...... 6 1.8 Conventional HHG schematic. Infrared femtosecond laser pulses are focused into a gas to achieve intensities in the strong field regime. A metallic filter blocks the fundamental driving pulses ...... 7 1.9 (a) Attosecond photon burst at each half wave cycle. (b) Single attosecond burst each pulse. (c) Spectrum of (a). ω0 is the central frequency of fundamental driving laser. ωc is the cut off frequency where the yield of harmonics start to drop. (d) Spectrum of (b)...... 8 1.10 Setup of intracavity HHG chamber. Fundamental driving pulses are focused to argon gas to generate XUV pulses. The XUV pulses are coupled out by using a crystal at Brewster angle...... 9 1.11 Illustration of phase locking (frequency domain)...... 9 1.12 Schematic of a high-power, double-clad fibre amplifier...... 10 1.13 (a) Fiber end image of NKT DC-200/40-PZ-Yb. (b) Fiber end image of NKT aeroGAIN-ROD-PM85. The little circle structures are air holes...... 10 1.14 Absorption and emission cross section of Ytterbium [45]...... 11 1.15 MATLAB simulation of gain narrowing (code from Donald Willcox)...... 12 1.16 MATLAB simulation of SPM of pulse after propagation along a piece of fiber (dispersion in the fiber is ignored). New frequency component can be observed. 13 1.17 Simulation by MATLAB (code from Donald Willcox). The upper figures show the power distribution along the fiber. The lower figures show the accumulated B-integral along the fiber. CTP stands for counter propagating between pump laser and signal laser. COP stands for co-propagating...... 14 2.1 The main parts of the high power IR laser ...... 16 2.2 Scheme of oscillator. Detailed information of parts is in table 1...... 17 2.3 Spectrum of oscillator with two different WDMs...... 19 2.4 Spectrum teeth beat with Nd:YAG laser. Rep rate stands for repetition rate. Four of the beat note signals are marked (n = 0 and n = 1)...... 19

v 2.5 Repetition rate signal and beat note signal measured by spectrum analyzer. Signal at 156 MHz is the harmonic of the repetition rate signal. The beat note signals with n = 1 is shown...... 20 2.6 Beat signal measured with different RBW ...... 20 2.7 Scheme of stretcher (Figure from OFS website) ...... 21 2.8 Schematic of optical amplifier. The 5 m crystal fiber is the pre-amplifier and the 0.8 m crystal fiber is the rod-type power amplifier. The detailed information of the parts (L1, L2, D1, etc) can be found in table 2. L stands for lens. D stands for dichroic filter. I stands for isolator. M stands for plane mirror. HWP stands for half wave plate. BD stands for beam damp. . . . . 22 2.9 (a) Amplification Curve of Pre-amplifier. (b) Amplification Curve of power amplifier before compression and after compression...... 24 2.10 (a) Power amplifier spectrum of its seed light, 25 W amplified light and 70 W amplified light. The spectrum of oscillator is also shown. (b) The reflectivity of the dichroic mirrors D1 and D2 (D4), which show cutoff at ∼1010 nm and ∼1030 nm, respectively. This is single measurement without averaging. The data for D2 has been squared because the output of pre-amplifier will be reflected twice (D2 and D4) before going into the power amplifier...... 24 2.11 A schematic of FROG measurement. BS is Beamsplitter. M1 and M3 are plane mirrors. M2 is a focusing mirror. The stage can control the delay time of split pulses ...... 26 2.12 Raw data of FROG, measured SHG intensity at different delay and different wavelength ...... 26 2.13 (a) Reconstructed temporal pulse shape at low power and high power. Du- ration is 150 fs. The Fourier transform limited pulse (120 fs) is obtained by Fourier transform from measured spectrum (figure 2.10a). (b) Reconstructed spectrum and spectral phase at 55 W...... 27 2.14 (a) Temporal pulse shape when third order phase dominates. (b) Spectrum and spectral phase when third order phase dominates...... 27 2.15 (a) Beam mode at low output power (2 W) (b) Beam mode at high output power (55 W). Unit in µm...... 28 2.16 Measured RIN of oscillator, pre-amplifier and power-amplifier. Each curve is combined by three measurements from left to right: 6.25 kHz span using FFT spectrum analyzer, 100 kHz span using FFT spectrum analyzer, 2 MHz span using Rigol spectrum analyzer, ...... 29 2.17 Circuit diagram of the interlock (Designed by Melanie Raber and Yuning Chen) 31 2.18 Laser Control Program by LabVIEW ...... 32 2.19 Beam damp. BD1 in figure 2.8...... 33 2.20 Beam damp. BD2 in figure 2.8...... 33 2.21 Fully water cooling for rod fiber. Water flows in from port 1 and flows our from port 2...... 34 3.1 Schematic of cavity HHG, monochromator and surface experiment...... 35 3.2 Photo of high power ultrafast laser. Pre-amplifier (green fiber) and power amplifier (straight rod) are shown...... 36 3.3 Photo of HHG chamber and monochromator chamber...... 36

vi 3.4 Photo of surface sciences chamber...... 37 A1 LabView code part 1 ...... 43 A2 LabView code part 2 ...... 43 A3 LabView code part 3 ...... 44 A4 LabView code part 4 ...... 44 A5 LabView code part 5 ...... 45 A6 LabView code part 6 ...... 45

vii List of Tables

1 Detailed information of parts in the oscillator (figure 2.2)...... 18 2 Detailed information of parts in the optical amplifier (figure 2.8)...... 23 3 Detailed information of parts in the compressor (figure 1.5). GD stands for groove density...... 25 4 Dispersion parts in the laser. Normal dispersion: φ2 < 0, φ3 < 0. Anomalous dispersion: φ2 > 0, φ3 > 0. FS stands for fused silica. TGG stands for Terbium Gallium Garnet crystal...... 25

viii Acknowledgement

This work owes much to the people who provided me help and opportunity. I want to thank my advisor professor Thomas Allison who allowed me to join his research group and choose this project for me. I have learned a lot of knowledge and skills in this project. I want to thank Christopher Corder for the instruction and cooperation during this project. I also want to thank Peng Zhao who worked with me. Thanks to Melanie Reber and Yuning Chen for their initial work and continuous help in this project. Thanks to Donald Willcox for providing me the MATLAB code. Besides, I want to thank professor Harold Metcalf for his MSI program and choosing committee members for me. Thank professor Eden Figueroa, Matthew Dawber, Meigan Aronson and Michael Rijssenbeek for being my MSI and defense committee members. I also want to thank my parents who provide me support in all the aspects in my life. Also, My success is strongly indebted to my ﬁanc´eeBoni. Her intelligence and assistance has made me smarter and better.

ix 1 Introduction

High power ultrafast laser pulses have broad applications in many fields such as micromachining [2], real time imaging of ultrafast process [3], and frequency-comb-based precision spectroscopy [4], enabling large numbers of breakthroughs in science and technology. They even open the door to the attosecond (10−18 s) world via high harmonic generation (HHG) [5, 6] thus gaining the insight into a wide range of electron dynamics [7, 8]. Up to date, a variety types of lasers have been built to produce high energy femtosecond pulses. The wave packet of these pulses occupy only a few times of its wavelength along its propagation direction and also are in a diffracted-limited beam and hence can be focused to a spot size comparable to the wavelength. Therefore, these pulse can provide peak power in Petawatts level [9] and peak intensity as high as 1020 W/cm2 [10, 9]. Even at much lower intensity, the interaction between light and matter becomes highly nonlinear. As a consequence, the laser field is strong enough to trigger optical-field ionization [11] and other strong nonlinear effects such as HHG. In this thesis, I present a linearly amplified fiber laser with 55 W average output power and 150 fs pulse duration. This laser is used for cavity-enhanced high harmonic generation to produce high-repetition-rate (78 MHz) extreme ultraviolet (XUV) femtosecond pulses. This thesis is organized as follows. Chapter 1 will introduce some basic concepts such as mode-locking, frequency comb, fiber lasers and so on. Chapter 2 will introduce the details of our high power fiber laser, such as oscillator, amplifier, etc. Chapter 2 will also present the experimental datas of the fiber laser such as spectrum, pulse duration, noise, etc.

