Development of Ultrashort Pulse Fiber Lasers for Optical
Communication Utilizing Semiconductor Devices
by
Erik R. Thoen
B.S. Engineering, Swarthmore College, 1995
M.S. Electrical Engineering and Computer Science,
Massachusetts Institute of Technology, 1997
Submitted to the Department of Electrical Engineering and Computer
Science in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Electrical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2000
© 2000 Massachusetts Institute of Technology.
All rights reserved.
Signature of Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Electrical Engineering and Computer Science
May 19, 2000
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Erich P. Ippen
Elihu Thompson Professor of Electrical Engineering and Computer Science
Professor of Physics
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arthur C. Smith
Chairman, Committee on Graduate Students
Department of Electrical Engineering and Computer Science
Development of Ultrashort Pulse Fiber Lasers for Optical
Communication Utilizing Semiconductor Devices
by
Erik R. Thoen
Submitted to the Department of Electrical Engineering and Computer
Science in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Electrical Engineering
Abstract
The nonlinear reflectivity of semiconductor saturable absorber mirrors is investigated
with ultrafast time-resolved and time-averaged reflectivity measurements. The relative contributions of absorption bleaching and induced absorption are studied as a
function of fluence and wavelength. The impact of induced absorption on the stability
of continuous-wave mode-locking is considered theoretically. Picosecond pulses are
produced from an Er/Yb waveguide laser using a semiconductor saturable absorber
mirror, and the influence of two-photon absorption on mode-locking is studied. A
semiconductor mirror exhibiting only induced absorption is used to stabilize a GHz
repetition rate active harmonically mode-locked fiber laser, improving supermode
suppression by eliminating pulse dropouts.
Thesis Supervisor: Erich P. Ippen
Title: Elihu Thomson Professor of Electrical Engineering and Computer Science
Professor of Physics
3
4
ACKNOWLEDGMENTS
My deepest gratitude goes to Professor Erich Ippen for being a fantastic mentor, role
model, and friend during my graduate studies. He has been the ideal advisor for me; I could
not have found better. I can only aspire to his intuition, thoughtfulness, and kindness. Working with Professor Leslie Kolodziejski has been a wonderful experience because of her high
standards, honesty, and sense of humor. The close collaboration with her group has made this
thesis possible. Professor Hermann Haus has been an inspiration both for his astounding theoretical insight and endless energy. I thank all of them for supporting my research and serving
on my thesis committee.
The best part of this thesis has been working with Elisabeth Koontz. This project has
been truly collaborative, and without her expertise it never would have worked. I have developed a deep appreciation for her technical abilities, but more important I have enjoyed her
generous friendship. I thank both Elisabeth and her husband Carl for making MIT a little bit
more livable.
Many other people have participated in this research, and I appreciate their contributions. Professor Franz Kärtner provided key insights at critical junctures and has become a
wonderful friend. Patrick Langlois and Markus Joschko did a ton of fantastic pump-probe
that was critical to understanding these devices. One of the most productive students I have
ever met is Thomas Schibli, who contributed greatly to our theoretical understanding of stabilization. David Jones started me on the waveguide laser and has blazed a path for me to follow ever since Swarthmore. Joe Donnelly provided expert advice on proton bombardment
and has been a long-time friend, answering my countless questions. Igor Bilinsky’s comments prompted much of the work on TPA. Gale Petrich was always happy to help (but
always had a broken pump). Denis Barbier provided the Er-Yb waveguide, Chris Cook
deposited a number of evaporative coatings, and Libby Shaw and Tim McClure provided
expert guidance in the CMSE Analytical Shared Experimental Facilities. I leave future work
(and my office window) behind in the competent hands of Juliet Gopinath, Matt Grein, and
Dan Ripin. It has been a joy coming to know Juliet and helping her discover the wonders of
pump-probe measurements. Matt has been a enjoyably intriguing officemate for years, and
now we have even built lasers together. Finally Dan has always offered a helping hand, generated PBG results, and brought incredibly interesting lunches to the conference room.
ACKNOWLEDGEMENTS
5
I've learned from quite a number of other people who passed through the group over
the years (before and during my time). Lynne Molter has been encouraging and supportive
before and ever since I arrived at MIT. Katie Hall provided advice, equipment, lots of laughs
(often with Kristin Rauchenbach), and source of revenue in the form of a book chapter. Gadi
Lenz has been a great friend and source of advice since when I first visited the group. I'm still
thankful that Siegfried Fleischer and Dave Dougherty put up with me as a young, optimistic,
and eager grad student. Günter Steinmeyer was one of my first mentors, and I learned a great
deal from him. Lynn Nelson was always generous with her time to me. I appreciate the
friendship of others connected with the group including Luc Boivin, Steve Boppart, Brett
Bouma, Yijiang Chen, Wolfgang Drexler, Jim Foresi, Boris Golubovic, Farzana Khatri, Ed
Lim, Brent Little, Stefano Longhi, Moti Margalit, Masayuki Matsumoto, Uwe Morganer, Shu
Namiki, Gaston Tudury, and William Wong. Quite a number of current group members have
shared the struggle, including Pat (and Suky) Chou, John Fini, Leaf Jiang, Jalal Khan, J. P.
Laine, Christina Manolatou, Milos Popovic, Peter Rakich, Mike Watts, Charles Yu, and Serhii
Zhak, and the Fujimoto contingent of Seong-Ho Cho, Christian Chudoba, Ravi Ghanta, Ingmar Hartl, Pei-Lin Hsiung, Tony Ko, Xingde Li, Costas Pitris, Rohit Prasankumar, and Kathleen Saunders. I wish them all the best of luck in the rest if their time at MIT. I also
appreciate the kindness of Mrs. Ippen and Mrs. Haus over the years. Finally, thanks go to
Cindy Kopf, Donna Gale, and Mary Aldridge who all keep the group running both in terms of
administration and group parties.
I am thankful for the support of the Beinecke Brothers Memorial Scholarship and Tom
Parkinson, its wonderful administrator. I have also benefitted from the support of a Joint Services Electronics Program fellowship.
Outside of the lab I am grateful to a number of friends including Tom Murphy (a fabulous roommate for a really, really long time), James Hockenberry (godson and fellow Swattie), Thomas Ta (Banc-er), Nina Santos (who climbs tall buildings), Tonet Santos (The Man),
Kaori Shingledecker, Joel Broveleit, Bill Hoffman, Dan Smoot, and Jen Zimmer. My thanks
go out to all the people from CF, P2K (Forever!), and the whole South Dakota crew.
Finally I thank God for blessing me with wonderful parents and brothers who have
watched over me, encouraged me, and supported me in everything I do. Without them, I
would not have made it this far.
6
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
Acknowledgments
5
Table of Contents
7
List of Figures
11
Chapter 1 Introduction
19
1.1 Passively Mode-Locked Fiber Lasers............................................... 20
1.2 Active Harmonically Mode-Locked Fiber Lasers ............................ 22
1.3 Semiconductor Saturable Absorbers for Mode-Locking .................. 24
1.4 Outline of Thesis............................................................................... 25
Chapter 2 Semiconductor Saturable Absorber Mirrors
27
2.1 Structure Design ............................................................................... 27
2.2 Growth of Semiconductor Saturable Absorber Mirrors ................... 32
2.3 Optical Characterization ................................................................... 32
Chapter 3 Time-Resolved Nonlinear Response
39
3.1 Pump-Probe Measurements .............................................................. 39
3.2 Fluence Dependence ......................................................................... 40
3.3 Wavelength Dependence .................................................................. 44
3.4 Induced Absorption........................................................................... 45
TABLE OF CONTENTS
7
3.5 Hot-carrier Dynamics ....................................................................... 47
3.6 Below-Band Induced Absorption ..................................................... 48
3.7 Implications of Induced Absorption ................................................. 50
Chapter 4 Time-Averaged Nonlinear Response
53
4.1 Nonlinear Reflectivity Measurements .............................................. 53
4.2 Structural Design Effects .................................................................. 55
4.3 Resonant Coating Effects.................................................................. 58
Chapter 5 Stabilization of Passive Mode-Locking
67
5.1 Effect of Two-Photon Absorption on Reflectivity ........................... 67
5.2 Relating Time-Averaged and Time-Resolved Measurements.......... 71
5.3 Mode-Locking Stabilization ............................................................. 74
Chapter 6 Erbium-Ytterbium Waveguide Laser
79
6.1 Waveguide Laser Design .................................................................. 79
6.2 Operation Without Filtering.............................................................. 81
6.3 Absorber Operation........................................................................... 83
6.4 Operation With Filtering................................................................... 84
Chapter 7 Stabilization of Harmonic Mode-Locking
91
7.1 Stabilizing Harmonically Mode-Locked Lasers ............................... 91
7.2 Laser Design ..................................................................................... 92
7.3 Operation Without TPA.................................................................... 94
7.4 Operation With TPA ......................................................................... 96
7.5 Advantages of TPA........................................................................... 99
Chapter 8 Conclusions and Future Work
101
8.1 Conclusions....................................................................................... 101
8.2 Future Work ...................................................................................... 102
Appendix A Models for Nonlinear Reflectivity
105
A.1 Slow Saturable Absorber ................................................................. 105
8
TABLE OF CONTENTS
A.2 Fast Saturable Absorber ................................................................... 107
A.3 Slow Saturable Absorber with Spatial Effects................................. 110
A.4 Fast Saturable Absorber with Spatial Effects .................................. 112
A.5 Two-Photon Absorption................................................................... 113
A.6 Time-Averaged Reflectivity ............................................................ 115
Appendix B Passively Mode-Locked Fiber Laser
117
B.1 Dispersion Management................................................................... 117
B.2 Polarization Sidebands ..................................................................... 118
B.3 Stabilization with Two-Photon Absorption ..................................... 121
B.4 Absorber Lifetime Reduction........................................................... 123
Appendix C Actively Mode-Locked Fiber Laser
127
References
131
TABLE OF CONTENTS
9
10
TABLE OF CONTENTS
LIST OF FIGURES
Figure 2.1 ................................................................................................................ 28
Schematic of an anti-reflection coated semiconductor saturable absorber mirror
containing two quantum wells. The refractive index and magnitude squared of
the electric field (λ=1.54 mm) are plotted as a function of distance from the
GaAs substrate-DBR interface.
Figure 2.2 ................................................................................................................ 30
Schematic of an anti-reflection coated semiconductor saturable absorber mirror
containing four quantum wells. The refractive index and magnitude squared of
the electric field (λ=1.54 mm) are plotted as a function of distance from the
GaAs substrate-DBR interface.
Figure 2.3 ................................................................................................................ 31
Schematic of a resonantly coated semiconductor saturable absorber mirror containing four quantum wells. The refractive index and magnitude squared of the
electric field (λ=1.54 mm) are plotted as a function of distance from the GaAs
substrate-DBR interface.
Figure 2.4 ................................................................................................................ 31
Schematic of an anti-reflection coated semiconductor saturable absorber mirror
containing a quasi-bulk absorption region. The refractive index and magnitude
squared of the electric field (λ=1.54 mm) are plotted as a function of distance
from the GaAs substrate-DBR interface.
Figure 2.5 ................................................................................................................ 33
Transmission as a function of wavelength for a two quantum well structure deposited on GaAs.
LIST OF FIGURES
11
Figure 2.6 ................................................................................................................ 34
Transmission as a function of wavelength for various quantum well structures
deposited on GaAs. For comparison, the room temperature photoluminescence
of each structure is also plotted in arbitrary intensity units, with an arrow indicating the peak
Figure 2.7 ................................................................................................................ 35
Transmission as a function of wavelength for a typical GaAs/AlAs DBR. For
comparison the normalized photoluminescence intensity of a quantum well
structure deposited on GaAs is plotted.
Figure 3.1 ................................................................................................................ 41
Differential reflectivity measurements as a function of excitation fluence at 1.5
µm. At low fluence, the bleaching dynamics of the QWs are dominant. At
higher fluences, TPA and FCA develop and eventually dominate the ultrafast
dynamics.
