THE DEVELOPMENT OF NOVEL YTTERBIUM FIBER LASERS AND THEIR
APPLICATIONS
By
Bai Nie

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics—Doctor of Philosophy
2014

ABSTRACT
THE DEVELOPMENT OF NOVEL YTTERBIUM FIBER LASERS AND THEIR
APPLICATIONS
By
Bai Nie
The aim of my Ph.D. research is to push the fundamental limits holding back the development of
novel Yb fiber lasers with high pulse energy and short pulse duration. The purpose of developing
these lasers is to use them for important applications such as multiphoton microscopy and laserinduced breakdown spectroscopy.
My first project was to develop a short-pulse high-energy ultrafast fiber laser for
multiphoton microscopy. To achieve high multiphoton efficiency and depth resolved tissue
imaging, ultrashort pulse duration and high pulse energy are required. In order to achieve this, an
all-normal dispersion cavity design was adopted. Output performances of the built lasers were
investigated by varying several cavity parameters, such as pump laser power, fiber length and
intra-cavity spectral filter bandwidth. It was found that the length of the fiber preceding the gain
fiber is critical to the laser performance. Generally, the shorter the fiber is, the broader the output
spectrum is. The more interesting parameter is the intra-cavity spectral filter bandwidth. Counter
intuitively, laser cavities using narrower bandwidth spectral filters generated much broader
spectra. It was also found that fiber lasers with very narrow spectral filters produced laser pulses
with parabolic profile, which are referred to as self-similar pulses or similaritons. This type of
pulse can avoid wave-breaking and is an optimal approach to generate pulses with high pulse
energy and ultrashort pulse duration. With a 3nm intra-cavity spectral filter, output pulses with
about 20 nJ pulse energy were produced and compressed to about 41 fs full-width-at-halfmaximum (FWHM) pulse duration. Due to the loss in the compression device, the peak power of

the compressed pulses is about 250 kW. It was the highest peak power generated from a fiber
oscillator when this work was published. This laser was used for multiphoton microscopy on
living tissues like Drosophila larva and fruit fly wings. Several imaging methods, such as twophoton-excited fluorescence, second harmonic generation, and third harmonic generation, were
performed. Not only were single layers of thin tissue imaged, but also depth resolved imaging of
thick samples was tested, and three-dimensional image reconstruction was demonstrated.
The other project was to develop a simple fiber oscillator for laser-induced breakdown
spectroscopy (LIBS). Laser pulses with high energy, high ablation efficiency and low ablation
threshold are desirable for this application. We built a fiber laser using up to 200 m long fiber
and scaled the output pulse energy up to 450 nJ. This laser was operated in an unusual
mode-locking regime and produced noise-like pulses, which have a picosecond long pulse
envelope containing multiple irregular femtosecond sub-pulses. This type of pulse was mostly
ignored by many earlier researchers. Intra-cavity spectral filters did not affect the laser
performance as much as in the similariton lasers and were removed from the laser cavity.
Characteristics of our noise-like laser, such as MHz repetition rate, broad spectrum, and
picosecond-long pulse envelope containing multiple femtosecond sub-pulses, were found to meet
the requirement of an ideal laser source for LIBS. A simple LIBS setup using our laser was
demonstrated and atomic emission spectra with very good signal-to-noise ratio were obtained.
Composition detection, qualitative concentration determination, and trace detection were also
tested. These tests show that our noise-like fiber laser is an ideal laser source for a low-cost and
portable LIBS system.

ACKNOWLEDGMENTS

My time here at Michigan State University has been a great learning experience scientifically
and personally. Thinking about the decision to come to US for my Ph.D. study, I do not have any
regrets. Professor Chong-Yu Ruan and other committee members recruiting for Physics and
Astronomy Department at MSU thank you for giving me the chance of this great adventure.
My advisor, Professor Marcos Dantus, allowed me to learn a great deal of science in his lab.
I am so lucky to have joined your group. The variety of research projects in your group gave me
chance to learn and try many different things; and you always supported me for exploring new
things. You also sent me to various conferences and encouraged me to discuss my research with
people in the same field. I was very impressed by your determination and enthusiasm to
approach new concepts. I feel this attitude is crucial for successful in any field. I hope that I can
replicate this attitude in my following career. I really appreciate all your support during my
research and job hunting.
I also would like to thank current and former members of Dantus group: Dr. Vadim
Lozovoy, Dr. Marshall Bremer, Dr. Paul Wrzesinski, Dr. Sergey Arkhipov, Dr. Alexander van
Rhijn, Arkaprabha Konar, Anton Ryabtsev, Ilyas Saytashev, Gennady Rasskazov, Gregory
Parker, Jay Shah and Orin Yue. Thank you for sharing your toys and helping me carry out my
experiments. It was a lot of fun working with you together. I would like to thank Dr. Vadim
Lozovoy for the many great discussions we have had. I was always impressed by your insightful
thoughts. I want to thank Ilyas Saytashev for teaching me many aspects of optical microscopy. I
have bothered you the most in this group. I owe you a great debt of gratitude. Gregory Parker
worked together with me on the LIBS project and helped me a lot.

iv

Our collaborators from Cornell University, Professor Frank Wise, Andy Chong, William
Renninger, Simon Lefrancois and Hui Liu, are a group of people I must thank. You were so kind
to share your experience on fiber laser research and answer all my questions. Without your help,
I would not have made my fiber laser work so quickly. I was always amazed by your creative
thoughts.
I would like to thank Biophotonics Solutions Inc. Especially, Dr. Dmitry Pestov and Dr.
Bingwei Xu, for their help with my questions and concerns regarding pulse shaper alignment and
pulse compression technology. I owe a lot of gratitude to Dr. Dmitry Pestov, for purchasing
equipment and components for my first fiber laser project before I joined the group. He has
helped save a tremendous amount of time.
During the first week of my US adventure, I met a group of Chinese students and we
remained friends in the past six years. It was a great journey with all of you together. I appreciate
your help and support during my hard time. Thank you to Xianbo Yang, Xingyi Yang, Bite Zhou,
Hongmei Li, Zhe Chen, Cheng Sun, Zhensheng Tao, Ding Wang, Xu Lu, Yutian Shu, Mingjie
Jin.
I would like to thank my mother and father. You always supported me with patience and
love. If I have ever accomplished anything, the real credit should go to you. I cannot say thank
you enough.
Finally, I would like to thank my beautiful wife. I really appreciate your support and
patience. Without your understanding, I could not reach the end of this adventure. I feel deeply
sorry that we were mostly geographically separated in the past two years. And special thank goes
to my lovely son, your smile is the strongest motivation for me to finish my Ph.D. study. Sorry, I

v

missed so many important moments in your life. I hope that we will get together soon and will
never be separated again.

vi

TABLE OF CONTENTS

LIST OF FIGURES ....................................................................................................................... ix
KEY TO SYMBOLS AND ABBREVIATIONS ..........................................................................xv
Chapter 1 Introduction .....................................................................................................................1
1.1
Introduction to ultrafast lasers .......................................................................................... 2
1.2
Introduction of optical fibers ............................................................................................ 6
1.3
Introduction to fiber lasers ............................................................................................. 16
1.4
Mode-locking methods in fiber lasers ............................................................................ 23
1.5
Ultrashort Pulse Compression ........................................................................................ 27
Chapter 2 Sub-50 fs High Energy Ultrafast Fiber Laser................................................................32
2.1
Introduction .................................................................................................................... 32
2.2
All-normal dispersion fiber laser.................................................................................... 35
2.2.1
Experimental setup.................................................................................................. 35
2.2.1.1 Nonlinear polarization evolution .............................................................................36
2.2.1.2 Spectral filter ...........................................................................................................38
2.2.2
Experimental results and discussion ....................................................................... 40
2.2.2.1 Fiber length dependence ..........................................................................................42
2.2.2.2 Filter bandwidth dependence...................................................................................45
2.2.3
Conclusion .............................................................................................................. 47
2.3
Similariton fiber lasers ................................................................................................... 48
2.3.1
Introduction to the similariton ................................................................................ 48
2.3.2
Numerical Simulations............................................................................................ 52
2.3.3
Experimental setup of similariton fiber laser .......................................................... 57
2.3.4
Experimental results................................................................................................ 58
2.3.5
Discussion ............................................................................................................... 64
2.4
Conclusion...................................................................................................................... 73
Chapter 3 Application of Ultrafast Fiber Laser – Multiphoton Microscopy .................................74
3.1
Introduction .................................................................................................................... 74
3.2
Multiphoton microscopy using low power sub-30 fs fiber laser .................................... 76
3.2.1
Experimental setup.................................................................................................. 76
3.2.2
Space time coupling ................................................................................................ 80
3.2.3
Experimental results................................................................................................ 83
3.2
Multi-photon microscopy using high pulse energy sub-50 fs fiber laser ....................... 87
3.2.1
Experimental setup.................................................................................................. 87
3.2.2
Experimental results................................................................................................ 87
3.3
Conclusion...................................................................................................................... 92
Chapter 4 Development of Noise-like Fiber Laser and Their Applications in Laser-Induced
Breakdown Spectroscopy...............................................................................................................93
4.1
Introduction .................................................................................................................... 93
vii

4.2
Experimental setup of noise-like lasers ........................................................................ 100
4.3
Experimental results ..................................................................................................... 101
4.4
LIBS using noise-like laser .......................................................................................... 109
4.4.1
Experimental setup................................................................................................ 110
4.4.2
Experimental results.............................................................................................. 111
4.4.3
Ablation threshold ................................................................................................. 114
4.5
Conclusion.................................................................................................................... 115
Chapter 5 Summary and Outlook ................................................................................................116
5.1
Similariton fiber laser and applications ........................................................................ 116
5.2
Noise-like fiber laser and applications ......................................................................... 117
5.3
Future work .................................................................................................................. 117
APPENDICES .............................................................................................................................119
Appendix-I Matlab Code ......................................................................................................... 120
Appendix-II Fiber Laser Setup and Alignment ....................................................................... 137
Appendix-III Publication List ................................................................................................. 140
BIBLIOGRAPHY ........................................................................................................................141

viii

LIST OF FIGURES

Figure 1: Schematic of a standard single-clad optical fiber [11]. ................................................... 6
Figure 2: Schematic of a double-clad optical fiber. [12] ................................................................ 7
Figure 3: Variation of material (blue), waveguide (dot) and total (red) dispersion for a silica fiber.
[17] .................................................................................................................................................. 9
Figure 4: Simulation results. Pulse profiles of a) input pulse; b) pulse after propagating through
3*LD-long fiber with β3=0; c) pulse after propagating through 3*LD'-long fiber with β2=0; d)
combined effects of (b) and (c). .................................................................................................... 11
Figure 5: Simulation results. Top: (a) input pulse spectrum and (b) temporal profile; Bottom: (c)
spectrum and (d) temporal profile of pulse after propagating a distance LNL in fiber. Red line:
frequency chirp induced by SPM. ................................................................................................. 12
Figure 6: Simulated SPM induced spectral broadening of the pulse experiencing a maximum
nonlinear phase shift of a) 0; b) π; c) 3.5π. φmax is the maximum nonlinear phase shift. ............. 14
Figure 7: Simulation showing pulse intensity and spectrum after propagating through a fiber with
both dispersion and nonlinear refraction. Top: fiber length of 0.01LD; middle: fiber length of
0.04LD; bottom: fiber length of 0.08LD. ........................................................................................ 15
Figure 8: Energy levels of a few isolated 3+ rare earth ions. n is the number of electrons in the
partially filled 4f orbital. [33]........................................................................................................ 17
Figure 9: Energy level diagram of Yb3+ ions containing split sub-levels [36]. 940 nm transition
is for the pump light, 1030 nm and 1050 nm transitions correspond to the emissions wavelengths.
....................................................................................................................................................... 18
Figure 10: Illustration of pulse evolution in different fiber laser cavities. [44] ............................ 21
Figure 11: Spectral filtering of highly chirped pulse. T: transmittance. ....................................... 23
Figure 12: Nonlinear Optical Loop Mirror. [49] .......................................................................... 24
Figure 13: NOLM Fiber laser [29]. NALM: nonlinear amplifying loop mirror. .......................... 25
Figure 14: Mode-locked fiber laser based on nonlinear polarization evolution. [50] .................. 26
Figure 15: Schematic of a 4-f pulse shaper. .................................................................................. 28
Figure 16: MIIPS simulation results. Top: sinusoidal scan of pulses with (a) flat phase, (b)
second order dispersion, (c) third order dispersion, (d) fourth order dispersion and (e) all of them;
bottom: second order dispersion scan of pulses with (f) flat phase, (g) second order dispersion, (h)
ix

third order dispersion, (i) fourth order dispersion and all (j) of them. Dot lines: local maxima of
SHG signal. ................................................................................................................................... 31
Figure 17: Pulse duration dependent multiphoton efficiency. Symbols: experimental results;
Lines: fit of experimental data. ..................................................................................................... 32
Figure 18: Schematic of an all-normal dispersion fiber laser. PBS: polarizing beam splitter; QWP
and HWP: quarter- and half-wave plate respectively; SMF: single mode fiber; coll.: fiber
collimator; SF: spectral filter. ....................................................................................................... 35
Figure 19: Schematic of artificial saturable absorber. PBS: polarizing beam splitter, HWP and
QWP: half- and quarter-wave plate, and +z is the pulse propagation direction. Note: color has no
meaning in this figure. .................................................................................................................. 36
Figure 20: Illustration of propagation of electric field through the artificial saturable absorber. α1,
α2, α3 are the angles between the fast axis of the wave plates and the x-axis, θ1 and θ2 are the
angles between the axis of the polarizers and the x-axis, x, y, z are the coordinate axes, and +z is
the pulse propagation direction. Note: color has no meaning in this figure. ................................ 37
Figure 21: Illustration of spectral filter. PBS: polarizing beam splitter, BF: birefringent plate, and
+z is the pulse propagation direction. ........................................................................................... 38
Figure 22: Transmittance of spectral filter using a) a 3 mm thick birefringent plate and b) a 5 mm
thick birefringent plate .................................................................................................................. 40
Figure 23: Laser performance of all-normal dispersion fiber laser. (a) Output spectrum; (b)
Experimentally measured interferometry autocorrelation of de-chirped output pulses................ 42
Figure 24: Measured pump-to-laser conversion efficiency. ......................................................... 43
Figure 25: Output spectra of laser cavities using (top) 7.5 m, (middle) 2.4 m and (bottom) 1.7 m
SMF-I. ........................................................................................................................................... 44
Figure 26: Dependence of the output spectra on the spectral-filter bandwidth (a) Cavity with 7.5
m SMF-I and a 20 nm (top) or a 12 nm (bottom) spectral filter; (b) Cavity with 2.5 m SMF-I and
a 20 nm (top) or a 12 nm (bottom) spectral filter. ........................................................................ 46
Figure 27: Amplified spontaneous emission of the gain fiber. .................................................... 47
Figure 28: Numerical solution of the nonlinear Schrödinger equation for the pulse amplitude at
different propagation distance. [62] .............................................................................................. 49
Figure 29: Similariton in passive (left) and gain (right) fiber [44] ............................................... 50
Figure 30: Evolution of pulse amplitude as functions of propagation distance in a normal-GVD
fiber amplifier. [63] ....................................................................................................................... 50

x

Figure 31: Top: scheme of cavity used for simulation. Bottom: pulse duration (black) and
spectral bandwidth (red) evolution through the laser cavity with a 12 nm bandwidth spectral filter.
....................................................................................................................................................... 53
Figure 32: Simulation results of laser cavity using a 12 nm bandwidth spectral filter. (a) 2D
spectral evolution through the cavity; (b) laser spectrum at the end of SMF-II ........................... 54
Figure 33: Pulse duration and spectral bandwidth evolution through the laser cavity with a 3 nm
bandwidth spectral filter. Top: scheme of the cavity used for simulation. ................................... 55
Figure 34: Simulation results of laser cavity using a 3 nm bandwidth spectral filter. (a) Twodimensional spectral evolution through the cavity; (b) Laser spectrum at the end of SMF-II. .... 55
Figure 35: Simulated pulse shape of the pulse at the end of SMF-II plotted on a logarithmic scale.
Red dots: parabolic fit; Insert: same plot on a linear scale. .......................................................... 56
Figure 36: Schematic of the double-clad Yb all-normal-dispersion fiber laser cavity and the setup
for pulse characterization. SMF-I and SMF-II: single mode passive fiber section I and II; QWP
and HWP: quarter- and half-wave plates; PBS: polarizing beam splitter; coll.: collimator; OSA:
optical spectrum analyzer; L: lens; spec.: spectrometer. .............................................................. 57
Figure 37: Two output modes with the same pump power. (a) and (c) Output spectrum; (b) and
(d) Interferometric autocorrelation. Note: the gray or dark color in (b) and (d) has no meaning. It
is caused by the varying density of lines. ..................................................................................... 59
Figure 38: Output laser spectrum (black) and measured spectral phase of the output pulses (red).
....................................................................................................................................................... 60
Figure 39: Laser performance. (a) pulse train form oscilloscope. Repetition rate 42.5 MHz; (b)
RF spectrum analyzer result, 1 MHz frequency span; (C) RF spectrum analyzer result, 500 MHz
span. .............................................................................................................................................. 61
Figure 40: (a) Experimental and calculated SHG spectra shown in linear (solid curve) and log-10
(dashed curve) scales. (b) Experimental THG spectrum obtained by focusing TL pulses at the
surface of a glass slide. (c) Experimental and calculated interferometric autocorrelation traces for
compressed laser pulses in the range of -150 fs to 150 fs. Insert: Same data in the range of -500
fs to 500 fs. .................................................................................................................................... 63
Figure 41: (a) Output spectrum of a similariton fiber laser using more than 1 m long SMF-II; (b)
Comparison of experimental (solid line) and calculated (dash line) SHG spectra. ...................... 67
Figure 42: Calculated (red) and experimental (black) (a) interferometric and (b) background-free
intensity autocorrelation traces. .................................................................................................... 67
Figure 43: Calculated (left) and experimental (right) sinusoidal phase scan traces. δ is the scan
parameter....................................................................................................................................... 68

xi

Figure 44: Left: calculated and experimentally measured two-dimensional SOD scan; Right:
experimental (black) and calculated (red) SHG-integrated SOD scan. ........................................ 69
Figure 45: Output spectrum of a similariton fiber laser using more than 1 m long SMF-II with
lower pump power. ....................................................................................................................... 70
Figure 46: Left: calculated and experimentally measured two-dimensional SOD scan; Right:
experimental (solid line) and calculated (dash line) integrated SOD scan. .................................. 70
Figure 47: Experimental setup of the similariton fiber laser using the UHNA fiber. UHNA: ultrahigh numerical aperture fiber; SMF: single mode fiber; HWP and QWP: half- and quarter-wave
plate; coll.: collimator; PBS: polarizing beam splitter; WDM: wavelength division multiplexer.71
Figure 48: Experimental spectra from (a) port 1; (b) port 2; (c) port 3. ....................................... 72
Figure 49: Experimental setup of PCF similariton fiber laser. PCF: photonic crystal fiber; SMF:
single mode fiber; HWP and QWP: half- and quarter-wave plate; PBS: polarizing beam splitter.
....................................................................................................................................................... 73
Figure 50: Experimental results. (a) spectrum before PBS; (b) output spectrum; (c)
autocorrelation results ................................................................................................................... 73
Figure 51: Schematic of imaging setup. (a) Fiber laser cavity layout. PCF: photonic crystal fiber;
SMF: single mode fiber; WDM: wavelength-division multiplexer; HWP and QWP: half- and
quarter-wave plate; PBS: polarizing beam splitter; coll.: fiber collimator. (b) 4f-folded pulse
shaper. SLM: spatial light modulator; M: mirror. (c) Microscopy setup. DM: dichroic mirror;
GM: galvanic mirror; AMP: amplifier; PMT: photomultiplier tube. ........................................... 77
Figure 52: (a) Laser spectrum after the microscope objective. (b) Comparison of experimental
(black) and calculated (red) SHG spectrum in linear scale. (c) Comparison of SHG spectrum in
log-10 scale. (d) Comparison of experimental (black) and calculated (red) interferometric
autocorrelation trace. Insert: calculated temporal profile based on the measured laser spectrum 79
Figure 53: Sketch of 4-f shaper with output beam focused using a lens. [91].............................. 80
Figure 54: Multiphoton microscopy images of polystyrene microspheres. (a) TPEF image, (b)
THG image and (c) THG image of single bead. Scale bar: 10 µm. .............................................. 84
Figure 55: Multiphoton microscopy images of live tissues. (False color) Top line: images of a
guppy fish (Poecilia reticulata) tail. (a) SHG image (false color, red), (b) THG image (false color,
cyan), and (c) Composition of SHG and THG images. (d) Bright-field microscope image.
Bottom line: images of fruit fly (Drosophila melanogaster) wings. (e) SHG image (false color,
red) (f) THG image (false color, cyan) (g) Composition of SHG and THG images. (h) Brightfield microscope image. Scale bar: 10 µm. ................................................................................... 85
Figure 56: Experimental setup. (a) Fiber laser. HWP and QWP: half- and quarter-wave plate;
PBS: polarizing beam splitter; SMF: single mode fiber; UHNAF: ultra-high numerical aperture
fiber; coll.: fiber collimator. (b) 4-f folded pulse shaper. M: mirror; SLM: spatial light modulator.
xii

(c) Laser-scanning microscope. DM: dichroic mirror; GM: galvanic mirror; obj.: objective; PMT:
photon multiplier tube; AMP: amplifier. ...................................................................................... 87
Figure 57: Composition of TPEF (green, false color) and THG (blue, false color) imaging of
mouse intestine (left) and mouse kidney (right), 150 µm x150 µm area represented................... 88
Figure 58: Projection of three-dimensional images at different angles of SHG (left) and THG
(right) microscopy of Drosophila Larva. 150 µm x150 µm area represented............................... 90
Figure 59: Projection of three-dimensional images at different angles of SHG (left) and THG
(right) microscopy of fruit fly eyes. 150 µm x150 µm area represented. ..................................... 91
Figure 60: LIBS spectra captured by using multi-pulse (black) and single-pulse (red)
configurations. [109] ..................................................................................................................... 95
Figure 61: Spectral bandwidth dependence of the LIBS threshold. [116] .................................... 96
Figure 62: Experimental results of noise-like laser. (a) output spectrum (b) background-free
autocorrelation trace. [117] ........................................................................................................... 97
Figure 63: (a) Calculated time-dependent intensity and (b) autocorrelation trace. [117] ............. 98
Figure 64 Net gain per roundtrip vs. initial pulse power. Curves 1-3 correspond to slightly
different cavity parameters close to the boundary of the single-pulse generation regime. [119] . 99
Figure 65 Experimental setup of the fiber laser. SMF-I and SMF-II: single mode fiber; HWP and
QWP: half- and quarter-wave plate; PBS: polarizing beam splitter. .......................................... 100
Figure 66: Pulse train of mode-locked fiber laser with 100 m long SMF-I. ............................... 101
Figure 67: a) Experimental output spectrum; b) Experimental SHG spectrum with second-order
dispersion compensation (SOD) applied (red) and calculated SHG spectrum with flat phase
based on the fundamental spectrum. ........................................................................................... 102
Figure 68: (a) Calculated and experimental two-dimensional SOD scan. The SOD range of the
calculated plot is 10 times smaller than experimental plot. (b) Calculated and experimental SHGintegrated SOD scan. .................................................................................................................. 103
Figure 69: (a) Interferometric AC, peak-to-base-line ratio is less than 8:1; (b) background-free
non-collinear intensity AC. ......................................................................................................... 104
Figure 70: Simplified noise-like fiber laser setup without any spectral filter. SMF: single mode
fiber; HWP and QWP: half- and quarter-wave plate; PBS: polarizing beam splitter; coll.: fiber
collimator. ................................................................................................................................... 105
Figure 71: Pump-power-dependent output spectra. Black: pump power 1.8 W; Red: pump power
3.9 W. .......................................................................................................................................... 105
Figure 72: 1 MHz pulse train of noise-like laser with 200 m long SMF-I. ................................ 106
xiii

Figure 73: Output spectrum of 1 MHz noise-like laser. ............................................................. 106
Figure 74: Non-collinear AC trace from 0 ps to +180 ps. Insert: the same AC trace on a small
range from -1 ps to +1 ps. ........................................................................................................... 107
Figure 75: Setup of fiber amplifier using a noise like laser as the seed...................................... 108
Figure 76: Output spectrum of fiber amplifier. ........................................................................... 109
Figure 77: LIBS setup using noise-like laser. DM: dichroic miror; L: lens; spec: spectrometer;
obj: objective. SMF: single mode fiber; HWP and QWP: half- and quarter-wave plate; PBS:
polarizing beam splitter............................................................................................................... 110
Figure 78: LIBS spectra of brass (top) and copper (bottom). ..................................................... 111
Figure 79: LIBS spectra of three aluminum alloys, Al1100 (black), Al6061 (red) and Al7075
(blue). Insert: the full LIBS spectra. ........................................................................................... 112
Figure 80: LIBS spectra of pure Al1100 alloy (black) and PbNO3 contaminated Al1100 (red). 113
Figure 81: (a) Picture of Galena rock; (b) LIBS spectra of Galena rock. ................................... 113
Figure 82: Threshold measurement. LIBS intensity for copper as a function of incident laser
fluence. ........................................................................................................................................ 114
Figure 83: Layout of the similartion fiber laser. ......................................................................... 137
Figure 84: Layout of the spectral filter. ...................................................................................... 138
Figure 85: Splicing between gain fiber and SMF-II ................................................................... 139

xiv

KEY TO SYMBOLS AND ABBREVIATIONS

AC

Autocorrelation

ANDi

All-Normal Dispersion

AOM

Acoustic Optical Modulator

ASE

Amplified Spontaneous Emission

BBO

Barium Borate

BW

Bandwidth

CPA

Chirped-Pulse Amplification

CW

Continuous Wave

DCF

Double-Clad Fiber

EOM

Electrical Optical Modulator

Er

Erbium

FWHM

Full Width Half Maximum

GVD

Group Velocity Dispersion

HWP

Half-Wave Plate

LIBS

Laser-Induced Breakdown Spectroscopy

LMA

Large Mode Area

KDP

Potassium Dihydrogen Phosphate

MIIPS

Multiphoton Intrapulse Interference Scan

Nd

Neodymium

NLOM

Nonlinear Loop Optical Mirror

NPE

Nonlinear Polarization Evolution

OPO

Optical Parametric Oscillator
xv

OSA

Optical Spectrum Analyzer

PBS

Polarizing Beam Splitter

PDD

Polarization Dependent Delay

PMT

Photomultiplier Tubes

QWP

Quarter-Wave Plate

RF

Radio Frequency

SA

Saturable Absorber

SESAM

Semiconductor Saturable Absorber Mirror

SF

Spectral Filter

SMF

Single Mode Fiber

SOD

Second Order Dispersion

SWCN

Single-Wall Carbon Nanotube

Tm

Tellurium

TOD

Third Order Dispersion

SBS

Stimulated Brillouin Scattering

SHG

Second Harmonic Generation

SPM

Self-Phase Modulation

SRS

Stimulated Raman Scattering

THG

Third Harmonic Generation

TPEF

Two Photon Excited Fluorescence

UHNA

Ultra-High Numerical Aperture

WDM

Wavelength-Division Multiplexing

XPM

Cross-Phase Modulation

xvi

Yb

Ytterbium

xvii

Chapter 1 Introduction
In this thesis, two types of fiber lasers – similariton and noise-like – are studied. Both
experimental and numerical simulation results are presented and compared. The laser
performance is mainly described in terms of the pulse energy, the pulse duration and the peak
power. A few cavity parameters, such as fiber length and intra-cavity spectral filter bandwidth,
are investigated to see how they affect the laser performance. Meanwhile, our developed fiber
lasers are demonstrated for applications, such as multiphoton microscopy and laser-induced
breakdown spectroscopy.
The rest of this thesis is organized as follows:
Chapter 1 provides the background knowledge necessary to understand the subjects of this
thesis. First, the development and science of ultrafast lasers are introduced. Following that, the
properties of optical fibers and pulse propagation in passive fibers are discussed. Then, the
principles of ultrafast fiber lasers and several types of ultrafast fiber laser designs are discussed.
At the end of chapter 1, an ultrafast pulse shaping and characterization technology is introduced.
In Chapter 2, systematic study of sub-50 fs fiber lasers based on all-normal-dispersion
cavities is presented. The dependence of laser performance on several cavity parameters is
investigated. Experimentally, it is found that a narrow intra-cavity spectral filter can attract laser
pulses into self-similar evolution. This result is also verified by numerical simulations.
Using our developed sub-50 fs fiber lasers, multiphoton microscopy of living tissues is
demonstrated in Chapter 3. Results of second harmonic generation (SHG) imaging and third
harmonic generation imaging (THG) are compared. Depth resolved imaging on Drosophila larva
and fruit fly eyes is also presented.