1.1 Mode-Locking

Mode-locking is a tequenue to produce ultrafast lasers [12]. According to the Heisenberg’s uncertainty principle ∆t∆ω > 4ln2 (1.1)

Figure 1.1: Spectrum consists of discrete lines with equal spacing.

It needs a broad spectrum to create short pulses. For example, a 150 fs pulse requires 8 THz of bandwidth, far exceeding that available from electronics. The spectrum of a Gaussian pulse is also in Gaussian shape within a frequency range. The spectrum of a series of pulses has a interference structure like a comb (ﬁgure 1.1). The electric ﬁeld of an mode-locked laser can be expressed in the frequency domain X Etot = E0 exp[i(ω0 + nωs)t + iφn(t)] (1.2)

1 (a) (b)

Figure 1.2: (a) 10 frequency modes without model-locking. (b) Mode-locking with 2, 5, 10 frequency modes, respectively.

Here we have assumed the spectrum consist of a series of lines of constant amplitude spaced by constant frequency mode ωs (figure 1.1). If the φn(t) is a random distributed 2 phase, the laser intensity (∝ E0 ) will behave like noise (figure1.2a). If we have a mechanism for locking φn(t) of all the lines, the field of different lines will interfere with each other sinNω t/2 iω0t+iφn(t) X inωst iω0t+iφn(t) s Etot = E0e e = E0e (1.3) sinωst/2 then we can get mode-locking. Figure 1.2a shows the light intensity consisting of 10 frequency modes with random phase. It is very noisy. Figure 1.2b shows the pulsed laser intensity consisting of 2, 5, 10 frequency modes with mode-locking. Notice that the more frequency modes we have, the shorter pulses we can get. Also, shorter pulses have larger peak intensity.

Mode-locking can be realized by using a saturable absorber. Shown in ﬁgure 1.3, The saturable absorber has larger loss at low intensity and less loss at high intensity. So shorter pulses, which have larger intensity, experience less loss in the absorber, thus is more stable and preferred by the laser cavity. The saturable absorber can be a real absorber, such as a semiconductor, or an ”artiﬁcial saturable absorber” based on nonlinear optics [12].

Figure 1.3: Schematic of a conventional pulse laser.

2 1.2 Frequency Comb

The spectrum of a pulse train can be expressed as

νn = fCEO + nfr (1.4)

where νn (ﬁgure 1.4) is the optical frequency of each mode, fCEO is called carrier-envelop 6 oﬀset (CEO) frequency, fr is the mode spacing and n is an integer O(10 ). The mode spacing frequency, fr, is the inverse of the laser cavity round trip time T and is determined by the laser cavity round trip length lc. It is also called the repetition rate.

1 lc fr = = (1.5) T vg

where vg is the average group velocity inside the oscillator cavity. CEO frequency, fCEO, is determined by the round trip carrier-envelop phase (CEP) shift ∆Φ f = CEO (1.6) CEO 2πT As seen in ﬁgure 1.4, ∆ΦCEO is caused by the diﬀerence between phase velocity, vp, and group velocity, vg. It can be determined by [13] 1 1 ∆ΦCEO = lcωc( − ) (1.7) vg vp

where ωc is the central frequency of the spectrum. So the CEO frequency is

∆ΦCEO ωc vg fCEO = = (1 − ) (1.8) 2πT 2π vp

We can see fCEO is dependent on the diﬀerence between group velocity and phase velocity, which is a result of dispersion inside the laser cavity. Therefore, by stabilizing the length and dispersion of the laser cavity, we can ﬁx the frequency of all the teeth and then we can call this spectrum a frequency comb [14][15]. Also, because both fr and fCEO are in radio frequency range (kilohertz level or megahertz level), we can count the frequency very accurately by using electronic instruments: (1) fr is just the repetition rate of pulses and can be measured directly using a counter. (2) fCEO can be obtained by measure the beat note between comb tooth f2n and comb tooth 2fn in the second harmonic of the frequency comb

fCEO = 2νn − ν2n = (2fCEO + 2nfr) − (fCEO + 2nfr) (1.9)

With these two measurements, we can know the optical frequency νn with great accuracy, which helps us carry on precision spectroscopy experiments, which means we not only can measure the relative frequency between transitions very precisely, but also can know the absolute transition frequency very precisely. John L. Hall and Theodor W. H¨ansch, in 2005, were awarded the Nobel Prize “for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb” [16][17]. In addition, XUV comb-based precision spectroscopy has been reported in 2012 [4]. In addition, to measure fCEO using above method needs a octave spectrum. For some applications, we do not need to measure fCEO, just need to control it.

3 (a) (b)

Figure 1.4: (a) The spectrum of frequency comb. Each comb tooth is equally spaced and has a very narrow bandwidth of usually kHz level.. (b) Pulse train in the time domain. Pulses are equally spaced by the time T = 1/f. The phase diﬀerence between carrier and envelope is shifted by ∆Φ between adjacent pulses.

1.3 Pulse Propagation

The refractive index is a function of frequency in a material. Thus the phase shift during propagating in a crystal (e.g. optical fiber) is also a function of frequency. Using j(ωt−βz) the convention E = E0e we can expand the wave propagation phase factor in Taylor series [12] ω 1 1 β(ω) = n(ω) = β + β (ω − ω ) + β (ω − ω )2 + β (ω − ω )3 + ··· (1.10) c 0 1 0 2 2 0 6 3 0 Assuming the optical path the pulses propagate is L, then the phase shift can be expressed 1 1 φ(ω) = −β(ω)L = φ + φ (ω − ω ) + φ (ω − ω )2 + φ (ω − ω )3 + ··· (1.11) 0 1 0 2 2 0 6 3 0 where β1 is equal to the inverse of the group velocity dβ 1 β1 = = (1.12) dω vg and the first order phase, φ1, is called group delay L φ1 = −Lβ1 = − = −T (1.13) vg which is equal to the round trip time of pulse in the laser cavity as well as the time delay between the output adjacent pulses. The zeroth order phase, φ0, is frequency independent and do not affect the pulse shape. The first order phase, φ1, determines the group velocity of the pulses and also do not affect the pulse shape. The second order phase, φ2, which starts to affect the pulse shape, is also called group delay dispersion (GDD), and φ3 is just called the third order phase (TOD).

4 Given a spectrum, the shortest pulse we can get is the inverse Fourier transform of it with a flat spectral phase φ(ω) =const. This is called transform-limited pulse. This pulse has zero GDD or higher order dispersion. Usually, the pulses will gain dispersion during its propagating in a fiber (φ2 < 0,φ3 < 0) and hence broadened and become longer pulses. This is because red light travels faster than blue light in the fiber, which is called normal dispersion. To compress the pulses to nearly transform-limited duration, we need anomalous dispersion to compensate the normal dispersion of the fibers. Usually we realize this pulse compression by using a pair of gratings [18].

Figure 1.5: Schematic of compressor (top view). Light with longer wavelength will travel longer distance than shorter wavelength. G1 and G2 are gratings. G: normal distance between gratings. Roof reﬂector changes the beam hight so we can sort out the output beam of the compressor. Detailed information of parts is in table 3.