Figure 3.2 ................................................................................................................ 43
Differential reflectivity measurements as a function of excitation fluence at 1.54
µm. The change of reflection ∆R/R0 = (R - R0)/R0 (R, R0: reflection with and
without pump, respectively) is plotted versus delay between pump and probe
pulses. The autocorrelation (AC) depicts the temporal resolution.
Figure 3.3 ................................................................................................................ 44
Differential reflectivity measurements under high fluence excitation as a function of wavelength. The wavelength is tuned from above to below the QW
bandgap (~1.53 µm). Below the QW bandgap, TPA and FCA in InP are dominant.
Figure 3.4 ................................................................................................................ 45
Differential reflectivity measurements for a pump fluence of 250 µJ/cm2 with
the probe fluence varied as indicated.
Figure 3.5 ................................................................................................................ 46
Differential reflectivity measurements at a pump fluence of 320 µJ/cm2 for low
(solid curve) and high (dashed curve) probe fluence, and the difference between
the two (dash-dotted curve).
Figure 3.6 ................................................................................................................ 48
Differential reflectivity measurements with excitation by Ti:sapphire pulses for
a saturable absorber mirror with low (solid curve) and high (dashed curve)
probe fluence exhibits a 2.8 ps time constant. Dynamics of an identical structure
without QWs (high probe fluence, dotted curve) shows no fast time constant.
12
LIST OF FIGURES
Figure 3.7 ................................................................................................................ 49
Differential reflectivity measurements under high fluence excitation at 1.56 µm
for a saturable absorber mirror structure in which absorption bleaching is negligible (solid curve). The ~5 ps decay for FCA is attributed to carrier diffusion
across the InP half-wave layer. The dashed curve shows the differential absorption of a ~350 µm thick InP substrate in which a standing-wave pattern is not
formed. Inset: linear and quadratic fluence dependence of the TPA and FCA
components respectively, in the saturable absorber mirror structure.
Figure 4.1 ................................................................................................................ 54
Transmitted power has a function of knife-edge position in the beam after passing through a focusing lens. The fit to an error function provides the Gaussian
width.
Figure 4.2 ................................................................................................................ 55
The beam waist as a function of distance from a focusing lens as determined
from several knife-edge measurements. The fit of the waist as a function of position gives the focused spot size
Figure 4.3 ................................................................................................................ 56
Measured reflectivity as a function of fluence at 1.542 microns for an antireflection coated sample similar to the structure of Figure 2.2 except containing six
quantum wells. The solid line is the result of a fit to a slow saturable absorber
model with the coefficients indicated.
Figure 4.4 ................................................................................................................ 57
Measured reflectivity as a function of fluence at 1.542 microns for the antireflection coated structure of Figure 2.4. The solid line is the result of a fit to a
slow saturable absorber model with the coefficients indicated.
Figure 4.5 ................................................................................................................ 59
Measured reflectivity as a function of fluence at 1.542 microns for the antireflection coated structure of Figure 2.2. The solid line is the result of a fit to a
slow saturable absorber model with the coefficients indicated.
Figure 4.6 ................................................................................................................ 60
The reflectivity as a function of wavelength of the resonantly coated structure
of Figure 2.3 (solid line) and a DBR mirror (dashed line) measured with a Fourier transform infrared spectrometer.
Figure 4.7 ................................................................................................................ 61
The total change in reflection as a function of wavelength for the structure of
Figure 2.3. The measurement was performed with a single 20 cm lens. The solid line is a Gaussian fit to the data.
LIST OF FIGURES
13
Figure 4.8 ................................................................................................................ 62
Measured reflectivity as a function of fluence at 1.5 microns for the resonantly
coated structure of Figure 2.3. The solid line is the result of a fit to a slow saturable absorber model with the coefficients indicated.
Figure 4.9 ................................................................................................................ 63
Measured reflectivity as a function of fluence at 1.53 microns for the resonantly
coated structure of Figure 2.3. The solid line is the result of a fit to a slow saturable absorber model with the coefficients indicated.
Figure 4.10 .............................................................................................................. 64
Predicted variation in the saturable loss as a function of wavelength for the
structure of Figure 2.3. The data points are taken from Figures 4.8 and 4.9 and
extrapolated from Figure 4.8, and the solid line is a Gaussian fit.
Figure 4.11 .............................................................................................................. 64
Predicted variation in the saturation fluence as a function of wavelength for the
structure of Figure 2.3. The data points are taken from Figures 4.8 and 4.9 and
extrapolated from Figure 4.8, and the solid line is a Gaussian fit.
Figure 4.12 .............................................................................................................. 65
Predicted variation in the AStruct parameter as a function of wavelength for the
structure of Figure 2.3. The data points are taken from Figures 4.8 and 4.9 and
extrapolated from Figure 4.8, and the solid line is a Gaussian fit.
Figure 5.1 ................................................................................................................ 69
Saturation fluence measurements at 1.5 microns for the antireflection coated
structure of Figure 2.1. The solid line is a fit using the model described in Section 5.3. The inset depicts the time-resolved differential reflectivity measured
at ~80 µJ/cm2.
Figure 5.2 ................................................................................................................ 70
Saturation fluence measurements 1.5 microns for the antireflection coated
structure of Figure 2.3. The solid line and dashed lines are calculated using the
model described in Section 5.3. The insets depict the time-resolved differential
reflectivity measured at (i) ~10 µJ/cm2 and (ii) ~200 µJ/cm2.
Figure 5.3 ................................................................................................................ 72
The change in reflectivity as a function of fluence at 1.54 microns for the antireflection coated sample of Figure 2.2 as obtained from pump-probe measurements at zero delay. (Open squares - low fluence probe, filled circles - high
fluence probe, filled triangles - subtracted)
Figure 5.4 ................................................................................................................ 73
Measured reflectivity as a function of fluence at 1.54 microns for the antireflection coated sample of Figure 2.2. The solid line is the result of a fit to a slow
saturable absorber model.
14
LIST OF FIGURES
Figure 5.5 ................................................................................................................ 74
The change in reflectivity as a function of fluence at 1.54 microns for the antireflection coated sample of Figure 2.2 as obtained from pump-probe measurements at a delay of 2.5 ps. (Open squares - low fluence probe, filled circles high fluence probe, filled triangles - subtracted)
Figure 5.6 ................................................................................................................ 76
Effect of optical limiting on mode-locking stability. In the presence of TPA,
following a perturbation the pulse envelope returns to a CWML state (dashed
line). In the absence of TPA, following a perturbation the pulse envelope enters
a QSML state (solid line).
Figure 5.7 ................................................................................................................ 77
Calculated stability contours for a fast saturable absorber mode-locked laser.
QSML is present in the regions labeled "unstable". CWML is present in the regions labeled "stable". The area within the solid line is the instability region
without TPA included in the model. The area within the dashed line is the instability region with TPA included in the model.
Figure 6.1 ................................................................................................................ 80
Schematic of the laser cavity based on an Er-Yb planar waveguide. The dotted
box surrounds the filtering elements.
Figure 6.2 ................................................................................................................ 82
Second harmonic generation autocorrelation of the pulses obtained with the
cavity configuration of Figure 6.1 without filtering (data – solid, sech fit –
dashed).
Figure 6.3 ................................................................................................................ 82
Optical spectrum centered at 1534 nm of the pulses obtained with the cavity
configuration of Figure 6.1 without filtering.
Figure 6.4 ................................................................................................................ 84
The semiconductor saturable absorber mirror reflectivity measured as a function of incident energy fluence with 150 fs pulses at 1530 nm (dots). The solid
lines are the saturable absorption (SA) and two-photon absorption (TPA 150 fs)
components fit to the measured data. The dotted (TPA 9 ps) and dashed (TPA
1 ps) lines are calculated TPA components. The shaded region depicts the range
of fluences where CWML was obtained with 9.8 ps pulses.
Figure 6.5 ................................................................................................................
Fluorescence of erbium-doped fiber as a function of pump power.
85
Figure 6.6 ................................................................................................................ 85
Fluorescence of the erbium-ytterbium waveguide as a function of pump power.
LIST OF FIGURES
15
Figure 6.7 ................................................................................................................ 87
Second harmonic generation autocorrelation of the pulses obtained with the
cavity configuration of Figure 6.1 with filtering (data – filled circles, sech fit –
solid line).
Figure 6.8 ................................................................................................................ 87
Optical spectrum centered at 1545 nm of the pulses obtained with the cavity
configuration of Figure 6.1 with filtering.
Figure 6.9 ................................................................................................................ 88
Optical spectrum of tunable pulses obtained at 100 MHz in the cavity configuration of Figure 6.1 by adjusting the bandedge filter.
Figure 7.1 ................................................................................................................ 93
Schematic of an anti-reflection coated two-photon absorption mirror containing
an ~5.2 micron thick InP layer. The refractive index and magnitude squared of
the electric field (λ=1.54 mm) are plotted as a function of distance from the
GaAs substrate-DBR interface.
Figure 7.2 ................................................................................................................ 93
Schematic of actively mode-locked fiber laser. Wavelength division multiplexer (WDM), Erbium-doped fiber (EDF).
Figure 7.3 ................................................................................................................ 94
Second harmonic generation autocorrelation of the pulses obtained without focusing on TPA mirror.
Figure 7.4 ................................................................................................................
Optical spectrum of the pulses obtained without focusing on TPA mirror.
95
Figure 7.5 ................................................................................................................ 95
Rf spectrum of output pulses obtained without focusing on TPA mirror. Resolution bandwidth of 30 kHz.
Figure 7.6 ................................................................................................................ 96
Digitizing oscilloscope trace obtained without focusing on TPA mirror exhibiting dropouts of output pulses.
Figure 7.7 ................................................................................................................ 97
Second harmonic generation autocorrelation of the pulses obtained with focusing on TPA mirror.
Figure 7.8 ................................................................................................................
Optical spectrum of the pulses obtained with focusing on TPA mirror.
97
Figure 7.9 ................................................................................................................ 98
Rf spectrum of output pulses obtained with focusing on TPA mirror. Resolution
bandwidth of 30 kHz.
16
LIST OF FIGURES
Figure 7.10 .............................................................................................................. 99
Digitizing oscilloscope trace obtained with focusing on TPA mirror exhibiting
no pulse dropouts is shown in the upper trace. The detector and instrument
noise background in the absence of the optical input is shown in the lower trace.
Figure B.1 ............................................................................................................... 118
Schematic of fiber laser. Wavelength Division Multiplexer (WDM), Erbium
Doped Fiber (EDF), Single-Mode Fiber (SMF).
Figure B.2 ............................................................................................................... 119
Optical spectrum obtained for anomalous dispersion operation.
Figure B.3 ............................................................................................................... 120
Optical spectrum obtained for slightly normal dispersion operation.
Figure B.4 ............................................................................................................... 121
Optical spectrum for various intracavity quarter-wave-plate settings. From top
to bottom the wave-plate is varied in five degree increments.
Figure B.5 ............................................................................................................... 122
Optical spectrum through a polarizing beam splitter with various external-cavity half-wave-plate settings. From top to bottom the wave-plate is varied from
45 to 0 degrees.
Figure B.6 ............................................................................................................... 123
Spectral width versus pulse energy for a soliton fiber laser mode-locked with
saturable absorber mirrors having different thicknesses of InP.
Figure B.7 ............................................................................................................... 124
Spectral width and number of pulses versus pump current for a soliton fiber laser mode-locked with a saturable absorber mirror.
Figure B.8 ............................................................................................................... 125
Autocorrelations of a bunched multiple pulse state at several pump currents.
From bottom to top the pump current is 390, 475, 550, and 650 mA.
Figure B.9 ............................................................................................................... 126
Autocorrelation of a bunched multiple pulse state with an exponential fit of the
long background envelope.
