High Power Ultrafast Yb:fiber Laser

A Thesis presented

by

Xinlong Li

to

The Graduate School

in Partial Fulfillment of the

Requirements

for the Degree of

Master of Science

in

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 AdvisorAssistant Professor, Department of Physics and Astronomy, Department of Chemistry

Eden Figueroa - Committee MemberAssistant Professor, Department of Physics and Astronomy

Matthew Dawber - Committee MemberAssociate Professor, Department of Physics and Astronomy

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

This thesis is accepted by the Graduate School

Charles TaberDean of the Graduate School

ii

Abstract of the Thesis

High Power Ultrafast Yb:fiber Laser

by

Xinlong Li

Master of Science

in

Instrumentation

(Physics)

Stony Brook University

2015

High power ultrafast laser pulses have broad applications in many fields such as mi-cromachining, real time imaging of ultrafast process, and frequency-comb-based precisionspectroscopy, enabling large numbers of breakthroughs in science and technology. Theyeven open the door to the attosecond (10−18 s) world via high harmonic generation thusgaining the insight into a wide range of electron dynamics. In this thesis, I present a linearlyamplified Yb:fiber laser with 55 W average output power and 150 fs pulse duration. Thislaser 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 11.1 Mode-Locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Frequency Comb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Pulse Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 High Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 Fiber Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Nonlinear Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 High Power Yb:Fiber Comb 162.1 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Comb Tooth Linewidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Stretcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4 Optical Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.6 FROG Measurement and Pulse Duration . . . . . . . . . . . . . . . . . . . . 252.7 Beam Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.8 Relative Intensity Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.9 Interlock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.10 LabVIEW Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.11 Mechanical Design and Cooling system . . . . . . . . . . . . . . . . . . . . . 32

3 Conclusion 35

Bibliography 38

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

iv

List of Figures

1.1 Spectrum consists of discrete lines with equal spacing. . . . . . . . . . . . . . 11.2 (a) 10 frequency modes without model-locking. (b) Mode-locking with 2, 5,

10 frequency modes, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Schematic of a conventional pulse laser. . . . . . . . . . . . . . . . . . . . . 21.4 (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 timedomain. Pulses are equally spaced by the time T = 1/f . The phase differencebetween carrier and envelope is shifted by ∆Φ between adjacent pulses. . . . 4

1.5 Schematic of compressor (top view). Light with longer wavelength will travellonger distance than shorter wavelength. G1 and G2 are gratings. G: normaldistance between gratings. Roof reflector changes the beam hight so we cansort out the output beam of the compressor. Detailed information of parts isin table 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Refractive index distribution of dressed cladding fiber [1] . . . . . . . . . . . 61.7 Three step model for HHG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.8 Conventional HHG schematic. Infrared femtosecond laser pulses are focused

into a gas to achieve intensities in the strong field regime. A metallic filterblocks the fundamental driving pulses . . . . . . . . . . . . . . . . . . . . . . 7

1.9 (a) Attosecond photon burst at each half wave cycle. (b) Single attosecondburst each pulse. (c) Spectrum of (a). ω0 is the central frequency of funda-mental driving laser. ωc is the cut off frequency where the yield of harmonicsstart to drop. (d) Spectrum of (b). . . . . . . . . . . . . . . . . . . . . . . . 8

1.10 Setup of intracavity HHG chamber. Fundamental driving pulses are focusedto argon gas to generate XUV pulses. The XUV pulses are coupled out byusing a crystal at Brewster angle. . . . . . . . . . . . . . . . . . . . . . . . . 9

1.11 Illustration of phase locking (frequency domain). . . . . . . . . . . . . . . . . 91.12 Schematic of a high-power, double-clad fibre amplifier. . . . . . . . . . . . . 101.13 (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. . . . . . . . 101.14 Absorption and emission cross section of Ytterbium [45]. . . . . . . . . . . . 111.15 MATLAB simulation of gain narrowing (code from Donald Willcox). . . . . . 121.16 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. 131.17 Simulation by MATLAB (code from Donald Willcox). The upper figures show

the power distribution along the fiber. The lower figures show the accumulatedB-integral along the fiber. CTP stands for counter propagating between pumplaser and signal laser. COP stands for co-propagating. . . . . . . . . . . . . . 14

2.1 The main parts of the high power IR laser . . . . . . . . . . . . . . . . . . . 162.2 Scheme of oscillator. Detailed information of parts is in table 1. . . . . . . . 172.3 Spectrum of oscillator with two different WDMs. . . . . . . . . . . . . . . . 192.4 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 beatnote signals with n = 1 is shown. . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Beat signal measured with different RBW . . . . . . . . . . . . . . . . . . . 202.7 Scheme of stretcher (Figure from OFS website) . . . . . . . . . . . . . . . . 212.8 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 detailedinformation of the parts (L1, L2, D1, etc) can be found in table 2. L standsfor lens. D stands for dichroic filter. I stands for isolator. M stands for planemirror. HWP stands for half wave plate. BD stands for beam damp. . . . . 22

2.9 (a) Amplification Curve of Pre-amplifier. (b) Amplification Curve of poweramplifier before compression and after compression. . . . . . . . . . . . . . . 24

2.10 (a) Power amplifier spectrum of its seed light, 25 W amplified light and 70 Wamplified light. The spectrum of oscillator is also shown. (b) The reflectivityof the dichroic mirrors D1 and D2 (D4), which show cutoff at ∼1010 nmand ∼1030 nm, respectively. This is single measurement without averaging.The data for D2 has been squared because the output of pre-amplifier will bereflected twice (D2 and D4) before going into the power amplifier. . . . . . . 24