As seen in ﬁgure 1.5, the compressor consists of two gratings and a roof reﬂector. The light with longer wavelength will travel longer distance than the light with shorter wavelength, which realizes anomalous dispersion. We can get the frequency dependent phase shift [19] 2ω φ(ω) = − Gcosθ (ω) + const (1.14) c D

d2φ(ω) d3φ(ω) From equation (1.14), we can get φ2 = dω2 > 0 and φ3 = dω3 < 0. We can notice that the setup in figure 1.5 brings anomalous second order dispersion (φ2 > 0) but normal third order dispersion (φ3 < 0), which tells it can not compensate the dispersion of the fiber (φ2 < 0, φ3 < 0). However, this is not always true. We previously defined the propagation constant ω β(ω) = n(ω) (1.15) c This is true for a plane wave not subject to boundary conditions. When the wave equation is subject to boundary conditions, there still exists a relation β(ω), but equation 1.15 needs to ω be modified. The difference β(ω) − n(ω) c is called waveguide dispersion, and becomes more important as the light is confined to smaller volumes such as fibers. Therefore, although the materials, such as fused silica, always have normal dispersion at ∼1 µm, the waveguide character of fibers enable us to set a certain boundary conditions for light propagating, thus changing the dispersion regime. For example, the dressed cladding fiber (DCF) has normal

5 Figure 1.6: Refractive index distribution of dressed cladding ﬁber [1]

second order dispersion (φ2 < 0) and anomalous third order dispersion (φ3 > 0)). The index structure of DCF is shown in figure 1.6. Therefore, with different length combination of normal single mode fiber (SMF) and DCF, we can get different ratio of second to third order dispersion [20, 21], which enables matching to the diffraction-grating-based compressor. (higher order dispersion has much less influence on pulse duration).

1.4 High Harmonic Generation

The high power femtosecond laser I will present in this thesis is used for high harmonic negeration (HHG) experiment. HHG can be used to convent optical lasers to the XUV or even soft X-ray. And it is currently the only method to generate attosecond (10−18 s) pulses.

Figure 1.7: Three step model for HHG.

It is extremely diﬃcult to build conventional laser at short wavelength (XUV, soft-Xray and hard X-ray). The lifetime of the high-energy excited state is so short that it needs incredible power to realize population inversion [22]. However, rely on HHG process, people

6 has got coherent laser pulses down to a few nanometer or even sub-nanometer level [23]. Usually, HHG is achieved by focusing high-intensity pulses to a gas jet or a waveguide filled with gas to create highly nonlinear processes, in which high harmonics of the focusing beam can be generated. Popmintchev et al. have recently reported ultrahigh harmonics greater than 5000 [23]. As shown in figure 1.7, HHG is a strong field ionization process, which can be described by the three step semiclassical model [24]. First, the electron is tunnel-ionized out of the atom and gain kinetic energy by the strong laser field. Second, after a half wave cycle, the laser field changes its direction and pulls the electron back to the ion. In the last step, the electron will recombine with the ion and emits a high-energy photon (XUV or even soft X-ray) with an energy as high as

~ω = 3.17Up + Ip (1.16) where Up is the pondermotive energy and Ip is the ionization potential. Therefore, every

Figure 1.8: Conventional HHG schematic. Infrared femtosecond laser pulses are focused into a gas to achieve intensities in the strong field regime. A metallic filter blocks the fundamental driving pulses half cycle of laser wave, there will be an XUV attosecond photon burst (figure 1.9a) and its spectrum consists of odd-order harmonics of fundamental driving light (figure 1.9c). There are also methods to produce single attosecond pulse (figure 1.9b) such as polarization gating [25] and ionization gating [26]. In this situation, the isolated spectrum of harmonics (figure 1.9c) will spread and form a continuous broad spectrum (figure 1.9d). Besides, if we can select one of the harmonics like what we propose to do in our lab, the isolated attosecond pulses (figure 1.9a) will spread and form one long XUV pulse. Usually, HHG is achieved by focusing laser pulses on noble gas like argon [27] (figure 1.8). One of the reasons is noble gas atoms have the highest ionization potentials in the periodic table, allowing them to survive the rising edge of a laser pulse without being ionized early in the pulse before the intensity reaches its maximum. Another reason is the spherical symmetry of noble gas can let us ignore the orientation of the atoms or molecules with respect to the laser field. Generally speaking, an intensity of 1014 W/cm2 is required to achieve HHG [28]. For conventional HHG (figure 1.8), it needs kilowatts average power to produce 100-MHz-level repetition-rate XUV pulses. This is why conventional HHG is limited by < 100 kHz repetition

7 (a) (b)

Figure 1.9: (a) Attosecond photon burst at each half wave cycle. (b) Single attosecond burst each pulse. (c) Spectrum of (a). ω0 is the central frequency of fundamental driving laser. ωc is the cut oﬀ frequency where the yield of harmonics start to drop. (d) Spectrum of (b). rate [29]. However, relying on optical cavity, where the pulses are constructively added, we can get XUV pulses with repetition rate larger than 100 MHz [30].

2 × 50 W × 200 repetition rate ≈ ≈ 200 MHz (1.17) 1014 W/cm2 × π × (15 µm)2 × 150 fs where 50 W is the average power we propose to send into the HHG cavity, 200 is the designed cavity build up (number of pulses can be stored in the cavity at the same time), 15 µm is the focused beam radius at the argon gas jet, 150 fs is the pulse duration of our laser. We can conclude the higher the cavity finesse (build up) is, the lower fundamental power we need to send into the cavity. However, the finesse can not be infinite high. It is limited by intensity clamping and optical bistability [29]. As shown in figure 1.10, the fundamental driving pulses are sent into a six-mirror optical enhancement cavity inside a vacuum chamber to achieve intracavity HHG. The round trip time of this cavity is adjusted to be the same as the time delay between adjacent pulses and the ∆φCEO of this cavity is the same as that of oscillator. Thus pulses arriving at different time can overlap in the cavity. As long as the pulses are coherent and mode-maching with the cavity, they can be added and stored in the cavity, leading to an intensity that is hundreds of times higher. To make the pulses coherent, we need to lock the cavity with the oscillator. And the spectrum linewidth of the pulses should be narrower than the cavity mode linewideth (figure 1.11) to avoid power loss and noise.

8 Figure 1.10: Setup of intracavity HHG chamber. Fundamental driving pulses are focused to argon gas to generate XUV pulses. The XUV pulses are coupled out by using a crystal at Brewster angle.

Figure 1.11: Illustration of phase locking (frequency domain).

1.5 Fiber Laser

Optical fibers were first used for telecommunications, realizing low-attenuation, high- capacity channels as a substitute for conventional cables [31]. However, they experienced rapid development in producing high power lasers after the demonstration of the concept of double cladding [32]. In the early 1990s, only a few watts output power was reached [33]. It rapidly becomes more than 100 W in 1999 [34], 1 kW in 2004 [35], and ∼10 kW in 2010 [36]. The pulse fiber laser was also under rapid development. The average power reached 100 W in 2005 [37] and near 1 kW in 2009 [38]. Most HHG sources are achieved by using Ti:sapphire lasers [39]. However, population inversion in Ti:sapphire requires pumping around 532 nm, where powerful laser diodes are not available. What’s more, although sapphire (monocrystalline Al2O3) has an excellent thermal conductivity, there is also some thermal issue such as thermal lensing. In addition, the energy of pump photon is ∼2.5 eV while the signal photon is only ∼1.5 eV, which indicates a relative big quantum defect. Instead, fiber lasers deliver extremely high beam quality due to their waveguide structure. The guiding character can help avoid thermal lensing and self-focusing . The large surface to volume ratio leads to better thermal performance. Take Yb:fiber as an example, the energy of pump photon is ∼1.3 eV while the signal photon is ∼1.1 eV, which indicates a much smaller quantum defect. Furthermore, the double cladding structure of most rare-earth-doped fiber allows the pump laser to be multimode diodes, which are easily obtained for very high power.