Figure C.1 ............................................................................................................... 128
Schematic of active harmonically mode-locked linear laser. Wavelength Division Multiplexer (WDM).
Figure C.2 ............................................................................................................... 129
Low frequency operation. Optical spectrum (Top) and autocorrelation (Bottom).
LIST OF FIGURES
17
Figure C.3 ............................................................................................................... 130
High frequency operation. Optical spectrum (Top) and autocorrelation (Bottom).
18
LIST OF FIGURES
CHAPTER 1
INTRODUCTION
The explosive growth of the Internet has recently driven the development of optical
communications. To meet the increasing bandwidth demands, both wavelength-division multiplexing (WDM) [14, 81] and time-domain multiplexing (TDM) [13, 5] are being investigated with ever increasing numbers of channels and higher bit rates. Fiber lasers play an
important role in the development of telecommunications systems. Active harmonically
mode-locked fiber lasers have been developed at very high repetition rates and have been used
as pulse sources in high bit-rate system demonstrations in a research setting [25]. Passively
mode-locked fiber lasers exhibiting sub-picosecond pulses have been developed, and the corresponding broad spectrum has been used for a variety of applications including spectral slicing [8], optical coherence tomography [9], and solid-state amplifier seeding [75].
This thesis focuses on the use of semiconductor structures to improve the characteristics of passively and actively mode-locked fiber and waveguide lasers. Obtaining self-starting
mode-locking, suppressing Q-switched mode-locking, and attaining high repetition rates can
all be difficult in a passively mode-locked fiber laser. In active harmonically mode-locked
fiber lasers, stabilization against energy fluctuations is a significant challenge. Nonlinear
semiconductor mirrors offer potential solutions for a number of the problems in passively and
actively mode-locked fiber lasers.
INTRODUCTION
19
1.1
Passively Mode-Locked Fiber Lasers
Three primary methods have been used to passively mode-locked fiber lasers. Nonlinear polarization rotation, also known as polarization additive pulse mode-locking (P-APM),
has been used to generate 63 fs pulses, the shortest from an Er-doped fiber laser [111]. PAPM is based on the intensity-dependent rotation of the polarization state in optical fiber [46,
80, 106]. The polarization state of the peak of the pulse will change differently than the wings
of the pulse, so the transmission of a pulse through a polarizer can be adjusted with waveplates to eliminate the wings of a pulse. P-APM acts as a fast saturable absorber because the
Kerr effect in optical fiber is virtually instantaneous. Nonlinear polarization rotation has been
used to mode-lock a wide range of fiber lasers to produce femtosecond pulses [32, 108, 109,
110, 88, 74, 89].
The nonlinear amplifying loop mirror (NALM) is a second technique for mode-locking fiber lasers which is also based on the Kerr effect in fiber [31, 94, 28]. The NALM is a
fiber Sagnac interferometer with the gain medium placed asymmetrically in the loop.
Because of the asymmetry, a pulse traveling in one direction undergoes greater polarization
rotation than a pulse traveling in the reverse direction. With proper biasing of the incident
polarization, the NALM transmits high-intensity while reflecting low intensity, producing a
fast saturable absorber. Pulses as short as 98 femtoseconds have been generated in an Erdoped fiber laser with an NALM [85].
Semiconductor saturable absorbers have also been used to either initiate other pulse
shaping mechanisms (such as P-APM) or to serve as the primary mode-locking mechanism in
fiber lasers. A semiconductor absorber was used in a fiber laser for the first time in 1991 in a
transmission geometry [129]. Later a linear cavity incorporating a semiconductor saturable
absorber deposited on a semiconductor Bragg reflector produced sub-picosecond pulses [76,
77]. Because a semiconductor saturable absorber can insure self-starting, combining a semiconductor saturable absorber with P-APM has been used to generate 330 fs pulses [47].
Finally, mode-locking with a semiconductor saturable absorber does not require the long
interaction lengths to produce polarization rotation, so shorter cavities are possible. Using a
semiconductor Bragg reflector in a linear Er/Yb fiber laser, fundamental repetition rates as
high as 290 MHz have been demonstrated with 350 fs pulses [16].
One of the major difficulties with passively mode-locked lasers is self-starting of
mode-locking. Simple conditions for mode-locking start-up have been derived, which depend
on the gain cross-section [50] or the linewidth of the first beat note of the power spectrum
[69]. Spurious reflections in a cavity [45] and a standing-wave in the gain medium [70] can
20
CHAPTER 1
both prevent self-starting of mode-locking. To overcome these difficulties, ring cavities
instead of standing-wave cavities have been implemented [107], especially for fiber lasers
mode-locked with only nonlinear polarization rotation or an NALM. However semiconductor
saturable absorbers have been used successfully in linear cavities, either as the primary modelocking mechanism [16] or as a self-starting mechanism [47]. Semiconductor saturable
absorbers offer a great potential for overcoming self-starting difficulties in fiber lasers
because their properties can be tailored to the cavity.
A second obstacle to attaining a continuous-wave mode-locked (CWML) laser is the
tendency for many lasers to Q-switch at the relaxation oscillation frequency. The stability
condition for CWML over Q-switching has been derived analytically in a perturbational analysis [43]. The theory has been expanded to include the stability of CWML against Q-switching mode-locking (QSML) [QSML consists of a burst of ultrashort pulses with a Q-switching
envelope.] [60]. Stability in the presence of soliton-shaping effects has been derived [87].
Stabilization against QSML with a semiconductor saturable absorber has also been considered
for both the picosecond and femtosecond regime [48]. In terms of laser parameters, preventing Q-switching instabilities is more difficult for shorter cavities and longer upper-state lifetimes. Semiconductor saturable absorbers have been used quite successfully to mode-lock
even lasers with long upper-state lifetimes, because a number of parameters can be controlled
[63, 64, 16]. The long upper-state lifetime of erbium (~10 ms [95]) makes Q-switching an
acute problem in fiber lasers, so the proper design of a semiconductor saturable absorber mirror is particularly important.
The use of a reverse saturable absorber has also been proposed to suppress Q-switching in lasers. Originally, a reverse saturable absorber based on excited-state absorption was
suggested as an intensity limiter for preventing Q-switching [41]. Later the effect of a time
constant in the reverse saturable absorber was studied in fast and slow regimes [11]. Experimentally, two-photon absorption (TPA) in a GaAs platelet was used to stabilize the output of a
Nd:YAG laser [23]. The same technique was used to stabilize an actively mode-locked
Nd:YAG laser [79]. In the context of fiber laser gain media exhibiting a long upper-state lifetime, intensity-limiting mechanisms could be quite useful for stabilization against Q-switching.
A third major difficulty in designing fiber lasers is that the doping density of erbium in
silica-based fibers is typically quite low, requiring very long lengths (meters) of fiber for sufficient gain in a laser [84]. While solid-state lasers have been mode-locked at fundamental
repetition rates in the GHz regime [68], fiber lasers have not been demonstrated with fundamental repetition rates above a few hundred MHz because of the long lengths of doped fiber
INTRODUCTION
21
required [16]. Recently erbium-doped planar waveguide amplifiers have been introduced
with significantly higher doping densities than silica fiber [90]. A 4.5 cm Er-Yb phosphate
glass waveguide has been used as an amplifier in system experiments at 10 Gb/s with 16.5 dB
gain [22]. A similar waveguide was operated as a continuous-wave laser producing output
powers greater than 2 mW [125]. With the incorporation of a modulator into the cavity, a Qswitched laser was demonstrated with kW peak powers [126]. However, none of these
designs have taken advantage of the short length of Er-Yb waveguides to produce a high repetition rate fundamentally mode-locked laser.
A number of obstacles remain in the development of advanced passively mode-locked
fiber lasers, but potential solutions also exist. Semiconductor saturable absorber mirrors are
one solution to self-starting difficulties in fiber lasers. Properly designed semiconductor
structures might also be useful for suppressing Q-switching instabilities in long upper-state
lifetime lasers. Finally Er-Yb waveguides offer one method for producing significantly
shorter fundamental cavity round-trip times, and when combined with a semiconductor saturable absorber, waveguide lasers could produce ultrashort pulses, high repetition-rate sources.
1.2
Active Harmonically Mode-Locked Fiber Lasers
One method to attain very high repetition rates (>GHz) is to operate a laser harmonically, such that multiple pulses are present in the cavity at one time. A high-speed electrooptic modulator is driven at a harmonic of the round-trip time of the cavity, creating multiple
pulse slots in the cavity. With this active mode-locking technique, the repetition rate is no
longer dictated by the fundamental length of the cavity. Such a laser has the additional advantage that the repetition rate is controlled by an electronic frequency synthesizer, so the pulses
can be "locked-to-clock," an important functionality in a communications system. This technique has been applied to fiber lasers to generate 6 ps pulses at 40 GHz [93]. Improvements
have been made to generate sub-picosecond pulses tunable across the Er bandwidth at 40 GHz
[128], and the output could be scaled to 160 Gb/s [30]. The harmonic mode-locking technique has been used quite successfully to produce fiber laser sources that are useful in a
research setting.
One significant problem for harmonically mode-locked lasers is suppressing pulse-topulse energy fluctuations. Because the upper-state lifetime of erbium is quite slow (~10 milliseconds), the gain does not respond rapidly enough to equalize pulses energies. By Fourier
transform, when pulse energy fluctuations occur cavity frequencies other than the desired har-
22
CHAPTER 1
monic and its integer multiples are excited. A group of equally spaced axial modes in the frequency domain is referred to as a supermode [103]. In the presence of fluctuations,
supermodes other than integer multiples of the harmonic frequency are excited. The degree of
fluctuations can be quantified by the supermode suppression in the radio frequency spectrum
of the pulse train. Supermode suppression >50 dB is generally considered sufficient for communications applications.
One of the first techniques used to stabilize a harmonically mode-locked fiber laser
involved controlling the cavity length. The length of the cavity was adjusted by stretching
fiber with a PZT to match the phase of the cavity round-trip time to that of the oscillator driving the electro-optic modulator [100]. Later modifications of this technique involved dithering the cavity length [101] or detecting noise at frequencies other than the mode-locked
harmonic [102]. Given the thermal sensitivity of optical fiber, the fundamental cavity roundtrip time will drift with temperature variations, so some type of cavity length stabilization is
required for any harmonically mode-locked fiber laser to be stable over a long period of time.
However, techniques used to stabilize supermodes with cavity-length control require more
complicated signal processing [102] than simply matching the phase of the oscillator and output pulses.
A second technique to suppress supermodes involves introducing an additional cavity
into the laser (a ring sub-cavity or Fabry Perot) with a free spectral range matching the repetition rate [127, 42]. In the frequency domain, the filter prevents the excitation of modes other
than the harmonic at which the laser is operated. In the time domain this corresponds to
equalizing energy across all the pulses. The primary difficulty with this technique is that the
cavity length and sub-cavity free spectral range must be stabilized to match one another. In a
practical system the cavity length would be matched to the modulation frequency and the subcavity would also be matched to that frequency. With both the length control technique and
the sub-cavity technique, active stabilization is required, so passive solutions would clearly
offer advantages.
A third method for stabilizing harmonically mode-locked lasers employs polarization
rotation to produce a fast intensity-dependent loss. As described in the previous section,
polarization rotation in a fiber is intensity dependent, so when combined with polarization
control and a polarizer, an artificial fast saturable absorber can be created. However with
proper adjustment of the polarization, intensity-dependent limiting can also be produced,
which is referred to as additive-pulse limiting (APL) [26]. The technique was used successfully to produce a stable 1-GHz harmonically mode-locked laser. However because the technique is dependent on polarization rotation, thermal drift of the fiber inducing linear
INTRODUCTION
23
polarization rotation leads to bias drift, therefore foiling APL. A passive technique not sensitive to environmental conditions is more desirable.