1

In Chapter 4, fiber lasers delivering higher energy noise-like pulses are studied. The
noise-like fiber lasers behave very differently than the similariton fiber lasers. It is found that the
output pulses have the characteristic of a picosecond-long wave packet containing multiple
irregular femtosecond sub-pulses. Laser-induced breakdown spectroscopy (LIBS) is tested on a
few samples using a noise-like fiber laser. Based on the strong atomic emission signal, good
signal-to-noise ratio and low ablation threshold, we believe that the noise-like fiber lasers can be
incorporated as ideal light source for a simple LIBS system.
Our work is summarized in Chapter 5 and future directions of our work are discussed.
1.1

Introduction to ultrafast lasers
The concept of laser, Light Amplification by Stimulated Emission of Radiation, was

initially proposed in the late 1950s [1] and the first functioning laser was operated by Theodore
Maiman in 1960 [2]. In the past several decades, all sorts of lasers were developed, varying in
emission wavelength, pulse duration or output power. Numerous scientific discoveries and
innovations have been aided by lasers. Besides serving as a powerful tool for fundamental
research, lasers are also widely used in industrial fields. From simple laser pointers to high
power military-use lasers, from LASIK surgery to three-dimensional printing, lasers are
permeating our daily life. Today’s laser market is worth billions of dollars and continues to grow
at an accelerating pace [3].
Most lasers follow the same principle and depend on a laser cavity. A simple laser cavity
can be just two mirrors with a gain medium in between. One of the mirrors is fully reflective and
the other one is partially transmitting and acts as an output coupler. The gain medium is pumped
by an external optical source (not including electrically pumped lasers such as diode lasers) that
provides photons with higher energy than the band-gap of the gain medium, such that electrons
2

in the upper energy level out-number the electrons in the lower level, a condition called
population inversion. Once this state is achieved, stimulated emission happens and the cavity
starts lasing. Laser light is emitted through the partially transparent mirror. The emission
wavelength is determined by the band-gap of the gain medium.
There are two major modes of laser operation – continuous wave (CW) and pulsed. CW
means that the output power is continuous over time. However, pulsed mode is very different; it
delivers laser pulses with finite temporal duration. Each laser pulse has the same duration, which
can vary from several nanoseconds to several femtoseconds. The pulsed mode can be achieved
using either Q-switching or mode-locking methods. Q-switching is usually used to generate high
power nanosecond laser pulses, such as from a Nd:YaG laser. To get shorter pulse duration,
mode-locking is normally used.
To understand these different operation modes, we can start from a basic resonator cavity.
Due to the wave-particle duality, light can be considered a wave. As light bounces back and forth
between two resonator mirrors, it will form standing waves due to constructive and destructive
interference. The modes of the standing waves are determined by the cavity properties. Generally,
the frequency can be presented as

ω=

Nπ c
,
nL

(1)

where ω is the mode frequency, N is an integer number representing the mode number, c is the
speed of light, n is the refractive index of the cavity medium , and L is the cavity length.
∆ω =

πc
nL

,

(2)

where ∆ω is the fundamental mode frequency (free spectral range), corresponding to the gap
between two adjacent modes.

3

In principle, a resonator cavity can support an infinite number of modes. However, due to
the limited gain bandwidth, only certain modes can be amplified. Meanwhile, if all these modes
have random relative phase, then the summation of all these modes results in a constant output in
the temporal domain. If these modes are phase locked to each other, which means that their
phase difference is either 0 or multiples of 2π, constructive interference between these modes
happens and an intense pulse is generated. In this case, the laser is called mode-locked. Either a
passive saturable absorber (or artificial saturable absorber) or active modulation (amplitude,
phase, or frequency) can be used to achieve mode-locking.
Pulsed lasers are attractive for many practical applications due to their high peak power.
P0 =

E

τ

=

P ∆t

τ

,

(3)

where P0 is peak power, E is pulse energy that is the product of average power P and period
6

time ∆t, and τ is pulse duration. If the pulse duration is 1 ps, the peak power can be 10 times
higher than the average power at 1 MHz repetition rate. With this high peak power, nonlinear
effects can be realized which leads to many useful and important applications. On the other hand,
regardless of the peak power, short pulse duration is also very useful. It is possible to resolve
ultrafast chemical processes. All these interesting characteristics have led to the development of
a new research field – ultrafast (~ ps to fs) science. There have been two Nobel Prize awarded to
scientist working on ultrafast science. One was for ultrafast chemistry, which enables the
observation of the transition state of molecules in chemical reactions [4]. The other one was for
frequency combs which are very useful in metrology [5]. Additionally, there are many other
important applications, such as multi-photon microscopy [6] and material processing [7].

4

Driven by the ultrafast science research and practical applications, many types of ultrafast
lasers have been developed. Among them, solid-state mode-locked lasers have emerged as the
most popular and useful ultrafast light sources. Currently the most popular femtosecond lasers
are based on the Ti:sapphire crystal, due to its high gain and very broad gain bandwidth [8].
From a simple oscillator, sub-100 fs pulses can be easily produced. But the pulse energy is
usually limited to tens of nJ due to self-focusing caused by high peak power, which can damage
the gain medium. Normally, chirped-pulse amplification (CPA) [9] is used to increase the pulse
energy. Chirped pulses means that the instantaneous frequency in pulses increases or decreases
with time, which broadens the pulses in time domain and lowers the peak power of the pulses.
The output pulses from an oscillator can be pre-chirped using pairs of gratings before being
amplified in another gain medium. After the pre-chirping, the pulse duration of the input pulses
usually becomes three or more orders of magnitude longer, which brings down the peak power
by the same magnitude. Thus, the input pulses can be safely amplified to the µJ or mJ level. The
amplified pulses are compressed back to short pulse duration afterward. Recently, pulse energy
up to 1.85 MJ has been achieved by the National Ignition Facility, corresponding to a peak
power of 414 TW [10].
Despite the improved performance and accelerated development of solid-state lasers, there
are still problems that are hard to overcome. For example, Ti:Sapphire femtosecond lasers are
sensitive to their environment because the gain crystal is exposed to the environment. Changes of
temperature or humidity can easily disturb the laser operation. Also they have to be set on tables
with excellent vibrational stability, otherwise mode-locking status is hard to sustain. Due to the
small volume of the gain crystal, heat dissipation also becomes a problem. Usually the crystal is
cooled using water, which adds complexity to the system and limits the output power or pulse

5

energy. Another drawback is the pump laser
laser, usually a frequency-doubled
doubled Nd:YaG CW laser,
which has low electric-to-optical
optical efficiency or wall-plug
plug efficiency. The size and cost are also
concerns. With the development of new research and technology, robust, compact and high
performance lasers are more and more desirable
desirable.

1.2

Introduction of optical fibers
In 2010, the Nobel Prize in Physics w
was awarded to Charles K. Kao for his contributions
contribution in

the development of optical fiberss. Optical fibers have many great characteristics
tics such as low loss
over long-distance propagation and flexibility. Optical fibers have made telecommunication and
the majority of Internet traffic possible
possible, and this is why they can be considered as one of the most
important developments in human history.
Effectively, an optical fiber is an optic
optical waveguide, which can propagate light along
confined modes. Typical optical
tical fiber
fibers have two layers called core and cladding, respectively
(see Figure 1) [11]. The difference in the refractive index between the core and cladding
c
causes
total internal reflection of the input light and confines it. In an active single-clad
clad fiber, the pump
light and laser radiation co-propagate
propagate through the core and have the same beam quality.

Figure 1: Schematic
chematic of a standard ssingle-clad optical fiber [11]..

6

Figure 2: Schematic of a double-clad optical fiber. [12]
Besides the single-clad
clad fiber
fibers, there are also double-clad fibers (DCF) [12]], which have one
core and two cladding layers (Figure
Figure 2). The inner cladding has higher refractive index than the
outer cladding. Since the refractive index is frequency dependent, it can confine certain
frequencies in the core while allowing some other frequencies to leak into the inner cladding,
clad
within which they are still confined by the outer clad
cladding. As shown in Figure 2, this design
allows clad pumping, where laser radiation and pump light propagate separately in the fiber core
and the inner cladding, which can be as large as 100 µm, enabling the coupling of high-power
h
pump light. These high power pump lasers are usually delivered by multimode fiber (~100 µm)
and have poor beam quality. However
However, laser radiation still propagates in the small core and
remains single mode. This new design greatly improvess the pump efficiency and average power
levels available form fiber lasers. Other than these, there are many more novel fibers developed,
such as photonic crystal fibers [13
13], chirally-coupled-core fibers [14], and highly nonlinear fibers
fiber
[15].
Fibers are also categorized as single
single-mode or multi-mode fibers and as passive or active
fibers. Usually multi-mode
mode fiber
fibers have larger diameter than single mode fiberss and can support
light with many spatial modes other than HE11 mode. The most common fiber is made
m
of fused
silica. Normally, germanium dioxide or aaluminum
luminum oxide is used as dopant to raise the refractive
7

index. Fluorine or boron trioxide doping is used for decreasing the refractive index. For active
fiber or gain fiber, the core is usually doped with rare earth ions.
There are several important parameters of optical fibers. Among them, the two most
important for ultrashort laser pulses are chromatic dispersion and third order susceptibility χ

(3)

,

which dominate the linear and nonlinear effects on the laser pulses, respectively. Chromatic
dispersion means that different frequencies travel with different group velocities due to the
frequency-dependent refractive index. Thus, a transform-limited pulse can be chirped to a longer
pulse after going through a fiber. The chromatic dispersion can be either positive, negative or
zero; the material used for fiber fabrication and the waveguide structure determine it. Waveguide
dispersion arises from the frequency-dependent effective mode index of a waveguide [16],
defined by
1 d β n2 n1 − n2  d
=
=
+
( bV )  ,

vg dω
c
c  dV


β=

ω
c

( n2 + ( n1 − n2 ) b (V ) ) ,

(

V = k0 a n12 − n22
b≈

β − k0 n2

k0 ( n1 − n2 )

)

1/ 2

(4)

,

,

k0 = 2π λ ,
where vg is the group delay due to waveguide, n1 and n2 are the refractive index of core and clad,
c is speed of light, a is core radius, and λ is the wavelength of light.
Normally waveguide dispersion is small compared to the material dispersion and can be
ignored. Figure 3 shows the variation of material, waveguide, and total dispersion for a standard
silica fiber [17]. But for a fiber with zero material dispersion, waveguide dispersion has to be
considered.
8

Figure 3: Variation of material (blue), waveguide (dot) and total (red) dispersion
for a silica fiber. [17]
Chromatic dispersion is a linear optical effect and can be easily dealt with.
with On the other
hand,, due to the small core size of a fiber, the high peak power of an ultrafast laser pulse can
result in very high peak intensity and cause significant nonlinear effects. The major effects
effec
include self-phase
phase modulation (SPM), cross
cross-phase
phase modulation (XPM), stimulated Raman
scattering (SRS) and stimulated Brillouin scattering (SBS).. All these effects originate from the
third order susceptibility χ

(3)

. SPM and XPM are due to the nonlinear refractive index change.

SRS and SBS are related to excitation of acoustic phonons and optical photons,
photons respectively, of
silica. All these linear and nonlinear effects in an optical fiber can be described
ed by [18]

∂A α
∂A i
∂ 2 A 1 ∂3 A
+ A + β1
+ β2
− β3
∂z 2
∂t 2
∂t 2 6
∂t 3
∞


i ∂ 
2

,
′
′
′
= iγ 1 +
A
z
,
t
R
t
A
z
,
t
−
t
dt
)
 ( ( )) ∫ ( ) (


ω
t
0 

0


(5)

where A is the pulse amplitude, which is a function of propagation distance z and time t , α is the
fiber loss, β1 is the group delay, β2 is the group-velocity dispersion (GVD), β3 is the third order

9

dispersion, ω0 is the carrier frequency of the pulse, and R(t) is the nonlinear response function,
which is related to higher order nonlinear effects such as SRS and self-steepening. γ is the
nonlinear coefficient, defined by

γ=

n2ω0
,
cAeff

where n2 is the nonlinear refractive index and is related to χ

(6)
(3)

, and Aeff is the effective fiber core

area.
In most cases, the higher order nonlinear effects such as SRS and SBS can be ignored and
the Equation (5) can be simplified as
∂A i
∂ 2 A 1 ∂3 A
2
+ β2
− β3
= iγ A A.
2
3
∂z 2
6
∂t
∂t

(7)

Only chromatic dispersion (left terms in Equation (7)) and nonlinear refraction (right term in
Equation (7)) terms need to be considered. Without the third order dispersion term, Equation (7)
becomes
∂A i
∂2 A
2
+ β2
− iγ A A = 0.
2
∂z 2
∂t

(8)

Equation (8) is sometimes referred to as a nonlinear Schrödinger equation (NLSE) [18, 19], since
it has the same form as a basic NLSE defined by [20, 21]

i

∂ψ 1 ∂ 2ψ
2
+
+ κ ψ ψ = 0,
∂t 2 ∂x 2

(9)

where ψ is a complex function, the variables t and x are frequently but not limited to time and
space coordinates, and κ is a nonlinear coefficient. Unlike the linear Schrödinger equation, the
NLSE does not describe the time evolution of a quantum state. Instead, it is generally used to

10

describe the evolution of slowly
ly varying wave packets in nonlinear media with dispersion [21].
Nonlinear effects, such as self-focusing
focusing [22] and pulse propagation in optical fibers [23], have
been successfully described using this equation
equation.
With only chromatic dispersion terms (γ = 0), Equation (7) is linear and can be solved
analytically. Pure dispersion affect
affects the pulse in the temporal domain while keeping its spectrum
unchanged. Some numerical simulation results are illustrated in Figure 4 (the simulation
imulation code is
presented in Appendix). Significant changes of temporal profile are observed. However, the
spectra remain the same.
The parameter used to characterize the effect of dispersion is the dispersion-length,
dispersion
which
is defined as

τ2
τ3
′
LD =
,L =
,
β 2 D β3

(10)

where LD and LD' represent the dispersion length corresponding to second order and third order
dispersion, respectively. τ is the full
full-width half-maximum
maximum (FWHM) pulse duration.

Figure 4: Simulation results. Pulse profiles of a) input pulse; b) pulse after
propagating through 3*
3*LD-long fiber with β3=0; c) pulse after propagating
through 3*LD'-long
long fiber with β2=0; d) combined effects of (b) and (c).
11

The introduction of the nonlinear refraction term makes the problem more complicated.
With a non-zero γ, Equation (7) can no longer be solved analytically.. The way to figure out the
effects of pulse propagation is to use numerical simulation with the split-step
step method [24, 25].

By using small steps for the pulse propagation, the linear (dispersion) and nonlinear parts in
NLSE can be treated separately. Figure 5 shows simulation results of the effects caused by
nonlinear refraction without dispersion introduced (the simulation
imulation code is presented in
Appendix). A pulse propagates through a length LNL of fiber, and a spectral broadening is
observed while the pulse profile is preserved. LNL is the nonlinear length, defined as

LNL =

1
.
γ P0

(11)

Figure 5: Simulation results. Top: (a) input pulse spectrum and (b) temporal
profile; Bottom: (c) spectrum and (d) temporal profile
le of pulse after propagating a
distance LNL in fiber. Red line: frequency chirp induced by SPM.
This phenomenon is called self
self-phase modulation (SPM).. The spectral broadening is due to
the time dependence of the selfself-induced nonlinear phase shift (φNL) experienced by an optical

12

pulse during its propagation through the fiber. The SPM induced chirp, or the difference between
instantaneous optical frequency and central frequency, is plotted in Figure 5(d). Though the
pulse has the same profile, it is not transform-limited any more.
The nonlinear phase shift is a very important parameter for pulse evolution in the fiber, and
is defined by

φ NL =
max
φ NL

2π

λ

2

n2 L E ,

(12)

= L LNL = γ P0 L ,

where L is the fiber length, λ is the carrier wavelength of optical pulse, E is the electric field in
the temporal domain, and P0 is the peak power of pulse. The pulse experiences a maximum
max
nonlinear phase shift ( φ NL
) of 1 radian after propagating through LNL long fiber. Simulation

results of the spectral broadening corresponding to different maximum nonlinear phase shifts are
max
shown in Figure 6. The larger φ NL
is, the broader the output spectrum is.

13

Figure 6: Simulated SPM induced spectral broadenin
broadening
g of the pulse experiencing a
maximum nonlinear
linear phase shift of a) 0; b) π; c) 3.5π. φmax is the maximum
nonlinear phase shift.
Previously, we only consider
considered the effects of chromatic dispersion and nonlinear refraction
independently. In reality, they always exist together and affect each other, and this causes more
complicated and interesting effects. As shown in Figure 7, the optical pulse experiences
experience changes
in both the spectral and temporal domain
domains, unlike the effects
ffects demonstrated previously
(simulation
mulation code seen in Appendix
Appendix). Here, we choose the case for which
hich SPM effects are much
larger than those of dispersion, which means LNL is much greater than LD. For a fiber with a
length of only 0.04LD, there are significant changes of the pulse profile and spectrum
spec
(see Figure
7(c) and (d)).

14

Figure 7: Simulation showing ppulse intensity and spectrum after propagating
propa
through a fiber with both dispersion and nonlinear refraction. Top: fiber length of
0.01LD; middle: fiber length of 0.04
0.04LD; bottom: fiber length of 0.08LD.
As shown in Figure 7(e) and (f), there are oscillations near the edges of the temporal profile
and side lobes in the spectrum. This phenomenon is called temporal wave-breaking
breaking [26]. This
only happens
ns in a normal dispersion fiber where longer wavelengths travel faster.
faster As shown in
Figure 5(d),, SPM induces frequency chirp. The SPM-induced red-shifted
shifted light (negative change
of frequency) travels faster, which makes the frequency chirp function steeper while the pulse
propagates, see Figure 7(d). Eventually, the red
red-shifted light can overtake the un-shifted
un
light in
the leading edge of the pulse.. Then, the lead edge of the pu
pulse
lse contains two frequencies at the
same time, which causes interference. Also, blue
blue-shifted
shifted light travels slower and is caught by the
un-shifted
shifted light on the trailing edge. The oscillations near the leading and trailing edges of the

15

pulse are due to these interferences [26]. It is very important to avoid wave-breaking in fiber
laser development, since it breaks one pulse into pieces.

1.3

Introduction to fiber lasers
Not only for optical communication, optical fibers are also used to make lasers [27].

Compared to conventional solid-state lasers, fiber lasers have many advantages. First of all, all
light can be confined within the fibers. Thus it is environmentally more stable and insensitive to
changes in humidity or temperature. Also no optical alignment is needed, unlike the complicated
optical setups of normal solid-state lasers. Meanwhile, the output beam profile can be a pure
single mode, without being affected by different powers. This is very important for microscopic
imaging or precise micro-machining. Second, due to the large surface-to-volume ratio, the heat
dissipation of fiber is much better than that of bulk gain crystals, which enables high power or
energy laser delivery without any cooling. Third, because of the large telecom industry, the
fabrication of fibers is very well developed and the cost is considerably low. Fourth, fiber lasers
can be directly diode pumped. Laser diodes are widely available, inexpensive and compact. The
electrical-to-optical efficiency of fiber lasers can be more than 30%. Based on all the advantages
mentioned above, fiber lasers have attracted considerable attention in the past two decades. [2732]

16

Figure 8: Energy levels of a few isolated 3+ rare earth ions. n is the number of
electrons in the partially filled 44f orbital. [33]
Rare earths or lanthanides are normally used as dopants for most gain fibers.
fibers They have a
2

6

partially filled 4f electron shell, which is shielded from external fields by 5s and 5p electrons
[18, 33].. The variety of lanthanides also enables a wide range of emission wavelengths,
wavelength see
Figure 8. When doped in an amorphous host, they are triply ionized and through the loss of two
2

6

6s electrons and one 4f electron. Due to the shielding from 5s and 5p electrons, their ion
energy levels or optical properties are largely independent of the host. This is one of the reason
that rare earth doped gain fibers are widely used. However, full
ull Stark splitting is observed for
rare-earth ions in glasses, due to the low point symmetries of the rare-earth
earth sites in amorphous
matrices [33-35]. This leads to more possible transitions than those between the original ion
energy levels, see Figure 9 [[36]. The Stark levels broaden and overlap to produce an
17

inhomogeneously broadened emission band [33]. The millisecond long fluorescence lifetime
(upper-state
state time) of lanthanides also results in the need for only a relatively low pump power to
maintain a significant population inversion [18],, which means a relatively low lasing threshold.
threshold

Figure 9:: Energy level diagram of Yb3+ ions containing split sub-levels [36]. 940
nm transition is for the pump light, 1030 nm and 1050 nm transitions correspond
to the emissions wavelengths
wavelengths.
Depending on the rare earth dopant, emission wavelength varies with different gain
ga fibers.
Nd, Er, Tm and Yb doped gain fiber
fibers are most commonly used. The
he first fiber laser was based on
a Nd gain fiber [37]. For Er-doped
doped fiber, the emission wavelength is around 1500 nm, which
coincides with the minimum loss of silica and is the standard wavelength for optical
communication. Tm doped fiber emits around 2000 nm, which is in the near IR and considered
an ‘eye-safe’ laser.
r. It has important applications in both medical an
and
d sensing technology. As for
Yb-gain
gain fiber, the solubility of Yb in glass is much better than Er, which can result in a much
higher gain. Also the emission wavelength of Yb is around 1030 nm
nm,, which is close to the
common diode pump laser wavelength of 976 nm. The Yb gain fiber has very good quantum
efficiency and is suitable for maki
making high-power fiber lasers. The average power of a CW Yb
fiber laser can be routinely scaled up to 10 kW [38]. Recently, the first commercial 100 kW CW
18

fiber laser has been developed by IPG Photonics [39]. In the past decade, mode-locking ultrafast
fiber lasers have also developed greatly, in terms of both pulse duration and pulse energy.
Benefiting from the development of fiber technology, fiber lasers delivering different output
pulses such as soliton [40], Gaussian pulse [41] and all-normal-dispersion [31], have been
developed. By manipulating cavity dispersion and intra-cavity pulse shaping, different modelocking regimes can be achieved or switched between.
Soliton fiber lasers were studied and developed in the early years of the history of fiber
lasers. John Scott Russell first observed the phenomenon of soliton formation in 1983 [42]. He
noticed that solitary waves could form on water and propagate long distances without change in
its profile. The optical soliton was studied after the invention of optical fibers and attracted much
attention [43]. It was discussed above that the phase distortion induced by dispersion and SPM in
a fiber can change the pulses in the temporal or spectral domains or both. In order to support the
formation of solitons in a fiber, the phase induced by dispersion needs to balance that of SPM.
According to Equation (12), the nonlinear phase shift induced by SPM is always positive. The
dispersion can be either positive or negative, depending on the optical wavelength and fiber
materials. So, a fiber that has appropriate anomalous dispersion to compensate the positive
nonlinear phase shift can support solitons. After solitons are formed, they can propagate a long
distance while keeping their spectral and temporal profile unchanged.
Since solitons have zero phase distortion, it should be possible to produce transformlimited pulses directly out of soliton lasers. No extra phase correction or pulse compression is
needed, which is ideal for many laser applications. In order to generate soliton-like pulses,
anomalous dispersion components are needed in laser cavities and net cavity dispersion must be
negative. In a standard solid-state Ti:sapphire laser, prism pairs are normally used to provide

19

negative dispersion. For fiber lasers, anomalous dispersion fiber can be used. Fox example,
normal silica fiber has negative dispersion for wavelength > 1.3 µm. The first soliton fiber laser
was demonstrated in 1989 by Kafka et al. [40] and later, an all-fiber soliton laser was developed
[29]. Both of them were Er fiber lasers with emission wavelength at 1.5 µm. The pulse evolution
through the laser cavity is illustrated in Figure 10 [44]. Soliton pulses take the form

U (t ) = U 0sech(t / τ ) exp(iφ )

(13)

where the FWHM pulse duration ∆t = 1.763τ . Since soliton results from the cancellation of
negative phase due to dispersion and positive phase due to SPM in a negative dispersion cavity,
the requirement can be expressed as [18]

L
L
τ2
1
=
⇒
=
.
LD LNL
β 2 γ P0

(14)

where L is the length of fiber used in the soliton fiber laser, LD is the dispersion length, LNL is
the nonlinear length, β2 is second order dispersion, γ is nonlinear coefficient, and P0 is the peak
power of soliton. The peak power P0 is defined by

P0 = 0.88

E E
= ,
∆t 2τ

(15)

where E is the soliton pulse energy. Based on Equation (14) and (15), the pulse energy can be
presented as
E=

2 β 2 3.53 β 2 3.53 D
=
=
,
γτ
γ∆ t
γ L ∆t

(16)

where D = β 2 L is total cavity dispersion (negative for soliton fiber laser). Meanwhile, the
length of fiber used in solition fiber laser is limited by [18]

20

L = 0.322

π∆t 2
⇒ ∆t =
β2

D.