9 Figure 1.12: Schematic of a high-power, double-clad ﬁbre ampliﬁer.

(a) (b)

Figure 1.13: (a) Fiber end image of NKT DC-200/40-PZ-Yb. (b) Fiber end image of NKT aeroGAIN-ROD-PM85. The little circle structures are air holes.

Double-clad fiber is widely used in optical amplifier [40, 41]. For single-cladding fiber, both pump laser and seed (or signal) laser is guided in the core of the fiber. This requires a very high beam quality to focus the pump light into a small spot to couple it into the core. Unfortunately, it is quite difficult to find such pump source with very high brightness. However, for double-clad fiber, as shown in figure 1.12, the pump laser is delivered in the inner cladding whose diameter is hundreds of micrometers, which allows us to use multimode pump laser. And high power multimode diode lasers are available [42]. Also, the seed laser is propagating in the core of the fiber and can effectively maintain its fundamental (Gaussian-like) beam mode. To date, different from conventional optical fibers, photonic-crystal fiber (PCF) are widely used to produce much better optical performance [43]. Conventional fibers have different materials for core and claddings to produce refractive index difference. This limits the size of the core and hence the power the fiber can hold. However, pioneered by the research group of Philip St. J. Russell in the 1990s [44], the PCF can support much larger mode field diameter (MFD), which is defined as 2w where w is the radius at which the field amplitude drops by 1/e and intensity drops by 1/e2 from their peak values. Figure 1.13 shows the structure of PCF used in our lab. The whole fiber is made of one material with complicated air holes structure (the little circle structures in the figure). This kind of structure can guide single mode beam with MFD up to 100 µm at wavelength of ∼1 µm, which allows much

10 more power propagating in the fiber. Another character to be stressed is that the pump laser counter propagates with respect to the seed laser (figure 1.12 and figure 1.12). This helps to reduce the B integral (will be introduced in a later section) of pulse propagating in the fiber very efficiently. In our lab, we use Yb:fiber as our gain medium in the oscillator and amplifiers. The wavelength dependence of the Yb absorption and emission cross sections are shown in figure 1.14, There is a tall and narrow absorption peak at 975 nm and a broad peak around 915 nm. The emission cross section, however, exhibits a broad peak around 1030 nm and slowly falls at longer wavelengths. Thus, Yb is ideal for amplifying a laser with a broad spectrum at ∼1030 nm with laser pumping either the 915 nm or 975 nm absorption peaks depending on the efficiency and available pump width constraints. We notice there is also a tall emission peak at 975 nm. But we can not amplify femtosecond pulses at this wavelength due to its narrow width. Besides, the nonuniform of the emission cross section leads to different

Figure 1.14: Absorption and emission cross section of Ytterbium [45]. amplification efficiency at different wavelength, which brings gain narrowing [22, 46]. A MATLAB simulation (code from Donald Willcox) is shown in figure 1.15. Pulses with 35 nm spectrum FWHM and 16 mW average power is sent into 5 m Yb doped double- clad fiber and amplified to 10 W. We can notice that the output spectrum of the pulses is narrowed to ∼14 nm.

1.6 Nonlinear Eﬀect

Average power scaling is straightforward in fiber lasers. However, it is quite more difficult to obtain high peak power using fiber lasers due to their tiny core radius. The pulses focused into the core of the fiber have a very high intensity, which can cause nonlinear effects quite easily. Besides, the long path length of fibers can easily accumulate the nonlinear effects even at modest powers.

11 Figure 1.15: MATLAB simulation of gain narrowing (code from Donald Willcox).

One of the nonlinear effects is called stimulated Brillouin scattering (SBS, which usually dominates the narrowband signals), which arises from the interaction between light and acoustic waves in the fiber. SBS is characterized by a sharp power threshold, beyond which the energy starts to transfer from the signal laser to a frequency-downshifted (by ∼11 GHz in fused silica [31]) beam propagating to the opposite direction to the signal laser. This not only limits the amplified power but also easily destabilizing the seed oscillator or amplifier due to its counter-propagating character. Another nonlinear effect is stimulated Raman scattering (SRS, which usually dominates the broadband signals), which arises from the interaction between light and vibrations of the glass lattice. The same as SBS, SRS also transfer energy from the signal laser to a frequency-downshifted (by ∼13 GHz in fused silica [31]) beam. The difference is SRS can transfer energy to beams propagating in both forward and backward direction. Also, SRS can be seeded by amplified spontaneous emission (ASE). SBS and SRS set the fundamental power limits of fiber lasers [47]. In our lab, we do not output such high power and we can ignore these two nonlinear effects. The third nonlinear effect is called Kerr effect, which is the main consideration in our fiber laser. Because the peak intensity is quite big for ultrafast pulses, so the refractive index of fiber is modified n = n0 + n2I (1.18) where I is the intensity, n0 is the linear index, n2 is the nonlinear index. For example, fused silica has a nonlinear index of ∼ 3 × 10−16 cm2/W [48]. One of the phenomena caused by kerr effect is self-phase modulation (SPM) [49]. For a Gaussian pulse, the intensity in the time domain is 2 2 −t /tp I(t) = I0e (1.19)

12 where I0 is the peak intensity, tp is related to the FWHM of pulse √ ∆t = 2ln2tp (1.20) So the refractive index is also a function of time

2 2 −t /tp n(t) = n0 + n2I0e (1.21) The phase evolution in the ﬁber of length l is 2πl φ(t) = ω0t − n(t) (1.22) λ0 where ω0 and λ0 are the central frequency and central wavelength of the pulse, respectively. The phase shift along time results in an instantaneous frequency

dφ 4πn lI t 2 2 2 0 −t /tp ω(t) = = ω0 + 2 e (1.23) dt λ0tp

Figure 1.16: MATLAB simulation of SPM of pulse after propagation along a piece of ﬁber (dispersion in the ﬁber is ignored). New frequency component can be observed.

We can notice that new frequency has been generated via SPM. Figure 1.16 shows the spectrum broadening of pulses after propagation along a piece of fiber. If we have two laser beams with different frequency or different polarization propagating in the fiber, we can also observe cross-phase modulation (XPM). The kerr effect is not always detrimental for fiber lasers. For example, we need this nonlinear effect to realize mode-locking in our oscillator (see next chapter). Besides, the

13 SPM can help broaden the spectrum of pulses and thus we can compress the pulses to much shorter duration [27]. However, for our laser, we need a very quiet frequency comb locked with the HHG enhancement cavity. From the above equation we can see the SPM can transfer noise from amplitude to phase. For our amplifier, the noise of pump source will be transferred to the phase of the frequency comb. The main parameter to evaluate kerr effect is the B integral, which is defined as

2π Z l B = n2Ipeak(z)dz (1.24) λ 0 where l is the length of the fiber. This B integral evaluate the total on-axis nonlinear phase shift accumulated in the fiber. The criteria B < 1 rad defines linear amplification. So the phase difference between the center of the pulse (high intensity) and the edges of the pulse (low intensity) is less than 1 rad. Therefore, we need large pulse duration at high average power to reduce the peak intensity and then reduce the nonlinear effect. There is a simulation shown in figure 1.17. I use a 19 W pump laser (915 nm) to amplify the signal (or seed) laser (1030 nm) from 15 mW to 10 W with counter propagating (CPT) and co-propagating (COP), respectively, in a 5 m fiber. The pulse duration is 300 ps. Then I calculate the accumulated B integral.

Figure 1.17: Simulation by MATLAB (code from Donald Willcox). The upper figures show the power distribution along the fiber. The lower figures show the accumulated B-integral along the fiber. CTP stands for counter propagating between pump laser and signal laser. COP stands for co-propagating.