An additional passive technique for supermode suppression employs self-phase modulation and spectral filtering, which creates peak intensity limiting similar to APL [86]. By virtue of the nonlinearity in optical fiber, as a pulse propagates its spectrum is broadened in
proportion to its peak intensity by self-phase modulation. If a spectral filter is introduced after
such broadening, then a higher peak intensity pulse exhibiting a broader spectrum is filtered
more strongly then a lower peak intensity pulse exhibiting a narrower spectrum. This technique has been used successfully to suppress supermodes by >50 dB in a 10 GHz fiber laser
[86]. However, because the energy is distributed among a large number of pulses in a harmonically mode-locked fiber laser, the peak intensity of individual pulses is relatively low. To
obtain the required spectral broadening for supermode suppression the interaction length must
be enhanced, requiring a cavity hundreds of meters long. A further limitation of this technique is that it only works in the anomalous dispersion regime, limiting its applicability to
soliton lasers [112].
All of the techniques presented for stabilizing harmonically mode-locked fiber lasers
exhibit some disadvantages. The active techniques require significant external circuitry. For
passive techniques, APL is environmentally unstable and self-phase modulation (SPM) with
filtering requires very long cavities and anomalous dispersion. A semiconductor structure
which could provide a fast intensity-dependent loss with a small footprint would be particularly attractive for stabilizing supermodes.
1.3
Semiconductor Saturable Absorbers for Mode-Locking
Semiconductor saturable absorber structures offer a potential solution to a number of
the problems encountered in both passively and actively mode-locked fiber lasers. Semiconductor nonlinearities were used to passively mode-lock a semiconductor laser for the first time
20 years ago [49]. Later, but still more than a decade ago, a semiconductor saturable absorber
was first applied to mode-locking a solid-state color-center laser [51]. However in both of
these cases the upper state lifetime was short, reducing the tendency to Q-switch. A solidstate laser with a long upper-state lifetime was mode-locked for the first time with a semiconductor saturable absorber mirror in a coupled cavity in 1990 [62]. An intracavity semiconductor saturable absorber, referred to as an antiresonant Fabry-Perot saturable absorber (AFPSA), was employed to CW mode-lock a long upper-state lifetime Nd:YLF solid-state laser
24
CHAPTER 1
shortly afterwards [63]. A semiconductor saturable absorber mirror, termed a saturable Bragg
reflector (SBR), which requires no growth post-processing has also been used as an intracavity saturable absorber in a variety of solid-state lasers [122]. Some of the shortest pulses ever
attained (<6 fs, in the two-cycle regime) were produced from a Kerr-lens mode-locked Ti:sapphire with an intracavity semiconductor saturable absorber mirror [105]. Variations on all of
these designs have been used to mode-locked a wide range of solid-state and fiber lasers [64,
65, 16].
For fiber lasers in particular, semiconductor saturable absorber mirrors offer a number
of advantages. A semiconductor saturable absorber can be used to obtain repeatable self-starting in a fiber laser, even when another mechanism may be used for pulse shaping. The properties of a semiconductor saturable absorber can be designed to enhance the stability of a fiber
laser against QSML. As a mode-locking mechanism, a semiconductor saturable absorber
does not require the interaction length of nonlinear polarization rotation or an NALM, so it is
usable with very short cavities. For actively mode-locked systems, semiconductor structures
may be used to provide optical limiting to stabilize against unwanted supermodes. Therefore
leveraging on the established base of semiconductor saturable absorber mirror technology,
this thesis investigates a number of new applications of semiconductor structures to fiber and
waveguide lasers.
1.4
Outline of Thesis
The thesis is organized as follows. In Chapter 2 the basic design of the semiconductor
saturable absorber mirrors used throughout this thesis is discussed. A short description of the
gas source molecular been epitaxial growth technique used to create the structures follows.
Finally the basic optical techniques used to initially characterize the properties of the semiconductor layers are discussed.
Chapter 3 presents an investigation of the time-resolved nonlinear response of the
semiconductor structures. Pump-probe measurements as a function of fluence and wavelength are shown, and the corresponding ultrafast nonlinear dynamics are discussed. More
detailed studies of induced absorption both above- and below-band are presented along with
two-color experiments used to investigate hot-carrier dynamics. The implications of induced
absorption on mode-locking of lasers are discussed briefly.
The measurements of the time-averaged nonlinear response of the semiconductor saturable absorber mirrors are discussed in Chapter 4. The details of the technique used to mea-
INTRODUCTION
25
sure the nonlinear reflectivity are presented along with measurements of a wide range of
structures. The impact of structural design and post-growth optical coatings on the nonlinear
reflectivity is discussed in detail for a number of cases.
In Chapter 5 the impact of induced absorption on mode-locking is discussed. Initially
the role of two-photon absorption on the nonlinear reflectivity of the various structures is
investigated. The time-averaged and time-resolved reflectivity are compared to clarify the
physical mechanisms responsible for changes in reflectivity. Finally the theoretical impact of
induced absorption on mode-locking stability is presented.
The results of mode-locking an Er-Yb waveguide laser using a semiconductor saturable absorber mirror are presented in Chapter 6. The design and operation of the laser without
an intracavity filtering element is presented, and the effect on mode-locking of two-photon
absorption in the absorber structure is studied. Intracavity filtering is investigated and shown
to produce significantly shorter pulses.
Stabilization of an active harmonically mode-locked fiber laser with a semiconductor
mirror is described in Chapter 7. The design of the laser and operation without two-photon
absorption is studied initially. Then the stabilizing effect of a two-photon absorbing semiconductor mirror is investigated, and the advantages of using two-photon absorption over other
stabilizing techniques are discussed.
Appendix A outlines the mathematical details of the various models for the nonlinear
reflectivity used throughout the thesis. Cases of both slow and fast saturable absorbers are
considered, and the impact of a Gaussian beam distribution is considered.
Results from a passively mode-locked fiber laser are discussed in Appendix B. Issues
of dispersion management, polarization sidebands, stabilization with two-photon absorption,
and lifetime reduction are investigated.
Appendix C presents preliminary results of active harmonic mode-locking of a fiber
laser in a linear geometry using a travelling-wave phase modulator.
Finally Chapter 8 presents the conclusions of the thesis, and outlines various areas for
future work.
26
CHAPTER 1
CHAPTER 2
SEMICONDUCTOR SATURABLE ABSORBER MIRRORS
In this chapter1 the results are presented of studies performed on a variety of semiconductor saturable absorber mirrors designed for different applications. Depending on the application, variations in the design of the structure including placement of the absorbing region,
amount of absorbing material, and optical coatings were investigated. The design, growth,
and basic optical characterization of the devices is discussed here.
2.1
Structure Design
All of the semiconductor structures considered in this thesis consist of a distributed
Bragg reflector (DBR) with additional top layers producing saturable absorption or induced
absorption. The structures are tailored to the requirements of particular lasers. Depending on
the design of the absorbing layers and additional coatings, the amount of saturable loss, the
amount of induced absorption, the amount of non-saturable loss, the wavelength dependence,
and the saturation fluence can be controlled.
Initial design of a structure involves calculating the electric field profile within the
structure using matrix and interface techniques [7]. One example of such a calculation is
shown in Figure 2.1, where the magnitude of the electric field as a function of position is plotted on the right axis. On the left axis the refractive index of the various material layers is plot1
Many of the results of this chapter were attained in collaboration with Elisabeth M. Koontz, Prof. Franz
X. Kärtner, and Prof. Leslie Kolodziejski. Optical coatings were provided by Chris Cook of Lincoln Laboratory and assistance with the spectrophotometer was provided by Elisabeth L. Shaw of the Analytical
Shared Experimental Facilities, MIT Center for Materials Science and Engineering.
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
27
Figure 2.1
Schematic of an anti-reflection coated semiconductor saturable absorber mirror containing two
quantum wells. The refractive index and magnitude squared of the electric field (λ=1.54 µm)
are plotted as a function of distance from the GaAs substrate-DBR interface.
ted as a function of position. This structure is similar to that demonstrated by other research
groups for mode-locking solid-state lasers [15]. From left to right in the figure, the last few
pairs of the 22 pair GaAs/AlAs λ/4 DBR stack used to produce a high reflector centered at
~1.55 microns are shown. Next is a λ/2 layer which contains the saturable absorbing material.
In the case of Figure 2.1 this layer consists of a λ/2 layer of InP with two InGaAs quantum
wells located ~15 nm from the top surface of the layer. The last layer is a λ/4 thickness of
Al2O3 which acts as an antireflection coating.
In Figure 2.1 the electric field magnitude squared is depicted; to obtain the intensity,
the electric field magnitude squared would be multiplied by a term proportional to the refractive index, which would lead to discontinuities in the plot of the intensity. Inspection of the
field may be somewhat misleading because of the large index difference between air, n=1, and
the semiconductor material, n~3. In Figure 2.1 the field magnitude in the InP region is much
smaller than external to the structure. However when appropriately multiplied by factors proportional to the refracted index, the intensity in the structure is equal to the external intensity,
because of the antireflection coating.
28
CHAPTER 2
The electric field in Figure 2.1 is calculated for the single wavelength of 1.54 microns.
Because all of the layers of the structure are designed for a particular center wavelength, the
positions of the peaks and nulls of the electric field will change with wavelength. In saturable
absorber design, the most critical information that the electric field calculation provides is the
overlap between the field and the absorbing region. For the structure shown in Figure 2.1, the
absorbing quantum wells are located near the surface of the structure, close to a null of the
electric field. With such simulations one can evaluate the placement of absorbing regions as a
function of operating wavelength and desired absorbing properties.
Figure 2.2 illustrates a second structure similar to that of Figure 2.1, except the position and number of quantum wells has been altered. In this case four quantum wells instead of
two are used, which increases the amount of available saturable absorption. Moving the position of the absorbing quantum wells from the null of the electric field to the peak of the field
lowers the saturation fluence. The saturation fluence is the energy density at which the
absorption is nearly bleached. As mentioned previously, because the position at which the
electric field peaks is dependent on wavelength, the saturation fluence is also dependent on
wavelength.
The absorption properties of structures may also be altered significantly based on the
choice of top coating [63, 65]. Figure 2.3 illustrates the same semiconductor structure as Figure 2.2, except the structure is coated with multiple layers of Si and Al2O3 instead of a single
λ/4 layer of Al2O3. In this case the coating has been designed to produce a resonant field in
the InP layer. A Fabry Perot is formed between the DBR back mirror and the top coating
which acts as a 70 % reflector. The field calculation shows that the magnitude squared of the
field in the InP is comparable to the magnitude-squared field incident upon the structure,
enhancing the intensity in the InP by roughly 3 times over the incident intensity. Such field
enhancement lowers the saturation fluence significantly and increases the saturable absorption
modulation depth of the structure.
Instead of the resonant coating shown in Figure 2.3, an antiresonant coating could be
applied [10]. Such a coating may be desirable in solid-state lasers in which the intracavity
power can be very high. Additionally in high-Q laser cavities, only a very small modulation
depth of saturable absorption may be necessary to mode-lock the laser, so antiresonant coatings are an option. An antiresonant coating produces less intensity in the absorbing region
than is incident on the structure. One special case of an antiresonant structure is an uncoated
structure, often referred to as a saturable Bragg reflector [122]. Because the top surface of the
structure is a high-index semiconductor, the Fresnel reflection off the top surface is reasonably
large (~30 %), producing an antiresonance.
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
29
Figure 2.2
Schematic of an anti-reflection coated semiconductor saturable absorber mirror containing
four quantum wells. The refractive index and magnitude squared of the electric field (λ=1.54
µm) are plotted as a function of distance from the GaAs substrate-DBR interface.
Instead of quantum wells, thicker layers of absorbing material could be used as illustrated in Figure 2.4. In this structure the region which contained quantum wells in the previous structures is now a single layer of InGaAs. Depending on the thickness of the material, it
may or may not exhibit quantum confinement effects, which alter the absorption characteristics. The structure of Figure 2.4 exhibits significantly more saturable absorption than the
structure of Figure 2.2, simply because more absorbing material is included. Although in the
various devices illustrated here only single λ/2 absorbing layers have been shown, significantly thicker absorbing regions could be deposited on the DBR stack to produce larger
absorption.