(17)

So the pulse energy E of soliton fiber laser can bbe approximated by
E=

3.53 D

γL

.

(18)

Figure 10: Illustration of pulse evolution in different fiber laser cavities.
cavities [44]
Besides cavities with negative net cavity dispersion, fiber lasers with zero net cavity
dispersion were also studied. These lasers typically have a normal dispersion component (normal
dispersion fiber) and a negative dispersion component (such as anomalous fiber or grating

compressor) that compensate each other. So these lasers are also called dispersion-managed
dispersion
or
dispersion-mapped fiber lasers.
rs. The output pulses have Gaussian profile [45],
2
U (t ) = U 0exp  − ( t / 2τ )  ,



21

(19)

in contrast to the sech profile of soliton pulses. They are called Gaussian pulses, or stretchedpulses. In this laser, pulses are stretched and compressed twice within each round trip of the
cavity, as shown in Figure 10. So there are two locations where the pulses are chirp free or
transform-limited, which can be selected as the desired output. The pulse energy and pulse
duration of Gaussian pulses can be expressed as [45]
E=

4.47 D

γL

,

(20)

∆t = 0.66 D .

Unlike previous laser cavities all containing anomalous dispersion components, more
recently all-normal dispersion (ANDi) fiber lasers were developed [31]. There is no pulse
compression or any component introducing negative dispersion inside the laser cavities. The
output pulses are normally highly chirped and can be compressed externally. In order to stabilize
the mode-locking, spectral filtering is normally applied in ANDi fiber lasers [44]. This idea was
first proposed in Kerr-lens mode-locked solid-state lasers [46, 47]. When an optical pulse is
highly chirped, different frequencies are distributed at different positions in the temporal domain.
In a positively chirped pulse, red frequency occupies the leading edge while blue frequency
occupies the trailing edge. So a spectral filter that blocks red and blue frequencies will also
shorten the pulse in the time domain (see Figure 11). Thus, the mode-locking can be stabilized.
Otherwise

the

pulse

broadens

forever,

and

non-self-sustaining.

22

the

system

becomes

dissipative

and

Figure 11: Spectral filtering of highly chirped pulse
pulse.. T: transmittance.

1.4

Mode-locking
locking methods in fiber lasers
There are two main categories of mode
mode-locking
locking methods. One is active, using acousticacoustic

optic modulators (AOM) and electric
electric-optic modulators (EOM); the other one is passive and uses
saturable absorberss or artificial sat
saturable absorbers.
Both AOM- or EOM-aided
aided mode
mode-locking generate up- and down-shifted
ed frequencies. If
these newly generated frequencies
ies match the cavity modes, they will be phase locked with the
original frequency and all the subsequently generated new frequencies will also be phase-locked.
phase
Thus mode-locking
locking is achieved. Another active mode
mode-locking
locking method is seeding the laser with
an already mode-locked
locked laser source, which is mostly used in laser amplifiers.
Passive mode-locking
locking usually uses saturable absorbers. A saturable absorber has two main
characteristics: intensity-dependent
dependent transmission and a fast response time. In solid-state
solid
lasers,
organic dyes, liquid crystals, and semiconductors are used as saturable absorbers. Among them, a
semiconductor saturable absorption mirror (SESAM) is used widely, while the other two have
been gradually replaced due to complexity and instability. SESAM
ESAM is also one of the main types
of saturable absorber used in fiber lasers, although it typically has a slower response time and is
not suitable for producing very short pulses. Meanwhile, ssingle wall carbon
arbon nanotubes
nanotube (SWCN)
and graphene are emerging saturable
turable absorbers, due to their broadband absorption and fast
fas
recovery time. [48]
23

Other than these devices, there are also some artificial saturable absorbers that use
nonlinear optical effects, such as Kerr
Kerr-lens mode-locking
locking used in Ti:sapphire lasers. Due to the
optical Kerr effect, the higher the intensity is, the more the refractive index is changed. For a
Gaussian beam, the central part has much higher intensity than the edge and will be focused
focu
more after a lens. This effect is also called self
self-focusing. In a Kerr-lens
lens mode-locking
mode
laser, a
hard or softer aperture is used to favor amplification of the pulsed light over the CW light, since
pulsed light has higher peak intensity
tensity. For fiber lasers,
rs, artificial saturable absorbers
absor
based on
nonlinear effects are most commonly used due to the large optical nonlinearity in fibers.

Figure 12
12: Nonlinear Optical Loop Mirror. [49]
One of the earliest developed fiber artificial saturable absorber
absorbers is the nonlinear optical
loop mirror (NOLM) [49],, based on the principle of nonlinear phase shift. A typical
ty
NOLM is
shown in Figure 12.. The input signal splits to two after going through the coupler. One of the
split pulses is going clockwise and the other one is counter
counter-clockwise.
clockwise. Depending on the power
of the pulses in eachh arm, the phase accumulated by going clockwise and counter-clockwise
counter
will
be different. They will have either constructive or destructive interference with each other at the
coupler. By properly adjusting the coupling ratio, NOLM can favor the output of high
h
intensity
light, which essentially is the same as Kerr
Kerr-lens mode-locking.

24

Figure 13: NOLM Fiber
iber laser [29]. NALM: nonlinear amplifying loop mirror.
Figure 13 shows a typical fiber laser using NOLM [29].. A setup of two rings is used and
looks like a figure ‘8’, which is why this type of laser is also called a ‘figure-8’
8’ fiber laser. On
the right side, a piece of gain fiber is added and a coupler is used to couple the pump laser in. In
between two rings, a 50% couple
coupler is used. The left ring is usually called the resonator,
resonator and the
right one is the NOLM or nonlinear amplifying loop mirror (NALM), since it contains gain fiber.
fiber
Light from the resonator equally splits and propagates in opposite directions in the NOLM. In
I the
clockwise direction, light goes through a large segment of passive fiber and gets amplified later.
For the counterclockwise direction
direction, it is amplified first and gains additional phase shift through
the long passive fiber than does the clockwise one. If the phase
se difference happens to be π,
interference will send all the light to the bottom of the resonator where it gets ejected out of the
output coupler. The non-pulsed
pulsed signal, exp
experiencing
eriencing very little phase difference in the clockwise
and counterclockwise directions in the NOLM, is couple
coupled back to the top of the resonator and
rejected by the isolator. In this case, the residual signal in the resonator is mainly from the pulsed
laser and mode-locking
locking is achieved.

25

Figure 14: Mode-locked
locked fiber laser based on nonlinear polarization evolution.
evolution
[50]
Nonlinear polarization evolution (NPE) [50, 51] is another popular mode-locking
mode
method
used for fiber lasers, see Figure 14. In addition to rotation by the natural birefringence of the
fiber, the polarization of the input light is also rotated by the effects of SPM and XPM. As
mentioned above, SPM induces an intensity-dependent
dependent nonlinear phase shift. XPM also
introduce a nonlinear phase shift to the optical pulse induced by a second propagating pulse
either with different wavelength or a different polarization. The total nonlinear phase shift caused
by SPM and XPM is approximately given by

φNL =

2π

λ

(

2

n2 L E1 + 2 E2

2

).

(21)

where E1 and E2 are the electric fields in two orthogonal polarization orientations.
orientations The
difference between the phase shifts of the two orthogonal polarization components is defined by

26

∆φ =

)

(

2π L n2
2
2
E1 − E2 .
λ 3

(22)

An input optical pulse, with either multiple frequencies or polarization not along the axis of the
fiber, will change its polarization in ellipticity and angle (see Figure 14), which is frequency or
intensity-dependent. By applying a polarizer after the fiber output, intensity dependent
transmission can be achieved, just like in Kerr-lenses or NOLM artificial saturable absorbers.
Among all the mode-locking methods mentioned above, SESAM, SWCNT and NOLM are
most favorable for all-fiber lasers. NPE is more often used for fiber lasers with free space
components, especially for producing high pulse energy and ultrashort pulse duration. Active
mode-locking is mainly used for picosecond fiber laser.

1.5

Ultrashort Pulse Compression
Due to the dispersion and the nonlinear phase shift, the output of an ultrafast fiber laser can

have a significant amount of phase distortion. It becomes very important to compensate phase
distortions and compress the pulse to its transform-limited duration for most applications. There
are many approaches used for pulse compression, such as grating compressors, prism
compressors, chirped mirrors, and fiber Bragg gratings. These passive compressors are quite
simple to assemble and easy to implement, but they are not able to compensate higher-order
phase distortions. In order to do so, active pulse compressors such as pulse shapers [52] are used.
A pulse shaper is a device to shape the optical pulse, either spatially or temporally. A normal
pulse shaper is illustrated in Figure 15, which is also called 4-f pulse shaper. It consists of two
gratings, two lenses and one mask in the Fourier plane. This mask can be used as either for phase
or amplitude modulation or both of them. Without the mask, it just acts as a grating compressor.

27

Figure 15: Schematic of a 4-f pulse shaper.
As shown in Figure 15, when the distance between grating and lens (L) is less than the
focal length (f), it behaves as a pulse stretcher, where red frequencies come ahead of blue
frequencies. In the case of L>f, it becomes a pulse compressor. However, this layout will cause
some spatial chirp in the output pulses, which is unwanted. So, it is better to keep the shaper at a
4-f layout. The 4-f scheme can be modified by folding the setup at the Fourier plane using a
reflection mirror. Lenses can also be replaced by curved mirrors.
With the development of liquid crystal based spatial light modulators (LC-SLM), it became
possible to make adaptive corrections rather than using fixed masks [52]. By applying certain
voltages to the pixels of liquid crystal arrays, the liquid crystals rotate and act as birefringent
materials. In the Fourier plane, frequencies focused on to different LC arrays accumulate
corresponding phase retardance. This applied phase is called the spectral phase and does not
change the output spectrum. However, the pulse is modified in the temporal domain.
Based on this technique, the Dantus research group developed a pulse characterization and
compression method – multiphoton intrapulse interference phase scan (MIIPS) [53-55]. By
adding a defined spectral phase to the laser spectrum and measuring the resulting change in the
SHG signal, the phase distortion in the original pulse can be determined. The principle of the

28

method is based on nonlinear interference, which depends on the spectral phase, and cause
changes in the SHG spectrum. The electric field of a pulse can be written as

E (ω ) = E (ω ) exp(iφ (ω )),

(23)

where E(ω) is the electric field of the pulse in frequency domain, and φ(ω) is the spectral phase
of the pulse. If this pulse is focused into a SHG crystal, the generated SHG signal can be
presented by

I (2ω ) =

∫ E (ω + ∆)

2

E (ω − ∆ ) exp ( i (φ (ω + ∆ ) + φ (ω − ∆) ) ) d ∆ ,

( )
( )

1
1
φ ′′(ω )∆ 2 + φ ′′′(ω )∆ + O ∆ 4 ,
2!
3!
1
1
φ (ω − ∆) = φ0 − φ ′(ω )∆ + φ ′′(ω )∆ 2 − φ ′′′(ω )∆ + O ∆ 4 ,
2!
3!

φ (ω + ∆) = φ0 + φ ′(ω )∆ +

(24)

φ (ω + ∆) + φ (ω − ∆) = 2φ0 + φ ′′(ω )∆ 2 + O (∆ 4 ),
I (2ω ) =

∫

((

))

2

E (ω + ∆ ) E (ω − ∆ ) exp i 2φ0 + φ ′′(ω ) ∆ 2 + O ( ∆ 4 ) d ∆ ,

(25)

where I(2ω) is the SHG signal, ∆ is the frequency deviation from ω and the variable of
integration, and φ0 , φ ′ (ω ) , φ ′′ (ω ) and φ ′′′ (ω ) are the zero order, first order, second order and
third order derivatives of the spectral phase φ (ω ) , respectively. According to Equation (25), the
SHG signal I(2ω) is maximized when φ ′′ (ω ) = 0 .
When a reference phase φref(ω) is introduced, the SHG intensity at certain frequency is
maximized when
′′ (ω ) ,
φ ′′ (ω ) = −φref

(26)

where ω is the angular frequency, φ ′′(ω ) is the second derivative of the original phase of input

′′ (ω ) is the second derivative of the reference phase. Normally a sinusoidal
pulses, and φref
29

reference phase or second order dispersion phase is applied, as defined by either of the two
expressions, respectively:

φref (ω ) = α cos ( γ (ω − ω0 ) + δ ) ,
1
2

φref (ω ) = β 2 (ω ) (ω − ω0 ) ,
2

(27)

where α is a modulation amplitude with value around 2π, γ is the FWHM pulse duration of
transform-limited pulse, δ is the scanning phase parameter, and β2 is the scanning second order
dispersion. The SHG signal will be maximized when

ϕ ′′ (ω ) = αγ 2 cos (γ (ω − ω0 ) + δ max (ω ) ) ,
ϕ ′′ (ω ) = − β 2max (ω ) .

(28)

In the case of a transform limited pulse, ϕ ′′ (ω ) is 0 and

δ max (ω ) = (2n ± 1)
β2

max

π
2

− γ ( ω − ω0 ) ,

(29)

(ω ) = 0,

where δ max (ω ) and β 2max (ω ) are the scanning parameters corresponding to the local
maximum SHG signal. It can be easily noticed that δ max (ω ) is simply a straight line with slope
of γ and repeats every π; β 2max (ω ) is simply a horizontal line equal to zero. If there is second
order phase dispersion, then ϕ ′′ (ω ) is a non-zero constant. δ max (ω ) is still a straight line but
the spacing becomes smaller or larger than π; and β 2max (ω ) is just a constant meaning a
straight line across all frequencies. With higher order dispersions, the functions will change
correspondingly, as illustrated in Figure 16.

30

Figure 16: MIIPS simulation results. Top: sinusoidal scan of pulses with (a) flat
phase, (b) second order dispersion, (c) third order dispersion, (d) fourth order
dispersion and (e) all of them
them; bottom: second order dispersion scan of pulses
with (f) flat phase, (g) second order dispersion, (h) third order dispersion, (i)
fourth order dispersion and all (j) of them.. Dot lines: local maxima of SHG signal.

31

Chapter 2 Sub
Sub-50 fs High Energy Ultrafast Fiber Laser
This chapter discusses the development of sub
sub-50 fs fiber lasers producing tens of nJ pulse
energy,, which achieved the highest peak power of the pulses from a single
single-mode
mode fiber laser.
laser
Different cavity designs are discussed. Dependence of laser performance on several key cavity
parameters is studied. Both simulation and experimental results are demonstrated.

2.1

Introduction
One principal application of ultrafast fiber lasers is biomedical imaging, such as

multiphoton microscopy [6].. It is known that multiphoton efficiency is dependent on pulse
duration [56]. As shown in Figure 17, the SHG signal is inversely proportional to the laser pulse
duration and the THG is inversely
ly proportional to pulse duration squared [Figure
Figure 17] [57].

Figure 17: Pulse duration dependent multiphoton efficiency
efficiency.. Symbols:
experimental results; Lines: fit of experimental data.
It is clear that shorter pulse
pulses increase the multiphoton signal. On the other hand, in order to
image biological samples,, laser pulse
pulses need to overcome the large loss from tissue scattering.
scattering So
a fiber laser that can provide both ult
ultrashort pulse duration (sub-50
0 fs) and high pulse energy

32

(tens of nJ) is highly desirable for this application. As discussed in Chapter 1, there are several
types of fiber laser designs. A proper design needs to be chosen to produce pulses as mentioned
above.
Intuitively, a soliton or Gaussian pulse fiber laser is considered as the first option, since
both of them can deliver transform-limited pulses. It is known that pulse energy E and FWHM
pulse duration ∆t of soliton pulses are approximately [45]
E=
∆t =

3.53 D

γL

,

(30)

D,

or

E 3.53
=
,
∆t γ L

(31)

where D is the net cavity dispersion (usually negative), γ is the nonlinear coefficient, and L is
total fiber length in laser cavity. As shown in Equation (30), the larger the net cavity dispersion,
the higher the pulse energy and the longer the pulse duration. In other words, pulse duration is
proportional to pulse energy. For a typical 100 MHz soliton fiber laser using about 2 m long 6µm
core diameter fiber operating at 1.5 µm wavelength, the ratio between pulse energy and pulse
duration or peak power is limited to about 400 W according to Equation (31). This means that a
100 fs pulse from a soliton fiber laser can only contain about 40 pJ of energy, which is too low
for most imaging applications. While a 10 ps soliton pulse can deliver 4 nJ pulse energy, the
pulse duration is too long. Therefore, soliton fiber lasers would be ideal for producing transformlimited picosecond pulses, which is not suitable for biomedical imaging. This limitation can also
be understood as follows. Since soliton pulses are transform-limited through the whole laser
cavity, the corresponding peak power will be very high for femtosecond pulses with nJ pulse
33

energy. This will cause significant high order nonlinear effects such as self-steepening,
stimulated Raman scattering and even self-focusing (for peak power larger than 6 MW). Soliton
propagation cannot be sustained under those conditions.
For Gaussian pulse fiber lasers, pulse energy and pulse duration can be expressed as
E=

4.47 D

γL

,

(32)

∆t = 0.66 D ,

or
E 6.77
=
.
∆t γ L

(33)

According to the energy-to-pulse-duration ratio, Gaussian pulses can deliver about twice the
pulse energy as soliton pulses with the same pulse duration. This higher pulse energy is
attributed to partial stretching of the pulses due to the normal dispersion components. However,
the pulse energy for femtosecond pulses is still not high enough.
Different from soliton and Gaussian pulse fiber lasers, all-normal dispersion fiber lasers
have pulses that are highly chirped through the entire cavity; and higher pulse energy can be
tolerated without generating significant nonlinear effects in fibers, so an all-normal dispersion
fiber laser is a better option for high pulse energy delivery. On the other hand, Yb fiber lasers are
favored for high power fiber laser designs. The emission wavelength is around 1 µm, fused silica
has normal dispersion at this wavelength. Therefore, the output pulses of all-normal dispersion
fiber lasers usually have significant phase distortion since there is no dispersion compensation
inside the cavity. External pulse compression is needed for this type of lasers. The maximum
nonlinear phase shift experienced by pulses in a normal dispersion cavity can be as large as ~10π
[58], compared to only ~π in soliton and Gaussian pulse fiber lasers [44]. In previous report [59],

34

pulse energy as high as 31 nJ was delivered from an all
all-normal
normal dispersion fiber laser. The output
pulses were compressed to about 80 fs FWHM pulse duration, resulting in a peak power of 200
kW. It is desirable to explore the limit of this fiber laser design in terms of the pulse energy, the
pulse duration and the peak power.

2.2

All-normal
normal dispersion fiber laser

2.2.1

Experimental setup

Figure 18: Schematic of an aall-normal dispersion fiber laser.. PBS: polarizing
beam splitter; QWP and HWP: quarter
quarter- and half-wave plate respectively;
respectively SMF:
single mode fiber; coll.: fiber collimator; SF: spectral filter.
A typical all-normal dispersion fiber lase
laser is illustrated in Figure 18. It has a ring cavity
with some free-space
space components used. A pump laser (976 nm laser diode) is coupled into an Yb
doped gain fiber by a fiber combiner. The gain fiber used here is a double-clad
clad fiber with 10 µm
core diameter (CorActive, 6 dB/m absorption @ 975 nm). The pump
ump laser is delivered by a 100

µm core diameter multi-mode
mode fiber and coupled into the inner cladding of the gain fiber. The
excess pump laser is forced to leak out by applying index
index-matching gel at the end of gain fiber.
Two segments of passive single mode fiber (SMF
(SMF-I and SMF-II) are fusion spliced to gain fiber
using a fiber splicer (Fujikura LMA
LMA-PM-400). Two fiber collimators are used to couple the input
and output light of the fiber, respectively. Several quarter- and half-wave plates are used to help

35

the mode-locking
locking based on nonlinear polarization eevolution
volution (NPE). The polarizing beam splitter
(PBS) acts as an output coupler and is also part of the NPE mode-locking. The isolator
i
is a very
important component. It establishes the direction of the laser propagation and prevents
prevent damage to
the gain fiber. If even a small amount of light couples back to the gain fiber,, it can destroy the
fiber cavity due to the high gain. A spectral filter is used to stabilize the mode-locking.
mode
In
principle, all the free-standing
standing components mentioned above can be replaced by all-fiber
all
components. For example, the wave plates can be easily replaced with a fiber polarization
controller. By adding forces to a non
non-polarization
polarization maintaining fiber, the birefringence of the fiber
can be easily changed. Thus the polarization of the output light will also be changed. The PBS
can be replaced with a fiber coupler. However, our research focuses on developing the concept
co
of a fiber laser design instead of engineering an integrated all-fiber laser. (Detailed fiber laser
cavity alignment is presented in the Appendix.)
The principles behind using each of these components to achieve mode-locking
mode
is
described below.

2.2.1.1

Nonlinear polarization
olarization eevolution

Figure 19: Schematic of aartificial saturable absorber. PBS: polarizing beam
splitter, HWP and QWP: half
half- and quarter-wave plate, and +z is the pulse
propagation direction. Note: color has no meaning in this figure.
As mentioned in Chapter 1, a fiber laser can be mode-locked using an artificial saturable
absorber based on NPE of the optical field in the fiber. A schematic of the artificial saturable

36

absorber used in our laserr is shown in Figure 19.. It is formed by a PBS, three wave plates, and
the fiber.

Figure 20: Illustration of propagation of electric field through the artificial
saturable absorber. α1, α2, α3 are the angles between the fast axis of the wave
plates and the x-axis, θ1 and θ2 are the angles between the axis of the polarizers
polarizer
and the x-axis, x, y, z are the coordinate axes, and +
+z is the pulse propagation
direction. Note: color has no meaning in this figure.
As shown in Figure 20, a pulse after the PBS is horizontally polarized. The
T input optical
field E0 is

1 
E0 = a   ,
 0

(34)

where a is the amplitude of the input optical field. Due to cross-phase
phase modulation (XPM), the
phase change for each frequency through the fiber can be written as
∆φ (ω ) =

)

(

2π L n2
2
2
E+ (ω ) − E− (ω ) .
λ 3

(35)

where L is the length of the fiber, λ is the wavelength of the input pulse, n2 is the nonlinear
refractive index, and E+ and E- are the electric field of the two orthogonal polarization
components along the fast and slow axes of the fiber, respectively
respectively. Here, we assume that the fast
axis of the fiber is along x axis and the slow axis of the fiber is along y axis. The evolution of the

37

electric field through these components can be calculated using Jones vectors. Two simple
results are shown below,
If α1 = 0, α 2 = 0, α 3 = 0, I out (ω ) = a 2 sin 2 ( ∆φ (ω ) ) .

If α1 =

π
4

,α2 =

π
4

, α3 =

π
4

, I out (ω ) = a 2 (1 + cos ( ∆φ (ω ) ) ) .

(36)
(37)

So, by rotating these wave plates, the transmission function of this setup varies. With fixed wave
plate angles, the transmittance of each frequency is different, depending on their intensities and
input polarizations. Thus, by properly adjusting the wave plates, the coupling and amplification
of frequencies with high intensity can be favored t. After a number of round trips,
trips mode-locking
can be achieved.

2.2.1.2

Spectral filter

Figure 21: Illustration of spectral filter
filter.. PBS: polarizing beam splitter, BF:
birefringent plate, and +zz is the pulse propagation direction.
The spectral filter is another very important component in this cavity
cavity.. It is formed by a
birefringent quartz plate placed between the PBS and the isolator (see Figure 21).
21 The ordinary
axis of the birefringent plate is at 45° with the respect to the horizontal axis in the plane
perpendicular to the beam propagation direction
direction. The plate is also tilted at the Brewster
B
angle to
reduce reflection loss. Meanwhile, the polarization of the input port of the isolator is set as
horizontal. The input light from the PBS is horizontally polarized. Then we can get the equations
below,

38

v
Ein = E0eˆx = 2 E0eˆ0 + 2 E0eˆe ,
2
2
v
E ′ = 2 E0eˆ0 + 2 E0eˆe ⋅ e−i∆φ ,
2

2

v
E ′ = 2 E0 ( 2 eˆx + 2 eˆ y ) + 2 E0 ( 2 eˆx − 2 eˆ y ) ⋅ e−i∆φ ,
2
2
2
2
2
2

(38)

∆φ
v
∆φ −i 2
E ′ = E0 cos( )e
eˆx + ⋅⋅⋅eˆ y ,
2

Eout =

∆φ
∆φ −i 2
E0 cos( )e
eˆx .
2

v
where E ′ is the electric field after the birefringent plate. The transmission function of the output
pulse can be written as below,
∆φ

I out = E0 cos 2 ( ),
2
∆φ = 2π (ne − no )d .
λ

(39)

where ne and no are the refractive indices of extra-ordinary and ordinary axes of the birefringent
quartz plate, Iout is the pulse intensity after the spectral filter.
Here, ne and no are 1.53514 and 1.54392 at 1 µm, respectively. Using the
Equations (39) and the refractive indices, transmittance curves for different thicknesses of
birefringent plates are plotted in Figure 22. It shows that, the setup with a 3 mm thick
birefringent plate corresponds to a 20 nm FWHM bandwidth spectral filter, and the one with a 5
mm thick birefringent plate has a FWHM spectral bandwidth of 12 nm. By rotating the axis of
the spectral filter or changing the input or output polarization axis of the polarizers, the
wavelength of the peak transmittance can be shifted.