2.11 A schematic of FROG measurement. BS is Beamsplitter. M1 and M3 areplane mirrors. M2 is a focusing mirror. The stage can control the delay timeof split pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.12 Raw data of FROG, measured SHG intensity at different delay and differentwavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 byFourier transform from measured spectrum (figure 2.10a). (b) Reconstructedspectrum and spectral phase at 55 W. . . . . . . . . . . . . . . . . . . . . . 27

2.14 (a) Temporal pulse shape when third order phase dominates. (b) Spectrumand spectral phase when third order phase dominates. . . . . . . . . . . . . . 27

2.15 (a) Beam mode at low output power (2 W) (b) Beam mode at high outputpower (55 W). Unit in µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.16 Measured RIN of oscillator, pre-amplifier and power-amplifier. Each curve iscombined by three measurements from left to right: 6.25 kHz span using FFTspectrum analyzer, 100 kHz span using FFT spectrum analyzer, 2 MHz spanusing Rigol spectrum analyzer, . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.17 Circuit diagram of the interlock (Designed by Melanie Raber and Yuning Chen) 312.18 Laser Control Program by LabVIEW . . . . . . . . . . . . . . . . . . . . . . 322.19 Beam damp. BD1 in figure 2.8. . . . . . . . . . . . . . . . . . . . . . . . . . 332.20 Beam damp. BD2 in figure 2.8. . . . . . . . . . . . . . . . . . . . . . . . . . 332.21 Fully water cooling for rod fiber. Water flows in from port 1 and flows our

from port 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.1 Schematic of cavity HHG, monochromator and surface experiment. . . . . . 353.2 Photo of high power ultrafast laser. Pre-amplifier (green fiber) and power

amplifier (straight rod) are shown. . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Photo of HHG chamber and monochromator chamber. . . . . . . . . . . . . 36

vi

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

vii

List of Tables

1 Detailed information of parts in the oscillator (figure 2.2). . . . . . . . . . . 182 Detailed information of parts in the optical amplifier (figure 2.8). . . . . . . 233 Detailed information of parts in the compressor (figure 1.5). GD stands for

groove density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Dispersion parts in the laser. Normal dispersion: φ2 < 0, φ3 < 0. Anomalous

dispersion: φ2 > 0, φ3 > 0. FS stands for fused silica. TGG stands forTerbium Gallium Garnet crystal. . . . . . . . . . . . . . . . . . . . . . . . . 25

viii

Acknowledgement

This work owes much to the people who provided me help and opportunity. I want tothank my advisor professor Thomas Allison who allowed me to join his research group andchoose this project for me. I have learned a lot of knowledge and skills in this project. Iwant to thank Christopher Corder for the instruction and cooperation during this project. Ialso want to thank Peng Zhao who worked with me. Thanks to Melanie Reber and YuningChen for their initial work and continuous help in this project. Thanks to Donald Willcoxfor providing me the MATLAB code.

Besides, I want to thank professor Harold Metcalf for his MSI program and choosingcommittee members for me. Thank professor Eden Figueroa, Matthew Dawber, MeiganAronson 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 fiancee Boni. Her intelligence and assistancehas made me smarter and better.

ix

1 Introduction

High power ultrafast laser pulses have broad applications in many fields such as micro-machining [2], real time imaging of ultrafast process [3], and frequency-comb-based precisionspectroscopy [4], enabling large numbers of breakthroughs in science and technology. Theyeven 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 femtosecondpulses. The wave packet of these pulses occupy only a few times of its wavelength along itspropagation direction and also are in a diffracted-limited beam and hence can be focused toa spot size comparable to the wavelength. Therefore, these pulse can provide peak powerin Petawatts level [9] and peak intensity as high as 1020 W/cm2 [10, 9]. Even at muchlower intensity, the interaction between light and matter becomes highly nonlinear. As aconsequence, the laser field is strong enough to trigger optical-field ionization [11] and otherstrong nonlinear effects such as HHG.

In this thesis, I present a linearly amplified fiber laser with 55 W average output powerand 150 fs pulse duration. This laser is used for cavity-enhanced high harmonic generationto 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 asmode-locking, frequency comb, fiber lasers and so on. Chapter 2 will introduce the detailsof our high power fiber laser, such as oscillator, amplifier, etc. Chapter 2 will also presentthe 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’suncertainty 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 8THz of bandwidth, far exceeding that available from electronics. The spectrum of a Gaussianpulse is also in Gaussian shape within a frequency range. The spectrum of a series of pulseshas a interference structure like a comb (figure 1.1). The electric field of an mode-lockedlaser can be expressed in the frequency domain

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, 10frequency modes, respectively.

Here we have assumed the spectrum consist of a series of lines of constant amplitudespaced by constant frequency mode ωs (figure 1.1). If the φn(t) is a random distributedphase, the laser intensity (∝ E2

0) will behave like noise (figure1.2a). If we have a mechanismfor locking φn(t) of all the lines, the field of different lines will interfere with each other

Etot = E0eiω0t+iφn(t)

∑einωst = E0e

iω0t+iφn(t)sinNωst/2

sinωst/2(1.3)

then we can get mode-locking. Figure 1.2a shows the light intensity consisting of 10 frequencymodes with random phase. It is very noisy. Figure 1.2b shows the pulsed laser intensityconsisting of 2, 5, 10 frequency modes with mode-locking. Notice that the more frequencymodes 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, Thesaturable absorber has larger loss at low intensity and less loss at high intensity. So shorterpulses, which have larger intensity, experience less loss in the absorber, thus is more stableand preferred by the laser cavity. The saturable absorber can be a real absorber, such as asemiconductor, 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-envelopoffset (CEO) frequency, fr is the mode spacing and n is an integer O(106).