Considering the structures illustrated here, a variety of design parameters may be
altered to control the response of semiconductor saturable absorber mirrors. The placement of
the absorbing layers in the electric field standing wave can control the saturation fluence. Various coatings on the structures can be used to control the modulation depth of saturable
absorption and the saturation fluence. The number of quantum wells or the thickness of
absorbing layers can be used to control the modulation depth of saturable absorption. Analysis of the electric field in such structures provides considerable insight for design.
30
CHAPTER 2
Figure 2.3
Schematic of a resonantly coated semiconductor saturable absorber mirror containing four
quantum wells. The refractive index and magnitude squared of the electric field (λ=1.54 µm)
are plotted as a function of distance from the GaAs substrate-DBR interface.
Figure 2.4
Schematic of an anti-reflection coated semiconductor saturable absorber mirror containing a
quasi-bulk absorption region. The refractive index and magnitude squared of the electric field
(λ=1.54 µm) are plotted as a function of distance from the GaAs substrate-DBR interface.
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
31
2.2
Growth of Semiconductor Saturable Absorber Mirrors
A much more detailed description of the growth techniques used to produce the structures described in this thesis is given elsewhere [67]. However because an understanding of
the growth techniques is necessary for proper design of the structures, some issues will be
addressed here. All of the structures discussed in this thesis were deposited by gas source
molecular beam epitaxy (GSMBE) by Elisabeth M. Koontz in the laboratory of Professor
Leslie A. Kolodziejski.
A somewhat unusual characteristic of the structures shown in Figures 2.1-2.4 is the
GaAs-InP interface, because a large lattice mismatch exists between the two materials. In epitaxial growth, for the highest quality material, the structure should be lattice matched. A
semiconductor saturable absorber mirror containing InGaAs could be grown in a lattice
matched fashion if the DBR mirror was produced from InP-based material. However because
of the reduced index contrast, such a DBR would exhibit a reduced reflectivity bandwidth
compared to a structure fabricated from GaAs and AlAs. Therefore in the devices developed
in this thesis GaAs/AlAs DBRs are used.
Because of the lattice mismatch at the interface of the GaAs and InP, defects are created. High-quality crystalline InP/InGaAs material, with minimal defects, exhibits a very
long (ns) lifetime, which may not recover between incident pulses [33]. For mode-locking
applications, the defects produced by such a lattice mismatch have the fortuitous benefit of
shortening the recombination time. However, defects also smear the bandedge of the material
and correspondingly broaden the photoluminescence spectrum. For the applications of this
thesis such smearing is not problematic because it is possible to operate within the absorption
edge of the structure, so the defects are actually a benefit, because they reduce the recombination time.
The epitaxial deposition for this thesis was typically performed in stages. First, the
DBR structure was grown either by GSMBE or purchased from a metalo-organic chemical
vapor deposition (MOCVD) facility. Second, the top absorbing layers were deposited via
GSMBE on smaller pieces of the DBR structures. In some cases further growth was performed via GSMBE to add additional InP material. After epitaxial growth, evaporative coatings were deposited to enhance absorber characteristics, as detailed above.
2.3
Optical Characterization
A full understanding of the optical properties of the saturable absorption layers of the
structures is necessary for proper design. In the epitaxial growth of the devices, both the com-
32
CHAPTER 2
0.95
Transmission
0.94
0.93
0.92
0.91
0.90
1200
SBR98051401
1300
1400
1500
1600
1700
Wavelength (nm)
Figure 2.5
Transmission as a function of wavelength for a two quantum well structure deposited on GaAs.
position and thickness of the saturable absorbing layers must be controlled. Room temperature photoluminescence was used to calibrate the epitaxial growth to obtain the desired
absorption edge. The photoluminescence peak was also compared to wavelength dependent
transmission measurements to quantify the absorption depth and sharpness of the bandedge.
An example of the wavelength dependent transmission properties of a quantum well
structure is illustrated in Figure 2.5. Two quantum wells within a λ/2 layer of InP were deposited on a GaAs wafer for characterization purposes. The wavelength dependent transmission
was characterized in a dual-arm spectrophotometer, using a GaAs wafer without quantum
wells as the reference. From Figure 2.5 the bandedge falls at approximately 1580 nm. The
absorption characteristics are consistent with energy-level calculations based on the quantum
well thickness and composition [2].
For mode-locking applications, two characteristics of the absorption are significant.
First, the bandedge is clearly smeared over a large range, nearly 60 nm. In theory the absorption edge should be quite sharp, but the defects associated with the growth are the likely cause
of the smearing. However, as will be discussed in later chapters, the lasers in which these
devices were used operated at a wavelength well within the absorption band. Second, the first
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
33
1.01
1.00
0.99
Transmission
0.98
0.97
0.96
0.95
0.94
0.93
0.92
1400
SBR98051401
1450
1500
1550
1600
1650
1700
Wavelength (nm)
Figure 2.6
Transmission as a function of wavelength for various quantum well structures deposited on
GaAs. For comparison, the room temperature photoluminescence of each structure is also
plotted in arbitrary intensity units, with an arrow indicating the peak
step of absorption is relatively flat from 1370 nm to 1540 nm. Given that the bandwidth of the
DBR mirror is typically ~100 nm, with proper positioning of the bandedge, the saturable
absorption could be uniform across the entire mirror bandwidth. Such a constant saturable
loss as a function of wavelength is desirable for mode-locking the maximum bandwidth of the
laser.
The absorption spectrum of Figure 2.5 clearly quantifies the properties of the quantum
wells in the saturable absorber structure. However a referenced transmission measurement is
often more time-consuming than a photoluminescence measurement, which is typically used
to calibrate epitaxial growth. To verify that photoluminescence provides an accurate estimation of the bandedge, comparisons between wavelength dependent transmission and photoluminescence measurements were performed, as shown in Figure 2.6. In the figure the
transmission near the bandedge is compared to the photoluminescence for three different
quantum well structures deposited on GaAs wafers. Typically the peak of the room temperature photoluminescence is used as the estimate of the bandedge, so in Figure 2.6 an arrow
34
CHAPTER 2
1.1
1.0
DBR
0.9
DBR reflectivity
0.8
0.7
PL
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.3
1.4
1.5
1.6
1.7
1.8
Wavelength (µm)
Figure 2.7
Transmission as a function of wavelength for a typical GaAs/AlAs DBR. For comparison the
normalized photoluminescence intensity of a quantum well structure deposited on GaAs is
plotted.
denotes the peak of the photoluminescence for each of the three cases. In all cases the peak of
the photoluminescence corresponds to a wavelength where the absorption is changing, so the
photoluminescence appears to provide a reasonable estimation of the bandedge.
For a mirror used in mode-locking, the relationship between the absorption characteristics and the reflection characteristics of the DBR is critical for operation. Figure 2.7 shows
the measured transmission of a typical GaAs/AlAs DBR with the photoluminescence of a
quantum well structure superimposed. The reflectivity of the DBR is greater than 99 percent
over a bandwidth of nearly 100 nm centered at 1.55 microns. The photoluminescence peak is
near 1525 nm, but based on the results of Figure 2.6, the bandedge probably extends +/- 30
nm from the peak. Although for the center wavelength of this mirror, the bandedge is not
optimally located to mode-lock across the entire mirror bandwidth, the sample is quite useful
for measuring the nonlinear absorption characteristics across the bandedge on the mirror.
In this chapter the design, growth, and characterization of semiconductor saturable
absorber mirrors has been discussed. Depending on the application, structures can be
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
35
designed based on calculations of the electric field in the structure. The placement and type of
absorbing material along with evaporative coatings can be used to control the saturation properties of the devices. For the structures shown here, epitaxial deposition issues related to the
GaAs/InP interface are significant, but are actually beneficial for some applications. Optical
characterization by wavelength dependent transmission and photoluminescence provides sufficient information to characterize the bandedge of the absorption and optimize epitaxial
growth.
36
CHAPTER 2
SEMICONDCUTOR SATURABLE ABSORBER MIRRORS
37
38
CHAPTER 2
CHAPTER 3
TIME-RESOLVED NONLINEAR RESPONSE
In this chapter1, a detailed investigation of InGaAs/InP saturable absorber mirrors as a
function of fluence and wavelength is described which reveals both two-photon absorption
(TPA) and free-carrier absorption (FCA). Even at moderate excitation fluences, TPA and
FCA are present when short pulses are used at wavelengths where absorption bleaching is
dominant. A technique that makes it possible to separate, experimentally, the contributions of
bleaching from those of induced absorption is demonstrated, and a two-color experiment is
performed to investigate how hot carriers enhance FCA. Below-band dynamics are also studied, and the effect of carrier diffusion is observed.
3.1
Pump-Probe Measurements
Ultrafast absorption saturation dynamics in semiconductors play a crucial role in highspeed photonic applications such as optical pulse shaping in mode-locked lasers. Studies
reported to date on saturable absorber mirrors have focussed mainly on the nonlinear carrier
dynamics at wavelengths close to or above the absorber bandgap, where mode-locking operation is typically achieved. Excitation fluences less than those required for full saturation of
the absorption have generally been used and correspond to conditions where the bleaching
dynamics are dominant [65]. Pump-probe experiments on semiconductor saturable Bragg
1
Portions of this chapter appear in [72, 56, 57]. Many of the results of this chapter were attained in collaboration with Dr. Markus Joschko, Dr. Patrick Langlois, Elisabeth M. Koontz, Prof. Franz X. Kärtner, and
Prof. Leslie Kolodziejski. Juliet T. Gopinath provided additional useful insights.
TIME-RESOLVED NONLINEAR RESPONSE
39
reflectors operated in the tail of the excitonic absorption edge also showed dominant absorption bleaching dynamics [16]. However, investigation of InGaAsP active and passive
waveguide structures has revealed the presence of TPA [38, 21, 40] and hot electron-assisted
absorption [121] which reduces or eliminates the bleaching dynamics. Nonlinear absorption
in GaAs-based saturable absorber mirrors has been studied at high fluences, but these studies
focussed on thermalization and trapping of carriers and concluded that absorber bleaching
was dominant even at fluences many times the saturation fluence, Fsat [73]. In this chapter, a
detailed study of InGaAs/InP saturable absorber mirrors as a function of wavelength and excitation fluence ranging from low (F < Fsat) to ultrahigh (F >> Fsat) is presented.
The nonlinear absorption dynamics of various saturable absorber mirrors are studied
as a function of both fluence and wavelength using a collinear cross-polarized pump-probe
technique. The measurements were typically performed with degenerate pump and probe
pulses and a pump-to-probe fluence ratio of 10, unless otherwise noted. The samples were
studied in reflection using an optical parametric oscillator (OPO) producing ~150 fs pulses
tunable from 1.4 µm to 1.6 µm at a repetition rate of 82 MHz. Lenses with 2-15 mm focal
lengths were used to focus the pump and probe beams onto the mirror structure and to collect
the reflected signal, which was directed to a lock-in detection system.
3.2
Fluence Dependence
The structure under investigation was grown by gas source molecular beam epitaxy
and is shown in Figure 2.2. The mirror was a 22-pair GaAs/AlAs distributed Bragg reflector
(DBR) centered at 1.55 µm with a reflectivity >99% over a bandwidth of 100 nm. The
absorption layer contained four InGaAs quantum wells (QWs) (exhibiting a photoluminescence peak at 1.53 µm) centered in a half-wave layer of InP. A single quarter-wave Al2O3
antireflection coating was also deposited following epitaxial growth.