39

Figure 22: Transmittance
ttance of spectral filter using a) a 3 mm thick birefringent plate
and b) a 5 mm thick birefringent plate
The spectral filter plays a very important role in stabilizing mode
mode-locking.
locking. Initially by
adjusting the filter, only the desired spectral range is amplified in the gain fiber. After
amplification, high intensity pulse induced SPM will generate new frequencies and broaden the
spectrum. After each loop, the
he filter
filter-induced loss of both spectral bandwidth and pulse energy
also balances the gain, which keep
keeps the laser producing stable output pulses. Meanwhile, due to
the cavity dispersion (here we only discuss the case of normal dispersion),
), the generated red
frequencies lead the pulse and the blue frequencies lag the pulse. This dispersion broadens the
pulse duration. By applying the spectral filter, it not only cut
cuts the spectral bandwidth, but also
als
shortens the pulse in the temporal domain. Other ways in which the spectral filter affects the
laser performance will be discussed later in this chapter.

2.2.2

Experimental results and discussion
For the initial operation of the laser, the pump power should be set at a low level and the

alignment of the setup is adjusted by monitoring the output power.. The most critical thing is the
coupling between two fiber collimators. Both angle and height need to be adjusted. Once enough
coupling efficiency is reached, the cavity will start lasing and output power will increase
40

dramatically. Then, finer adjustment can be done to maximize the output power in CW mode.
The isolator has to be placed in between the two collimators all the time. Otherwise, the gain
fiber will be easily damaged.
Various mode-locking patterns can be obtained by varying the pump power and rotating the
wave plates. Typical output pulses from an all-normal dispersion fiber laser are shown in Figure
23. Output pulses with average power of 1.43 W at a repetition rate of 41.2 MHz, corresponding
to 34.7 nJ per pulse, are delivered from this laser. Output pulses are highly chirped and
compressed to about FWHM 80 fs pulse duration, which already beats the best all-normal
dispersion fiber laser (31 nJ and 80 fs) reported previously [59]. The cat-ear like structure of the
spectrum is the characteristic of all-normal dispersion fiber laser and is caused by SPM effects.
For this demonstrated laser, the parameters are as follows: 2.5 m long SMF-I, 1.9 m long gain
fiber, 0.2 m long SMF-II fiber and spectral filter of FHWM 20 nm bandwidth. The gain fiber is
pumped at about 6.1 W. Since all the cavity parameters listed above can be adjusted, it is
important to study the dependence of the laser performance on these parameters and find proper
guidance in cavity design. In the following sections, dependences of laser performance on fiber
length and filter bandwidth are mainly discussed.

41

Figure 23: Laser performance of all-normal dispersion fiber laser. (a) Output
spectrum; (b) Experimentally
xperimentally measured interferometry autocorrelation of dede
chirped output pulses.

2.2.2.1

Fiber length dependence
endence

According to their locations and functions, fibers in the cavity are categorized as SMF-I
SMF
(passive fiber preceding gain fiber and after spectral filter), gain fiber and SMF-II
SMF (passive fiber
following gain fiber and before output port).
Normally, the length of gain fiber is chosen to absorb most of the pump light. If the gain
fiber is too short, and it will not fully absorb the pump signal. Too long is not good either, since
the excess gain fiber absorbs no more pump light but the laser signal instead causing some
narrowing. Also it adds more dispersion and nonlinear phase shift to the cavity. Therefore, both
excessively long and short gain fiber should be avoided. The proper length can be determined by
the absorption
sorption rate of the gain fiber
fiber, which depends on the density of Yb ion dopant and pump

42

light wavelength. The gain fiber used here has an absorption rate of 6 dB
dB/m at 975 nm, which
means one meter of fiberr will absorb about 75% of the pump light. In our system, about 2 m gain
fiber is used and the pump-to-laser
laser conversion efficiency can be up to 50% (maximum CW
output power divided by the pump power), as shown in Figure 24. Since the length of the gain
fiber iss not a proper parameter to adjust, the remaining adjustable parameters other than spectral
filter bandwidth are the length of SMF
SMF-I and SMF-II.

Figure 24: Measured pump-to-laser conversion efficiency.
With other parameters kept the same, the length of SMF-I is changed from 7.5 m to 1.7 m.
It is found that the output spectral bandwidth increases with the decrease of SMF-I
SMF length, see
Figure 25. Shortening SMF-II from 7.5 m to 2.4 m, the output spectra change significantly.
significantly
However, further reducing SMF
SMF-I length does not affect the output spectra much, as seen by
comparing the results of 2.4 m and 1.7 m SMF
SMF-I.

43

Figure 25: Output spectra of laser cavities using (top) 7.5 m, (middle) 2.4 m and
(bottom) 1.7 m SMF-I.
In this laser, SMF-II is used to pre
pre-chirp the pulse before being amplified in the gain fiber.
Without pre-chirp,
chirp, it will just behave like a soliton fiber laser and cannot tolerate the high pulse
energy. The pre-chirp lowers the pulse peak power, which helps to avoid too much nonlinear
phase accumulation during amplification
amplification. To be noted, as shown in
n Chapter 1, the nonlinear
phase shift induced by SPM is associated with spectral broadening and a proper nonlinear phase
shift is helpful. When SMF-I becomes very long, the laser pulses would be too chirped to
accumulate enough nonlinear phase shift for spectral broadening. Also, SMF-I
SMF introduces
nonlinear phase shift. The excess nonlinear phase shift can be detrimental to the laser
performance. It is experimentally observed that, mode
mode-locking
g becomes less stable with long
SMF-I.
44

On the contrary, the lengthening of SMF-II broadens the output spectra. The opposite
correspondence is due to the different roles of SMF-I and SMF-II in the cavity. SMF-II guides
the light out of the gain fiber. Other than that, it also helps broaden the output laser spectra by
taking advantage of SPM effects. Ideally, it would be good to use long SMF-II to broaden the
laser spectra as much as possible, provided the entire bandwidth is coherent and compressible.
However, as we mentioned in Chapter 1, unwanted wave-breaking could happen to prevent this
expected pulse evolution. In order to prevent wave breaking, SMF-II length is limited to only
about 0.3-0.5 m.

2.2.2.2

Filter bandwidth dependence

As mentioned before, the spectral filter bandwidth varies due to the thickness of the
birefringent plate used. Three different spectral filters – 12 nm, 20 nm and 30 nm FWHM
bandwidth are tested, while keeping other cavity parameters the same.
It is very hard to mode-lock the laser with a 30 nm spectral filter. The narrower the filter
bandwidth, the easier the mode-locking becomes. This shows that spectral filtering does help
stabilize mode-locking in all-normal dispersion fiber laser. A FWHM 30 nm bandwidth filter is
too large to cause any pulse shaping of the pulses inside the cavity. When it is replaced with a 20
nm spectral filter, stable mode-locking is achieved. It is found that further reducing the filter
bandwidth to 12 nm increases the output spectra bandwidth, as shown in Figure 26. The
broadening of the output spectra is observed in both the 7.5 m long SMF-I and 2.4 m long SMF-I
cavities. The shifted central frequency of the output spectra is due to different axis angles of the
birefringent plates relative to the table axis, as mentioned early in this chapter.

45

Figure 26: Dependence of the output spectra on the spectral-filter
filter bandwidth (a)
Cavity with 7.5 m SMF--I and a 20 nm (top) or a 12 nm (bottom) spectral filter;
(b) Cavity with 2.5 m SMF
SMF-I and a 20 nm (top) or a 12 nm (bottom) spectral
filter.
The spectral filter bandwidth dependent output spectra are observed in various laser
cavities with different SMF-II length. Figure 26(a) and Figure 26(b) are the results from two
cavities using 7.5 m and 2.4 m SMF
SMF-I,
I, respectively. Both of them show the broadening of output

46

spectra due to narrower spectral filter
filter,, which results in shorter compressed pulses.
pulses However, it is
more significant in the cavity with shorter SMF
SMF-I.

2.2.3

Conclusion
Based on the studies shown above, it was found that the output spectrum bandwidth is

highly dependent on the length of SMF
SMF-I and the spectral filter bandwidth. Generally, the longer
the SMF-I is,, the narrower the output spectral bandwidth; the narrower the spectral filter
bandwidth, the broader the output spectral bandwidth. Increase of SMF-II
II can also broaden the
output spectrum to some extent,, but it is not a good parameter to tune in this laser.
laser Meanwhile,
the stability of mode-locking
locking is also influenced by these parameters.

Figure 27: Amplified spontaneous emission of the gain fiber.
Our lasers mentioned above can routinely deliver pulses with tens of nJ pulse energy and as
short as 80 fs pulse duration. Output pulses with 34 nJ pulse energy and 80 fs already beats the
best all-normal
normal dispersion fiber laser (31 nJ and 80 fs) reported previously [59
59]. However, it is
hard to further push the pulse duration below 50 fs with this design.. The output spectrum is not
near the gain bandwidth limit (Figure
Figure 27), which means there is still room for improvement. The
47

interesting fiber bandwidth dependence made us wonder whether we can further reduce the
spectral bandwidth to broaden the output spectrum though it sounds counter intuitive.

2.3

Similariton fiber lasers
In 2010, Bale et al. proposed that strong spectral filtering in a fiber laser can act as a

nonlinear attractor to generate similariton pulses [60], which have a parabolic pulse profile. Later
this regime was demonstrated experimentally and pulses with 55 fs FWHM pulse duration and 3
nJ energy per pulse were delivered from a similariton fiber laser with a very narrow spectral
filter. [61]

2.3.1

Introduction to the similariton
The similariton in an optical fiber was first investigated theoretically by Anderson et al.

[62]. In their work, they found a solution for which optical pulses can avoid wave-breaking and
preserve their pulse shape when propagating in optical fibers. The solution is defined by [62]

A( x,τ ) = Ap 1 −τ 2 τ 0 ( x)2 exp(− ibτ 2 2),

(40)

Where A(x,τ) is the pulse field, τ is instantaneous time, x is the position in the fiber, AP is the
peak amplitude, τ0 is the pulse duration, and b is the chirp parameter. In order to achieve this
solution, assumptions of high pulse intensity, strong nonlinearity and normal dispersion were
made [62]. The quadratic phase term, yielding a linear chirp, is the reason that optical pulses
described by this solution can avoid wave-breaking.

48

Figure 28: Numerical solution of the nonlinear Schrödinger equation for the pulse
amplitude at different propagation distance. [62]
As seen from Equation (40
40), an optical pulse with this solution has a parabolic profile.
profile The
parabolic profile is preserved with increasing width of the pulse as it propagates in the fiber( see
Figure 28) [62].. That is why this type of pulses is called ‘self-similar
similar pulse’ or ‘similariton’.
‘similar
Depending on the change of pulse intensity, they are categorized as passive similaritons,
similariton
which propagate in passive fiber
fibers and dissipate in peak power and amplifier similaritons,
similar
which
propagate in active fiber
er and gain peak power (see Figure 29) [44]. Since similaritons can
tolerate greater pulse energy than solitons without wave
wave-breaking,
breaking, it would be useful to design a
similariton fiber laser that delivers higher energy short pulses.

49

Figure 29: Similariton in passive (left) and gain (right) fiber [44]

Figure 30: Evolution of pulse amplitude as functions of propagation distance in a
normal-GVD
VD fiber amplifier. [63]
Experimentally self-similar
similar pulse evolution was first observed in a fiber amplifier [64],
because the requirement for high pulse intensity can be easily achieved in a fiber amplifier.
amplifier
Based on the results in reference [64], the same group of researchers also theoretically studied
the amplifier similariton [63]. They found that only the initial
ial pulse energy mattered
matter to determine
whether the similariton would form in the gain fiber. As shown in Figure 30,
30 the theoretical
50

predictions for the asymptotic parabolic pulse evolution (solid curve) were compared with the
results obtained for simulations with input pulses of different pulse durations yet identical pulse
energy. The pulse duration of the input pulses only determines how fast the input pulse is
transformed into a self-similar pulse. The input pulse energy giving the fastest convergence to
self-similar evolution is defined by [63]

2TP3 (0) g 2
U in =
,
27γβ 2

(41)

where Uin is the input pulse energy, TP(0) is the input pulse duration, g is the gain, γ is the Kerrcoefficient of the fiber, and β2 is the GVD of the fiber.
However, similariton generation in a fiber oscillator is not as simple as that in a fiber
amplifier. Self-similar pulse propagation in a passive fiber section of a dispersion-managed fiber
oscillator was experimentally demonstrated first [65]. The passive similariton pulses stretch in
time while their spectral bandwidth stays nearly constant. Recently, Oktem et al. [32], Renninger
et al. [61], and Aguergaray et al. [66] have reported similariton formation in the amplifier
sections of lasers. Amplifier similaritons undergo strong spectral and temporal breathing in the
cavity. In the report of amplifier similariton formation in an all-normal-dispersion cavity [61],
the authors focused on the new pulse evolution, not the performance limits. Amplifier similariton
pulses having 3 nJ per pulse and compressed down to 55 fs were generated from an Yb fiber
laser [61], but there was no attempt to maximize the pulse energy. The short pulses and smooth
spectra of amplifier similariton lasers will be attractive for applications, so it is desirable to see if
these solutions will be stable at higher energies.

51

2.3.2

Numerical Simulations
To verify the presence of amplifier similaritons in the cavity, numerical simulations based

on the modified Ginzburg-Landau equation [67-69], with a gain term added to the nonlinear
Schrödinger equation (8), are performed with the actual fiber parameters, using the split-step
Fourier method [70]. The modified Ginzburg-Landau equation is given by [18]

β2 ∂ 2 A
∂A
g
2
+i
− iγ A A − A = 0,
2
∂z
2 ∂t
2

(42)

2

-1

where group-velocity dispersion β2 = 23 fs /mm and nonlinear coefficient γ = 0.0016 (W m)
are used. The gain is defined by

g=

g0
1 + ω / ω0 + (ω − ω0 )

2

∆ω 2

,

(43)

where ω is the frequency, ω0 is the pulse carrier frequency, ∆ω is the gain bandwidth, and g0 is
called a small-signal gain, which means that the gain is small enough to avoid any gain
saturation. In a fiber laser, the small-signal gain is normally limited by the parasitic lasing. g0
-1

can be calculated by ( 30dB 10 ) × ln(10) 2 = 3.45 in unit of m . 30dB is the highest gain that
should be used, since higher gain will generate significant spontaneous emission. An
instantaneous saturable absorber is used for NPE. The saturable absorber function is given by
S (t ) = 1 −

m
,
1 + P (t ) P0

(44)

where m is the unsaturated loss, corresponding to the modulation depth, and P0 is the saturation
power.

52

This numerical simulation is based on a ring cavity design. The sequence of each
component is the same as the experimental setu
setup. The saturable absorber precedes the spectral
filter. Starting from white noise, puls
pulsing in the cavity is formed after a number of iterations.

Figure 31: Top: scheme of cavity used for simulation. Bottom: ppulse
ulse duration
(black) and spectral bandwidth (red) evolution through the laser cavity with a 12
nm bandwidth spectral filter
filter.
First, a laser cavity with a spectral filter of 12 nm bandwidth is simulated. The change of
pulse duration and spectral bandwidth through the cavity is plotted in Figure 31.
31 A parameter –
the breathing ratio – is used to characterize the change, which is defined as the change of the
pulse durations or spectral bandwidths. It can be seen that the breathing ratio of both pulse
53

duration and spectrum is about 22-3 through the entire cavity.. To better illustrate
illu
the pulse
evolution, a two-dimensional plot of spectral change is illustra
illustrated in Figure 32(a).
(a). The spectrum
at the end of SMF-II
II is shown in Figure 32(b). The ‘cat-ear’-like
like spectrum matches
match the
experimental results very well. The match between the numerical simulation and the
experimental results helps to validate our simulation model.

Figure 32: Simulation results of laser cavity using a 12 nm bandwidth spectral
filter. (a) 2D spectral evo
evolution through the cavity; (b) laser
aser spectrum at the end of
SMF-II

54

While keeping other fiber parameters the same, the bandwidth of the spectral filter is
changed to 3 nm and the corresponding simulation results are shown in Figure 33 and Figure 34.

Figure 33: Pulse duration and spectral bandwidth evolution through the laser
cavity with a 3 nm bandwidth spectral filter
filter.. Top: scheme of the cavity used for
simulation.

Figure 34: Simulation results of laser cavity using a 3 nm bandwidth
andwidth spectral
filter. (a) Two-dimensional
dimensional spectral evolution through the cavity; (b) Laser
spectrum at the end of SMF
SMF-II.
55

The pulses experience both large temporal and spectral breathing in the gain segment
(Figure 33).
). The spectral breathing ratio is up to 15 throughout the cavity. The saturable absorber
and spectral filter shape the pulse and make it self
self-consistent
consistent over the cavity round-trip.
round
Note that
the spectral filter does not only cuts the spectral bandwidth, but also reduces the
th pulse duration
significantly.. It shapes the pulse more than the saturable absorber and is the key component to
attract pulse evolution to this special regime. The spe
spectrum at the end of SMF-II
II (Figure 34(b)) is
also very different from the ‘cat
‘cat-ear’ shape and shows a parabolic profile, which is the
characteristic of similariton pulses. The temporal pulse shape of the simulated results is also
checked, as seen in Figure 35. Parabolic fit is applied to the pulse at the end of SMF-II
SMF and
shows very good match, which further verifies the formation of similaritons.

Figure 35: Simulated pulse shape of the pulse at the end of SMF-II
II plotted on a
logarithmic scale. Red dot
dots: parabolic fit; Insert: same plot on a linear scale.

56

2.3.3

Experimental setup of similariton fiber laser

Figure 36: Schematic of the double
double-clad Yb all-normal-dispersion
dispersion fiber laser
cavity and the setup for pulse characterization. SMF
SMF-I and SMF-II:
II: single mode
passive fiber section I and II; QWP and HWP: quarter
quarter- and half-wave
wave plates;
PBS: polarizing beam splitter; coll.: collimator; OSA: optical
ical spectrum analyzer;
L: lens; spec.: spectrometer
spectrometer.
An all-normal-dispersion
dispersion laser cavity is designed to support similariton formation in the
gain medium. The narrow intra--cavity
cavity spectral filter is formed by the combination of a grating
g
and a collimator [61],, as shown in Figure 36.. The collimator is set at a distance away from the
st

grating (300 groves per millimeter) and is aligned to couple the 1 order diffraction beam from
the grating back into the laser cavity. The small aperture of the collimator acts as a spatial and
spectral filter. Also due to the 10 µm diameter core size of the fiber mounted in the collimator,
st

only a very small amount of the 1 order beam couples into the rest of the cavity, as illustrated in
Figure 36.. Following the collimator is the si
single mode passive fiber (SMF--I) including the
extension fiber of the collimator and combiner. A short section of single mode passive fiber
(SMF-II)
II) follows the gain fiber. The 10 µm core diameter Yb doped double-clad
double
gain fiber
57

(CorActive DCF-YB-10/128) is spliced to SMF-I and SMF-II, respectively. The gain fiber is
pumped by a CW diode laser at 976 nm. A PBS, isolator, and several wave plates (HWP and
QWP on the left side, and QWP on the right side in Figure 36) act as an artificial saturable
absorber based on NPE [50]. By adjusting these wave plates, passive mode-locking can be
achieved. The HWP preceding the grating helps to maximize the efficiency of the 1
diffraction. The 0

th

st

order

order diffraction beam is directed onto a photodiode, connected to an

oscilloscope or a radio frequency (RF) spectrum analyzer.
The PBS acts as the output coupler. The output spectrum is measured by an Optical
Spectrum Analyzer (OSA, HP70451). A flip mirror near the output is used to direct the beam
into the MIIPS-enabled pulse shaper (MIIPS Box 640, Biophotonic Solutions Inc.). Before
entering the shaper, the beam is expanded by a 3x telescope. The output of the pulse shaper is
focused on a 10 µm BBO crystal (see Figure 36). The resulting SHG signal is detected by a
fiber-coupled spectrometer (Ocean Optics, USB4000). The MIIPS program measures the spectral
phase of the pulses at the nonlinear crystal and adaptively compensates high order dispersion to
obtain transform-limited pulses. A number of tests and shaper-assisted interferometric
autocorrelation (AC) are performed to ensure that the results are consistent with independent
theoretical calculations.

2.3.4

Experimental results
As learned from previous experimental tests, simulation results and other researchers’

reports [61], the length of each fiber segment affects the similariton laser similarly as in a
common all-normal dispersion fiber laser. Here, the fiber length of SMF-I and SMF-II is chosen
to be 1.7 m and 0.35 m, respectively. These parameters were found to be good in both previous

58

laser design and numerical simulations. The fiber collimator is placed about 13 cm away from
the grating and acts as a ~3 nm spectral filter.

Figure 37: Two output modes with the same pump power. (a) and (c) Output
spectrum; (b) and (d) Interferometric autocorrelation
autocorrelation. Note: the gray or dark color
in (b) and (d) has no meaning. It is caused by the varying density of lines.
Various mode-locked
locked states are possible depending on the diode laser pump power and the
orientation of the wave plates. With the pump power at 3.1 W, two different output
out
modes are
shown in Figure 37.. The fringes on the spectra are due to the interference in the multi-mode
multi
fiber
used for OSA measurement. The deviation of spectra from parabolic shape is caused by the NPE
induced frequency dependent transmission through PBS
PBS.. By inserting a beam sampler before the
PBS, a parabolic spectrum can be observed. The measured AC FWHM is ~80 fs and the
calculated deconvolution factor is 1.39, which gives the FWHM pulse duration as 57 fs (Figure

59

37(b) and (d)). By increasing the pump power, not only the output power but also the output
spectral bandwidth increases.

Figure 38: Output laser spectrum (black) and measured spectral phase of the
output pulses (red).
When being pumped at 4.1 W, a stable mode
mode-locked
locked state with an average output power of
930 mW is obtained (Figure 38)), corresponding to 21.9 nJ pulses emitted
itted at 42.5 MHz rep. rate
(Figure 39(a)).. The output pulse train is monitored by a fast photodiode on the oscilloscope.
There are power fluctuations observed from the pulse train, which are probably due to the
unfixed fibers in the cavity. To better check the stability of mode
mode-locking,
locking, a RF spectrum
analyzer is used to analyze the pulse train. With a 1 MHz frequency span, the RF spectrum
analyzer gives a single peak at 42.48 MHz with ~70 dB signal-to-background
background ratio (Figure
(
39(b)).. No sidebands are observed for the fundamental and higher harmonics over the 500 MHz
span [Figure 39(c)],
(c)], which confirms the stable mode-locking.

60

Figure 39: Laser performance
performance. (a) pulse train form oscilloscope. Repetition rate
42.5 MHz; (b) RF spectrum analyzer result, 1 MHz frequency span; (C) RF
spectrum analyzer result, 500 MHz span.
Output pulses are compressed and characterized using a MIIPS-enabled pulse shaper. The
MIIPS software scans a sinusoidal spectral phase function across the spectrum of the pulses,
pulse
collects the resulting SHG spectra and derives the corresponding spectral phase distortion [53, 54,
71].. Typically, seven iterations are run for the measure
measurements
ments presented here in order to obtain
compensation within 99.7% of the theoretical transform limit, defined by the input laser
spectrum. The phase function required to achieve transform limited pulses is the complementary
phase obtained after double integration
gration of the shaper
shaper-measured second-derivative.
derivative. To account for
phase distortions due to optics in the pulse shaper and thereby measure the pulse phase directly at
61

the laser output, we have independently measured the phase distortions due to the pulse shaper
itself by putting it in line with another pulse shaper. The measured phase at the laser output
2

pulses is shown in Figure 38. Polynomial fitting up to the third order gives ~35,000 fs of
3

second-order dispersion (SOD) and ~166,000 fs of third-order dispersion (TOD). Note that the
2

observed SOD is much less than the cavity dispersion of ~100,000 fs , calculated based on the
2

total fiber length and the fiber group-velocity dispersion β2 = 23 fs /mm. This is one of the
characteristic signatures of similariton formation in a gain medium [61].
After pulse compression, the pulse shaper has been used to create two pulse replica and
scan one of them in time to obtain interferometric autocorrelations [72], resulting in an AC trace
with full-width-half-maximum (FWHM) of 57 fs. Based on Fourier transformation of the
experimental laser spectrum and autocorrelation simulations, a deconvolution factor of 1.37 is
used to calculate the FWHM pulse duration, which is 41.6 fs for the compressed pulses. The
measurements show excellent agreement with calculations (Figure 40(c)). Similarly, we have
also compared the experimental SHG spectrum for compressed laser pulses with the calculated
SHG spectrum based on the measured fundamental spectrum of the laser and a flat spectral phase
(Figure 40(a)). Excellent agreement between theoretical and experimental results for both linear
and logarithmic scales gives us confidence in the measured parameters and that the laser pulses
at the BBO crystal are transform limited.

62

Figure 40: (a) Experimental and calculated SHG spectra shown in linear (solid
curve) and log-10
10 (dash
(dashed curve) scales. (b) Experimental THG spectrum
obtained by focusing TL pulses at the surface of a glass slide. (c) Experimental
and calculated interferometric autocorrelation traces for compressed laser pulses
in the range of -150
150 fs to 150 fs. Insert: Same data in the range of -500
500 fs to 500
fs.
Taking into account the throughput of our pulse shaper (~50% due to the reflection
efficiency of the grating and mirrors), we calculate the peak power for compressed pulses to be
about 250 kW. This peak power is sufficient to obtain THG at the interface of air and glass [73],
see Figure 40(b).
(b). For these measurements, the output from the pulse shaper is first focused via a
10x objective on a BBO crystal. Then
Then, the pulses are compressed at the objective focus. Once
pulse compression
ion is achieved, the BBO crystal is replaced by a 11-mm-thick
thick glass slide. The

63

broad THG spectrum indicates that the third order dispersion is fully corrected. Higher peak
power can be obtained by improving the throughput efficiency of the pulse shaper.
We have also observed that for a fixed filter bandwidth, the spectral breathing ratio through
the cavity is proportional to the pump power. However, when the pump power is increased over
4.1 W, the output laser spectrum continues to broaden but is no longer stable and fully coherent.
Only partial pulse compression has been achieved and the resulting SHG signal is observed to be
much weaker than when the output is fully coherent.
The filter bandwidth certainly affects the laser performance. When the collimator is moved
closer to the grating (~11 cm in between) and the spectral filter bandwidth is increased to ~4 nm,
compressed pulses as short as 52 fs are obtained. Further reducing the filter bandwidth is also
tested and no obvious improvement has been observed. The numerical simulations also predict
that, it is difficult to achieve stable mode-locking when the filter bandwidth is smaller than 3 nm.
According to numerical simulations, the transition from dissipative soliton to amplifiersimilariton happens when the filter bandwidth is reduced below ~6 nm. The simulation results
are in agreement with experimental results for several filter bandwidth conditions.
Energy loss material is also inserted into the cavity on purpose to increase the coupling loss
in between two collimators; losses increase the threshold pump power but do not improve the
breathing ratio.