The mode spacing frequency, fr, is the inverse of the laser cavity round trip time T andis determined by the laser cavity round trip length lc. It is also called the repetition rate.

fr =1

T=lcvg

(1.5)

where vg is the average group velocity inside the oscillator cavity. CEO frequency, fCEO, isdetermined by the round trip carrier-envelop phase (CEP) shift

fCEO =∆ΦCEO

2πT(1.6)

As seen in figure 1.4, ∆ΦCEO is caused by the difference between phase velocity, vp, andgroup velocity, vg. It can be determined by [13]

∆ΦCEO = lcωc(1

vg− 1

vp) (1.7)

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

fCEO =∆ΦCEO

2πT=ωc2π

(1− vgvp

) (1.8)

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 thefrequency 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 megahertzlevel), we can count the frequency very accurately by using electronic instruments: (1) fr isjust the repetition rate of pulses and can be measured directly using a counter. (2) fCEOcan be obtained by measure the beat note between comb tooth f2n and comb tooth 2fn inthe 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 canmeasure the relative frequency between transitions very precisely, but also can know theabsolute transition frequency very precisely.

John L. Hall and Theodor W. Hansch, in 2005, were awarded the Nobel Prize “for theircontributions to the development of laser-based precision spectroscopy, including the opticalfrequency comb” [16][17]. In addition, XUV comb-based precision spectroscopy has beenreported in 2012 [4].

In addition, to measure fCEO using above method needs a octave spectrum. For someapplications, 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 hasa very narrow bandwidth of usually kHz level.. (b) Pulse train in the time domain. Pulsesare equally spaced by the time T = 1/f . The phase difference between carrier and envelopeis shifted by ∆Φ between adjacent pulses.

1.3 Pulse Propagation

The refractive index is a function of frequency in a material. Thus the phase shiftduring propagating in a crystal (e.g. optical fiber) is also a function of frequency. Usingthe convention E = E0e

j(ωt−βz) we can expand the wave propagation phase factor in Taylorseries [12]

β(ω) = n(ω)ω

c= β0 + β1(ω − ω0) +

1

2β2(ω − ω0)

2 +1

6β3(ω − ω0)

3 + · · · (1.10)

Assuming the optical path the pulses propagate is L, then the phase shift can be expressed

φ(ω) = −β(ω)L = φ0 + φ1(ω − ω0) +1

2φ2(ω − ω0)

2 +1

6φ3(ω − ω0)

3 + · · · (1.11)

where β1 is equal to the inverse of the group velocity

β1 =dβ

dω=

1

vg(1.12)

and the first order phase, φ1, is called group delay

φ1 = −Lβ1 = − Lvg

= −T (1.13)

which is equal to the round trip time of pulse in the laser cavity as well as the time delaybetween 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 affectthe pulse shape. The second order phase, φ2, which starts to affect the pulse shape, is alsocalled 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 itwith a flat spectral phase φ(ω) =const. This is called transform-limited pulse. This pulsehas zero GDD or higher order dispersion. Usually, the pulses will gain dispersion duringits 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 normaldispersion.

To compress the pulses to nearly transform-limited duration, we need anomalous dis-persion to compensate the normal dispersion of the fibers. Usually we realize this pulsecompression by using a pair of gratings [18].

Figure 1.5: Schematic of compressor (top view). Light with longer wavelength will travellonger distance than shorter wavelength. G1 and G2 are gratings. G: normal distancebetween gratings. Roof reflector changes the beam hight so we can sort out the output beamof 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 lightwith 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]

φ(ω) = −2ω

cGcosθD(ω) + const (1.14)

From equation (1.14), we can get φ2 = d2φ(ω)dω2 > 0 and φ3 = d3φ(ω)

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 thedispersion of the fiber (φ2 < 0, φ3 < 0). However, this is not always true. We previouslydefined the propagation constant

β(ω) = n(ω)ω

c(1.15)

This is true for a plane wave not subject to boundary conditions. When the wave equation issubject to boundary conditions, there still exists a relation β(ω), but equation 1.15 needs tobe modified. The difference β(ω)−n(ω)ω

cis called waveguide dispersion, and becomes more

important as the light is confined to smaller volumes such as fibers. Therefore, althoughthe materials, such as fused silica, always have normal dispersion at ∼1 µm, the waveguidecharacter of fibers enable us to set a certain boundary conditions for light propagating, thuschanging 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 indexstructure of DCF is shown in figure 1.6.

Therefore, with different length combination of normal single mode fiber (SMF) andDCF, we can get different ratio of second to third order dispersion [20, 21], which enablesmatching to the diffraction-grating-based compressor. (higher order dispersion has much lessinfluence on pulse duration).

1.4 High Harmonic Generation

The high power femtosecond laser I will present in this thesis is used for high harmonicnegeration (HHG) experiment. HHG can be used to convent optical lasers to the XUV oreven 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-Xrayand hard X-ray). The lifetime of the high-energy excited state is so short that it needsincredible 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 filledwith gas to create highly nonlinear processes, in which high harmonics of the focusing beamcan be generated. Popmintchev et al. have recently reported ultrahigh harmonics greaterthan 5000 [23].