Differential reflectivity measurements at 1.50 µm, as a function of excitation fluence,
are presented in Figure 3.1. Three different regimes are clearly identified in the data. First, at
all pump fluences up to the 5.6 µJ/cm2 shown, the pump-probe trace shows a fast bleaching
component followed by a slow component reflecting the change in carrier density. This signature is typical for low fluence absorption dynamics of semiconductor saturable absorber structures [65, 16]. The fast component is attributed to spectral hole burning (SHB) [38], with a
time constant on the order of the pulse cross-correlation (~200 fs). On a longer time scale, the
slow component decays with a time constant of ~40 ps, which is considerably shorter than the
40
CHAPTER 3
nanosecond recovery times typically observed in lattice matched samples [33]. Carrier capture in defect states due to the large lattice mismatch between InP and GaAs is the most likely
cause of this lifetime shortening.
At higher fluences (~28 µJ/cm2), an additional component sets in that reduces the differential reflectivity, and decays with a time constant of ~1 ps, consistent with the cooling
dynamics of hot carriers in the QWs [39, 40]. Possible mechanisms for this component are
nonequilibrium free-carrier absorption (FCA) and a delayed bleaching corresponding to carrier cooling. However, delayed bleaching alone cannot explain the occurrence of an absolute
negative ~1 ps transient at high fluence levels (112-222 µJ/cm2); therefore an additional
absorption mechanism must also be present, as will be discussed. The reduction of the fast
bleaching component relative to the slow component with increased excitation fluence suggests that SHB begins to saturate while the ~1 ps negative transient continues to increase. At
higher fluence levels, TPA in both the QWs and the InP layer continues to increase, and eventually, TPA and FCA dominate the ultrafast dynamics. TPA has also been shown to be an
important mechanism of free-carrier generation and carrier heating in active waveguides
under high fluence excitation [39]. The duration of the TPA component corresponds to that of
the pulse cross-correlation and is consistent with the “instantaneous” virtual transition pro-
Change of Reflection ∆R / R0
-2
1.0x10
λ = 1.5 µm
-3
5.0x10
0.0
2
pump fluence (µJ/cm )
5.6
28
56
-3
-5.0x10
-2
0
2
4
112
222
6
8
Delay (ps)
Figure 3.1
Differential reflectivity measurements as a function of excitation fluence at 1.5 µm. At low
fluence, the bleaching dynamics of the QWs are dominant. At higher fluences, TPA and FCA
develop and eventually dominate the ultrafast dynamics.
TIME-RESOLVED NONLINEAR RESPONSE
41
cess. The oscillations near zero delay of the traces at intermediate fluence levels (~112 µJ/
cm2) may be attributed to the non-instantaneous SHB response, otherwise TPA and SHB
would perfectly cancel each other near 112 µJ/cm2. Dynamic spectral effects have also been
shown to contribute a similar effect [82]. Another feature associated with the increase of the
excitation fluence is the reduction of the longer-lived bleaching component. Some of this
reduction is attributed to FCA in the QWs and in the InP layer (via carriers created by pump
TPA in the latter case). Additionally because a 10 to 1 pump-probe power ratio is maintained,
the probe itself bleaches the absorption at higher fluences, thus reducing the modulation that
can be produced by the pump. To avoid this effect, a pump-to-probe fluence ratio of ~500
would be necessary. However as will be discussed, the present conditions actually help to
reveal the TPA and FCA components while simultaneously preserving the qualitative bleaching and absorption dynamics along with their respective time constants. It should be emphasized that TPA has also been confirmed from average saturation fluence measurements for
these fluence levels [116] as will be shown in a later chapter.
The data of Figure 3.1 was obtained at 1.5 µm, a wavelength within the absorption
band (bandedge ~1.53 µm). The nonlinear absorption of the same structure was also studied
with ~150-fs pulses at λ=1.54 µm, a wavelength near the bandedge and a wavelength at which
erbium- or erbium-ytterbium doped lasers are typically operated, in the same collinear crosspolarized pump-probe experiment as before. Both beams were focussed onto the sample by
an 11-mm focal length lens. The change of reflection was measured as a function of pumpprobe delay for a wider range of pump excitation fluences, from 0.01 µJ/cm2 to 1000 µJ/cm2.
Pump-probe differential reflectivity traces for a fixed probe fluence of 0.2 µJ/cm2 and
varying pump fluences as indicated are presented in Figure 3.2. The pump-probe trace for a
pump fluence of 5 µJ/cm2 (~Fsat) represents a typical saturable absorber response at low fluence [16, 58]. Because the QWs are positioned at the peak of the standing wave field (See
Figure 2.2), the bleaching reflects carrier density changes in the QWs, thus affecting the
probe. The absorption recovery exhibits an ultrafast time constant on the order of the pulse
autocorrelation (< 150 fs), an intermediate 1 ps time constant, and a longer ~40 ps time constant. The ultrafast component is attributed to carrier thermalization due to carrier-carrier
scattering, which fills the spectral hole (SH) formed by the pump. The thermalized but hot
carrier distribution then dissipates excess energy via carrier-phonon scattering, cooling to the
lattice temperature within 1 ps [39, 1]. The subsequent ~40 ps recombination time is shorter
than expected for a lattice-matched sample and is most likely related to carrier capture in
strain-related defect states in the QWs. At increased fluence (50 µJ/cm2), the signal deviates
from a linear increase with respect to pump fluence. The SH-peak saturates, but the slow
42
CHAPTER 3
Change of Reflection ∆R / R0
AC
0.01
5 µJ/cm
320 µJ/cm
2
2
600 µJ/cm
AC
0
2
50 µJ/cm
2
160 µJ/cm
2
4
960 µJ/cm
0.05
6
0
2
4
2
2
6
Delay (ps)
Figure 3.2
Differential reflectivity measurements as a function of excitation fluence at 1.54 µm. The
change of reflection ∆R/R0 = (R - R0)/R0 (R, R0: reflection with and without pump, respectively) is plotted versus delay between pump and probe pulses. The autocorrelation (AC)
depicts the temporal resolution.
bleaching component increases further with a 1 ps risetime; this indicates that the quasiFermi-level has risen above the pump-probe photon energy, so bleaching actually increases as
the carriers cool. At higher fluence (F ≥ 160 µJ/cm2) the SH broadens in time with respect to
the auto correlation due to saturation and TPA becomes visible at zero delay [116, 83]. At
ultrahigh fluence levels (320 µJ/cm2-960 µJ/cm2), an additional induced absorption component with a 2.8 ps time constant, not clearly observed in Figure 3.1 because of the lower fluence levels, begins to dominate the ultrafast nonlinear dynamics. A negative change is
observed for positive delays, and the magnitude increases with respect to the square of the fluence. This additional induced absorption can be attributed to free carriers that TPA created
high in the bands [83, 123]. The 2.8 ps partial recovery time constant of this signal is an indication that absorption by these highly excited carriers is greater than that of the cooler carriers
and that the relaxation rate from high lying states is slower than the ordinary carrier cooling.
TIME-RESOLVED NONLINEAR RESPONSE
43
Change of Reflection ∆R / R0
-3
4.0x10
-3
2.0x10
0.0
1.48 µm
1.50 µm
-3
-2.0x10
1.52 µm
2
pump: 83 µJ/cm
1.54 µm
1.58 µm
-3
-4.0x10
-2
0
2
4
6
8
Delay (ps)
Figure 3.3
3.3
Differential reflectivity measurements under high fluence excitation as a function of wavelength. The wavelength is tuned from above to below the QW bandgap (~1.53 µm). Below
the QW bandgap, TPA and FCA in InP are dominant.
Wavelength Dependence
To clarify the dynamics and characterize the wavelength dependence of the TPA and
FCA contributions, the structure investigated in Figures 3.1 and 3.2 was studied under conditions in which the bleaching of the QWs is negligible compared to TPA, even at low fluence
levels. Figure 3.3 depicts differential reflectivity measurements taken under moderate fluence
excitation as a function of wavelength. The most significant behavior is the vanishing of the
bleaching dynamics as the excitation wavelength is varied from 1.48 µm (above the QW
bandgap) to 1.58 µm (below bandgap), which is consistent with a reduction of the saturable
absorption at longer wavelengths. At 1.58 µm, the signal is dominated by strong TPA followed by an induced absorption component that persists for longer delays. The decay of the
induced absorption is no longer described by a single ~1 ps time constant, but rather by a combination of ~1 ps and ~5 ps components, with weighting factors that favor the ~5 ps component at longer wavelengths. The ~5 ps component is attributed mainly to FCA in the InP
layer, and its time constant is believed to originate from the diffusion of the TPA-induced car-
44
CHAPTER 3
Change of Reflection ∆R / R0
2
probe (µJ/cm )
0.10
0.25
1.00
2.50
10.0
pump: 250 µJ/cm
0
1000
2000
3000
4000
2
5000
Delay Time (fs)
Figure 3.4
Differential reflectivity measurements for a pump fluence of 250 µJ/cm2 with the probe fluence varied as indicated.
riers in the InP layer, as discussed below. As the excitation wavelength is changed from above
to below the QW bandgap, the bleaching dynamic in the QWs is reduced due to a decrease in
the density of absorbing states. Therefore, TPA and FCA in InP become the dominant dynamics. However, even at 1.58 µm, there are still some carriers excited in the quantum wells as
evidenced by the presence of a ~1 ps component. (Measurements further below the QW
bandgap were limited by the bandwidth of the DBR.)
3.4
Induced Absorption
To isolate TPA and FCA dynamics at wavelengths within the absorption band, pumpprobe experiments were performed at higher probe fluence. The effect of varying the probe
fluence while maintaining a constant pump fluence is illustrated in Figure 3.4 In the measurement, the power in the probe was varied. Since only the probe is detected, at low powers the
TIME-RESOLVED NONLINEAR RESPONSE
45
-2
∆R/R0 (x10 )
4
2
0
-2
0
Figure 3.5
2
4
Delay (ps)
6
Differential reflectivity measurements at a pump fluence of 320 µJ/cm2 for low (solid curve)
and high (dashed curve) probe fluence, and the difference between the two (dash-dotted
curve).
signal-to-noise ratio degraded. However the qualitative change from bleaching to induced
absorption is clearly observed as the probe power is varied. Depending on the operating
wavelength, the fluence of the probe required to eliminate bleaching effects varies. At sufficiently high fluences the probe pulse alone bleaches the available states. Excitation by the
pump cannot further increase transmission of the measured probe; it can only decrease the
reflection by inducing absorption.
Pump-probe experiments at 1.54 µm with a high probe fluence (80 µJ/cm2, well above
Fsat~5 µJ/cm2) were performed on the structure of Figure 2.2 to separate induced absorption
dynamics from those due to bleaching by state filling. Figure 3.5 compares pump-probe
traces at a pump excitation fluence of 320 µJ/cm2 taken with low (solid line) and high (dashed
line) probe fluences. These two traces are then subtracted to reveal the pure bleaching dynamics (dash-dotted line). The induced absorption dynamics (dashed line) are clearly a result of
TPA and FCA and are similar to the response of the structure when probed below band, as in
Figure 3.3 at 1.58 microns. The pure bleaching dynamics (dash-dotted line) exhibit hole burn46
CHAPTER 3
ing, carrier cooling, and a long recombination time, all of which are similar to the response of
the structure measured at 1.50 microns in Figure 3.3.
3.5
Hot-carrier Dynamics
A two-color pump-probe experiment was performed to further clarify the contribution
of hot carriers to the ultrafast dynamics observed at very high fluences (320 µJ/cm2-960 µJ/
cm2) in Figure 3.2. The sample of Figure 2.2 was excited by 100 fs pulses from the Ti:sapphire laser (λ = 810 nm) and probed by the ~150 fs OPO pulses (λ = 1.54 µm). Because a
standing wave is not produced at wavelengths outside the reflectivity band of the DBR, pumping at 810 nm generates a spatially uniform distribution of highly excited carriers in the
InGaAs with energies comparable to those generated by TPA in the previous experiment.