2.3.5

Discussion
The significant change of pulse evolution due to the spectral bandwidth can be understood

by the theoretical study of similaritons in fiber amplifiers. It was learned that only the pulse
energy of input pulses determines whether a similariton forms in a fiber amplifier. The input
pulse energy Uin giving the fastest convergence to similariton is defined by Equation (41). Here,
64

−1

γ = 0.0016 ( mW ) , β 2 = 23 × 103 fs 2 m and g = 2m −1 are used for calculation. According to
the simulation results in Figure 31 and Figure 33, the FWHM pulse duration of the pulses
reaching the gain fiber input is about 2.8 ps for the laser using 12nm bandwidth spectral filer;
and 0.8 ps for the one using 3 nm spectral filter. According to Equation (41), the calculated
critical input pulse energy Uin is about 177 nJ and 4 nJ for lasers with 12 nm and 3 nm spectral
filters, respectively. Even considering the loss caused by filters, the 12-nm-filter laser still
requires 10 times higher intra-cavity pulse energy to form similaritons in the same pace as the
3-nm-filter laser. In the case that the output pulse energy of the 12-nm-filter laser is 35 nJ, the
non-ejected intra-cavity pulse energy can be estimated to be about 70 nJ. Considering the ratio
between the spectral filter bandwidth and output spectral bandwidth of 30 nm, the input energy
for the gain fiber is about 28 nJ, which is too small compared to the critical value of 177 nJ. This
is not considering the ‘cat-ear’ like spectra profile, which should experience even higher loss
caused by the spectral filter. Hence, it will be impossible to generate similaritons in the laser
cavity with 12 nm or larger bandwidth spectral filter. For the 3-nm-filter laser, in the case of an
output pulse energy of about 20 nJ, the residual intra-cavity pulse energy is estimated to be 40 nJ
and the output spectral bandwidth 45 nm, considering a linear loss due to the spectral filter. Then
the input pulse energy to the gain fiber is about 2.7 nJ, which is close to the expected value.
Since the similariton pulse has a parabolic spectrum and the 3 nm spectral filter is applied around
the peak intensity, it should cause a less than 1/15 loss and result in better transmission.
Considering the error in the estimation, this gives us a basic idea about how the pulse evolution
is affected by the change of intra-cavity spectral bandwidth. Therefore, the narrow intra-cavity
spectral filter provides a good combination of pulse energy and pulse duration for fast
convergence to similariton in gain fiber.
65

The other reason that all the efforts have failed to increase the breathing ratio is due to the
gain bandwidth limit, as shown in Figure 27. When the laser spectrum reaches the gain
bandwidth limit, the gain fiber itself acts as a filter to stop the spectral broadening.
The only way of increasing the output spectral bandwidth beyond the gain limit is to
continue the self-similar evolution in a long SMF-II. It seems very practical since a similariton
can avoid wave-breaking while propagating in normal dispersion fiber. However, this idea does
not work for standard fibers, due to the high pulse intensity and strong nonlinearity requirements
of the similariton solution. A standard normal dispersion fiber does not have a very large
nonlinear coefficient. Without high pulse peak power, the corresponding nonlinearity will be
fairly weak. Meanwhile, the pulse intensity gets lower as it propagates in this fiber, which further
weakens the nonlinearity. In this case, the similariton cannot be sustained and wave-breaking
will happen again. This is verified by our experiments.
In one of our similariton fiber lasers, which uses single-clad 6 µm core diameter fiber,
about 2 m long SMF-II is used. One of the output spectra is shown in Figure 41(a), which has
typical structures of wave-breaking pulses as shown in Chapter 1 Figure 7. Pulse characterization
using a pulse shaper shows the existence of wave-breaking. Output pulses are compressed with a
MIIPS-enabled pulse shaper and the SHG spectra of compressed pulses match very well with the
calculation based on the fundamental spectrum; see Figure 41 (b). In Figure 42, both
interferometric AC and background-free intensity AC are measured and compared to the
calculations. They also show good match with small deviation on the side-lobes of the trace.
Based only on these measurements, it is hard to tell whether this pulse is indeed wave-breaking
or not. For further verification, MIIPS traces with sinusoidal phase scan and second order
dispersion scan are investigated.

66

Figure 41: (a) Output
utput spectrum of a similariton fiber laser using more than 1 m
long SMF-II; (b) Comparison of experime
experimental (solid line) and calculated (dash
line) SHG spectra.

Figure 42: Calculated (red) and experimental (black) (a) interferometric
nterferometric and
(b) background-free
free intensity au
autocorrelation traces.

67

Figure 43: Calculated (left) and experimental (right) sinusoidal phase scan traces.
traces
δ is the scan parameter.
The experimental and calculated sinusoidal scan tracess of compressed pulses are shown in
Figure 43. Some bi-fork
fork structure
structures are observed on the experimental data,, which are missing in
the calculated result. This indicates the exist
existence of multiple pulses that have different phase
responses and generate local maxim
maxima in the SHG signal with different reference phase.
phase Since
MIIPS traces the maxima of the SHG signal and the main pulse dominates the generation of
SHG,, the phase distortion of the main pulse is fully corrected and the sinusoidal scan
sc gives a
trace of straight lines. Meanw
Meanwhile phase distortion of minor breaking pulse is still left
uncorrected and causes the bi-fork
fork structure
structures. Based on the shape of the trace, it is estimated that
there is fourth order dispersion left in the minor breaking pulses, which is further proved with the
second order dispersion scan.

68

Figure 44: Left: calculated and experimentally me
measured two-dimensional
dimensional SOD
scan; Right: experimental (black) and calculated (red) SHG-integrated SOD scan.
Both the two-dimensional
dimensional and SHG
SHG-integrated SOD scans (also referred to as chirp-MIIPS
chirp
[74]) of compressed pulses are shown in Figure 44. On the simulated 2D trace
race, the SHG signal
quickly dissipates after the appearance of the maxima and the trace is symmetric with respective
to the scanned reference SOD. The experimentally me
measured 2D trace is very asymmetric, with
the left half matching the simulation very well. On the right half, there is still a significant SHG
2

signal observed when
en the reference SOD is about 55,000 fs , which is very different from the
simulated trace. The deviation
eviation ffrom the simulation results shows a parabolic-like
parabolic
profile that
corresponds to fourth-order
order dispersion, as shown in Chapter 1 Figure 16. Meanwhile, the
integrated SHG signal obtained by scanning of the second-order dispersion is also shown in
2

Figure 44. An obvious deviation after ~2,500 fs is observed.. These observed deviations are due
to the uncompressed phase distortion in the breaking pulses.. These extra scan results provide full
information of the
he pulses, not only the existence of wave-breaking
breaking pulses but also the different
phase distortions for each
ach part of the pulses.

69

Figure 45: Output
utput spectrum of a similariton fiber laser using more than 1 m long
SMF-II
II with lower pump power
power.

Figure 46: Left: calculated and experimentally measured two
two-dimensional
dimensional SOD
scan;; Right: experimental (solid line) and calculated (dash line) integrated SOD
scan.
These pulse characterization methods are very important.. This is because normal pulse
characterization approaches, such as autocorrelations, do not provide such detailed information
which may mislead researchers, especially for the spectra that do not show typical signatures of
70

wave-breaking. As seen in Figure 45, the side-lobes
lobes on the spectrum disappear by lowering the
pump power. However, wave-breaking
breaking still exists, as proved by tthe SOD scanss (see Figure 46).
Since
ince there is quite a lot of energy wasted and phase distortion in the breaking pulses, it is very
important to learn about and avoid wave
wave-breaking.

Figure 47: Experimental
xperimental se
setup of the similariton fiber laser using the UHNA fiber.
UHNA: ultra-high
high numerical aperture fiber; SMF: single mode fiber; HWP and
QWP: half- and quarter
quarter-wave
wave plate; coll.: collimator; PBS: polarizing beam
splitter; WDM: wavelength division multiplexer.
As mentioned previously, strong nonlinearity is one of the requirements for the validation
of the similariton solution. It is possible to use a passive highly nonlinear fiber to extend the selfsimilar evolution [75]. While kee
keeping
ping other cavity parameters the same as the wave-breaking
wave
fiber laser, part of the SMF-II
II is replaced with aan ultra-high
high numerical aperture (UHNA) fiber
(see Figure 47). UHNA fiber’s core has a higher GeO2 dopant than that of normal fiber, which
results in a high NA and reduces the effective core diameter to only about 2.5 µm. So the
nonlinear coefficient is also about 6 times higher than normal fibers. It also has larger dispersion
2

2

(~50fs /mm) than normal fiber (~23fs /mm) due to the high concentration of GeO2. However,
the high nonlinearity still makes the self
self-similar evolution available. The experimental spectra
71

are shown in Figure 48.. Spectra form port
ports 1, 2 and 3 are all measured. The output
o
spectrum
from port 2, before PBS, clearly sshows parabolic profile. Also compared to Figure 41(a), the
output spectrum is much broader. Further systematic study of this laser system and pulse
characterization is still under investigation.

Figure 48: Experime
Experimental
ntal spectra from (a) port 1; (b) port 2; (c) port 3.
Besides UHNA fiber, photonic crystal fiber can also have a very small effective core
diameter due to its microstructure
microstructure. The experimental work done by Chong et al. has
demonstrated that, FHWM 21 fs pulses with a pulse energy of ~ 1 nJ can be generated from a
similariton
ton laser using a long photonic crystal fiber (PCF) (see Figure 49 and Figure 50) [75].
The PCF used has an effective core diameter of 2 µm, resulting in about ten times
time higher
nonlinearity than standard fiber. Though the similariton evolution greatly extended after the gain
fiber, signs of wave-breaking
breaking pulses – side-lobes in spectrum – are observed in Figure 50 (a). So
the passive highly nonlinear fiber is not an ultimate solution to sustain similariton evolution in a
fiber laser. Hirooka et al. demonstrated that a passive dispersion
dispersion-decreasing
decreasing normal dispersion
fiber can be used to generate parabolic pulses with 1.5 µm wavelength [76].. This dispersiondispersion
decreasing fiber can effectively
ffectively act as a gain fiber, which supports the similariton evolution. [76]

72

Figure 49: Experimental setup of PCF similariton fiber laser. PCF: photonic
crystal fiber; SMF: single mode fiber; HWP and QWP: half
half- and quarter-wave
quarter
plate; PBS: polarizing beam splitter.

Figure 50: Experimental
xperimental results. (a) spectrum before PBS; (b) output spectrum;
(c) autocorrelation results

2.4

Conclusion
Systematic studies of all-normal
normal ddispersion fiber laser system were conducted. A few

cavity parameters such as fiber length, spectral filter bandwidth and pump power were tested to
see how they affect laser performance. It was found that a narrow spectral filter greatly improve
the output spectral bandwidth that resul
resulted in a 41 fs pulse duration. Meanwhile, more than 20 nJ
pulse energy was still delivered. The compressed pulses had a peak power of about 250 kW that
was the highest value achieved from a single-mode fiber laser. It will be important to test this
laser for applications
pplications such as multi
multi-photon microscopy.

73

Chapter 3 Application of Ultrafast Fiber Laser – Multiphoton Microscopy
This chapter discusses the application of an ultrafast fiber laser to multiphoton microscopy.
Different multiphoton imaging methods such as two-photon excitation microscopy (TPEF),
second harmonic generation (SHG) and third harmonic generation (THG) microscopy are
demonstrated. Several biological samples are imaged. Both single layer and depth-resolved
images are shown.

3.1

Introduction
Due

to

the

benefits

of

high

contrast

ratio,

sub-micrometer

resolution

and

depth-resolved imaging, multiphoton microscopy has proven to be a powerful tool for studying
living tissues [6, 56]. Especially for SHG or THG microscopy, no sample labeling is needed and
no limits are imposed by the two-photon absorption spectrum either, which makes those methods
preferable for non-invasive in vivo tissue imaging. In addition, SHG and THG provide
complementary information due to their different optical-response mechanisms. One property of
THG microscopy is that no signal is generated by a beam focused inside a homogeneous medium.
This is caused by the Gouy phase-shift across the focus of the excitation beam (normally
Gaussian profile) [19]. Gouy first observed that a spherical converging light wave experienced a
π phase change in passing through its focus. Different from an infinite plane wave, a Gaussian
beam contains a collection of wave vectors in many directions. The phase difference between a
Gaussian beam and an infinite plane wave is defined by [77]

(

φ ( z ) = arctan λ z πω02

)

(45)

where λ is the wavelength, z is the beam position, the beam is traveling in the +z direction, and

ω0 is the beam waist. When the Gaussian beam goes through its focus, z effectively changes
74

from -∞ to +∞ and the corresponding phase shift φ(z) is π. Therefore, THG from a homogenous
medium is canceled for the case of perfect phase matching (k3 - 3k1 = 0), where k3 is the wave
vector of the third-harmonic field and k1 is the wave vector of the fundamental field. [19]
In contrast, THG is sensitive to inhomogeneity, where the refractive index or third-order
susceptibility χ

(3)

changes. It makes THG microscopy ideal for revealing the fine structure of

biological samples [78, 79]. SHG is sensitive only to media without a center of symmetry; for
example structural proteins such as collagen and tubulin. For both SHG and THG imaging,
ultrashort laser pulses are preferred to achieve good multi-photon efficiency. It is found that
SHG or THG efficiency is inversely proportional to the pulse duration or pulse duration squared,
respectively [57,

80,

81],

making

them

amenable

to

ultrashort

pulse

excitation.

Laser-pulse-duration dependence has been confirmed for two-photon excitation microscopy
down to 10 fs pulses [80].
Different ultrafast solid state laser sources, such as Ti:sapphire at 800 nm [82], Cr:forsterite
at 1230 nm [83] and optical parametric oscillator (OPO) at 1500 nm [78], have been used for
third harmonic generation microscopy. For clinical use, a compact and environmentally stable
laser is preferred to a complicated solid-state laser. In the past decade, compact fiber lasers have
drawn increasing attention due to their compact size and greater stability [31, 61, 84]. Typical
fiber lasers are operated around 1,040 nm (Yb), 1,550 nm (Er) or 2,000 nm (Tm). Although
longer wavelengths increase the scattering length and allow deeper imaging, water absorption
beyond 1,200 nm increases rapidly. This makes Yb fiber lasers operating at 1,040 nm a good
option for multiphoton microscopy, especially because regular objectives have good
transmission in the 400 – 1,100 nm wavelength range. Furthermore, the corresponding THG, at

75

350 nm, can transmit through BK7 glass and does not cause as much photo-damage as the THG
from 800nm light, which occurs at 266nm and coincides with the absorption maximum of DNA.
In order to avoid laser induced damage to living tissue and enable microscopic imaging deeper
into living tissue, interest has shifted towards imaging using longer wavelength sources [85].
Here two fiber lasers delivering sub-50 fs pulses centered at 1030 nm are evaluated for
multi-modal microscopy using fluorescent polystyrene microspheres and a few biological
samples including guppy fish (Poecilia reticulata) tails, fruit fly (Drosophila melanogaster) wings,
mouse kidneys, mouse intestines and Drosophila larvae. Images generated by TPEF, SHG and
THG are compared.

3.2

Multiphoton microscopy using low power sub-30 fs fiber laser

3.2.1

Experimental setup
The experimental setup shown in Figure 51 consists of an Yb fiber laser oscillator (Figure

51(a)) that generates a broadband spectrum centered at 1030 nm with ~50 mW average output
power at a repetition rate of 62 MHz. It is based on an all-normal dispersion cavity scheme [61]
where self-similar amplification takes place in the gain medium. The pulses gain energy and
bandwidth while evolving into a parabolic temporal profile in the gain segment [61] and
maintain the parabolic profile in the PCF segment with the temporal and spectrum bandwidth
increasing. The condition for self-similar amplification is facilitated by introducing a narrow
spectral filter consisting of a grating and a collimator [61]. The self-similar pulses are further
extended in both temporal and spectral domains by an intra-cavity segment of normal dispersion
photonic crystal fiber (PCF). This novel scheme enables the laser spectral bandwidth to exceed
the gain bandwidth and leads to pulse durations as short as 20 fs. The detailed design and
principle of the fiber laser is discussed in Ref. [86].

76

Figure 51: Schematic of imaging setup. (a) Fiber laser cavity layout. PCF:
photonic crystal fiber; SMF: single mode fiber; WDM: wavelength-division
wavelength
multiplexer; HWP and QWP: half
half- and quarter-wave plate; PBS: polarizing beam
splitter; coll.:: fiber collimator
collimator. (b) 4f-folded
folded pulse shaper. SLM: spatial light
modulator; M: mirror. (c) Microscopy setup. DM: dichroic mirror; GM: galvanic
mirror; AMP: amplifier; PMT: photomultiplier tube.
A folded 4f pulse shaper (MIIPS Box 640, Biophotonic Soluti
Solutions) [Figure
Figure 51(b)], with a
dual mask 640-pixel
pixel spatial light modulator, is used to measure and compensate the dispersion of
the output pulses at the focal plane of the microscope [[Figure 51(c)] [53,, 54]. The results
obtained using automated pulse compression (MIIPS) are confirmed by interferometric AC and
by theoretical calculation. Due to the reflection efficiency of the grating and mirrors inside the
shaper, the average power out of the shaper is ~25 mW.
The laser beam is raster scanned by a pair of mirrors mounted on galvanometers
(QuantumDrive-1500, Nutfieldd Technology, Inc.) and coupled into a water-immersion
immersion objective
(Zeiss LD C-APOCHROMAT
APOCHROMAT 40x/1.1) mounted on an adapted Nikon TE-200
TE
inverted

77

microscope. Laser pulses are compressed to their transform-limit at the focus of the objective.
With the sample placed at the focus of the objective, the SHG or TPEF is collected in the epi
direction. The SHG/TPEF is separated from the fundamental light using a dichroic mirror
(700DCSPXR, Chroma Technology Corp.) and is further filtered by a short-pass emission filter
(ET680-SP-2P8, Chroma Technology Corp.). A photomultiplier tube (PMT, HC20-05MOD,
Hamamatsu) is used to collect the SHG/TPEF. THG, which is primarily generated in the forward
direction, is collected by a UV compatible objective (HP ReflX, NT59-886, NA 0.28, focal
length 13.3 mm, transmission more than 85% from 200 nm to 700 nm, Edmund Optics). The
THG is also separated from the excitation light by a UV-pass filter (UG11, transmission from
250 nm to 400 nm) and detected by a PMT (H10720-210, Hamamatsu) whose signal is amplified
(SRS445, Stanford Research Systems). Tens of frames are taken to generate one image and each
frame takes 1s to acquire.
The spectrum of the laser pulses, after the microscope objective, is shown in Figure 52(a).
Dispersion compensation for the laser as well as the microscope objective is achieved using
MIIPS program [53, 54]. Briefly, the pulse shaper scans reference phase functions across the
spectrum of the pulses and uses the SHG spectral information (generated by a KDP crystal
mounted at the focal plane of the objective) to measure the second derivative of the spectral
phase. Through double integration of the measurement the system determines the dispersion that
needs to be corrected and the pulse shaper implements the correction. In order to confirm that the
compression is complete, the measured SHG spectrum is compared with calculated results based
on the fundamental laser spectrum and assuming no phase distortions. The excellent agreement
between the calculated and experimentally measured SHG spectra in both linear and log-10
scales is shown in Figure 52(b) and (c).

78

Figure 52: (a) Laser spectrum after the microscope objective. (b) Comparison of
experimental (black) and calculated (red) SHG spectrum in linear scale. (c)
Comparison of SHG spectrum in log-10
10 scale. (d) Comparison of experimental
(black) and calculated (red) interferometric autocorrelation trace. Insert:
calculated temporal profile based on the measured laser spectrum
After pulse compression,
on, the pulse shaper is used to create two pulse replicas and scan one
of them in time to obtain an in--situ interferometric AC at the focal plane of the objective [72].
The full-width at half-maximum
maximum (FWHM) duration of the experimental interferometric AC,
shown in Figure 52(d),
(d), is 38 fs corresponding to FWHM pulse duration of 27 fs. This pulse
duration is confirmed by comparing experimental and calculated interferometric AC traces, as
shown in Figure 52(d).
(d). The small wings on the transform limited pulse are caused by the sharp
features of the laser spectrum (Figure
Figure 52(a)).
(a)). According to the calculated temporal profile based
on the measured laser spectrum, there is around 95% pulse energy within the main pulse. The
measured pulse duration after the microscope objective is longer than the 21 fs measured for the
compressed pulse duration measured before the objective. The additional pulse broadening is
caused by the reduced transmittance of the objective (70% to 50% in the 950 nm to 1150 nm

79

spectral range). After compression and characterization, the KDP crystal is replaced with the
microscopy samples.

3.2.2

Space time coupling
Given that a good spatial mode is required for microscopy, there has been some concern

whether 4f pulse shapers introduce spatial distortion
distortions due to space-time
time coupling (STC). It is an
important issue and needs to be taken care of when using a 4f pulse shaper. There have been a
number of studies about STC caused by 44f pulse shapers and by acousto-optic
optic programmable
dispersive filters (AOPDF) in the past two decades [87-90]. According to Ref.
ef. [88], under pure
phase modulation introduced by a 44f pulse shaper, the beam profile at the focal plane of the
objective is only determined by the incident beam profile. Basically, in our experiment setup, we
focus the laser beam using an objective after the pulse shaper. The spatial distribution of the
beam on the focal plane of the objective is only determined by the input beam profile and does
not depend on space-time
time coupling. Space-time coupling only contributes some temporal
distortion to the beam at the focal plane of the objective. The effect is very small and can be
ignored. Detailed discussion is shown below.

Figure 53: Sketch of 4-ff shaper with output beam focused using a lens. [91
91]

80

Figure 53 shows the scheme for a laser beam passing through a 4-f shaper and being
focused by an extra lens outside the shaper. As discussed in Ref. [91], the electric field of the
laser beam at the focal plane (Σ) of the focusing lens after the pulse shaper can be described as

 kc
  fγ
 κ − 1 kc 2 
fb 
Ω+
x, Ω  M 
x  exp  i
x ,
f2 
 f2
  kc
 2 f2 

ε% f ( x, Ω ) ∝ ε%i  −

(46)

where w0 is the beam waist, ε% f is the electric field at the focal plane of the lens after the shaper,

ε%i is the electric field of the input laser pulses, kc is the wave vector of the center wavelength of
the input pulses, f 2 is the focal length of the lens after the shaper, κf2 is the distance between
the shaper output and the lens after the shaper, Ω = ω − ωc is the relative frequency and ωc is
the center frequency, and grating parameters γ = 2π / (ωc d cos βc ) and b = cos θ / cos βc (d is the
groove spacing of the grating, θ is the incident angle, and βc is the diffraction angle at center
frequency ωc ).
Based on Equation (46), the spatial distribution of the beam at the focal plane of the lens
after shaper is determined by the incident pulse profile ε%i ( k x , Ω ) and the transfer function
M(

fγ
fb
Ω+
x ) . Since we only do pure phase modulation here, the transfer function
kc
f2

M(

fγ
fb
Ω+
x ) is supposed to be only a phase term and will not introduce amplitude
kc
f2

modulation to change the beam spatial distribution at the focal plane. Therefore the beam shape
at the focal plane is only determined by the incident pulse profile ε%i ( k x , Ω ) , which means the
input Gaussian beam will end up as a Gaussian beam at the focal plane of the objective in our
experiment. Space-time coupling does not affect the beam shape at the focal plane.
81

The dependence on the x coordinate will introduce some frequency shift to distort the
pulses in the temporal domain. This frequency shift can be described as

δΩ( x) = −

bkc
x.
γ f2

The relative frequency shift can be described as

(47)

δΩ
, where σ ω is the spectral bandwidth of the
σω

incident beam.

σw =
α=

N ∆x p

α

,

λc2 f
2π cd cos( β c )

(48)

,

where α is the spatial dispersion on the SLM, N is the number of pixels covered by input laser
spectrum, and ∆x p is the SLM pixel size.

δΩ bkc
α
x
=
=
σω γ f 2 N ∆x p

λc2 f

bkc
2π cd cos( βc )
b
f
x=
x,
2π
N ∆x p
N ∆x p f 2
f2
ωc d cos( βc )
f λ
x=2 2 c,
π win
fλ
w0SLM =
,
π win

(49)

(50)

where x is determined by the beam size at the focal plane of the focusing lens after the pulse
shaper, and w0SLM is the beam radius of monochromatic light on the SLM. Hence,

δΩ 2bw0SLM
=
,
σω
N ∆x p

82

(51)

where N is the effective pixel numbers. Here we also assume that 2 w0SLM is equal to ∆x p and
the grating is in Littrow configuration (b=1). In our experiment setup, 2 w0SLM is even smaller
than ∆x p . We have about 600 pixels of SLM covered by the input laser spectrum. By calculation,
the ratio of the shift in our experiment is about 0.17%. This small amount of distortion can be
neglected. If we re-organize the formula above,

σ 2wSLM
δΩ = b ω 0
.
N

In the Littrow configuration, b=1, and

σw
N

∆x p

(52)

is the spectral resolution per pixel, which is also the

2 w0SLM
spectral resolution of the shaper. Basically, the smaller
is, the less the space-time
∆x p

coupling. When

2w0SLM
= 1 , the frequency shift is equal to the spectral resolution of shaper.
∆x p

Further reducing the spot size of a single color on the SLM will not help to reduce the frequency
shift, which is limited by the spectral resolution of the shaper. So using a spot size on the SLM
equal to or smaller than the SLM pixel size is the way to minimize the space-time coupling.

3.2.3

Experimental results
Fluorescein (emission from 470 nm to 650 nm) stained polystyrene microspheres

(Fluoresbrite® YG Carboxylate Microspheres 6.00µm, Polysciences Inc.) were used to test the
system before imaging live tissues.