The simulation shown in ﬁgure 1.17 is based on the rate equation [22] between the ground state and excited state. The ﬁber is treated as a one-dimensional system. The populations

14 at steady state are

N1(z) = 1 − N2z (1.25)

R1→2 + W1→2 N2(z) = (1.26) R1→2 + R2→1 + W1→2 + W2→1 + A2→1 where N1 is the population of ground state and N2 is the population of the excited state. A is the Einstein coefficient of spontaneous emission. W is the coefficient of stimulated transition for the signal laser and is related to the laser power and the transition cross section shown in figure 1.14. R is the coefficient of stimulated transition for the pump laser. The simulation divides the spectrum into small frequency range and treats the transition cross section, σ, as a constant in each frequency range. Then the average power can be calculated as

dP (z) k = (σ N (z) − σ N (z))N P (z) (1.27) dz k,2→1 2 k,1→2 1 tot k X Ptot = Pk (1.28) k where k is the kth frequency range, Pk is the power of the kth frequency range, Ptot is the total power and Ntot is the total effective doping rate of the fiber. (Note the effective doping rate is different for pump light and seed light because pump light is propagating in the cladding while the seed is in the core.) We can notice that CPT and COP gives almost the same amplified signal power. However, the accumulated B integral is much less in CPT. That is why we choose the pump laser to propagate in the opposite direction to the signal light in double-clad fiber amplifier.

15 2 High Power Yb:Fiber Comb

In this thesis, I present a linearly amplified fiber laser with 55 W average output power and 150 fs pulse duration. This laser is used for cavity-enhanced high harmonic generation to produce high-repetition-rate (78 MHz) XUV femtosecond pulses. The main parts of this laser is shown in figure 2.1. We have a fiber based oscillator that output an average power of 38 mW. Then, there is an fully-fiber-based stretcher, stretching the pulses to several hundred picoseconds. With this large chirp, the peak intensity of pulses will be much lower thus reducing the nonlinear effects in the subsequent amplification process. The output of the stretcher is 16 mW. Next, the pulses are sent into a 5 m double- clad crystal fiber pumped by a commercial diode laser with wavelength at 915 nm. The maximum power of this pump laser is 30 W but we only turn it up to 16 W because it is already enough for seeding the power amplifier. At this pump power, the amplified signal power will be 6 W. Then we have a second amplifier, a rod-type LMA fiber pumped by 975 nm commercial diode laser. We turn this pump laser up to 170 W and amplify the signal power to 70 W. In these two amplifiers, the B integral is small enough (< 1 rad) to maintain a linear application. In the end, we have a pair of gratings to compress the pulses to 150 fs and the final average signal power is 55 W.

Figure 2.1: The main parts of the high power IR laser

2.1 Oscillator

The structure of the oscillator is shown in figure 2.2. The pump light is coupled into the laser cavity by a wavelength division multiplexer (WDM) and the Yb:fiber acts as a gain medium. We can change the cavity length by moving the roof reflector R1. We use a pair of gratings G1 and G2 to compensate this material dispersion of the fibers and optics. The waveplates HWP and QWP is used to set the polarization of the pulses. The polarizing beam splitter (PBS) is used as an output coupler and sends the pulses into the stretcher. The electro-optic modulator (EOM) is used to provide a phase modulation which is used to lock the oscillator with the HHG enhancement cavity. The detailed information of these parts can be found in table 1. In this oscillator, mode-locking is achieved by nonlinear polarization evolution [50, 51]. The light launched into the Yb:fiber contains two polarizations with intensity Ix and Iy,

16 Figure 2.2: Scheme of oscillator. Detailed information of parts is in table 1. respectively. The refractive index for each polarization is dependent on the intensity due to the kerr eﬀect

nx = n0 + n2Ix + 2n2Iy (2.1)

ny = n0 + n2Iy + 2n2Ix (2.2) where n0 is the linear refractive index, n2 is the second-order nonlinear refractive index. The second term on the RHS is SPM and the third term is XPM. Light with different intensity will experience different phase evolution inside the fiber thus have different output polarization. By putting a PBS after the fiber, the light intensity transmission through the PBS will become light intensity dependent. Therefore, by setting a proper position for the waveplates, an artificial saturable absorber effect with ultrafast response can be achieved, where light with higher intensity experiences less loss on the PBS. The envelop of pulses propagating inside the fiber can be described by a modified nonlinear Schrödingerequation [52] ∂A β ∂2A 1 x = i x x − iγ(|A |2 + 2|A |2)A + (g − l)A (2.3) ∂z 2 ∂t2 x y x 2 x ∂A β ∂2A 1 y = i y y − iγ(|A |2 + 2|A |2)A + (g − l)A (2.4) ∂z 2 ∂t2 y x y 2 y where g is the gain factor and l is the loss factor in the fiber, γ = (2πn2)/(λ0Aeff ) is the nonlinear parameter at the central wavelength λ0 and effective fiber core area Aeff . The first terms on the RHS of the equations are for dispersion where βx,y = 2π/λx,y. The second 2 terms in the parenthesis are SPM and XPM where |Ax,y| are proportional to intensities. The third terms describe the gain and loss in the fiber.

17 Part Name Details M1 D-shaped mirror, Thorlabs PFD10-03-P01 M2 Plane mirror, Thorlabs BB1-E03 R1 Right angle prism, Thorlabs PS908H-C C1&C2 Fiber port collimators, Thorlabs PAFA-X-5-C HWP Zeroth order half wave plate, Thorlabs WPH05M-1030 QWP Zeroth order quarter wave plate, Thorlabs WPQ05M-1030 PBS Polarizing beamsplitter cube, Thorlabs PBS103 G1 & G2 Gratings, Wasatch Photonics 2254-B-21 EOM United Crystals, LiTaO3, Y-cut, Cr, Au electrode coating WDM WD202G-APC Yb:Fiber Thorlabs YB1200-4/125 975 nm Pump Laser Oclaro Technology Limited LC96L76P-20R SMF Single mode ﬁber, Thorlabs P4-980AR-2 I1 Isolator, Thorlabs IO-3D-1030-VLP

Table 1: Detailed information of parts in the oscillator (ﬁgure 2.2).

The output spectrum of the oscillator is shown in figure 2.3. The large bandwidth (∼35 nm) of the spectrum can in principle support ∼50 fs pulses but it will experience gain narrowing process in the amplifiers. Initially, we used a WDM working at 1030 nm. Then because of the dichroic mirrors we used in the amplifier (see amplifier section), we replace the WDM with a 1053 nm one. Even though the bandwidth of both WDMs are ±5 nm, the output spectrum is still quite broad. We can see the spectrum shift to red after we replace the WDM and there is more power at 1064 nm and then we can produce beat note between our oscillator and 1064 nm Nd:YAG laser to measure the linewidth of comb tooth (see comb tooth linewidth section). In addition, changing the polarization status of pulses by rotating the waveplates can also change the spectrum to some extent.

2.2 Comb Tooth Linewidth

One of the interesting parameters of the oscillator is its comb tooth linewidth. To lock the oscillator to the HHG cavity with as small power loss and as low noise as we can, we need the linewidth of spectrum tooth narrower than the linewidth of the cavity mode. For a cavity with a ∼2% loss , this gives us the ﬁnesse

1/4 π(R1RM ) F = 1/2 ≈ 300 (2.5) 1 − (R1RM ) where R1 = 0.98 is the reflectivity of the lossy mirror and we treat other mirrors of the cavity as RM = 1. This finesse gives us the cavity mode linewidth FSR 78 MHz δν = = ≈ 260 kHz (2.6) F 300 18 Figure 2.3: Spectrum of oscillator with two different WDMs.