Probing with OPO pulses ensures preferential probing of the QWs. Figure 3.6 presents data
taken at excited carrier densities (N ≈ 1018cm-3) comparable to the number of TPA-induced
carriers at a fluence of 600 µJ/cm2 in the single-color experiment shown in Figure 3.2. The
810 nm pulse energy required for these excitation densities, however, is well below that which
would cause any significant TPA. The pump-probe trace for low probe fluence (solid line)
exhibits an initial fast absorption component followed by strong bleaching which rises with a
2.8 ps time constant. On a longer time scale this signal decays with the ~40 ps recombination
time of the QWs. The overall signal is composed of an initial negative signal due to FCA, followed by a positive component due to state filling, as the highly excited carriers drop to the
bottom of the band and block the probed interband transitions. Using a high probe fluence, as
described earlier, the change in reflection without bleaching components is isolated to reveal
the FCA component (dashed line). In these experiments FCA is the only process giving rise
to an induced absorption; no TPA at zero delay is observed. The decay of the induced FCA
exhibits a 2.8 ps time constant, similar to that observed for the increase in bleaching at low
probe fluence. The pump-probe trace of an identical structure but without InGaAs, only InP,
which is shown for comparison (dotted line), does not contain a fast time constant. This is
further evidence that a portion of the highly excited carrier distribution relaxes with a time
constant (2.8 ps) which is longer than that of ordinary carrier cooling (1 ps). This distinct time
constant is consistent with a process in which some of the carriers are initially excited high
into the band and are scattered to satellite valleys from which they return at the slower rate [6,
92, 27]. Other possibilities for a reduced relaxation rate might be a phonon bottleneck [99] or
a delay due to capture of carriers excited out of the wells [124].
TIME-RESOLVED NONLINEAR RESPONSE
47
Change of Reflection (a. u.)
x0.2
tbleach = 2.8 ps
tFCA = 2.8 ps
0
2
4
6
8
Delay (ps)
Figure 3.6
3.6
Differential reflectivity measurements with excitation by Ti:sapphire pulses for a saturable
absorber mirror with low (solid curve) and high (dashed curve) probe fluence exhibits a 2.8 ps
time constant. Dynamics of an identical structure without QWs (high probe fluence, dotted
curve) shows no fast time constant.
Below-Band Induced Absorption
To further study the dynamics of TPA and FCA without the QW bleaching contribution, the mirror structure of Figure 2.1, containing two InGaAs QWs located ~15 nm from the
top of the InP λ/2 layer, was considered. In this case, the QWs are located close to a null of
the electric field, where the bleaching is considerably reduced. Additionally, the bandgap of
the QWs is shifted to λ ~ 1.45 µm, which further reduces their bleaching contribution at wavelengths greater than 1.5 µm. Figure 3.7 presents the absorption dynamics of this structure at
1.56 µm under high fluence excitation (solid curve). A strong TPA peak is followed by
induced FCA with a single ~5 ps time constant. Both of these dynamics do not significantly
depend on the wavelength of the excitation, as long as the excitation remains below the QW
48
CHAPTER 3
0.0
-0.2
FCA
-0.4
0.004
-0.6
∆R/R0
Normalized ∆R / R0
λ = 1.56 µm
-0.8
TPA
0.002
FCA
0.000
-1.0
0
TPA
-2
50
100
2
Pump fluence (µJ/cm )
0
2
4
6
8
Delay (ps)
Figure 3.7
Differential reflectivity measurements under high fluence excitation at 1.56 µm for a saturable
absorber mirror structure in which absorption bleaching is negligible (solid curve). The ~5 ps
decay for FCA is attributed to carrier diffusion across the InP half-wave layer. The dashed
curve shows the differential absorption of a ~350 µm thick InP substrate in which a standingwave pattern is not formed. Inset: linear and quadratic fluence dependence of the TPA and
FCA components respectively, in the saturable absorber mirror structure.
bandgap. Power dependent measurements have shown that, even at low fluence, no bleaching
occurs at 1.56 µm, which confirms that induced absorption in the InP layer is the only significant contribution to the differential reflectivity. The inset in Figure 3.7 shows the power
dependence of the TPA and FCA components. As expected, TPA and FCA vary linearly and
quadratically, respectively, with the pump power. The pump-induced absorption of the probe
(TPA) is linearly dependent on the pump power. Since FCA is produced by carriers that are
generated by the pump alone via TPA, FCA scales with the square of the pump power. Figure
3.7 also displays the differential absorption dynamics in a ~350 µm thick InP substrate in
which a standing wave pattern is not formed (dashed curve). In the bulk case there is no decay
of the FCA on the time scale of ten picoseconds, and the absorption vanishes over a much
longer time scale. Consequently, the ~5 ps decay time observed in the saturable absorber mirror is most likely caused by the diffusion of carriers out of the high fluence excitation (high
carrier density) region located at the peak of the standing-wave field pattern, which occurs at
the center of the InP λ/2 layer, as illustrated in Figure 2.1. To verify this assumption, the one-
TIME-RESOLVED NONLINEAR RESPONSE
49
dimensional diffusion equation for carriers in the InP layer was solved. The time evolution of
the overlap integral between the standing-wave field pattern and the carrier distribution in the
InP layer, which is proportional to FCA, was then evaluated. Assuming an initial carrier distribution described by ~sin4(πx/L) (proportional to the square of the intensity) and a layer
thickness L = 230 nm, an ambipolar diffusion coefficient of Da = 2.7 cm2/s is found for an
FCA decay time of 5 ps. This value of Da is consistent with other estimates found in the literature for InP [59], and further supports the claim that the ~5 ps time constant of the FCA component originates from carrier diffusion in InP.
3.7
Implications of Induced Absorption
Results of this chapter clearly establish the significant presence of TPA and FCA in the
InP/InGaAs λ/2 layer of these saturable absorber mirrors and demonstrate that these components are strongly dependent on the fluence of the excitation, yet relatively wavelength independent. Consequently, TPA and FCA are also present at wavelengths close to or above the
QW absorption edge, e.g. in the traces of Figures 3.1 and 3.2 even at moderate excitation fluences, but they are dominated by absorption bleaching in the QWs. For this reason, TPA and
FCA are usually not observed in the low and moderate fluence pump-probe measurements
typically performed on saturable absorber mirrors, although quantitative results will be influenced.
The effects of TPA on mode locking dynamics and output pulse characteristics of
mode-locked lasers using saturable absorber structures have recently been illustrated and will
be discussed in a later chapter [116, 115, 52]. The fluences at which TPA and FCA become
important in the structures studied here are easily achieved with focussing in a femtosecond
solid-state laser. With resonant structures, TPA and FCA can be significant even in lowpower mode-locked fiber lasers [115]. For high energy picosecond pulses, FCA, which scales
with the number of carriers, hence with pulse energy squared and inversely with pulse duration, may also have a significant impact on the pulse shaping mechanism and stability against
Q-switching. The relative effect of TPA and FCA compared to absorption bleaching will
depend on the specific structure of the saturable absorber. In general, shorter pulses will
increase TPA relative to interband excitation and, therefore, increase the importance of hot
carrier dynamics. At sufficiently high fluences, these absorption effects will occur in most
structures and should be measurable via saturation fluence and pump-probe measurements.
Thus TPA and FCA could effectively influence output pulse characteristics, mode-locking
dynamics, and stabilization against Q-switched mode-locking.
50
CHAPTER 3
In summary, the nonlinear absorption dynamics of semiconductor saturable absorber
mirrors have been investigated over a wide parameter range. Fluence and wavelength dependent measurements have shown that carriers generated in both the InP and InGaAs material of
the structures contribute to the ultrafast dynamics. On a timescale of several picoseconds,
bleaching dominates at low and moderate fluence, but as the fluence is increased, TPA and
FCA begin to modify the saturable absorber dynamics considerably near zero delay. Detailed
analysis of these pump-probe measurements has provided a clear separation of the induced
absorption and the bleaching dynamics and revealed the importance of TPA and FCA at fluence levels relevant to mode-locked lasers. A two-color technique was used to investigate
effects of FCA from absorption due to highly excited carriers. TPA, FCA, and carrier diffusion in InP are revealed in pump-probe measurements at fluence levels typical of modelocked lasers. Since the fluence incident on semiconductor saturable absorber mirrors in
many ultrafast lasers is routinely many times the saturation fluence, the dynamics of saturable
absorber mirrors at high excitation fluence will become increasingly important.
TIME-RESOLVED NONLINEAR RESPONSE
51
52
CHAPTER 3
CHAPTER 4
TIME-AVERAGED NONLINEAR RESPONSE
In this chapter1, time-averaged measurements of the reflectivity as a function of fluence are presented and discussed. Measurements of a number of structures are compared to
illustrate how structural differences affect saturation fluence properties. The effect of optical
coatings is studied in detail for the case of a resonantly enhanced structure.
4.1
Nonlinear Reflectivity Measurements
Time-averaged nonlinear reflectivity measurements were performed at 1.5-1.6 µm
using ~150 fs pulses from a synchronously-pumped optical parametric oscillator (OPO) with a
repetition rate of 82 MHz. In the measurements incident and reflected beams were lock-in
detected simultaneously, the ratio being proportional to the reflectivity. This ratio was calibrated to the absolute reflectivity of a reference dielectric mirror, measured with a spectrophotometer. The incident fluence was controlled by varying the incident power and changing the
spot size on the sample, using lenses of different focal lengths. Power incident on the sample
was varied using a half wave plate on a rotary stepper stage and a polarizing beam splitter.
The incident fluence was determined by measuring the focused spot size and the
power incident. A knife-edge scanning technique was used to determine the spot size at sev1
Many of the results of this chapter were attained in collaboration with Elisabeth M. Koontz, Prof. Franz
X. Kärtner, and Prof. Leslie Kolodziejski. Assistance with the Fourier transform infra-red spectrometer
was provided by Timothy C. McClure of the Analytical Shared Experimental Facilities, MIT Center for
Materials Science and Engineering.
TIME-AVERAGED NONLINEAR RESPONSE
53
100
90
80
Power (mW)
70
60
50
40
30
20
10
0
3.50
3.75
4.00
4.25
Position (mm)
Figure 4.1
Transmitted power has a function of knife-edge position in the beam after passing through a
focusing lens. The fit to an error function provides the Gaussian width.
eral measured distances from the focusing lens. The transmitted power was measured as a
razor blade was translated through the beam on a precision stage. An example of the transmission as a function of knife-edge position is illustrated in Figure 4.1. A nonlinear regression to an error function was used to obtain the Gaussian width of the beam. The measured
width as a function of position along the focus was then fit to a Gaussian focusing equation
[95, 44] to obtain the beam waist at the focus as shown in Figure 4.2. Such a regression technique was accurate in determining the focused beam waist for lenses with focal lengths longer
than ~5 mm, but appeared to be less accurate for very tightly focusing lenses.
Measurements of the reflectivity as a function of fluence over nearly four orders of
magnitude are possible by changing lenses. For each lens the power was varied from the maximum to the lowest level where a reasonable signal-to-noise ratio was still attained. Typically
the results from four different lenses were concatenated to form a single reflectivity-as-a-function-of-fluence curve. Appendix A discusses the various models for the reflectivity as a func54
CHAPTER 4
0.25
0.20
wo (mm)
0.15
0.10
0.05
0.00
0
2
4
6
8
10
12
14
16
Z (mm)
Figure 4.2
The beam waist as a function of distance from a focusing lens as determined from several
knife-edge measurements. The fit of the waist as a function of position gives the focused spot
size
tion of fluence used to extract the saturable absorption parameters. Because the ~150
femtosecond pulses used for these measurements are on the order of or shorter than most of
the time response of the saturable absorber structure, the nonlinear response is fit to the slow
saturable absorber model detailed in Section A.1 of Appendix A. All of the data presented in
this chapter is fit with the same slow saturable absorber model to facilitate comparison.