83

Figure 54: Multiphoton m
microscopy
icroscopy images of polystyrene microspheres. (a)
TPEF image, (b) THG image and (c) THG image of single bead. Scale bar: 10
µm.
The signal in the epi
pi detection corresponds to TPEF, and the signal in the forward direction
corresponds to THG. The galvanic mirrors control the area of the sample imaged, as shown in
Figure 54.. Comparing the images generated by TPEF and THG in Figure 54(a)
(a) and (b), THG
images have much better contrast. By limiting the scan range (Figure 54(c)),, a ~1 µm feature that
arises from the fabrication of the microspheres can be seen on the 6 µm microspheres. The
conditions for THG in microscopy have been discussed by Silberberg [78]; essentially,
essentially a change
in index of refraction is required to break the backward
backward-forward
forward symmetry near the focal plane.
The index of refraction of polystyrene is ~1.57 for 1 µm wavelength light, a large change
compared to the index of refraction of air ~1. Therefore THG is expected and observed from the
surface of polystyrene microspheres. Unlike THG, the TPEF is due to the emission from
fluorescein that coats all over the mi
microspheres.

84

Figure 55: Multiphoton microscopy images of live tissues. (False color) Top line:
images of a guppy fish (Poecilia reticulata) tail. (a) SHG image ((false
false color, red),
red
(b) THG image (false
false color, cyan
cyan), and (c) Composition of SHG and THG
images. (d) Bright-field
field microscope image. Bottom line: images of fruit fly
(Drosophila
Drosophila melanogaster) wings. (e) SHG image (false color, red) (f) THG
image (false color, cyan)
yan) (g) Composition of SHG and THG images. (h) BrightBrigh
field microscope image. Scale bar: 10 µm.
Imaging of biological tissues, unstained samples of fly wings and fish tails, was used to
demonstrate the practical relevance of the laser. The samples were mounted on glass slides with
Tissue-Tek O.C.T. compound (Sakura, CA) and allowed to immobilize for 30min before
imaging. The laser intensity used for imaging the fish tail was 17 mW. The laser power for
imaging fly wings was reduced to 7 mW, because higher power was found to damage the sample.
Bright-field images
ges were checked before and after imaging to make sure there is no damage to
the sample after excitation (Figure
Figure 55(d) and (h)]. The SHG (Figure 55(a) and (e)) and THG
(Figure 55(b) and (f)) images are shown in false color.
SHG and THG results are complementary because they arise from different phase
conditions. SHG requires non-centrosymmetric
centrosymmetric structures while THG requires a change in the
85

index of refraction. By merging the SHG and THG images, we can clearly see the
complementary results in Figure 55(c) and (g). The THG from fish tail is not as intense as the
SHG because of sample thickness. However, there is some complementary information at the
edge of the cells provided in the THG images, which is due to the enhanced THG at the interface.
On fly wing, the strongest THG is from the fine hairs. Note that the use of sub-30 fs pulses
resulted in comparable SHG and THG signal levels from fruit fly wings even when using only
~0.1 nJ pulse energy from a fiber laser.
As shown above, this sub-30 fs fiber laser is successfully demonstrated for multi-modal
biomedical imaging. The shorter pulse durations achieved by the laser greatly enhance two- and
three-photon induced modalities in both stained and unstained living tissues. Complementary
results of SHG and THG from living tissue are shown under similar laser conditions. However,
due to the low pulse energy of this laser, it cannot deliver enough photons to deep tissue to
enable depth scan imaging. A high-power fiber laser while still providing ultrashort pulses is
needed. This led to the testing of a 40 fs high-energy similariton fiber laser for multi-photon
microscopy.

86

3.2

Multi-photon
photon microscopy using high pulse energy sub
sub-50
0 fs fiber laser

3.2.1

Experimental setup

Figure 56: Experimental setup. (a) Fiber laser. HWP and QWP: half- and quarterquar
wave plate; PBS: polarizing beam splitter; SMF: single mode fiber;; UHNAF:
ultra-high
high numerical aperture fiber; coll.: fiber collimator. (b) 4-ff folded pulse
shaper. M: mirror; SLM: spatial light modulator. (c) Laser
Laser-scanning
scanning microscope.
DM: dichroic mirror; GM: galvanic mi
mirror; obj.: objective; PMT: photon
multiplier tube; AMP: amplifier.
The experimental setup, shown in Figure 56, is similar to the previous setup but with the
laser source replaced with the similar
similariton
on fiber laser described in Chapter 2. Since these two laser
sources have similar spectral range, all th
thee optics and acquisition devices remain the same.

3.2.2

Experimental results
The pulse compression routine is the same as described previously. No loss of spectral

bandwidth is experience
ence for this laser due to its slightly narrower spectrum. After pulse
compression,
sion, samples are loaded at the focal plane of the objective. To calibrate the microscope,
two stained commercial samples (mouse kidney and mouse intestine, Molecular Probes) that

87

have uniform thickness were imaged. For these two ssamples, the signal detected in epi
e direction
is mainly from two- or three-photon
photon excited fluorescence, since these samples are stained
(Mouse intestine with Alexa Fluor® 350 WGA, Alex Fluor® 568 phalloidin and SYTOX®
Green; Mouse kidney with Alexa Fluor® 488 WGA, Alex Fl
Fluor® 568 phalloidin and DAPI). In
I
the forward direction,
ection, mainly THG/three
THG/three-photon-excited
excited fluorescence is detected.
detected By combining
the signal from epi
pi and forward directions, it is clearly seen that they provide complementary
information for each other (see Figure 57).

Figure 57: Composition of TPEF (green, false color) and THG (blue, false color)
imaging of mouse intestine (left) and mouse kidney (right), 150 µm x150 µm area
represented.
Beyond imaging processed and pre
pre-labeled
labeled samples, we are more interested in imaging
living tissues,, especially to elucidate their three-dimensional structures. Compared to the fiber
laser delivering 30 fs pulses used for multi
multi-photon
photon imaging of living tissues, this laser can
provides 10 times more pulse energy with only slightly longer pulse durat
duration,
ion, which enables
depth resolved imaging in thick biological samples, such as Drosophila larva
larvae.

88

Third instar (a stage in the life of an arthropod between two successive molts) Drosophila
larvae were mounted onto the sample platform. The trachea of a larva was centered within the
image. Here, depth-resolved imaging is achieved by moving the focal plane of the objective
across the sample in 2 µm steps. The total scanned depth is about 90 um. SHG and THG signals
are collected from epi and forward directions, respectively. Three-dimensional images are
constructed by stacking all the frames from each step in order. The projections of the constructed
SHG and THG three-dimensional images at different angles are shown in Figure 58. It can be
seen that the THG three-dimensional image shows a lot more fine structure and provides more
detailed information and less scattering than the SHG image.

89

Figure 58: Projection of three-dimensional images at different angles of SHG
(left) and THG (right)) microscopy of Drosophila Larva. 150 µm x150 µm area
represented.

90

Figure 59: Projection of three-dimensional images at different angles of SHG
(left) and THG (right)) microscopy of fruit fly eyes. 150 µm x150 µm area
represented.
The same SHG and THG three
three-dimensional reconstructed imaging were also demonstrated
using fruit fly eyes. In Figure 59
59,, a few projections are shown and compared. It is found that
THG three-dimensional imaging shows much better contrast ratio and is a better solution
so
for
depth scanning of biological tissues.

91

3.3

Conclusion
We have demonstrated the use of two ultrafast fiber lasers for multi-modal biomedical

imaging. The ultrashort pulse durations achieved by both lasers greatly enhance two- and threephoton induced modalities in both stained and unstained living tissues. Complementary results of
SHG and THG from living tissue are shown under similar laser conditions. Depth-resolved
imaging of Drosophila larva and fruit fly eyes using a high energy, sub-50 fs Yb fiber laser is
achieved. Three-dimensional reconstructed imaging based on THG shows much better contrast
in resolving the tissue structures. It shows that this high-power similariton fiber laser is a suitable
source for deep tissue imaging.

92

Chapter 4 Development of Noise-like Fiber Laser and Their Applications in Laser-Induced
Breakdown Spectroscopy
In this chapter, fiber oscillators that can deliver pulses with pulse energy up to 450 nJ is
demonstrated. These fiber lasers are operated in a very different mode-locking regime – noiselike – compared to all the lasers discussed in previous chapters. It is found that these lasers are
ideal light sources for laser-induced breakdown spectroscopy.

4.1

Introduction
One of the major laser applications is laser ablation [7]. When a laser pulse of sufficient

energy and intensity is focused onto a material, a small amount of the material is ablated,
forming a plasma spark that radiates on atomic emission lines. By detecting the atomic emission
spectra and comparing it to a standard database, elements present in the material can be analyzed.
This technique is known as Laser Induced Breakdown Spectroscopy (LIBS) and has become a
common analytical method because it is virtually instantaneous, highly sensitive, and suitable for
samples in any kind of physical states [92, 93]. Since its discovery, LIBS has been demonstrated
for a wide variety of applications including the analysis of products in the steel industry [94, 95],
works of art and archaeological artifacts [96], terrestrial and Martian geological samples [97, 98],
and the detection of toxic [99] or explosive materials [100]. It is even used for space exploration
and there is a LIBS system installed on the famous Mars Rover.
Since most of LIBS measurements are carried out outside the laboratory, portable LIBS
instruments are in high demand. As a key part of the system, a portable and powerful laser
source is needed. Recent developments in fiber laser technology have provided more robust laser
sources. Fber-laser-based LIBS systems in both the nanosecond [101] and femtosecond regimes
[102] have been demonstrated. For LIBS systems employing nanosecond laser pulses [103-106],
93

plasma ablation is a thermal effect with a timescale comparable to that of the laser pulse. The use
of nanosecond pulses results in a high ablation threshold due to heat diffusion during the pulse
arrival, and the resulting spectrum is mixed with a strong continuum of radiation caused by freestate transitions of electrons in the laser field. Nanosecond LIBS therefore requires a complex
gated spectrometer to isolate atomic emission and pulse energies of >10mJ, which leads to
extensive thermal damage to the sample. The use of ultrafast pulses can overcome these
problems by delivering energy on timescale orders of magnitude faster than thermal effects [107,
108].
Besides pulse duration, there are a few more parameters that affect laser ablation efficiency
and threshold. It has been found that a burst of laser pulses can significantly improve ablation
efficiency [109, 110]. LIBS results using single pulses and bursts of pulses are compared in
[109], see Figure 60. The burst contains multiple pulses with each pulse of about 20 ns and
separated by 10 µs interval. The temporal duration of the burst being about 700 µs. It has also
been shown that, there is a 5-fold increase in material ablation rates when six lower-energy
pulses separated by 20 ns are used, compared to a single pulse with energy equal to the sum of
the burst [110]. These observations indicate that a laser with a high repetition rate, like MHz, can
help improving ablation rate. Current Q-switched or amplified laser systems usually have low
repetition rates down to the kHz or Hz level. These results can be explained through a severalstep process. The sample surface absorbs the first laser pulse and gets heated above the melting
point, which causes explosive material ablation. If the second pulse comes before the vapor of
initially ejected material disappears (the restoration time about 100 µs), it can skip the step of
melting the material and generate more atomic emission.

94

Figure 60: LIBS spectra captured by using multi
multi-pulse
pulse (black) and single-pulse
single
(red) configurations. [109
109]
Although femtosecond laser ablation is not a thermal process, multiple femtosecond pulses
pu
also help LIBS by lowering the ablation threshold. These femtosecond pulses are more closely
spaced
ed than those of burst mode. It has also been reported that two femtosecond pulses separated
by 200 ps lowered the ablation thresh
threshold
old by half compared to a single femtosecond pulse [111].
In that study it was observed that two pulses yield a hotter and longer lived plasma, and pulse
delays greater than 50 ps were found to yield greater signal, pr
presumably
esumably because they allow time
for plasma dissipation [111, 112]].
There are also some other factors affecting the ablation threshold, such as pulse duration
and spectral bandwidth. The fluence threshold of ablation is known to increase
increas with τ

1/2

for τ

greater than 10 ps [113-115],, where τ is the laser pulse duration. When the pulse duration is less
than a few picoseconds, the ablation threshold is nearly constant for metals [114
114, 115]. It is also
found that increasing the spectral
ectral bandwidth of a femtosecond pulse lowers the laser ablation
threshold [116], see Figure 61
61. Although changes in the bandwidth also change the pulse
duration, it has been shown that pulse duration alone does not affect the ablation threshold by
applying second order dispersion to the pulses [116].

95

Figure 61: Spectral bandwidth dependence of the LIBS threshold. [116
116]
Based on these studies, an ideal LIBS laser source should have high pulse energy, high
repetition rate and broadband spectrum. It would be also good to have multiple femtosecond
pulses with ultrashort time interval
intervals.. This leads us to study an unusual mode-locking
mode
regime
producing noise-like pulses that can provide the laser parameters discussed above.
In the past two decades, ultrafast fiber laser research has led to the observation of different
mode-locking
locking pulse formation regimes such as soliton [29],, dissipative soliton [31], and
similariton [32].. Efforts to generate high
high-peak-power
power pulses using conventional single-mode
single
fibers are typically limited to 0.5 MW [84]. Under high-gain and high-dispersion
dispersion conditions the
single-pulses
pulses break into multiple pulses, a regime that has been considered as “noise-like”
“noise
pulses
[117-121].. This regime usually generates picosecond or nanosecond long trains of pulses, each
containing hundreds of sub-pulses.
pulses.

96

Figure 62: Experimental results of noise
noise-like laser. (a) output spectrum (b)
background-free
free autocorrelation trace
trace. [117]
This regime was first studied analytically and numerically in a soliton laser [122]. In this
work, authors found the generation of a train of quasi
quasi-stable
stable localized pulses in the region where
whe
a single soliton is unstable [122]].. Later, it was experimentally demonstrated in an Er fiber laser
[117, 123].. A broad output spectrum ((Figure 62(a)) was obtained from this laser [117],
corresponding to about 50 fs pulse duration. However, autocorrelation measurements
measurement showed a
much longer pulse duration that last
lasted over 10 picoseconds with a FWHM 190 fs sharp spike
sp
in
the middle of the trace (Figure 62
62(b)).. Numerical simulation was carried out to investigate
in
these
unusual pulses (Figure 63) [117
117]. The simulation showed noise-like pulses that contain a large
number of sub-pulses
pulses with random amplitude and phase within a temporal window lasting tenstens
of-picoseconds (Figure 63(a))
(a)).. The simulated autocorrelation trace also matched the
experimental results qualitatively (Figure 63(b)). However, this noise-like pulse is different from
pure noise or a CW laser. The laser is still mode
mode-locked
locked or at least partially mode-locked,
mode
which
is indicated by the broad spectrum. The narrow spike on the autocorrelation trace is an artificial
coherent spike. Polarization dependent delay (PDD) is explained as the main reason for the
generation of these noise-like pulses. Large PDD is caused by the significant birefringence in the
fiber, and corresponding nonlinear cavity transmission splits pulses.
97

Figure 63: (a) Calculated time
time-dependent intensity and (b) autocorrelation trace.
[117]
Several other Er noise-like
like fiber lasers [118, 124-126] were reported later and different
mechanisms of noise-like
like pulse formation were proposed. In [126],, an Er fiber laser with weak
birefringence also showed similar noise-like pulses, which ruled
led out the possibility that it is
generated by the large cavity birefringence [117].. Instead, it showed that the formation of the
noise-like pulse was caused by soliton collapse as proposed initially by theoretical work [122],
and it was also a genetic feature of passively mode
mode-locked soliton fiber lasers [118]. Basically,
these noise-like pulses are attributed
ttributed to peak-power clamping [118, 127]. In NPE based modemod
locking fiber lasers, once
nce the pulse peak power reaches a certain value, it cannot increase any
more due to the nonlinear cavity transmission property. Further increasing the pump power will
force one pulse to split into two or more pulses to avoid exceeding the peak-power
power limit. Also,
the extra pump will amplify the background noise and the dispersive wave [127
127]. Thus, pulse
collapse happens and noise-like pulses are generated. The highest pul
pulse
se energy from an Er noiselike fiber laser is 15 nJ [128].. The first Yb fiber laser generating noise-like pulses was reported in
[119], with an output pulse energy of 7.5 nJ. In reference [119],, numerical simulation was also
conducted to understand the noise
noise-like pulse formation.

98

Figure 64 Net gain per roundtrip vs. initial pulse power. Curves 11-3
3 correspond to
slightly different cavity parameters close to the boundary of the single-pulse
sin
generation regime. [119]
Figure 64 shows the net gain per roundtrip of the laser cavity, which depends on the initial
pulse power and cavity parameters. Plot 1 in Figure 64 represents a cavity that can switch
between regular single pulses and noise
noise-like pulses. It shows that the net gain decreases
decrease as the
initial pulse power increases on the left half of curve 1. Therefore,, if the initial pulse power is
less than 1, the pulse will experience gain more than 1 and increase its power after one roundtrip.
If the initial pulse power of the next round trip is great than 1, the pulse will have gain less than 1
and lower its power after this roundtrip. The cavity finally will be stabilized at the point when the
net gain is equal to 1. In this case, the laser is operated in the normal mode-locking
locking regime. If the
pulse evolves as in the right haft of plot 1, the net gain increases as the input pulse power
increases. In this case, the pulse evolution cannot converge and the laser will switch to noise-like
mode.
Due to the partiall coherence in temporal domain, this type of laser has been avoided by
most researchers and considered undesirable. However, some useful applications
applicat
such as
99

metrology, grating-based
based sensing [117-121] and supercontinuum generation [117
117-121] have been
demonstrated using these pulses. Also due to its broad spectrum and multiple femtosecond subsub
pulses with ultrashort time interval, it could also be a potential source for LIBS. Here, we scale
up the pulse energy using an unusually long Yb fib
fiber
er laser cavity and demonstrate its application
for LIBS.

4.2

Experimental setup of noise
noise-like lasers
Our noise-like fiber laser was first designed based on a ssimilariton
milariton laser. A schematic of the

laser design is shown in Figure 65. This fiber laser is based on an all-normal
normal dispersion cavity
using 10/125 µm single-mode
mode fibers
fibers. A double clad 10/125 µm Yb doped gain fiber (2 m) is
pumped with a diode laser (976 nm) through a fiber combiner. A fiber collimator with 0.35 m
passive single-mode fiber (SMF--II) is spliced to the gain fiber to guide the laser beam out. A few
wave-plates and a polarizing beam splitter (PBS) are used to enable mode
mode-locking
locking based on NPE.

Figure 65 Experimental setup of the fiber laser. SMF-I and SMF-II:
II: single mode
fiber;
ber; HWP and QWP: half
half- and quarter-wave
wave plate; PBS: polarizing beam
splitter.
The major change compared to the previous laser is the length of SMF-I.
I. As discussed in
Chapter
hapter 2, the increase of SMF
SMF-II length will narrow the output spectrum and increase the
corresponding transform-limited
limited pulse duration. But this trend stops when SMF-I
SMF becomes
excessively long and the laser will switch into the noise-like regime. About 100 m long SMF-I is
100

used here. Although lasers with shorter fibers have been shown to also reach the noise-like
regime, we extend the cavity length to a much larger scale in order to scale up the pulse energy.

4.3

Experimental results
With a 3 nm bandwidth intra-cavity spectral filter and about 100 m long SMF-I, different

mode-locking states can be achieved by adjusting the wave plates and pump power, due to the
NPE mechanism. In this laser, pump-power dependent variation of the mode-locking state is
similar to a normal fiber laser. At low pump power, single pulsing and a clean pulse train is
observed. A pulse train at ~2 MHz repetition rate is shown in Figure 66. When the laser is
pumped with higher power, mode-locking becomes unstable and multi-pulsing occurs preventing
one to define a repetition rate. The switch between CW and mode-locking status is instantaneous
and significant spectral broadening is observed.

Figure 66: Pulse train of mode-locked fiber laser with 100 m long SMF-I.

101

An output spectrum is shown in Figure 67(a). It is smooth and corresponds to coherent
pulses with about 150 fs FWHM pulse duration. The output spectral bandwidth does not change
obviously
ously by increasing pump power, while the output power increases.

Figure 67: a) Experimental output spectrum; b) Experi
Experimental
mental SHG spectrum with
second-order
order dispersion compensation (SOD) applied (red) and calculated SHG
spectrum with flat phase based on the fundamental spectrum.
The output pulses are characterized using a MIIPS-enabled 4-f pulse shaper. A chirp scan is
2

carried out to find the maximum integrated SHG signals around -60,000 fs (Figure
Figure 68 (b)). It is
2

significantly less than the cavity dispersion
dispersion, which is about 2,300,000 fs , indicating something
2

unusual. With a compensation SOD of -60,000 fs applied to the output pulses using the pulse
shaper, the normalized measured SHG signal is not far from the calculated SHG spectrum
spectru
(Figure 67 (b)),, which indicates that there is at least some coherence. Also, when the laser is
switched to CW mode and the output laser beam is focused on the same BBO crystal, no SHG
signal is detected even at much higher average power. This proves that these pulses are
ar real and
have much higher peak power than CW mode. However, the change of integrated SHG signal is
very small (only ~5 times) compared to a fully coherent pulse that can have three order
orde of
magnitude larger changes (see Figure 68(b)).
102

Figure 68: (a) Calculated and experimental two
two-dimensional SOD scan.. The SOD
range of the calculated plot is 10 times smaller than experimental plot. (b)
Calculated and experimental SHG-integrated SOD scan.
The calculated and experimental results of SOD scan are shown in Figure 68. The
calculation uses a fully coherent pulse based on the fundamental spectrum ((Figure
Figure 67 (a)). A
2

second order phase dispersion of 60,000 fs is added to the coherent pulse
puls to match the
systematic phase distortion in the real pulse
pulses. In order to see the difference more clearly, the
t
SOD range of the calculated two
two-dimensional
dimensional SOD scan is 10 times smaller than that of the
experimental results. Their
eir SHG spectral ranges shown on the y-axis
axis are very similar;
similar while the
2

SHG of the experimental result still have significant signal until 1 ps SOD (see Figure 68 (a)).
This is better illustrated in the SHG
SHG-integrated SOD scan results (see Figure 68 (b)). Compared
to the FWHM width of calculated scan, the experimental one is ~30
30 times larger,
larger which indicates
the existence of the incoherent pulses.
Meanwhile, when a sinusoidal phase scan is performed and no convergence of the MIIPS
trace is achieved, this also indicates that there is an incoherent part in the laser pulses. However,
it can be an advantage that these
ese pulses are much less phase sensitive, since they can be delivered
by a fiber with minimal pulse distortion.
103

To further characterize the pulse
pulses, interferometric AC using a pulse shaper and
background-free non-collinear
collinear SHG intensity AC are carried out. On the short range (± 600 fs)
interferometric AC trace (Figure
Figure 69(a)),, the ratio between the peak and base line is less than 8:1,
which indicates the pulse lasts much longer than this time range. A long range background-free
background
intensity AC trace is conducted to show that ((Figure 69(b)).. On the intensity AC trace, there is a
~200 fs coherent spike while the whole trace last over 15 ps. This matches the characteristics
chara
of
noise-like
like pulses observed in previous work [117, 119].

Figure 69: (a) Interferometric AC, peak-to-base-line
line ratio is less than 8:1; (b)
background-free non-collinear
collinear intensity AC.
The distance between collimator and grating is adjusted to vary the spectral filter
bandwidth. No noticeable change of output spectrum, chirp scan or autocorrelation result was
observed. With this type of narrow filter
filter, the maximum average output power is about 420 mW,
mW
corresponding to 210 nJ pulse energy.
In order
der to further study the filter
filter-bandwidth-dependence
ce of laser performance, the gratinggrating
based spectral filter is replaced by a birefringent spectral
ectral filter (12 nm or 20 nm). The resulting
output spectra are broadened while the coherence of the pulse
pulses stays the same. Since the spectral
filter does not play as important a role as in other lasers,, it is completely removed from the cavity
and the laser setup
etup is simplified as shown in Figure 70. Similar mode-locking
locking behavior is still
104

achieved with a much broader spectrum and higher output power. A maximum output power of
640 mW, corresponding
nding to 320 nJ, is delivered from this laser. Pump-power-dependent
dependent spectral
spec
changes are shown in Figure 71..

Figure 70: Simplified noise
noise-like fiber laser setup without any spectral filter.
filter SMF:
single mode fiber; HWP and QWP: half
half- and quarter-wave
wave plate; PBS: polarizing
beam splitter;; coll.: fiber collimator
collimator.

Figure 71: Pump-power--dependent output spectra. Black: pump power 1.8 W;
Red: pump power 3.9 W.
With higher pump power, the output spectrum broadens to match the amplified
spontaneous emission spectrum of the gain fiber. This also indicates the mechanism behind this

105

noise-like mode-locking – once the peak power iiss clamped, the excess pump amplifies the
background noise.
In order to further scale
ale up the pulse energy, an additional 100 m long fiber was added to
SMF-I, mode-locking
locking is achieved at a rrepetition rate of about 1 MHz [Figure 72]].

Figure 72: 1 MHz pulse train of noise
noise-like
like laser with 200 m long SMF-I.
SMF

Figure 73: Output spectrum of 1 MHz noise
noise-like laser.

106

A broad and smooth spectrum ((Figure 73) was obtained with a maximum output power of
450 mW, corresponding to 450 nJ per pulse. Efforts to further increase the output power did not
work. It was also noticed that, the change of maximum pulse energy is not linearly proportional
to the inverse of the repetition
epetition rate, as we obtained 320 nJ for 2 MHz and 450 nJ for 1 MHz.
Limited by gain bandwidth, no further broadening of the output spectrum was observed either.
Background-free non-collinear
collinear SHG AC measurement is used to characterize the output
pulses, as shown in Figure 74.. Limited by the scan range of the delay stage, only half of the AC
trace is scanned to get as much information as possible about the symmetric AC trace. It can be
seen that there is a large pedestal
edestal lasting over more than 180 ps with a very narrow spike on top
of the trace. The base line drops to below 0.1 at 180 ps and it is believed that it will be more than
200 ps before the signal reaches zero.

Figure 74: Non-collinear
collinear AC trace from 0 ps to +180 ps. Insert: the same AC trace
on a small range from -11 ps to +1 ps.
This means that the output is characterized by multiple femtosecond sub-pulses
sub
within a
200 ps envelope. The irregular femtosecond sub
sub-pulses result in the narrow spike in the center of
AC trace. Another possibility
ssibility is that each output pulse is about 200 ps long and that these pulses
107

fluctuate in amplitude and phase
phase.. However, according to the mechanism behind the formation of
noise-like pulses and numerical
umerical simulation, the explanation of a long pulse envelope
envelop with
multiple sub-pulses is more suitable for this case.
Output pulses from the noise
noise-like fiber oscillator were also tested as a seed for a fiber
amplifier. In common ultrashort pulse fiber amplifiers, a long pre-chirp
chirp fiber is needed to lower
the peak power to avoid too much nonlinearity during amplification. Also, a down-counter
down
is
also used to lower the repetition
ion rate in order to achieve higher pulse energy. Since our laser is
mainly designed for LIBS and high
high-repetition pulses are preferred, no down-counter
counter is used in
our amplifier system. Also, due to the insensitive phase response of these pulses, no pre-chirp
pre
is
needed before amplification.