As shown in figure 1.7, HHG is a strong field ionization process, which can be describedby the three step semiclassical model [24]. First, the electron is tunnel-ionized out of theatom and gain kinetic energy by the strong laser field. Second, after a half wave cycle, thelaser field changes its direction and pulls the electron back to the ion. In the last step, theelectron will recombine with the ion and emits a high-energy photon (XUV or even softX-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 intoa gas to achieve intensities in the strong field regime. A metallic filter blocks the fundamentaldriving pulses

half cycle of laser wave, there will be an XUV attosecond photon burst (figure 1.9a) and itsspectrum consists of odd-order harmonics of fundamental driving light (figure 1.9c). Thereare 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 (figure1.9c) will spread and form a continuous broad spectrum (figure 1.9d). Besides, if we canselect one of the harmonics like what we propose to do in our lab, the isolated attosecondpulses (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] (figure1.8). One of the reasons is noble gas atoms have the highest ionization potentials in theperiodic table, allowing them to survive the rising edge of a laser pulse without being ionizedearly in the pulse before the intensity reaches its maximum. Another reason is the sphericalsymmetry of noble gas can let us ignore the orientation of the atoms or molecules withrespect to the laser field.

Generally speaking, an intensity of 1014 W/cm2 is required to achieve HHG [28]. Forconventional HHG (figure 1.8), it needs kilowatts average power to produce 100-MHz-levelrepetition-rate XUV pulses. This is why conventional HHG is limited by< 100 kHz repetition

7

(a) (b)

(c) (d)

Figure 1.9: (a) Attosecond photon burst at each half wave cycle. (b) Single attosecond bursteach pulse. (c) Spectrum of (a). ω0 is the central frequency of fundamental driving laser. ωcis 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, wecan get XUV pulses with repetition rate larger than 100 MHz [30].

repetition rate ≈ 2× 50 W × 200

1014 W/cm2 × π × (15 µm)2 × 150 fs≈ 200 MHz (1.17)

where 50 W is the average power we propose to send into the HHG cavity, 200 is the designedcavity build up (number of pulses can be stored in the cavity at the same time), 15 µm is thefocused beam radius at the argon gas jet, 150 fs is the pulse duration of our laser. We canconclude the higher the cavity finesse (build up) is, the lower fundamental power we need tosend into the cavity. However, the finesse can not be infinite high. It is limited by intensityclamping and optical bistability [29].

As shown in figure 1.10, the fundamental driving pulses are sent into a six-mirror opticalenhancement cavity inside a vacuum chamber to achieve intracavity HHG. The round triptime of this cavity is adjusted to be the same as the time delay between adjacent pulses andthe ∆φCEO of this cavity is the same as that of oscillator. Thus pulses arriving at differenttime can overlap in the cavity. As long as the pulses are coherent and mode-maching with thecavity, they can be added and stored in the cavity, leading to an intensity that is hundredsof 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 toargon gas to generate XUV pulses. The XUV pulses are coupled out by using a crystal atBrewster 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 experiencedrapid development in producing high power lasers after the demonstration of the concept ofdouble cladding [32]. In the early 1990s, only a few watts output power was reached [33]. Itrapidly 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 Win 2005 [37] and near 1 kW in 2009 [38].

Most HHG sources are achieved by using Ti:sapphire lasers [39]. However, populationinversion in Ti:sapphire requires pumping around 532 nm, where powerful laser diodes arenot available. What’s more, although sapphire (monocrystalline Al2O3) has an excellentthermal 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, whichindicates 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 tovolume ratio leads to better thermal performance. Take Yb:fiber as an example, the energy ofpump photon is ∼1.3 eV while the signal photon is ∼1.1 eV, which indicates a much smallerquantum defect. Furthermore, the double cladding structure of most rare-earth-doped fiberallows 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 NKTaeroGAIN-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 requiresa very high beam quality to focus the pump light into a small spot to couple it into thecore. 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 theinner cladding whose diameter is hundreds of micrometers, which allows us to use multi-mode pump laser. And high power multimode diode lasers are available [42]. Also, the seedlaser 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 widelyused to produce much better optical performance [43]. Conventional fibers have differentmaterials for core and claddings to produce refractive index difference. This limits the sizeof the core and hence the power the fiber can hold. However, pioneered by the researchgroup of Philip St. J. Russell in the 1990s [44], the PCF can support much larger mode fielddiameter (MFD), which is defined as 2w where w is the radius at which the field amplitudedrops by 1/e and intensity drops by 1/e2 from their peak values. Figure 1.13 shows thestructure of PCF used in our lab. The whole fiber is made of one material with complicatedair holes structure (the little circle structures in the figure). This kind of structure can guidesingle 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 beintroduced 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. Thewavelength dependence of the Yb absorption and emission cross sections are shown in figure1.14, There is a tall and narrow absorption peak at 975 nm and a broad peak around 915nm. The emission cross section, however, exhibits a broad peak around 1030 nm and slowlyfalls 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 onthe efficiency and available pump width constraints. We notice there is also a tall emissionpeak at 975 nm. But we can not amplify femtosecond pulses at this wavelength due toits 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 isnarrowed to ∼14 nm.