In order to measure the linewidth of comb tooth, we observe the heterodyne beats between the output of the oscillator and our CW Nd:YAG laser (1064 nm, Mephisto from Coherent Inc.). As seen in ﬁgure 2.4, the Nd:YAG laser will beat with diﬀerent comb teeth, generating a lot of beat note signals with frequency of

f1n = f1 + nfr (2.7)

f2n = f2 + nfr (2.8) where n = 0, 1, 2, ....

Figure 2.4: Spectrum teeth beat with Nd:YAG laser. Rep rate stands for repetition rate. Four of the beat note signals are marked (n = 0 and n = 1).

Figure 2.5 shows two of the beat note signals between two repetition rate signal (78 MHz and its harmonic: 156 MHz) measured with an RF spectrum analyzer. By changing the distance of the gratings in the oscillator, we can change the frequency of the two beat note signals. When f1 = f2, there will only be one beat note signal between any of the repetition rate signals. When f1 = 0 or f2 = 0, we can not observe any beat note signal on the spectrum analyzer. In ﬁgure 2.5, the height of the repetition rate signal at 156 MHz is lower than

19 the one at 78 MHz. This is because the optical detector (Thorlabs PDA10CF) we use has a bandwidth of only 150 MHz.

Figure 2.5: Repetition rate signal and beat note signal measured by spectrum analyzer. Signal at 156 MHz is the harmonic of the repetition rate signal. The beat note signals with n = 1 is shown.

Figure 2.6: Beat signal measured with diﬀerent RBW

The Nd:YAG laser is quite stable (< 1 MHz/minute shift) and its linewidth (∼1 kHz [53]) is much less than the expected linewidth of the comb tooth. We can estimate the comb tooth linewidth by seeing at what resolution bandwidth (RBW) the power in the coherent carrier goes down. Seen from ﬁgure 2.6, we decrease the RBW from 100 kHz to 10 kHz, the signal level starts to drop after 30 kHz, which indicates the linewidth of beat note is comparable to the RBW of the spectrum analyzer. Ignoring the linewidth of Nd:YAG laser, the beat note linewidth is equal to the linewidth of comb tooth. So we conclude the

20 linewidth of comb tooth is less than 30 kHz. This is small enough to lock the oscillator to the HHG enhancement cavity with low noise and is among the smallest free-running comb tooth linewidths reported for a fiber frequency comb [54][55]. The linewidth of comb tooth depends critically on the net GDD of the oscillator cavity [51]. Adjusting the grating distance (figure 2.2) to compensate the GDD of the fiber, we can get zero overall GDD and thus get narrowest linewidth. If the overall GDD is not zero, there will be larger linewidth.

2.3 Stretcher

The stretcher enlarges the pulse duration (e.g. from femtoscond to picosecond) to lower the peak intensity. So the nonlinear effects in the amplifier fiber is avoided.

Figure 2.7: Scheme of stretcher (Figure from OFS website)

The stretcher was custom made by OFS Fitel Denmark ApS (Figure 2.7). It is fully fiber based. The single mode fiber (SMF) has normal dispersion (φ2 < 0, φ3 < 0). The dressed cladding fiber (DCF) has normal second order dispersion (φ2 < 0) and anomalous third order dispersion (φ3 > 0). Therefore, with different length combination of SMF and DCF, we can get different ratio of second to third order dispersion, which enables matching to our diffraction-grating-based compressor. Based on the design of our compressor, the second order dispersion is -5.22 ps2 and the third order 0.0216 fs3. The length of SMF is 31.9 m and the length of DCF is 11.8 m. There is also standard single mode fiber (SMF-980) pigtails for easy system integration. At this dispersion, we can estimate the duration of the stretched pulses. For a gaussian pulse, the electric field can be expressed as

ln2 2t 2 − ( ) jω0t+ψ(t) E(t) = Ete 2 ∆t e (2.9)

where ∆t is the FWHM of the pulse. The FWHM of the output pulse after propagating in the stretcher is [52] p∆t4 + 16(ln2)2φ2 ∆t = 2 (2.10) out ∆t Assume the input pulses are Fourier transform limited, which gives ∆t =∼ 50 fs with spectrum FWHM of ∼35 nm. The FWHM of output pulse is ∆tout = 292 ps.

21 2.4 Optical Ampliﬁer

A schematic of our amplifier chain is shown in figure 2.8. Our pre-amplifier is a 5 m Yb- doped polarization-maintaining photonic-crystal fiber with a mode field diameter (MFD) of 31 µm. The pump laser, counter propagating in the inner cladding of the fiber, is at 915 nm. Our power amplifier uses a 0.8 m Yb-doped rod-type photonic-crystal fiber with a very large MFD (65 µm). The wavelength of pump laser is at 975 nm. This is because this rod-type fiber is only 0.8 m. We want the fiber to efficiently absorb the pump light and the absorption peak at 975 nm is much larger than at 915 nm (figure 1.14).

Figure 2.8: Schematic of optical amplifier. The 5 m crystal fiber is the pre-amplifier and the 0.8 m crystal fiber is the rod-type power amplifier. The detailed information of the parts (L1, L2, D1, etc) can be found in table 2. L stands for lens. D stands for dichroic filter. I stands for isolator. M stands for plane mirror. HWP stands for half wave plate. BD stands for beam damp.

There are also other parts in the amplifier system. The isolator I1 is used to protect the oscillator, preventing the amplified spontaneous emission (ASE) in the pre-amplifier and the reflected seed laser from going back into the oscillator. I2 and I3 can protect the pre-amplifier and power amplifier, respectively. Because both isolators and fibers need the input seed laser to be at certain polarization, we place half wave plates in front of each isolator and fiber. Water cooling of various components is required because of the high optical power and we will talk about that in a later section. The detailed information of all the parts in figure 2.8 can be found in table 2. Even though D5 is designed for long wave pass, there is still significant amount of signal light reflected in such a high power. So we put another dichroic

22 Part Name Details L1 Lens, Thorlabs LA 1289-B, f = 30 mm L2 Lens, Thorlabs LA 4532-B, f = 32 mm L3 Lens, Thorlabs LA 3026-B, f = 26 mm L4 Lens, Thorlabs LA 1134-B, f = 60 mm L5 Lens, Thorlabs LA 4532-B, f = 32 mm L6 Lens, Thorlabs LA 5040-B, f = 40 mm D1 Layertec 103675 short wave pass filter, work at 30◦ D2 Layertec 109842 short wave pass filter, work at 45◦ D3 Layertec 108834 long wave pass filter, work at 22.5◦ D4 Layertec 109842 short wave pass filter, work at 45◦ D5 Layertec 108834 long wave pass filter, work at 22.5◦ D6 Layertec 109842 short wave pass filter, work at 45◦ I1 Isolator, Thorlabs IO-3D-1030-VLP I2 & I3 Isolator, EOT 1200462 HWP Zeroth order half wave plate, Thorlabs WPH10M-1030 M1 Altechna low GDD HR broad band mirror 5 m crystal fiber NKT Photonics DC-200/40-PZ-Yb, MFD = 31 µm 915 nm pump laser nLight Photonics 1040677, maximum output 30 W 0.8 m crystal fiber NKT Photonics aeroGAIN-ROD-PM85, MFD = 65 µm 975 nm pump laser LIMO200-F200-DL980-S1886, maximum output 200 W

Table 2: Detailed information of parts in the optical amplifier (figure 2.8). mirror D6 (short wave pass) to prevent this reflected signal laser from going into the pump diode and causing damage to the pump diode. Dichroic mirrors D2 and D3 realize the same function. The amplification curves of pre-amplifier and power amplifier are shown in figure 2.9. The maximum pump laser outputs for the pre-amplifier and the power amplifier, are 30 W and 200 W, respectively. However, we decide to only turn up the pre-amplifier to 16 W and power amplifier to 170 W. This can provide 55 W final output, which is enough power for subsequent experiments. From the power before and after compressor, the efficiency of our compressor is 80%, which implies a 94% efficiency of single grating diffraction. The spectrums are shown in figure 2.10a. The FWHM of the oscillator spectrum is about 35 nm, which is quite broad, and the central wavelength is at ∼ 1040 nm. The spectrum of pre-amplifier is a little narrower (∼30 nm) than the oscillator. The spectrum loss at low wavelength is because of the dichroic mirror D2 and D4 (figure 2.8) which allows the pump laser to pass through and reflects the signal laser. The cutoff wavelength of the dichroic mirror D2 and D4 is at 1030 nm (figure 2.10b). That is to say, the laser with wavelength smaller than 1030 nm does not get reflected by these two dichroic mirrors to seed the power amplifier. The spectrum of power amplifier is even narrower (14 nm.) This is because of gain narrowing. We can conclude from spectrums at different output power. We can see in the

23 (a) (b)

Figure 2.9: (a) Amplification Curve of Pre-amplifier. (b) Amplification Curve of power amplifier before compression and after compression.