Figure 75: Setup off ffiber amplifier using a noise like laser as the seed.
The
he amplifier setup is shown in Figure 75.. A backward pumping scheme is used to achieve
better efficiency. The pump laser is coupled into the output end of gain fiber using a fiber
combiner. A double-clad 30 µm core diameter gain fib
fiber
er (Nufern) is used. This large-mode-area
large
(LMA) fiber is not purely single mode. By coiling it tightly, higher order modes can be filtered.
The focusing lens and input end of the gain fiber are mounted on a 3-axis
axis stage that is adjusted to
optimize the coupling of seed laser into the gain fiber.
By gradually increasing the pump power, the output power increases correspondingly.
Since the seed laser already has a broad spectrum close to the gain-bandwidth
bandwidth limit, no
significant spectral broadening of the amplifier output is observed. Meanwhile, with the increase
108

of pump power, ASE from the gain fiber increases due to the excessive pump power. ASE can be
suppressed by adjusting the setup alignment and optimizing the coupling efficiency. When the
pump power reaches 15 W, the ASE signal becomes too dominant to be suppressed. The
maximum clean and stable amplifier output is ~3.87 W, corresponding to 3.87 µJ pulse energy.
The
he output spectrum is shown in Figure 76.

Figure 76: Output spectrum of fiber amplifier.

4.4

LIBS using noise-like
like laser
As described above, the laser can produce 1-2 MHz repetition rate pulses with high pulse

energy and broad spectrum. The picosecond long pulse envelop consists of a number of
femtosecond sub-pulses.
pulses. These characteristics of the unamplified laser match the requirement for
an ideal LIBS laser source. It is important to test this laser for LIBS.

109

4.4.1

Experimental setup

Figure 77: LIBS setup using noise
noise-like laser. DM: dichroic miror; L:: lens; spec:
spectrometer; obj: objective
objective. SMF: single mode fiber; HWP and QWP: halfhalf and
quarter-wave
wave plate; PBS: polarizing beam splitter.
As shown in Figure 77,, the output beam of the fiber oscillator is collimated with a
telescope before being directed to the LIBS detection setup, without pulse compression. A 20x
objective (NA = 0.4) is used to foc
focus
us the beam onto the sample, which is mounted on a spinning
wheel (rotation frequency 133 Hz) so that each pulse sees a fresh spot for ablation. The scattered
LIBS signal can be directly collected by placing a collection ffiber
iber next to the ablation spot.
spot The
other end of the collection fiber is coupled to a compact spectrometer (178 nm – 876 nm,
USB4000, Ocean Optics). The advantage of this direct side collection is to avoid any signal
filtered by the collecting optics since the atomic emission can extend below
low 300 nm wavelength
and normal glass optics will greatly attenuate those wavelengths.. However, this scheme is
susceptible to large background scattering in the spectrometer due to the strong excitation laser.
It is important to filter all non-atomic
atomic emis
emission
sion signals for ablation threshold measurement. So a
110

backward detection scheme, with a dichroic mirror to filter out the excitation laser, is used for
ablation-threshold
threshold measurement, though sacrificing the signals below 350 nm.

4.4.2

Experimental results
The results discussed below are obtained using the 2 MHz cavity output, since its pulse

energy is enough to cause ablation and too much energy will generate more unwanted plasma
emission that will mask the atomic emission spec
spectra. Several samples were tested.

Figure 78: LIBS spectra of brass (top) and copper (bottom).
LIBS spectra of Cu and brass pie
pieces are compared in Figure 78. Brass typically contains
~30% zinc (Zn) and ~70% Cu. On the brass spectrum, peaks are visible at 330.7 nm, 334.3 nm,
472.3 nm and 481.1 nm, which are absent in the C
Cu
u spectrum. These peaks match Zn
Z emission
lines. The other peaks, which are common to both spectra, correspond to Cu emission lines. The
spectra shown above are directly recorded without using a gated
gated-spectrometer
spectrometer and the continuum
emission signal is insignificant compared to the atomic emission peaks. The low continuum
emission also implies thatt there is little thermal emission, which indicates that the heat-affected

111

zone is limited.. The simple detection system requirements further reduce the complexity and cost
of the LIBS system. The fast repetition rate at 11-2 MHz, comparing to Q-switched
switched lasers,
las
also
enhances the accumulation of LIBS signals.

Figure 79: LIBS spectra of three aluminum alloys
alloys,, Al1100 (black), Al6061 (red)
and Al7075 (blue).. Insert: the full LIBS spectra
spectra.
It is also important to evaluate the system’s ability to qualitatively evaluate difference in
composition and concentration. The aluminum alloys, Al7075, Al6061 and Al1100, were used
for this test. In Al1100, there is no magnesium. Al6061 and Al7075 have about 0.8-1.2%
0.8
and
2.1-2.9%
2.9% magnesium, respectively. LIBS spectra of these three alloys are compared in
i Figure 79.
Each spectrum is normalized to its highest aluminum peak. As expected, there is no Mg peak
observed on Al1100 LIBS spectra. For spectra of Al6061 and Al7075, not only are multiple Mg
peaks (278.3, 285.2, 383.8, 518
518.4nm) observed, but the change of Mg peak magnitude also
qualitatively corresponds to the variation of Mg concentration in these two alloys. Quantitative
results would require calibrated samples, which were not available for these tests.
One of the important
nt LIBS applications is to detect hazardous materials. Often these
hazardous materials occur only in trace amounts surround by large amounts of other materials,
which makes the detection extremely hard. To evaluate our system’s ability of trace detection, a
PbNO3-contaminated Al plate was prepared. This sample was made by applying a few drops of
6.5 mg/mL PbNO3 solution on an aluminum plate an
and heating until the water evaporated. The
112

2

average concentration of PbNO3 on the surface is <15mg/cm . Compared to the LIBS spectrum
of Al 1100, Pb peaks are clearly distinguishable at 364.0, 368.3, and 405.8nm, see Figure 80.

Figure 80: LIBS spectra of pure Al1100 alloy (black) and PbNO3 contaminated
Al1100 (red).

Figure 81: (a) Picture of Galena rock; (b) LIBS spectra of Galena rock.
rock
In addition to these smooth metallic samples, a Galena (PbS) rock [Figure
Figure 81(a)] with a
rough surface was also tested. Strong Pb emissions can be observed (e.g. 364.0, 368.3, and
405.8nm), as shown in Figure 81
81(b).. This clear spectrum shows great potential for the system’s

113

use in the mining industry, for example, for analyzing samples in the field without sample
preparation.

4.4.3

Ablation threshold
The experimental threshold measurement is shown in Figure 82, which was carried out on
2

Cu. Nonlinear fitting of the experimental data gives threshold fluence values around 0.25 J/cm .
It was reported that when using a 5 ns Q-switched
switched Nd:YAG laser the threshold fluence for Cu is
2

1.46 J/cm [111], whichh is ~6 times larger than our result. The threshold is also smaller than 0.49
2

2

J/cm obtained using a 150 fs Ti:Sapphire chirped
chirped-pulse amplifier [116] or 0.5 J/cm obtained
using a 35 fs Ti:sapphire
apphire amplifier in our lab [129].

Figure 82: Threshold measurement. LIBS intensity for copper as a function of
incident laser fluence.
Lower threshold implies less pulse energy required for LIBS, which results in a lower
background plasma emission. Plasma emission can mask the LIBS signal and eliminating it
114

typically requires a time-gated spectrometer. As discussed above, the threshold measured from
our laser is lower than the results of both nanosecond and femtosecond lasers. The observed
lower ablation threshold, compared to that of single fs pulses, is probably due to the multiple
femtosecond sub-pulses as indicated by reference [15]. The lower threshold and high repetitionrate of our laser source results in significant improvements in the efficiency and signal-to-noise
ratio of LIBS spectra. Current portable LIBS systems typically use Q-switched nanosecond fiber
lasers [113-115]. The laser presented here can be developed as an ideal source for a portable
LIBS system.

4.5

Conclusion
We have built several noise-like fiber lasers by using more than 100 m of fiber inside a

laser cavity. By varying intra-cavity spectral-filter bandwidth, laser performance is studied and
the filter does not play as important a role as in similariton fiber lasers. By removing the spectral
filter, broader output spectra are achieved and output pulses with 320 nJ pulse energy are
delivered at 2 MHz repetition rate. These pulses are more than 100 ps long and contain irregular
multiple femtosecond sub-pulses. It is found that these pulses meet the requirements of an ideal
laser source for LIBS. A simple LIBS system has been built using this laser. Strong LIBS signals
have been generated with low fluence threshold and insignificant continuum background. The
system has also been tested to detect the change of atomic concentration in alloys and track trace
contaminant. These results have shown that this laser will be an ideal source for a low-cost and
portable LIBS system.
The pulse energy of this laser has been scaled up to 450 nJ at 1 MHz repetition rate by
extending the cavity fiber length to about 200 m. A fiber amplifier has also been built to further
increase the pulse energy to 3.87 µJ at 1 MHz repetition rate.
115

Chapter 5 Summary and Outlook
This chapter summarizes the work and results presented through this thesis. My work includes
the development of similariton fiber lasers and noise-like fiber lasers and some applications
using these developed lasers. Future directions of our work are discussed at the end.

5.1

Similariton fiber laser and applications
We have developed ultrafast fiber lasers based on all-normal dispersion cavity design.

Pulses with up to 34 nJ pulse energy and 80 fs pulse duration are delivered from one of our
regular all-normal dispersion fiber lasers. Fiber length and intra-cavity spectral-filter bandwidth
are found to be the most important parameters affecting laser performance. A very narrow
bandwidth intra-cavity spectral filter is used as an attractor for similariton pulse formation, which
is a solution characterized by a wave-breaking-free form in normal dispersion fiber. With a 3 nm
spectral filter, output pulses with about 20 nJ pulse energy are delivered and compressed to about
41 fs FWHM pulse duration using a MIIPS-enabled pulse shaper. Numerical simulations are
conducted to verify the formation of similaritons and match the experimental results very well.
The similariton fiber laser has been successfully demonstrated for multiphoton microscopy.
The ultrashort pulse durations greatly enhance two- and three-photon induced modalities in both
stained and unstained living tissues such as Drosophila larvae and fruit fly wings. Results of
SHG and THG from living tissue are compared under similar laser conditions and
complementary results show the full information of living tissue structures. Due to the high pulse
energy, depth-resolved imaging of Drosophila larva and fruit fly eyes is also achieved. Threedimensional constructed imaging based on THG shows much better contrast in resolving the
tissue structures than SHG. It shows that this high pulse energy ultrafast similariton fiber laser is
a suitable source for deep tissue imaging.
116

5.2

Noise-like fiber laser and applications
Also based on all-normal fiber laser cavity design, another type of laser has been developed

for laser-induced breakdown spectroscopy (LIBS). This laser is operated in an unusual modelocking regime and produces noise-like pulses, which have mostly been ignored by many
researchers. However, we have found that some characteristics of our noise-like laser, such as
broad spectra and picosecond long pulse envelope containing multiple femtosecond sub-pulses,
meet the requirements of an ideal laser source for LIBS. We have built a noise-like fiber laser
using ~200 m long fiber and scaled the output pulse energy up to 450 nJ at 1 MHz repetition rate.
The spectral filter does not affect the laser performance as much as in the similariton lasers and
can be removed from the laser cavity. Due to its phase insensitivity, external pulse shaping is not
necessary for this type of pulses in applications.
A simple LIBS setup using this noise-like laser has been demonstrated on several samples.
Atomic emission spectra with very good signal-to-noise ratio have been obtained. Abilities, such
as analyzing atomic composition, qualitatively detecting concentration changes and tracking
trace compounds, have also been tested. The results show that our noise-like fiber laser is an
ideal laser source for a low-cost and portable LIBS system.

5.3

Future work
To further improve the pulse energy of a similariton laser while still producing equally

short pulse durations, one option is to use LMA fibers. In principle, with the same cavity design,
the maximum output pulse energy delivered is proportional to the square of the fiber core
diameter. Currently available single mode LMA fibers are mainly photonic crystal fibers and
chirally coupled core fibers. Their core diameter is normally more than 30 µm, which can scale
the pulse energy up to 100 nJ. However, these LMA fibers are not as flexible as standard single
117

mode fibers and may suffer large losses from bending. The other drawback is that special fiber
splicing technology is required for them. The other option to scale up the pulse energy is to use
multiple-stage amplification. This is the most commonly used method for higher-energy
industrial fiber lasers. In terms of pulse duration, specially designed dispersion-decreasing fiber
can be used to sustain the similariton evolution after the gain fiber and further broaden the output
spectrum. Basically, new fiber technology is highly desirable for the development of fiber lasers.
For the noise-like fiber lasers, the limit of pulse energy should be further studied using
even longer fiber. It is also important to experimentally measure the profile of single short pulses
and understand the detailed structure of the sub-pulses. We have tried cross correlation using
another highly chirped broadband laser source but could not get it to work. New measurement
method is required.
To eliminate all the free-space components in our current fiber laser and modify them to an
integrated all-fiber system will also be desirable for future applications.

118

APPENDICES

119

Appendix-I Matlab Code
1. Pulse propagation in fibers with second order and third order dispersion
%% define basic parameters
T = 1000; % time window, in femtosecond
nt = 2^12; % sampling points
dt = T/nt; % time resolution
t = (-nt/2:1:nt/2-1)'*dt; % time vector
v = (-nt/2:1:nt/2-1)'/(dt*nt); % frequency vector
w = 2*pi*(-nt/2:1:nt/2-1)'/(dt*nt); % angular frequency
dw = w(2)-w(1); % angular frequency resolution
lambda = 2*pi*3e2./(w+2*pi*3e2/1050); % wavelength, in nonometer
lambda(lambda<0)=nan;
c = 3*10^8; % speed of light, m/s
w0 = 2*pi*c/1050*10^9; % carrier frequency
beta2 = 23000; % GVD, fs^2/m
beta3 = 0.1e6; % Third order dispersion, fs^3/m
tau = 50; % FWHM pulse duration of input pulse, fs
tau0 = tau/2/log(2)^0.5; % 1/e^2 pulse duration
Ld = tau0^2/abs(beta2); % second order dispersion length
Ld3 = tau0^3/abs(beta3); % third order dispersion length
u0 = exp(-t.^2/2/tau0^2); % input intensity field
uw = fftshift(ifft(fftshift(u0)))*dt; % FFT of temporal field to frequency
filed
dispersion1 = exp(1i*beta2/2.*w.^2*3*Ld); % phase distortion
dispersion2 = exp(1i*beta3/6.*w.^3*3*Ld3); % phase distortion
uw1 = uw.*dispersion1;
uw2 = uw.*dispersion2;
uw3 = uw.*dispersion1.*dispersion2;
u1 = fftshift(fft(fftshift(uw1)))*1/dt;
u2 = fftshift(fft(fftshift(uw2)))*1/dt;
u3 = fftshift(fft(fftshift(uw3)))*1/dt;
%% make plots
ha=tight_subplot(2,4,[.1 .01]);
axes(ha(1));
plot(t,abs(u0).^2,'linewidth',2);
ylim([0 1]);
xlim([-500 500]);
set(gca,'xTick',-500:250:500,'xticklabel',[],'yticklabel',[]) ;
axes(ha(2));
plot(t,abs(u1).^2,'linewidth',2);
ylim([0 1]);
xlim([-500 500]);
set(gca,'xTick',-500:250:500,'xticklabel',[],'yticklabel',[]) ;
axes(ha(3));
plot(t,abs(u2).^2,'linewidth',2);
ylim([0 1]);
xlim([-500 500]);
set(gca,'xTick',-500:250:500,'xticklabel',[],'yticklabel',[]) ;
axes(ha(4));
plot(t,abs(u3).^2,'linewidth',2);
ylim([0 1]);

120

xlim([-500 500]);
set(gca,'xTick',-500:250:500,'xticklabel',[],'yticklabel',[]) ;
axes(ha(5));
plot(lambda,abs(uw).^2/max(abs(uw).^2),'linewidth',2);
ylim([0 1]);
xlim([950 1150]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[]) ;
axes(ha(6));
plot(lambda,abs(uw1).^2/max(abs(uw1).^2),'linewidth',2);
ylim([0 1]);
xlim([950 1150]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[]) ;
axes(ha(7));
plot(lambda,abs(uw2).^2/max(abs(uw2).^2),'linewidth',2);
ylim([0 1]);
xlim([950 1150]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[]) ;
axes(ha(8));
plot(lambda,abs(uw3).^2/max(abs(uw3).^2),'linewidth',2);
ylim([0 1]);
xlim([950 1150]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[]) ;

2. Pulse propagation in fibers with nonlinear coefficient
T=1000; %fs
nt=2^12;
dt=T/nt;
% timestep (dt)
t=(-nt/2:1:nt/2-1)'*dt;
% time vector
v=(-nt/2:1:nt/2-1)'/(dt*nt);
w=2*pi*(-nt/2:1:nt/2-1)'/(dt*nt);
dw=w(2)-w(1);
lambda=2*pi*3e2./(w+2*pi*3e2/1050);
lambda(lambda<0)=nan;
lambda2w=2*pi*3e2./(w+2*pi*3e2/1050*2);
c=3*10^8;%m/s
w0=2*pi*c/1050*10^9;
beta2=23000;
tau=50;
tau0=tau/2/log(2)^0.5;
Ld=tau0^2/abs(beta2);
beta3=0.1e6;
Ld3=tau0^3/abs(beta3);
I0=1e11;
u0=exp(-t.^2/2/tau0^2);
uw=fftshift(ifft(fftshift(u0)))*dt;
n2=2.6*10^-16;%cm^2/W
%%%gamma=n2*w0/c/Aeff;
Lnl=1/(0.0044*I0);
L=Lnl;
nstep=100;
h=L/nstep;
u=u0;
for i=1:1:nstep
u=u.*exp(1i*abs(u).^2*h/Lnl);
end

121

uw1=fftshift(ifft(fftshift(u)))*dt;
ha=tight_subplot(2,2,[.01 .02]);
axes(ha(1))
plot(lambda,abs(uw).^2/max(abs(uw).^2),'-k','linewidth',2);
xlim([950 1150]);
ylim([0 1]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[])
axes(ha(2))
plot(t,abs(u0).^2/max(abs(u0).^2),'-k','linewidth',2);
xlim([-100 100]);
set(gca,'xTick',-100:50:100,'xticklabel',[],'yticklabel',[])
ylim([0 1]);
hold on;
plot(t,[-diff(phase(u0))/dw;0],'-r','linewidth',2)
ylim([-1.1 1.1]);
hold on;
plot(t,0,'-k')
axes(ha(3))
plot(lambda,abs(uw1).^2/max(abs(uw).^2),'-k','linewidth',2);
xlim([950 1150]);
% ylim([0 1]);
set(gca,'xTick',950:50:1150,'xticklabel',[],'yticklabel',[])
axes(ha(4))
% [haxes,hline1,hline2] =
plotyy(t,abs(u).^2/max(abs(u).^2),t,[diff(phase(u))/dw;0])
plot(t,abs(u).^2/max(abs(u).^2),'-k','linewidth',2);
xlim([-100 100]);
set(gca,'xTick',-100:50:100,'xticklabel',[],'yticklabel',[])
ylim([-1.1 1.1]);
hold on;
plot(t,[-diff(phase(u))/dt*tau0;0],'-r','linewidth',2)
ylim([-1.1 1.1]);
hold on;
plot(t,0,'-k')

;

;

;

;

3. Pulse propagation in fibers with second order dispersion and nonlinear coefficient
T=1000; %fs
nt=2^12;
dt=T/nt;
% timestep (dt)
t=(-nt/2:1:nt/2-1)'*dt;
% time vector
v=(-nt/2:1:nt/2-1)'/(dt*nt);
w=2*pi*(-nt/2:1:nt/2-1)'/(dt*nt);
dw=w(2)-w(1);
lambda=2*pi*3e2./(w+2*pi*3e2/1050);
lambda(lambda<0)=nan;
lambda2w=2*pi*3e2./(w+2*pi*3e2/1050*2);
c=3*10^8;%m/s
w0=2*pi*c/1050*10^9;
beta2=23000;
tau=50;
tau0=tau/2/log(2)^0.5;
Ld=tau0^2/abs(beta2);
beta3=0.1e6;
Ld3=tau0^3/abs(beta3);

122

I0=1e11;
u0=exp(-t.^2/2/tau0^2);
uw=fftshift(ifft(fftshift(u0)))*dt;
n2=2.6*10^-16;%cm^2/W
%%%gamma=n2*w0/c/Aeff;
Lnl=1/(0.0044*I0);
L=pi*Lnl;
nstep=100;
h=L/nstep;
u=u0;
for i=1:1:nstep
u=u.*exp(1i*abs(u).^2*h/Lnl);
end
uw1=fftshift(ifft(fftshift(u)))*dt;
Lnl=1/(0.0044*I0);
L=3.5*pi*Lnl;
nstep=100;
h=L/nstep;
u=u0;
for i=1:1:nstep
u=u.*exp(1i*abs(u).^2*h/Lnl);
end
uw2=fftshift(ifft(fftshift(u)))*dt;
ha=tight_subplot(1,3,0.02);
axes(ha(1))
plot(lambda,abs(uw).^2/max(abs(uw).^2),'-k','linewidth',2);
xlim([750 1550]);
ylim([0 1.1]);
set(gca,'xTick',750:200:1550,'xticklabel',[],'yticklabel',[]) ;
axes(ha(2))
plot(lambda,abs(uw1).^2/max(abs(uw).^2),'-k','linewidth',2);
xlim([750 1550]);
% ylim([0 1]);
set(gca,'xTick',750:200:1550,'xticklabel',[],'yticklabel',[]) ;
axes(ha(3))
plot(lambda,abs(uw2).^2/max(abs(uw).^2),'-k','linewidth',2);
xlim([750 1550]);
ylim([0 0.17]);
set(gca,'xTick',750:200:1550,'xticklabel',[],'yticklabel',[]) ;

4. Wave-breaking pulse simualtion
T=1000; %fs
nt=2^12;
dt=T/nt;
% timestep (dt)
t=(-nt/2:1:nt/2-1)'*dt;
% time vector
v=(-nt/2:1:nt/2-1)'/(dt*nt);
w=2*pi*(-nt/2:1:nt/2-1)'/(dt*nt);
dw=w(2)-w(1);
lambda=2*pi*3e2./(w+2*pi*3e2/1050);
lambda(lambda<0)=nan;
lambda2w=2*pi*3e2./(w+2*pi*3e2/1050*2);
c=3*10^8;%m/s
w0=2*pi*c/1050*10^9;
beta2=23000;

123

tau=50;
tau0=tau/2/log(2)^0.5;
Ld=tau0^2/abs(beta2);
u0=exp(-1/2*(t/tau0).^2);
Lnl=Ld/30^2;
ha=tight_subplot(3,2,[.01 .02]);
L=0.01*Ld;
a=length(L);
nstep=100;
h=L/nstep;
halfstep=exp(1i*1/2*beta2*w.^2*h/2);
u=fftshift(ifft(fftshift(u0)))*dt;
spec0=abs(u).^2;
u=u*ones(1,a);
for i=1:1:nstep
u=u.*halfstep;
u=fftshift(fft(fftshift(u)))*1/dt;
u=u.*exp(1i/Lnl*abs(u).^2*h);
u=fftshift(ifft(fftshift(u)))*dt;
u=u.*halfstep;
end
axes(ha(1))
spec=abs(u).^2/max(spec0);
plot(v*tau0,spec,'-k','linewidth',2);
xlim([-10 10]);
ylim([0 0.2]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
axes(ha(2))
u=fftshift(fft(fftshift(u)))*1/dt;
int=abs(u).^2;
plot(t/tau0,int,'-k','linewidth',2);
xlim([-4.5 4.5]);
ylim([0 1]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
hold on;
plot(t/tau0,[-diff(phase(u))/dt/0.6+0.5;0],'-r','linewidth',2)
ylim([0 1]);
xlim([-4.5 4.5]);
L=0.04*Ld;
a=length(L);
nstep=100;
h=L/nstep;
halfstep=exp(1i*1/2*beta2*w.^2*h/2);
u=fftshift(ifft(fftshift(u0)))*dt;
spec0=abs(u).^2;
u=u*ones(1,a);
for i=1:1:nstep
u=u.*halfstep;
u=fftshift(fft(fftshift(u)))*1/dt;
u=u.*exp(1i/Lnl*abs(u).^2*h);
u=fftshift(ifft(fftshift(u)))*dt;
u=u.*halfstep;
end

124

axes(ha(3));
spec=abs(u).^2/max(spec0);
plot(v*tau0,spec,'-k','linewidth',2);
xlim([-10 10]);
ylim([0 0.07]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
axes(ha(4))
u=fftshift(fft(fftshift(u)))*1/dt;
int=abs(u).^2;
plot(t/tau0,int,'-k','linewidth',2);
xlim([-4.5 4.5]);
ylim([0 0.6]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
hold on;
plot(t/tau0,[-diff(phase(u))/dt/3+0.3;0],'-r','linewidth',2)
ylim([0 0.6]);
xlim([-4.5 4.5]);
L=0.08*Ld;
a=length(L);
nstep=100;
h=L/nstep;
halfstep=exp(1i*1/2*beta2*w.^2*h/2);
u=fftshift(ifft(fftshift(u0)))*dt;
spec0=abs(u).^2;
u=u*ones(1,a);
for i=1:1:nstep
u=u.*halfstep;
u=fftshift(fft(fftshift(u)))*1/dt;
u=u.*exp(1i/Lnl*abs(u).^2*h);
u=fftshift(ifft(fftshift(u)))*dt;
u=u.*halfstep;
end
axes(ha(5));
spec=abs(u).^2/max(spec0);
plot(v*tau0,spec,'-k','linewidth',2);
xlim([-10 10]);
ylim([0 0.04]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
axes(ha(6))
u=fftshift(fft(fftshift(u)))*1/dt;
int=abs(u).^2;
plot(t/tau0,int,'-k','linewidth',2);
xlim([-4.5 4.5]);
ylim([0 0.4]);
set(gca,'xticklabel',[],'yticklabel',[]) ;
hold on;
plot(t/tau0,[-diff(phase(u))/dt/15+0.15;0],'-r','linewidth',2)
ylim([0 0.35]);
xlim([-4.5 4.5]);