1.6 Nonlinear Effect

Average power scaling is straightforward in fiber lasers. However, it is quite more difficultto obtain high peak power using fiber lasers due to their tiny core radius. The pulses focusedinto the core of the fiber have a very high intensity, which can cause nonlinear effects quiteeasily. Besides, the long path length of fibers can easily accumulate the nonlinear effectseven 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 usuallydominates the narrowband signals), which arises from the interaction between light andacoustic waves in the fiber. SBS is characterized by a sharp power threshold, beyond whichthe energy starts to transfer from the signal laser to a frequency-downshifted (by ∼11 GHzin fused silica [31]) beam propagating to the opposite direction to the signal laser. This notonly limits the amplified power but also easily destabilizing the seed oscillator or amplifierdue to its counter-propagating character.

Another nonlinear effect is stimulated Raman scattering (SRS, which usually dominatesthe broadband signals), which arises from the interaction between light and vibrations ofthe glass lattice. The same as SBS, SRS also transfer energy from the signal laser to afrequency-downshifted (by ∼13 GHz in fused silica [31]) beam. The difference is SRS cantransfer energy to beams propagating in both forward and backward direction. Also, SRScan be seeded by amplified spontaneous emission (ASE). SBS and SRS set the fundamentalpower limits of fiber lasers [47]. In our lab, we do not output such high power and we canignore these two nonlinear effects.

The third nonlinear effect is called Kerr effect, which is the main consideration in ourfiber laser. Because the peak intensity is quite big for ultrafast pulses, so the refractive indexof 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, fusedsilica has a nonlinear index of ∼ 3 × 10−16 cm2/W [48]. One of the phenomena caused bykerr effect is self-phase modulation (SPM) [49]. For a Gaussian pulse, the intensity in thetime domain is

I(t) = I0e−t2/t2p (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

n(t) = n0 + n2I0e−t2/t2p (1.21)

The phase evolution in the fiber of length l is

φ(t) = ω0t−2πl

λ0n(t) (1.22)

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

ω(t) =dφ

dt= ω0 +

4πn2lI0t

λ0t2pe−t

2/t2p (1.23)

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 thespectrum broadening of pulses after propagation along a piece of fiber. If we have two laserbeams with different frequency or different polarization propagating in the fiber, we can alsoobserve cross-phase modulation (XPM).

The kerr effect is not always detrimental for fiber lasers. For example, we need thisnonlinear 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 muchshorter duration [27]. However, for our laser, we need a very quiet frequency comb lockedwith the HHG enhancement cavity. From the above equation we can see the SPM cantransfer noise from amplitude to phase. For our amplifier, the noise of pump source will betransferred to the phase of the frequency comb.

The main parameter to evaluate kerr effect is the B integral, which is defined as

B =2π

λ

∫ l

0

n2Ipeak(z)dz (1.24)

where l is the length of the fiber. This B integral evaluate the total on-axis nonlinear phaseshift accumulated in the fiber. The criteria B < 1 rad defines linear amplification. So thephase 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 averagepower 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 amplifythe 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. ThenI calculate the accumulated B integral.

Figure 1.17: Simulation by MATLAB (code from Donald Willcox). The upper figures showthe power distribution along the fiber. The lower figures show the accumulated B-integralalong 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 groundstate 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)

N2(z) =R1→2 +W1→2

R1→2 +R2→1 +W1→2 +W2→1 + A2→1

(1.26)

where N1 is the population of ground state and N2 is the population of the excited state. A isthe Einstein coefficient of spontaneous emission. W is the coefficient of stimulated transitionfor the signal laser and is related to the laser power and the transition cross section shown infigure 1.14. R is the coefficient of stimulated transition for the pump laser. The simulationdivides 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

dPk(z)

dz= (σk,2→1N2(z)− σk,1→2N1(z))NtotPk(z) (1.27)

Ptot =∑k

Pk (1.28)

where k is the kth frequency range, Pk is the power of the kth frequency range, Ptot is thetotal power and Ntot is the total effective doping rate of the fiber. (Note the effective dopingrate is different for pump light and seed light because pump light is propagating in thecladding 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 topropagate 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 powerand 150 fs pulse duration. This laser is used for cavity-enhanced high harmonic generationto 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 thatoutput an average power of 38 mW. Then, there is an fully-fiber-based stretcher, stretchingthe pulses to several hundred picoseconds. With this large chirp, the peak intensity ofpulses will be much lower thus reducing the nonlinear effects in the subsequent amplificationprocess. 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. Themaximum power of this pump laser is 30 W but we only turn it up to 16 W because it isalready enough for seeding the power amplifier. At this pump power, the amplified signalpower will be 6 W. Then we have a second amplifier, a rod-type LMA fiber pumped by 975nm commercial diode laser. We turn this pump laser up to 170 W and amplify the signalpower to 70 W. In these two amplifiers, the B integral is small enough (< 1 rad) to maintaina linear application. In the end, we have a pair of gratings to compress the pulses to 150 fsand 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 thelaser cavity by a wavelength division multiplexer (WDM) and the Yb:fiber acts as a gainmedium. We can change the cavity length by moving the roof reflector R1. We use a pairof gratings G1 and G2 to compensate this material dispersion of the fibers and optics. Thewaveplates HWP and QWP is used to set the polarization of the pulses. The polarizingbeam 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 usedto lock the oscillator with the HHG enhancement cavity. The detailed information of theseparts 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 tothe 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 differentintensity will experience different phase evolution inside the fiber thus have different outputpolarization. By putting a PBS after the fiber, the light intensity transmission through thePBS will become light intensity dependent. Therefore, by setting a proper position for thewaveplates, 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 pulsespropagating inside the fiber can be described by a modified nonlinear Schrodinger equation[52]