(a) (b)

Figure 2.10: (a) Power amplifier spectrum of its seed light, 25 W amplified light and 70 W amplified light. The spectrum of oscillator is also shown. (b) The reflectivity of the dichroic mirrors D1 and D2 (D4), which show cutoff at ∼1010 nm and ∼1030 nm, respectively. This is single measurement without averaging. The data for D2 has been squared because the output of pre-amplifier will be reflected twice (D2 and D4) before going into the power amplifier.

24 ﬁgure that the higher the output power is, the narrower the spectrum will be.

2.5 Compressor

The pulses have duration of hundreds of picoseconds coming out of the stretcher. We can compress them back to femtosecond pulses after ampliﬁcation. This is realized by using a pair of gratings shown in ﬁgure 1.5. The detailed information of the parts is in table 3.

Part Name Details G1 & G2 GD=1250 mm−1, Wasatch Photonics custom diﬀraction gratings Roof reﬂecter two mirrors, Altechna low GDD HR broad band mirror, size: 300 × 100

Table 3: Detailed information of parts in the compressor (ﬁgure 1.5). GD stands for groove density.

The lasers is designed to work at λ =1030 nm. And we set the gratings working at Littrow angle. ◦ 2sinθi = Nλ ⇒ θi = 40 where N = 1250 mm−1 is the groove density of gratings. By setting the normal distance of grating G = 40 cm. We can calculate the second order dispersion and third order dispersion of the compressor according equation 1.14. Now we list all the dispersion parts of our laser in table 4.

Part Name GDD (ps2) TOD (fs3) notes Stretcher -5.27 2.16×107 Ampliﬁers -0.11 -2.39×105 FS, total length = 5.8 m Isolators -0.017 -9.9×103 TGG, total length = 12 cm Compressor 5.4 -2.14×107

Table 4: Dispersion parts in the laser. Normal dispersion: φ2 < 0, φ3 < 0. Anomalous dispersion: φ2 > 0, φ3 > 0. FS stands for fused silica. TGG stands for Terbium Gallium Garnet crystal.

2.6 FROG Measurement and Pulse Duration

After compression, we can get high-power ultrafast pulses. We use frequency-resolved optical gating (FROG) to measure the pulse duration and its spectral phase. FROG is a standard method to measure ultrashort laser pulses [56]. The basic setup for FROG is shown in ﬁgure 2.11. Like a Michelson interferometer, the input pulse is ﬁrst split and sent to two arms. The path length of one of the arms can be scanned by a delay stage, so the delay between pulses can be scanned. After the focusing mirror M2, the two pulses are sent to the BBO crystal, generating three second harmonic (SH) beams. Two of

25 the SH beams are just generated by each of the input pulses and they are always generated no matter how big the delay is. When the delay is small enough, the two pulses will overlap at the BBO crystal and non-collinear second harmonic generation (SHG) will occur. Then we send this beam into the spectrometer and record the spectrum at diﬀerent time delay. In the end, using a phase reconstruction algorithm [57], we reconstruct the shape and phase of input pulse in both time and frequency domain.

Figure 2.11: A schematic of FROG measurement. BS is Beamsplitter. M1 and M3 are plane mirrors. M2 is a focusing mirror. The stage can control the delay time of split pulses

In our lab, we use a commercial FROG (from MesaPhotonics Corp.) to measure our output pulses of the laser. The raw data is shown in figure 2.12. It is basically the intensity of the middle SHG beam at different time delay and different wavelength. The software coming with the FROG can let us adjust the laser status in real time. By adjusting the distance of the compressor gratings and their diffraction angle, we minimize the size of raw data along time axis, which indicates the shortest pulses we can obtain.

Figure 2.12: Raw data of FROG, measured SHG intensity at diﬀerent delay and diﬀerent wavelength

26 (a) (b)

Figure 2.13: (a) Reconstructed temporal pulse shape at low power and high power. Duration is 150 fs. The Fourier transform limited pulse (120 fs) is obtained by Fourier transform from measured spectrum (ﬁgure 2.10a). (b) Reconstructed spectrum and spectral phase at 55 W.

(a) (b)

Figure 2.14: (a) Temporal pulse shape when third order phase dominates. (b) Spectrum and spectral phase when third order phase dominates.

27 (a) (b)

Figure 2.15: (a) Beam mode at low output power (2 W) (b) Beam mode at high output power (55 W). Unit in µm

The reconstructed pulses are shown in figure 2.13. In the time domain, we present the pulse shape in low power, high power and the Fourier transform limited pulse obtained by Fourier transform from the measured spectrum in figure 2.10a. The pulse width, 150 fs, is quite close to the transform limited pulse (120 fs). Also, it shows almost no difference between low power and high power without changing the distance of the two compressor gratings. This is because we make use of linear amplification. In nonlinear amplification, the spectrum of the pulses will be broadened due to SPM, and the output spectrum and spectral phase will be different at different output power. So for each output power, there will be a different grating distance to optically compress the pulses. In the frequency domain, we present the pulse spectrum and spectral phase at high power (figure 2.13b). We can see there is some residual second order phase. This is because we are minimizing the size of raw data in time axis. We can also minimize the second order phase (make the phase flat and zero in the pulse spectrum range) and then we can see third order phase will dominate and there are undesired satellite pulses (figure 2.14a). Even though the main pulse in figure 2.14a is shorter (130 fs) than that in figure 2.13a, the satellite pulses occupy a lot of power thus the peak power in figure 2.14a is lower than that in figure 2.13a. Therefore, we choose the one with larger peak power even though it has larger chirp (there is residual second order phase).

2.7 Beam Mode

The output beam measured at the output of compressor is shown in figure 2.15. To capture the whole beam in the camera, I use a telescope with a magnification of 1/2. So the beam size shown in the figure is half of the original beam size. At low power, the beam mode diameter (BMD) is 3.2 mm. And at high power, the beam size is smaller with a BMD = 2.7 mm. This is likely due to the thermal lensing in the isolator I3 (figure2.8). The high power laser will heat the crystal (∼3 cm long) in the isolator. Because the center of the

28 beam has a higher power level than the edge of the beam, the temperature at the center of the crystal will be higher than the edge of the crystal. So the refractive index at the center will be larger than that at the edge. Therefore, the crystal will act as a lens and focus the beam. The higher the laser power is, the stronger the focusing eﬀect will be [48].

2.8 Relative Intensity Noise

The relative intensity noise (RIN) describes the ﬂuctuations of the laser intensity. It can be generated by the vibration of optics, the instability of the pump source and the quantum noise. Since the intensity noise (IN) is proportional to the intensity, we usually use RIN, which is independent of laser power, to describe the noise level. The standard deﬁnition of RIN is [58] P (ω) R(ω) = E PDC where PE(ω) is the measured electrical noise power per unit bandwidth from a square law detecter and PDC is the electrical DC power from the same detector.