5. Fiber laser simulation
5.1 Pulse propagation function
function uout=prop(u0,g0,gamma,beta2,beta3,L,alpha,T,nt,Esat,lambda0)
if L<0.01

125

h=0.001;
else
h=0.02;
end
nz=L/h;
u=fftshift(fft(ifftshift(u0)));
% halfstep=exp((gain-alpha).*(h/2)-1i*beta2/2*w.^2*(h/2));
for n=1:1:nz
dt = T/nt;
% timestep (dt)
w = 2*pi*(-nt/2:1:nt/2-1)'./(dt*nt);
% w=fftshift(w);
% Esat=1500; %pJ
% Esat=2100;%38nJ saturation gain energy used in Simon's CCC fiber laser%
ue=fftshift(ifft(ifftshift(u)));
Ei=(abs(ue).^2)*dt*10^-3;
E0=sum(Ei);
% Tr=(4.3+0.5)/(3*10^8/1.458)*10^15;
% E0=E0*Tr/T;
bw=50;%nm
BW=(2*pi*3*10^8)/(lambda0-bw/2)/(lambda0+bw/2)*bw*10^-6;%gain bandwith
corresponding to the frequency
% if E0<Esat
gain=g0./(1+E0/Esat+((w+2*pi/2/T)./BW).^2);
% else gain=g0./(2+(w./BW).^2);
% end
% plot(w,gain)
halfstep=exp((gainalpha).*(h/2)+1i*beta2./2.*(w.^2)*(h/2))+1i*beta3/6*(w.^3)*(h/2);
u=halfstep.*u;
u=fftshift(ifft(ifftshift(u)));
u=u.*exp(1i*gamma*((abs(u)).^2)*(h));
u=fftshift(fft(ifftshift(u)));
u=halfstep.*u;
end
uout=fftshift(ifft(ifftshift(u)));

5.2 Laser cavity function
folder='';
mkdir(folder);
% prameters for fourier transforms
T=50000; %fs
nt=2^11;
dt = T/nt
t = (-nt/2:1:nt/2-1)'*dt;
w = 2*pi*(-nt/2:1:nt/2-1)'/(dt*nt);
% vs=w./2/pi;
lambda0=1070;
w0=2*pi*3e2/lambda0;
w1=w+w0;
lambda=2*pi*3e2./w1;
lambda_min=max(lambda)
lambda_max=min(lambda)
DATA=rand(1,5);
g0=3.45;
beta3=0;

% timestep (dt)
% time vector

126

Esat=5000;%gain saturation energy, in pJ
L_gain=2.5;
gamma_10um=0.001584;
%setting the maximum value of
L_GVD_max=1.7;
bw_max=1.5;
Esat_max=200;
for nm=1:1:1000
Esat=Esat+100
bw=2.5;
for j=1:1:1000
bw=bw+0.5
L_GVD=1.2;
count_L_GVD=0
for m=1:1:1000
L_GVD=L_GVD+0.5
%--%initial pulse%--%
% u0 = sqrt(p0)*exp(-((1+1i*C)/2)*((t-t0)/T0).^(2*m));%initial pulse
u0=wgn(nt,1,-40,'complex');
% u0=fftshift(fft(ifftshift(u0)));
% int_u0=abs(u0).^2;
% plot(t,int_u0);
% ylim([-0.1 1])
% spec_u0 = fftshift(abs(dt*fft(ifftshift(u0))/sqrt(2*pi)).^2);
% plot(lambda,spec_u0);
% xlim([960 1100]);
% ylim([-0.1 1]);
iteration=100;
for n=1:iteration
%--%the first segment of passive fiber%--%
%prameters for fiber
gamma1=gamma_10um;
beta2_1=23*10^3;
beta3;
% gamma1=0;
alpha1=0;
g1=0;
L1=L_GVD;
%pulse after propagating through the passive fiber
u1=prop(u0,g1,gamma1,beta2_1,beta3,L1,alpha1,T,nt,Esat,lambda0);
% spec1=fftshift(abs(dt*fft(ifftshift(u1)))/sqrt(2*pi).^2);
% spec1=spec1./max(spec1);%normalized spectrum
% int1=abs(u1).^2;
%--%segment of gain fiber%--%
% prameters for gain fiber
gamma=gamma_10um; %(W*m)^-1
% gamma=0;
% beta2=0;
beta2=23*10^3; %fs^2/m, 23 fs^2/mm
beta3;
alpha=0;

127

g0; %small signal gain corresponding to a ~30dB fiber amplifier,
30dB/10*ln10=6.9, then since the energy is square of power, so it is divided
by to get 3.45
% FWHM=rand(1,100);
% for i=1:1:100
%
L_gain=i*0.02;
L_g=L_gain;
%pulse after propagating through the gain fiber
u_gain=prop(u1,g0,gamma,beta2,beta3,L_g,alpha,T,nt,Esat,lambda0);
% spec_gain =
fftshift(abs(dt*fft(ifftshift(u_gain))/sqrt(2*pi)).^2);%spectrum
% spec_gain=spec_gain./max(spec_gain);%normalized spectrum
% int_gain=abs(u_gain).^2;

%--%the second segment of passive fiber%--%
%prameters for passive fiber
% gamma2=gamma_10um;
gamma2=gamma_10um;
beta2_2=23*10^3;
beta3;
alpha2=0;
g2=0;
L2=1;
%pulse after propagating through the passive fiber
u2=prop(u_gain,g2,gamma2,beta2_2,beta3,L2,alpha2,T,nt,Esat,lambda0);
% spec2=fftshift(abs(dt*fft(ifftshift(u2))/sqrt(2*pi)).^2);
% spec2=spec2./max(spec2);%normalized spectrum
int2=abs(u2).^2;
%%%saturable absorber%%%
SA=1-1./(1+int2./max(int2));
u_sa=u2.*(SA.^0.5);
%%%spectral filter%%%
bw;%nm
BW=(2*pi*3e2)/(lambda0-bw/2)/(lambda0+bw/2)*bw/2/((2*log(2))^0.5);%spectral
filter bandwidth
SF=exp(-1/2*(w/BW).^2);%setting up spectral filter
u_sa=fftshift(fft(ifftshift(u_sa)));
u_sf=u_sa.*(SF).^0.5;
u_sf=fftshift(ifft(ifftshift(u_sf)));
u_sf=(0.2^0.5)*u_sf;
% int_sf=abs(u_sf).^2;
% spec_sf = fftshift(abs(dt*fft(ifftshift(u_sf))/sqrt(2*pi)).^2);
% u0=(0.2^0.5)*u_sf;
u0=u_sf;
end
%%input for the last run of cavity%%
int0=abs(u0).^2;
spec0=fftshift(abs(dt*fft(ifftshift(u0))/sqrt(2*pi)).^2);
% spec0=spec0./max(spec0);

128

%%fwhm of pulse%%
fwhm_t=find(int0>(max(int0)/2));
fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=fwhm_t;
% %%fwhm of spectrum%%
fwhm_f=find(spec0>(max(spec0)/2));
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=fwhm_f;
spec_2d=spec0;%initiate the 2D spec database
%%plot the evolution of pulse duration and sepctrum bandwidth%%
%--%the first segment of passive fiber%--%
%prameters for fiber
gamma1=gamma_10um;
beta2_1=23*10^3;
beta3;
alpha1=0;
g1=0;
% L1=1.5;
%pulse after propagating through the passive fiber
for L1=0.05:0.05:L_GVD
u1=prop(u0,g1,gamma1,beta2_1,beta3,L1,alpha1,T,nt,Esat,lambda0);
spec1=fftshift(abs(dt*fft(ifftshift(u1))/sqrt(2*pi)).^2);
int1=abs(u1).^2;
%%fwhm of pulse%%
fwhm_t=find(int1>(max(int1)/2));
fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=horzcat(FWHM_t,fwhm_t);
% %%fwhm of spectrum%%
fwhm_f=find(spec1>(max(spec1)/2));
% fwhm_f=3e2*2*3.14./(w(min(fwhm_f))+2*3.14*3/1060*1e2)3e2*2*3.14./(w(max(fwhm_f))+2*3.14*3/1060*1e2);
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=horzcat(FWHM_f,fwhm_f);
spec_2d=horzcat(spec_2d,spec1);%save the spectrum for each position withou
normalization
spec1=spec1./max(spec1);%normalized spectrum
end
%--%segment of gain fiber%--%
% prameters for gain fiber
gamma=gamma_10um; %(W*m)^-1
% gamma=0;
% beta2=0;
beta2=23*10^3; %fs^2/m, 23 fs^2/mm
beta3;
alpha=0;
g0; %small signal gain corresponding to a ~30dB fiber amplifier
for L_g=0.05:0.05:L_gain;
%pulse after propagating through the gain fiber
u_gain=prop(u1,g0,gamma,beta2,beta3,L_g,alpha,T,nt,Esat,lambda0);
spec_gain = fftshift(abs(dt*fft(ifftshift(u_gain))/sqrt(2*pi)).^2);%spectrum
int_gain=abs(u_gain).^2;
%%fwhm of pulse%%
fwhm_t=find(int_gain>(max(int_gain)/2));

129

fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=horzcat(FWHM_t,fwhm_t);
% %%fwhm of spectrum%%
fwhm_f=find(spec_gain>(max(spec_gain)/2));
% fwhm_f=3e2*2*3.14./(w(min(fwhm_f))+2*3.14*3/1060*1e2)3e2*2*3.14./(w(max(fwhm_f))+2*3.14*3/1060*1e2);
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=horzcat(FWHM_f,fwhm_f);
spec_2d=horzcat(spec_2d,spec_gain);%save spectrum to the 2d database
spec_gain=spec_gain./max(spec_gain);%normalized spectrum
end

%--%the second segment of passive fiber%--%
%prameters for passive fiber
% gamma2=gamma_10um;
gamma2=gamma_10um;
beta2_2=23*10^3;
beta3;
alpha2=0;
g2=0;
for L2=0.05:0.05:1;
%pulse after propagating through the passive fiber
u2=prop(u_gain,g2,gamma2,beta2_2,beta3,L2,alpha2,T,nt,Esat,lambda0);
spec2=fftshift(abs(dt*fft(ifftshift(u2))/sqrt(2*pi)).^2);
int2=abs(u2).^2;
%%fwhm of pulse%%
fwhm_t=find(int2>(max(int2)/2));
fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=horzcat(FWHM_t,fwhm_t);
% %%fwhm of spectrum%%
fwhm_f=find(spec2>(max(spec2)/2));
% fwhm_f=3e2*2*3.14./(w(min(fwhm_f))+2*3.14*3/1060*1e2)3e2*2*3.14./(w(max(fwhm_f))+2*3.14*3/1060*1e2);
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=horzcat(FWHM_f,fwhm_f);
spec_2d=horzcat(spec_2d,spec2);
spec2=spec2./max(spec2);%normalized spectrum
end
u2_w=fftshift(fft(ifftshift(u2)));
phi=log(u2_w./abs(u2_w))*(-1i);
phi=real(phi);
phi=unwrap(phi);
plot(lambda,phi);
phase=[w,phi];
phase_filename=[folder,'phase.dat'];
saveascii(phase,phase_filename);
Etot=(abs(u2).^2)*dt*10^-3;
Etot=sum(Etot)
%%%saturable absorber%%%
SA=1-1./(1+int_gain./max(int_gain));
u_sa=u2.*(SA.^0.5);
int_sa=abs(u_sa).^2;

130

Ei=(abs(u_sa).^2)*dt*10^-3;
E0=sum(Ei)
Eout=Etot-E0
spec_sa=fftshift(abs(dt*fft(ifftshift(u_sa))/sqrt(2*pi)).^2);
%%fwhm of pulse%%
fwhm_t=find(int_sa>(max(int_sa)/2));
fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=horzcat(FWHM_t,fwhm_t);
% %%fwhm of spectrum%%
fwhm_f=find(spec_sa>(max(spec_sa)/2));
% fwhm_f=3e2*2*3.14./(w(min(fwhm_f))+2*3.14*3/1060*1e2)3e2*2*3.14./(w(max(fwhm_f))+2*3.14*3/1060*1e2);
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=horzcat(FWHM_f,fwhm_f);
spec_2d=horzcat(spec_2d,spec_sa);
spec_sa=spec_sa./max(spec_sa);
%%%spectral filter%%%
bw;%nm
BW=(2*pi*3e2)/(lambda0-bw/2)/(lambda0+bw/2)*bw/2/((2*log(2))^0.5);%spectral
filter bandwidth
SF=exp(-1/2*(w/BW).^2);%setting up spectral filter
u_sa=fftshift(fft(ifftshift(u_sa)));
u_sf=u_sa.*(SF).^0.5;
u_sf=fftshift(ifft(ifftshift(u_sf)));
u_sf=(0.2^0.5)*u_sf;
int_sf=abs(u_sf).^2;
spec_sf = fftshift(abs(dt*fft(ifftshift(u_sf))/sqrt(2*pi)).^2);
%%fwhm of pulse%%
fwhm_t=find(int_sf>(max(int_sf)/2));
fwhm_t=t(max(fwhm_t))-t(min(fwhm_t));
FWHM_t=horzcat(FWHM_t,fwhm_t);
% %%fwhm of spectrum%%
fwhm_f=find(spec_sf>=(max(spec_sf)/2));
% fwhm_f=3e2*2*3.14./(w(min(fwhm_f))+2*3.14*3/1060*1e2)3e2*2*3.14./(w(max(fwhm_f))+2*3.14*3/1060*1e2);
fwhm_f=lambda(min(fwhm_f))-lambda(max(fwhm_f));
FWHM_f=horzcat(FWHM_f,fwhm_f);
spec_2d=horzcat(spec_2d,spec_sf);
spec_sf=spec_sf./max(spec_sf);%normalized spectrum
%%final fwhm bandwidth and pulse duration%%
% FWHM_t=FWHM_t(1:1,2:length(FWHM_t));
% FWHM_f=FWHM_f(1:1,2:length(FWHM_f));
u0=u_sf;
%configure filename for saving data%
% folder='E:\RESEARCH\Dantus Group\FiberLaser\simulation\051311\';
filename=strcat('Esat',num2str(Esat),'pJ_','bw',num2str(bw),'nm_Lgvd',num2str
(L_GVD),'m_Eout',num2str(Eout),'pJ_Lgain_',num2str(L_gain),'m_');
spec1_file=strcat(folder,filename,'Spec1.dat');
int1_file=strcat(folder,filename,'Int1.dat');
spec_gain_file=strcat(folder,filename,'SpecGain.dat');
int_gain_file=strcat(folder,filename,'IntGain.dat');

131

spec2_file=strcat(folder,filename,'Spec2.dat');
int2_file=strcat(folder,filename,'Int2.dat');
spec_sf_file=strcat(folder,filename,'SpecSF.dat');
int_sf_file=strcat(folder,filename,'IntSF.dat');
FWHM_f_file=strcat(folder,filename,'FWHMf.dat');
FWHM_t_file=strcat(folder,filename,'FWHMt.dat');
figure1=strcat(folder,filename,'PulseEvolution.png');
figure2=strcat(folder,filename,'FWHM.png');
spec_2d_file=strcat(folder,filename,'spec_2d.data');

%check whether it is multi-pulsing for the loop using variable GVD segment
%length
delta=max(int2);
delta=delta*0.1;
peaks=peakdet(int2,delta);
[pix val]=size(peaks);
if pix>1
% if max(FWHM_t)>12000
count_L_GVD=count_L_GVD+1
if count_L_GVD>10
%to check whether this length of GVD segment is not quite possible
%to get stable single pulsing, the tolerance is 10 cycles, if it is
%over 10, then just continute to the next length of GVD segment
L_GVD;
strcat('first segment of ',num2str(L_GVD),'m is a not stable
solution')
count_L_GVD=0;
data=[Esat bw L_GVD Eout 0];
DATA=vertcat(DATA,data);

%

%

figure(1);
subplot(421);
plot(lambda,spec1);
xlim([900 1200]);
title('1st SMF-spectrum');
xlim([950 1160]);
ylim([-0.05 1.05]);
subplot(422);
plot(t,int1);
title('1st SMF-time');
spec1=horzcat(lambda,spec1);
int1=horzcat(t,int1);
saveascii(spec1,spec1_file);
saveascii(int1,int1_file);
subplot(423);
plot(lambda,spec_gain);
xlim([900 1200]);
title('gain-spectrum');
xlim([1000 1120]);
ylim([-0.05 1.05]);
subplot(424);
plot(t,int_gain);
title('gain-time');
spec_gain=horzcat(lambda,spec_gain);

132

int_gain=horzcat(t,int_gain);
saveascii(spec_gain,spec_gain_file);
saveascii(int_gain,int_gain_file);
subplot(425);
plot(lambda,spec2);
xlim([900 1200]);
title('2nd SMF-spectrum');
xlim([1000 1120]);
ylim([-0.05 1.05]);
subplot(426);
plot(t,int2);
title('2nd SMF-time');
spec2=horzcat(lambda,spec2);
int2=horzcat(t,int2);
saveascii(spec2,spec2_file);
saveascii(int2,int2_file);
subplot(427);
plot(lambda,spec_sf);
xlim([900 1200]);
title('Spectral Filter-spectrum');
xlim([1000 1120]);
ylim([-0.05 1.05]);
xlabel('wavelength(nm)');
subplot(428);
plot(t,int_sf);
title('Spectral Filter-time');
xlabel('time(fs)');
spec_sf=horzcat(lambda,spec_sf);
int_sf=horzcat(t,int_sf);
saveascii(spec_sf,spec_sf_file);
saveascii(int_sf,int_sf_file);
print('-f1', '-dpng', figure1);
figure(2);
position=0:0.05:(L_GVD+L_gain+L2+0.1);
length(position);
subplot(121);
plot(position,FWHM_t);
ylabel('pulse duration (fs)');
xlabel('position (m)');
subplot(122);
plot(position,FWHM_f);
ylabel('bandwidth (nm)');
xlabel('position (m)');
FWHM_f=horzcat(position',FWHM_f');
FWHM_t=horzcat(position',FWHM_t');
saveascii(FWHM_f,FWHM_f_file);
saveascii(FWHM_t,FWHM_t_file);
print('-f2', '-dpng', figure2);
saveascii(spec_2d,spec_2d_file);

%

%

else
L_GVD=L_GVD-0.5;
end
else

133

L_GVD;
count_L_GVD=0;
bandwidth=max(FWHM_f);
data=[Esat bw L_GVD Eout bandwidth];
DATA=vertcat(DATA,data);
figure(1);
subplot(421);
plot(lambda,spec1);
title('1st SMF-spectrum');
xlim([1000 1130]);
ylim([-0.05 1.05]);
subplot(422);
plot(t,int1);
title('1st SMF-time');
spec1=horzcat(lambda,spec1);
int1=horzcat(t,int1);
saveascii(spec1,spec1_file);
saveascii(int1,int1_file);
subplot(423);
plot(lambda,spec_gain);
title('gain-spectrum');
xlim([1000 1130]);
ylim([-0.05 1.05]);
subplot(424);
plot(t,int_gain);
title('gain-time');
spec_gain=horzcat(lambda,spec_gain);
int_gain=horzcat(t,int_gain);
saveascii(spec_gain,spec_gain_file);
saveascii(int_gain,int_gain_file);
subplot(425);
plot(lambda,spec2);
title('2nd SMF-spectrum');
xlim([1000 1130]);
ylim([-0.05 1.05]);
subplot(426);
plot(t,int2);
title('2nd SMF-time');
spec2=horzcat(lambda,spec2);
int2=horzcat(t,int2);
saveascii(spec2,spec2_file);
saveascii(int2,int2_file);
subplot(427);
plot(lambda,spec_sf);
title('Spectral Filter-spectrum');
xlim([1000 1130]);
ylim([-0.05 1.05]);
xlabel('wavelength(nm)');
subplot(428);
plot(t,int_sf);
title('Spectral Filter-time');

134

xlabel('time(fs)');
spec_sf=horzcat(lambda,spec_sf);
int_sf=horzcat(t,int_sf);
saveascii(spec_sf,spec_sf_file);
saveascii(int_sf,int_sf_file);
print('-f1', '-dpng', figure1);
figure(2);
position=0:0.05:(L_GVD+L_gain+L2+0.1);%change step to 0.02, then the 0.04
is for two steps of saturable absorber and spectral filter
length(position);
subplot(121);
plot(position,FWHM_t);
ylabel('pulse duration (fs)');
xlabel('position (m)');
subplot(122);
plot(position,FWHM_f);
ylabel('bandwidth (nm)');
xlabel('position (m)');
FWHM_f=horzcat(position',FWHM_f');
FWHM_t=horzcat(position',FWHM_t');
saveascii(FWHM_f,FWHM_f_file);
saveascii(FWHM_t,FWHM_t_file);
print('-f2', '-dpng', figure2);

%
%
%
%
%

saveascii(spec_2d,spec_2d_file);
size(spec_2d)
size(FWHM_t)
size(position)
size(lambda)
figure(3);
spec_2d=log10(spec_2d);
contour(position,lambda,spec_2d,500);
colorbar;

end
%check whether the length of the first segment of passive fiber is over the
%desired value
if (L_GVD+0.5)>L_GVD_max
break;
else
end
end
%
%check whether it is multi-pulsing for the loop using varibale filter
%
%bandwidth
% if max(FWHM_t)>12000
%
count_bw=count_bw+1;
%
if count_bw>10
%
bw;
%
strcat('filter bandwidth of ',num2str(bw),'nm is a not stabel
solution')

135

%
else
%
bw=bw-1;
%
end
%
else
%
bw;
% end
%
% %check whether the filter bandwith is over the desired one%
if (bw+1)>bw_max
break;
else
end
end
if (Esat+100)>Esat_max
break;
else
end
end
DATA_file=strcat(folder,'data_051311.dat');
saveascii(DATA,DATA_file);

136

Appendix
Appendix-II Fiber Laser Setup and Alignment
1. Overview of the whole setup of a similariton fiber laser

Figure 83
83: Layout of the similartion fiber laser.
2. Fiber laser alignment
Step #1, splice all fiber together and use fiber combiner to couple the pump laser to gain fiber
Step #2, put fiber collimators to their mount
Step #3, put in HWP, QWP and PBS
Step #4, turn on pump laser and operate it at low power
Step #5, adjust both collimators, make their output beam at the same height and propagate a
long distance without changing height. Then, by putting a IR card or a piece of paper in front
of one of the collimators, adj
adjust
ust the other collimator to overlap its output to the beam on the
back of the card or paper from the other collimator, vice versa. Important: DO NOT
COUPLE THEIR OUTPUT INTO EACH OTHER WITHOUT GOING THROUGH THE
ISOLATOR.

137

Step #6, after the beams overlapped at the output of both collimators, put in isolator and
adjust the isolator to pass the light. Up to this step, the rough alignment is done. Most likely
the cavity is not lasing yet.
Step #7, adjust the wave plates to maximize the output power after the PB
PBS
Step #8, adjust both collimators very carefully by monitoring the output power, once enough
coupling efficiency reaches, the cavity starts lasing and the output power changes
dramatically.
Step #9, once cavity start lasing, adjust wave plates again to m
maximize
aximize the output
Step #10, adjust collimators until the output power cannot be increased
Step #11, adjust the isolator to see if the output power can be improved
Step #12, adjust collimators again to maximize the output power
Step #13, cavity alignment iss done.
3. Spectral filter

Figure 84: Layout of the spectral filter.
4. Splicing between gain fiber and SMF
SMF-II

138

Different than passive fiber-to
to-passive
passive fiber splicing, splicing between gain fiber and SMF-II
SMF
fiber needs special care. In order to remove the excess pump to avoid it mixed in the laser
output, the pump light has to be removed at the end of gain fiber. Index matching gel is
applied to the splicing joint between gain fiber and SMF
SMF-II.
II. This index matching gel has
refractive index
ex larger than cladding, which will cause the leak of the gain fiber. After the
index matching gel is applied, the splicing joint should be cover since there is strong
scattering light coming out.

Figure 85
85: Splicing between gain fiber and SMF-II

139

Appendix-III Publication List
1. B. Nie, V. V. Lozovoy, M. Dantus, “Complete pulse characterization based on multiphoton
intrapulse interference,” to be submitted.
2. B. Nie, I. Saytashev, and M. Dantus, “Towards a compact fiber laser for multimodal
imaging,” Proc. SPIE 8948, 89480A (2014).
3. B. Nie, G. Parker, V. V. Lozovoy, M. Dantus, “Energy scaling and application of Yb fiber
oscillators producing clusters of femtosecond pulses,” Optical Engineering 53, 051505
(2013).
4. A. Ryabtsev, B. Nie, M. Dantus, “45 fs optical pulses from phase corrected broadband
cascaded four wave mixing products,” Laser Phys. Lett. 10, 125109 (2013).
5. G. Rasskazov, A. Ryabtsev, D. Pestov, B. Nie, V. V. Lozovoy, M. Dantus, “Anomalous
laser-induced group velocity dispersion in fused silica,” Opt Express, 21 (15), 17695-17700
(2013).
6. B. Nie, I. Saytashev, A. Chong, H. Liu, S. N. Arkhipov, F. W. Wise, M. Dantus,
“Multimodal microscopy with sub-30 fs Yb fiber laser oscillator,” Biomed Opt Express, 3 (7),
1750-1756 (2013).
7. A. Chong, H. Liu, B. Nie, B. Bale, S. Wabnitz, W. Renninger, M. Dantus, F. W. Wise,
“Pulse generation without gain-bandwidth limitation in a laser with self-similar evolution,”
Opt Express, 20 (13), 14213 (2012).
8. B. Nie, D. Pestov, F. W. Wise, M. Dantus, “An Ultrafast Fiber Laser with Self-Similar
Evolution in the Gain Segment,” Optics and Photonics News, 22 (12), 47 (2011). ('Optics in
2011')
9. B. Nie, D. Pestov, F. W. Wise, M. Dantus, “Generation of 42-fs and 10-nJ pulses from a fiber
laser with self-similar evolution in the gain segment,” Opt Express, 19 (13), 12074-12080
(2011). (Vol. 6, Iss. 7 Virtual Journal for Biomedical Optics)

140

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141

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