∂Ax∂z

= iβx2

∂2Ax∂t2

− iγ(|Ax|2 + 2|Ay|2)Ax +1

2(g − l)Ax (2.3)

∂Ay∂z

= iβy2

∂2Ay∂t2

− iγ(|Ay|2 + 2|Ax|2)Ay +1

2(g − l)Ay (2.4)

where g is the gain factor and l is the loss factor in the fiber, γ = (2πn2)/(λ0Aeff ) is thenonlinear parameter at the central wavelength λ0 and effective fiber core area Aeff . Thefirst terms on the RHS of the equations are for dispersion where βx,y = 2π/λx,y. The secondterms in the parenthesis are SPM and XPM where |Ax,y|2 are proportional to intensities.The third terms describe the gain and loss in the fiber.

17

Part Name DetailsM1 D-shaped mirror, Thorlabs PFD10-03-P01M2 Plane mirror, Thorlabs BB1-E03R1 Right angle prism, Thorlabs PS908H-C

C1&C2 Fiber port collimators, Thorlabs PAFA-X-5-CHWP Zeroth order half wave plate, Thorlabs WPH05M-1030QWP Zeroth order quarter wave plate, Thorlabs WPQ05M-1030PBS Polarizing beamsplitter cube, Thorlabs PBS103

G1 & G2 Gratings, Wasatch Photonics 2254-B-21EOM United Crystals, LiTaO3, Y-cut, Cr, Au electrode coatingWDM WD202G-APC

Yb:Fiber Thorlabs YB1200-4/125975 nm Pump Laser Oclaro Technology Limited LC96L76P-20R

SMF Single mode fiber, Thorlabs P4-980AR-2I1 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 (∼35nm) of the spectrum can in principle support ∼50 fs pulses but it will experience gainnarrowing process in the amplifiers. Initially, we used a WDM working at 1030 nm. Thenbecause of the dichroic mirrors we used in the amplifier (see amplifier section), we replacethe WDM with a 1053 nm one. Even though the bandwidth of both WDMs are ±5 nm, theoutput spectrum is still quite broad. We can see the spectrum shift to red after we replacethe WDM and there is more power at 1064 nm and then we can produce beat note betweenour oscillator and 1064 nm Nd:YAG laser to measure the linewidth of comb tooth (see combtooth linewidth section).

In addition, changing the polarization status of pulses by rotating the waveplates canalso 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 lockthe oscillator to the HHG cavity with as small power loss and as low noise as we can, weneed the linewidth of spectrum tooth narrower than the linewidth of the cavity mode. Fora cavity with a ∼2% loss , this gives us the finesse

F =π(R1RM)1/4

1− (R1RM)1/2≈ 300 (2.5)

where R1 = 0.98 is the reflectivity of the lossy mirror and we treat other mirrors of the cavityas RM = 1. This finesse gives us the cavity mode linewidth

δν =FSR

F=

78 MHz

300≈ 260 kHz (2.6)

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 betweenthe output of the oscillator and our CW Nd:YAG laser (1064 nm, Mephisto from CoherentInc.). As seen in figure 2.4, the Nd:YAG laser will beat with different comb teeth, generatinga 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 MHzand its harmonic: 156 MHz) measured with an RF spectrum analyzer. By changing thedistance of the gratings in the oscillator, we can change the frequency of the two beat notesignals. When f1 = f2, there will only be one beat note signal between any of the repetitionrate signals. When f1 = 0 or f2 = 0, we can not observe any beat note signal on the spectrumanalyzer. 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 abandwidth 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 withn = 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 thecomb tooth linewidth by seeing at what resolution bandwidth (RBW) the power in thecoherent carrier goes down. Seen from figure 2.6, we decrease the RBW from 100 kHz to 10kHz, the signal level starts to drop after 30 kHz, which indicates the linewidth of beat noteis comparable to the RBW of the spectrum analyzer. Ignoring the linewidth of Nd:YAGlaser, 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 tothe HHG enhancement cavity with low noise and is among the smallest free-running combtooth 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, wecan 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 lowerthe 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 fullyfiber based. The single mode fiber (SMF) has normal dispersion (φ2 < 0, φ3 < 0). Thedressed cladding fiber (DCF) has normal second order dispersion (φ2 < 0) and anomalousthird order dispersion (φ3 > 0). Therefore, with different length combination of SMF andDCF, we can get different ratio of second to third order dispersion, which enables matchingto our diffraction-grating-based compressor.

Based on the design of our compressor, the second order dispersion is -5.22 ps2 and thethird order 0.0216 fs3. The length of SMF is 31.9 m and the length of DCF is 11.8 m. Thereis 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 gaussianpulse, the electric field can be expressed as

E(t) = Ete− ln2

2( 2t

∆t)2ejω0t+ψ(t) (2.9)

where ∆t is the FWHM of the pulse. The FWHM of the output pulse after propagating inthe stretcher is [52]

∆tout =

√∆t4 + 16(ln2)2φ2

2

∆t(2.10)

Assume the input pulses are Fourier transform limited, which gives ∆t =∼ 50 fs withspectrum 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) of31 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 largeMFD (65 µm). The wavelength of pump laser is at 975 nm. This is because this rod-typefiber is only 0.8 m. We want the fiber to efficiently absorb the pump light and the absorptionpeak 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 the0.8 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. Istands for isolator. M stands for plane mirror. HWP stands for half wave plate. BD standsfor beam damp.