Figure 2.16: Measured RIN of oscillator, pre-ampliﬁer and power-ampliﬁer. Each curve is combined by three measurements from left to right: 6.25 kHz span using FFT spectrum analyzer, 100 kHz span using FFT spectrum analyzer, 2 MHz span using Rigol spectrum analyzer,

Usually we use a spectrum analyzer to analyze the electrical signal from the photodetec- tor. Since the noise in the electrical domain is proportional to the square of the electrical

29 current, which is proportional to the optical power, RIN is usually presented as relative fluctuation of the square of the laser intensity with the unit dBc/Hz over the measured bandwidth. We measured RIN using a homemade (by Yuning Chen) AC-coupled detecter. Also, we use the Stanford Research SR760 FFT spectrum analyzer to measure the low frequency (0 - 100 kHz) noise and use the Rigol DSA815 spectrum analyzer to measure the high frequency (100 kHz - 2 MHz) noise. The result is shown in figure 2.16. The main noise is coming from oscillator and power amplifier. In addition, turning up the power amplifier will not add noise to the laser. The noise will show up as long as the power amplifier is on. We can see that the pre-amplifier doesn’t add much noise to the laser.

2.9 Interlock

Without seed laser, the pump power absorbed in the amplifier will accumulate a very large population inversion. A spontaneous emission of one atom will cause stimulated emission of other atoms. This can cause a very big energy release within a very short time scale and generate a large pulse with very high intensity, leading to catastrophic failure of the fiber. To avoid this kind of fiber damage, the pump laser must be shut down when any accident happens to the seed laser. In addition. we want our laser working at pulse mode but sometimes the laser will lose mode-locking due to some interruption. So we built the circuit shown in figure 2.17 to monitor the power level and mode-locking of the laser. For each optical amplifier, there is a detector (Thorlabs PDA10CF) monitoring seed power. The detector measures the train of optical pulses produced by the oscillator, putting out an RF waveform consisting of repetition rate frequency ωr and its harmonics. Considering the fundamental ωr V = V0cos(ωt) (2.11) An RF splitter (Mini-Circuits ZFSC-2-4+) splits the electrical power into two channels of a frequency mixer (Mini-Circuits ZAD-1+) V V V V 0 = 0 cos(ωt) × 0 cos(ωt + φ) = 0 [cos(2ωt + φ) + cosφ] (2.12) 2 2 8 where the phase term φ is caused by the length difference of the BNC cables. After the low V0 pass filter, only the DC signal 8 cos φ is sent in to the circuit in figure 2.17. In the circuit, we can set a voltage reference to compare with the DC signal. If the seed laser is off, the DC signal is small compared to the reference, the circuit will disable the power supply of the pump laser. If the seed laser is on and the power is large enough for seeding the amplifier, the circuit will enable the pump laser. What’s more, if the oscillator loses mode-locking, the laser will be in CW mode. Then V0 = 0 and the DC signal will also be zero. The circuits shown in figure 2.17 is controlling not only my 55 W laser setup, but also another 10 W laser setup used for cavity enhanced transient absorption spectroscopy (CETAS) experiment. Among all the connection, Oscillator 2 controls my oscillator, 30 W Diode #2 controls my pre-amplifier and 200 W Diode controls my power amplifier. Also, There is a switch that can shut down all the laser setup in sequence. The lab warning sign can indicates the status of the switch to protect the people in the lab.

30 Figure 2.17: Circuit diagram of the interlock (Designed by Melanie Raber and Yuning Chen) 31 2.10 LabVIEW Control

To better control the whole laser system, we developed a control program (ﬁgure 2.18) using LabVIEW.

Figure 2.18: Laser Control Program by LabVIEW

The purpose of developing this program is to make the laser safer. First, we freeze the preamplifier part when the power amplifier is on. That is to say, as long as the power amplifier is on, we cannot turn off the pre-amplifier or change its power. Second, when the pre-amplifier is off, we cannot turn on the power amplifier. Even though we already setup the physical interlock, this acts as a secondary protection. Third, we monitor the temperature of the cooling preamplifier. When the temperature is higher than 32 ◦C or there is insufficient water flow, the program will shut down the amplifiers in sequence (shutting down the pre- amplifier 500 ms later than the power amplifier). The program can also monitor the seed powers of the pre-amplifier and power amplifier. It keeps talking with the power supplies of the pump laser. Once something dangerous happens, the program will shut down the amplifiers.

2.11 Mechanical Design and Cooling system

32 The main issue for high power laser is heating. For example, there is 200 W of pump power going into the rod fiber where ∼40 W will come out of the other end. We must setup a water-cooled beam dump to collect this unused power. The beam dump is shown in figure 2.19. It can be water cooled and collect unabsorbed light with beam size as big as 1 inch. The black part can be replaced to realize more function. Shown in figure 2.20, the beam damp is placed between the lens and the seed end of the fiber. The beam size of the seed laser is only about 1 mm but the output pump beam size is large, because the inner cladding of the fiber, where the pump is propagating in, has a numerical aperture (NA) of 0.5, which means the output pump light has a divergence of

θ = arcsin(NA) = 30◦ (2.13)

So the output pump light will illuminate and heat the mount of lens, which can cause misalignment. This is dangerous for the reasons mentioned before. If we place the beam damp like ﬁgure 2.20, we can block most of the pump light to protect the lens mount while the seed laser can still go into the ﬁber.

Figure 2.19: Beam damp. BD1 in ﬁgure 2.8.

Figure 2.20: Beam damp. BD2 in ﬁgure 2.8.

What’s more, ∼160 W pump power is absorbed by the rod fiber where only ∼70 W is converted to the signal power. The rod-type fiber is also water cooled along its length to efficiently remove unconverted pump power. The design of the water cooled fiber support is

33 shown in figure 2.21. We put the fiber in V-groove of a aluminum pipe and make water flow through the pipe.

Figure 2.21: Fully water cooling for rod fiber. Water flows in from port 1 and flows our from port 2.

34 3 Conclusion

In this thesis, I presented a linearly amplified fiber laser with 55 W average output power and 150 femtosecond pulse duration (figure 3.2). The comb tooth linewidth is less than 30 kHz and the relative intensity noise is low. However, the pulse duration is limited by the gain narrowing in the power amplifier. And the output power is limited by the efficiency of gratings. Also, the dichroic mirror at the output end of pre-amplifier cuts a little spectrum and also lower the seed power sent to the power amplifier. In addition, we build the water cooling system and interlock system to protect the laser. A LabView program is developed to control the laser system. In the future, we will replace the dichroic mirror D2. So we may have more spectrum around 1030 nm, where the emission cross section of Yb is higher. This laser is used for cavity-enhanced high harmonic generation to produce high-repetition- rate extreme ultraviolet (XUV) femtosecond pulses. In the end, we will use these XUV pulses to carry on a pump-probe experiments on clean surfaces in ultrahigh vacuum, as illustrated in figure 3.1. Figure 3.3 and figure 3.4 show the vacuum chambers.

Figure 3.1: Schematic of cavity HHG, monochromator and surface experiment.

35 Figure 3.2: Photo of high power ultrafast laser. Pre-amplifier (green fiber) and power amplifier (straight rod) are shown.

Figure 3.3: Photo of HHG chamber and monochromator chamber.

36 Figure 3.4: Photo of surface sciences chamber.

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42 Appendix

A. LabView code

Figure A1: LabView code part 1

Figure A2: LabView code part 2

43 Figure A3: LabView code part 3

Figure A4: LabView code part 4

44 Figure A5: LabView code part 5

Figure A6: LabView code part 6