There are also other parts in the amplifier system. The isolator I1 is used to protect theoscillator, preventing the amplified spontaneous emission (ASE) in the pre-amplifier and thereflected seed laser from going back into the oscillator. I2 and I3 can protect the pre-amplifierand power amplifier, respectively. Because both isolators and fibers need the input seed laserto 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 wewill talk about that in a later section. The detailed information of all the parts in figure2.8 can be found in table 2. Even though D5 is designed for long wave pass, there is stillsignificant amount of signal light reflected in such a high power. So we put another dichroic

22

Part Name DetailsL1 Lens, Thorlabs LA 1289-B, f = 30 mmL2 Lens, Thorlabs LA 4532-B, f = 32 mmL3 Lens, Thorlabs LA 3026-B, f = 26 mmL4 Lens, Thorlabs LA 1134-B, f = 60 mmL5 Lens, Thorlabs LA 4532-B, f = 32 mmL6 Lens, Thorlabs LA 5040-B, f = 40 mmD1 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-VLPI2 & I3 Isolator, EOT 1200462HWP Zeroth order half wave plate, Thorlabs WPH10M-1030M1 Altechna low GDD HR broad band mirror

5 m crystal fiber NKT Photonics DC-200/40-PZ-Yb, MFD = 31 µm915 nm pump laser nLight Photonics 1040677, maximum output 30 W0.8 m crystal fiber NKT Photonics aeroGAIN-ROD-PM85, MFD = 65 µm975 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 pumpdiode and causing damage to the pump diode. Dichroic mirrors D2 and D3 realize the samefunction.

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 Wand 200 W, respectively. However, we decide to only turn up the pre-amplifier to 16 W andpower amplifier to 170 W. This can provide 55 W final output, which is enough power forsubsequent 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 about35 nm, which is quite broad, and the central wavelength is at ∼ 1040 nm. The spectrumof pre-amplifier is a little narrower (∼30 nm) than the oscillator. The spectrum loss at lowwavelength is because of the dichroic mirror D2 and D4 (figure 2.8) which allows the pumplaser to pass through and reflects the signal laser. The cutoff wavelength of the dichroicmirror D2 and D4 is at 1030 nm (figure 2.10b). That is to say, the laser with wavelengthsmaller than 1030 nm does not get reflected by these two dichroic mirrors to seed the poweramplifier.

The spectrum of power amplifier is even narrower (14 nm.) This is because of gainnarrowing. 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 poweramplifier before compression and after compression.

(a) (b)

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

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. Wecan compress them back to femtosecond pulses after amplification. This is realized by usinga pair of gratings shown in figure 1.5. The detailed information of the parts is in table 3.

Part Name DetailsG1 & G2 GD=1250 mm−1, Wasatch Photonics custom diffraction gratings

Roof reflecter two mirrors, Altechna low GDD HR broad band mirror, size: 3′′ × 1′′

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

The lasers is designed to work at λ =1030 nm. And we set the gratings working atLittrow angle.

2sinθi = Nλ ⇒ θi = 40◦

where N = 1250 mm−1 is the groove density of gratings. By setting the normal distance ofgrating G = 40 cm. We can calculate the second order dispersion and third order dispersionof the compressor according equation 1.14. Now we list all the dispersion parts of our laserin table 4.

Part Name GDD (ps2) TOD (fs3) notesStretcher -5.27 2.16×107

Amplifiers -0.11 -2.39×105 FS, total length = 5.8 mIsolators -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. Anomalousdispersion: φ2 > 0, φ3 > 0. FS stands for fused silica. TGG stands for Terbium GalliumGarnet crystal.

2.6 FROG Measurement and Pulse Duration

After compression, we can get high-power ultrafast pulses. We use frequency-resolvedoptical gating (FROG) to measure the pulse duration and its spectral phase.

FROG is a standard method to measure ultrashort laser pulses [56]. The basic setupfor FROG is shown in figure 2.11. Like a Michelson interferometer, the input pulse is firstsplit and sent to two arms. The path length of one of the arms can be scanned by a delaystage, so the delay between pulses can be scanned. After the focusing mirror M2, the twopulses 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 generatedno matter how big the delay is. When the delay is small enough, the two pulses will overlapat the BBO crystal and non-collinear second harmonic generation (SHG) will occur. Thenwe send this beam into the spectrometer and record the spectrum at different time delay. Inthe end, using a phase reconstruction algorithm [57], we reconstruct the shape and phase ofinput pulse in both time and frequency domain.

Figure 2.11: A schematic of FROG measurement. BS is Beamsplitter. M1 and M3 are planemirrors. 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 ouroutput pulses of the laser. The raw data is shown in figure 2.12. It is basically the intensityof the middle SHG beam at different time delay and different wavelength. The softwarecoming with the FROG can let us adjust the laser status in real time. By adjusting thedistance of the compressor gratings and their diffraction angle, we minimize the size of rawdata 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 differentwavelength

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(a) (b)

Figure 2.13: (a) Reconstructed temporal pulse shape at low power and high power. Durationis 150 fs. The Fourier transform limited pulse (120 fs) is obtained by Fourier transform frommeasured 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 andspectral phase when third order phase dominates.

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(a) (b)

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

The reconstructed pulses are shown in figure 2.13. In the time domain, we present thepulse shape in low power, high power and the Fourier transform limited pulse obtained byFourier 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 differencebetween low power and high power without changing the distance of the two compressorgratings. 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 andspectral phase will be different at different output power. So for each output power, therewill 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 areminimizing 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 orderphase will dominate and there are undesired satellite pulses (figure 2.14a). Even though themain pulse in figure 2.14a is shorter (130 fs) than that in figure 2.13a, the satellite pulsesoccupy 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 (thereis residual second order phase).

2.7 Beam Mode

The output beam measured at the output of compressor is shown in figure 2.15. Tocapture the whole beam in the camera, I use a telescope with a magnification of 1/2. Sothe beam size shown in the figure is half of the original beam size. At low power, the beammode 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 highpower laser will heat the crystal (∼3 cm long) in the isolator. Because the center of the

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beam has a higher power level than the edge of the beam, the temperature at the center ofthe crystal will be higher than the edge of the crystal. So the refractive index at the centerwill be larger than that at the edge. Therefore, the crystal will act as a lens and focus thebeam. 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 canbe generated by the vibration of optics, the instability of the pump source and the quantumnoise. 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]

R(ω) =PE(ω)

PDC

where PE(ω) is the measured electrical noise power per unit bandwidth from a square lawdetecter 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 iscombined by three measurements from left to right: 6.25 kHz span using FFT spectrumanalyzer, 100 kHz span using FFT spectrum analyzer, 2 MHz span using Rigol spectrumanalyzer,

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 relativefluctuation of the square of the laser intensity with the unit dBc/Hz over the measuredbandwidth.

We measured RIN using a homemade (by Yuning Chen) AC-coupled detecter. Also, weuse 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 upthe power amplifier will not add noise to the laser. The noise will show up as long as thepower 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 largepopulation inversion. A spontaneous emission of one atom will cause stimulated emissionof other atoms. This can cause a very big energy release within a very short time scaleand generate a large pulse with very high intensity, leading to catastrophic failure of thefiber. To avoid this kind of fiber damage, the pump laser must be shut down when anyaccident happens to the seed laser. In addition. we want our laser working at pulse modebut sometimes the laser will lose mode-locking due to some interruption. So we built thecircuit 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 seedpower. The detector measures the train of optical pulses produced by the oscillator, puttingout an RF waveform consisting of repetition rate frequency ωr and its harmonics. Consideringthe fundamental ωr

V = V0cos(ωt) (2.11)

An RF splitter (Mini-Circuits ZFSC-2-4+) splits the electrical power into two channels of afrequency mixer (Mini-Circuits ZAD-1+)

V ′ =V02

cos(ωt)× V02

cos(ωt+ φ) =V08

[cos(2ωt+ φ) + cosφ] (2.12)

where the phase term φ is caused by the length difference of the BNC cables. After the lowpass filter, only the DC signal V0

8cosφ 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, theDC signal is small compared to the reference, the circuit will disable the power supply of thepump 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, thelaser 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 an-other 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 #2controls my pre-amplifier and 200 W Diode controls my power amplifier. Also, There is aswitch that can shut down all the laser setup in sequence. The lab warning sign can indicatesthe 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)

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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 thepreamplifier part when the power amplifier is on. That is to say, as long as the poweramplifier is on, we cannot turn off the pre-amplifier or change its power. Second, when thepre-amplifier is off, we cannot turn on the power amplifier. Even though we already setup thephysical interlock, this acts as a secondary protection. Third, we monitor the temperature ofthe cooling preamplifier. When the temperature is higher than 32 ◦C or there is insufficientwater 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 dangeroushappens, the program will shut down the amplifiers.

2.11 Mechanical Design and Cooling system

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The main issue for high power laser is heating. For example, there is 200 W of pumppower going into the rod fiber where ∼40 W will come out of the other end. We must setupa water-cooled beam dump to collect this unused power. The beam dump is shown in figure2.19. 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 beamdamp is placed between the lens and the seed end of the fiber. The beam size of the seedlaser is only about 1 mm but the output pump beam size is large, because the inner claddingof the fiber, where the pump is propagating in, has a numerical aperture (NA) of 0.5, whichmeans 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 causemisalignment. This is dangerous for the reasons mentioned before. If we place the beamdamp like figure 2.20, we can block most of the pump light to protect the lens mount whilethe 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 isconverted to the signal power. The rod-type fiber is also water cooled along its length toefficiently 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 flowthrough the pipe.

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

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3 Conclusion

In this thesis, I presented a linearly amplified fiber laser with 55 W average output powerand 150 femtosecond pulse duration (figure 3.2). The comb tooth linewidth is less than 30kHz and the relative intensity noise is low. However, the pulse duration is limited by thegain narrowing in the power amplifier. And the output power is limited by the efficiency ofgratings. Also, the dichroic mirror at the output end of pre-amplifier cuts a little spectrumand also lower the seed power sent to the power amplifier. In addition, we build the watercooling system and interlock system to protect the laser. A LabView program is developedto control the laser system.

In the future, we will replace the dichroic mirror D2. So we may have more spectrumaround 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 pulsesto carry on a pump-probe experiments on clean surfaces in ultrahigh vacuum, as illustratedin 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.

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

Figure 3.3: Photo of HHG chamber and monochromator chamber.

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Figure 3.4: Photo of surface sciences chamber.

37

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Appendix

A. LabView code

Figure A1: LabView code part 1

Figure A2: LabView code part 2

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Figure A3: LabView code part 3

Figure A4: LabView code part 4

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Figure A5: LabView code part 5

Figure A6: LabView code part 6

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