4.2
Structural Design Effects
The measured nonlinear reflectivity at 1.54 µm of a semiconductor saturable absorber
mirror is shown in Figure 4.3 along with a fit to the data. The structure is similar to that
shown in Figure 2.2, excepts it contains six quantum wells, instead of the four quantum wells
depicted in Figure 2.2, centered at the peak of electric field in the standing wave. Each quan-
TIME-AVERAGED NONLINEAR RESPONSE
55
0.94
0.93
Qo
Fsat
ao
Res
0.92
0.07277
3.58805
0.05758
10.35587
±0.00046
±0.07206
±0.00048
±0.24895
Reflectivity
0.91
0.90
0.89
0.88
0.87
0.86
0.1
1
10
100
2
Energy Density (µJ/cm )
Figure 4.3
Measured reflectivity as a function of fluence at 1.542 microns for an antireflection coated
sample similar to the structure of Figure 2.2 except containing six quantum wells. The solid
line is the result of a fit to a slow saturable absorber model with the coefficients indicated.
tum well was ~100 Å thick and was separated by ~70 Å of InP. In Figure 4.3 from approximately 0.1 to 50 µJ/cm2 the structure exhibits a typical saturable absorber response; as the
fluence increases, the reflectivity increases. However for fluences of 50 µJ/cm2 and higher,
the reflectivity drops dramatically. This reduction in reflectivity is due to TPA and FCA as
discussed in the time-resolved results of the previous chapter and will be further discussed in
the next chapter. The properties of the saturable absorption are the primary focus of this section.
The solid line in Figure 4.3 is the result of the regression with the parameters indicated. From the fit, the saturation fluence (Fsat) is 3.6 µJ/cm2. Based on the data, at this fluence roughly half of the potential modulation depth is saturated. The fitted full modulation
depth (Qo) is 7.3 percent. This value is somewhat lower than the reflectivity difference
between the reflectivity at the lowest fluence and the peak reflectivity because the onset of
56
CHAPTER 4
0.93
Qo
Fsat
ao
Res
0.92
0.06190
4.66532
0.05921
6.53554
±0.00067
±0.13822
±0.00068
±0.15653
Reflectivity
0.91
0.90
0.89
0.88
0.87
0.1
1
10
100
2
Energy Density (µJ/cm )
Figure 4.4
Measured reflectivity as a function of fluence at 1.542 microns for the antireflection coated
structure of Figure 2.4. The solid line is the result of a fit to a slow saturable absorber model
with the coefficients indicated.
induced absorption occurs before the saturable absorption is fully bleached. Finally the nonsaturable loss (ao) is 5.8 percent, which is due to the absorbing layer because the mirror is
100% reflective. The non-saturable loss and the saturable loss sum to the difference between
the reflectivity at the lowest fluence and 100 percent reflectivity.
A comparison was performed between the quantum well structure measured in Figure
4.3 and the structure of Figure 2.4, which replaces the quantum well section with a single
layer ~1018 Å thick. The thickness of the layer was designed such that the same portion of
the standing wave that previously overlapped quantum wells, overlaps the absorbing layer.
The measured nonlinear reflectivity at 1.54 µm as a function of fluence is shown in Figure 4.4
along with a fit. From the fit the modulation depth is 6.2 percent, and the saturation fluence is
4.7 µJ/cm2. Even though the quantum well structure measured in Figure 4.3 contained less
absorbing material because of the InP spacing layers, it exhibited slightly more saturable
TIME-AVERAGED NONLINEAR RESPONSE
57
absorption and a lower saturation fluence. In theory a lower saturation fluence would be
expected with quantum wells because the density of states exhibits a sharp step compared to
the gradual rise in states for bulk material. However as discussed previously, significant
smearing of the bandedge occurs in these structures, so such small differences in saturation
fluence and modulation depth are difficult to attribute to differences in the bandedge. For all
practical mode-locking purposes, the two devices appear to have a virtually identical
response.
4.3
Resonant Coating Effects
The effect of post-growth evaporative coatings was studied by comparing an antireflection coated sample to a resonantly coated sample. Figure 2.2 shows the antireflection
coated structure, and Figure 2.3 shows the resonantly coated structure. The DBR and absorption layer of the two structures are identical; only the evaporative coating is different. Initially
the antireflection coated sample was characterized. The nonlinear reflectivity at 1.54 µm as a
function of fluence is shown in Figure 4.5. In comparison to the measurement in Figure 4.3,
the modulation depth is reduced. Less saturable absorption occurs in the sample because the
number of quantum wells is fewer, and the bandedge is at a shorter wavelength. However
qualitatively the response is similar and is fit with the same function.
The resonant coating shown in Figure 2.3 was added to increase the modulation depth
and lower the saturation fluence of the structure at the resonant wavelength. To characterize
the effect of the resonant coating, the linear reflectivity of the structure was measured using a
Fourier transform infrared spectrometer (FTIR). A spectrophotometer could not be used for
the measurement because the sample size was only a few mm on a side, and the sample was
mounted with indium on the backside, preventing transmission measurements. The FTIR was
capable of measuring and imaging through an optical microscope, enabling measurements of
reflectivity over a very small spot. However neither the wavelength nor absolute reflectivity
calibration of FTIR were always accurate in reflection at the wavelengths of interest. Still the
instrument provided a qualitative picture of the effect of the resonant coating.
The FTIR measurement of the linear reflectivity of the resonant structure is shown in
Figure 4.6 (solid line). For comparison, a measurement of a GaAs/AlAs DBR without an
absorbing layer is also shown in Figure 4.6 (dashed line). Both curves have been shifted in
wavelength and scaled in reflectivity based on secondary measurements. The reflectivity of
the resonant structure was measured as a function of wavelength for low incident powers
58
CHAPTER 4
0.99
Reflectivity
0.98
0.97
0.96
Qo
Fsat
ao
Res
0.95
0.02400
4.26770
0.00198
7.83177
±0.00042
±0.25876
±0.00038
±0.08893
0.94
0.1
1
10
100
2
Energy Density (µJ/cm )
Figure 4.5
Measured reflectivity as a function of fluence at 1.542 microns for the antireflection coated
structure of Figure 2.2. The solid line is the result of a fit to a slow saturable absorber model
with the coefficients indicated.
using a tunable external-cavity laser diode with the wavelength monitored by an optical spectrum analyzer. The lowest reflectivity occurred at 1530 nm, so the FTIR trace was shifted to
match this measurement. Figure 4.6 shows the dramatic effect of the resonant coating. The
reflectivity on the long wavelength side of the resonance approaches that of the DBR. On resonance the reflectivity drops to nearly 60 percent. On the short wavelength side of the resonance the reflectivity does not to return to that of the DBR, partially because short
wavelengths are further into the absorption band. As designed, the resonant coating has produced a dramatic increase in absorption at certain wavelengths. However given the limitations of the FTIR spectrometer, careful nonlinear characterization is necessary.
To quickly and consistently estimate the nonlinear properties of the resonantly coated
structure, the nonlinear reflectivity change was measured over a limited fluence range with a
single lens as a function of wavelength. The wavelength of the OPO was tuned from 1500 to
1550 nm in 10 nm increments. At each wavelength the incident power was varied from maxi-
TIME-AVERAGED NONLINEAR RESPONSE
59
100
95
90
Reflectivity
85
80
75
70
65
sbr98060301.opj
60
1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900
Wavelength (nm)
Figure 4.6
The reflectivity as a function of wavelength of the resonantly coated structure of Figure 2.3
(solid line) and a DBR mirror (dashed line) measured with a Fourier transform infrared spectrometer.
mum to minimum, and the total change in reflectivity for that power change was measured. A
20 cm focal length lens was used for all of the measurements, and no change in alignment or
focusing was necessary as the laser was tuned. The change in reflectivity as a function of
wavelength is shown in Figure 4.7. The fluence produced by the lens is not sufficient to fully
bleach the sample at all wavelengths, but the wavelength dependence of the resonantly
enhanced nonlinearity can be ascertained. As with the linear measurement of Figure 4.6, the
maximum modulation depth occurs at 1530 nm. A Gaussian fit to the data of Figure 4.7 was
used to determine the center wavelength and bandwidth of the resonance. The center wavelength was 1529.6 nm, and the width was 23.1 nm. This data indicates the wavelengths at
which measurements should be made to fully characterize the nonlinear response of the resonantly coated sample.
Based on the nonlinear response measured in Figure 4.7, full reflectivity as a function
of fluence measurements were performed at 1.5 microns and 1.53 microns. The measurement
at 1.5 microns is shown in Figure 4.8 along with results of a fit. Although in the measurement
60
CHAPTER 4
12
10
∆R/R
8
6
4
2
980611
0
1500
1510
1520
1530
1540
1550
Wavelength (nm)
Figure 4.7
The total change in reflection as a function of wavelength for the structure of Figure 2.3. The
measurement was performed with a single 20 cm lens. The solid line is a Gaussian fit to the
data.
of Figure 4.7 no significant change in reflectivity was observed at 1.5 microns, in the full measurement of Figure 4.8 the modulation depth approaches 3.2 percent. The difference occurs
because in the measurement of Figure 4.8 several more tightly focusing lenses were used. In
comparison Figure 4.9 shows the measurement of the reflectivity as a function of fluence at
1.53 microns along with results of a fit. At 1.53 microns the modulation depth is 13.9 percent,
and the saturation fluence is 0.8 µJ/cm2. Clearly both the modulation depth and the saturation
fluence have changed considerably as a function of wavelength due to resonant enhancement.
The modulation depth measured in Figure 4.9 compares favorably to the change in reflectivity
measured in Figure 4.7 because the saturation fluence on resonance is significantly lower.
Based on the regression in Figure 4.7, the nonlinear properties of the resonant structure can be estimated with a Gaussian function. The more careful measurements at 1.5 and
1.53 microns in Figures 4.8 in 4.9 can be used as a basis for extrapolating the other properties
TIME-AVERAGED NONLINEAR RESPONSE
61
0.905
0.900
Qo
Esat
ao
Res
Reflectivity
0.895
0.03162
11.22923
0.09055
6.91703
±0.00048
±0.64711
±0.00057
±0.33957
0.890
0.885
0.880
SBR98071002.opj
0.875
0.1
1
10
100
2
Energy Density (µJ/cm )
Figure 4.8
Measured reflectivity as a function of fluence at 1.5 microns for the resonantly coated structure
of Figure 2.3. The solid line is the result of a fit to a slow saturable absorber model with the
coefficients indicated.
of the resonantly coated structure. Because of the symmetry of the Gaussian fit about 1.53
microns, the saturation properties of the structure at 1.56 microns are extrapolated to be identical to those at 1.5 microns. This assumption is not entirely accurate because the band edge
of the quantum wells was measured to be ~1.53 microns, so the absorption is asymmetric
about that point. Figure 4.10 shows the measured modulation depth of saturable absorption
from Figure 4.8 and 4.9 as a function of wavelength along with a Gaussian fit. The saturable
loss is enhanced by greater than a factor of 4 on resonance. Figure 4.11 shows the saturation
fluence as a function of wavelength with a Gaussian fit. The saturation fluence is lowered by
more than an order of magnitude on resonance. Finally Figure 4.12 illustrates how the AStruct
parameter (described in Appendix A) varies as a function of wavelength with a Gaussian fit.
The enhancement improves by nearly a factor of 5. This characterization of the resonantly
coated structure illustrates that post-growth coatings can be used effectively to alter the properties of semiconductor saturable absorber mirrors.
62
CHAPTER 4
0.90
0.88
0.86
Qo
Fsat
ao
Res
0.13922
0.80447
0.10529
33.63101
±0.00092
±0.01543
±0.0005
±0.17707
Reflectivity
0.84
0.82
0.80
0.78
0.76
0.74
0.72
SBR98061502CorW.opj
0.70
0.01
0.1
1
10
100
2
Energy Density (µJ/cm )
Figure 4.9
Measured reflectivity as a function of fluence at 1.53 microns for the resonantly coated structure of Figure 2.3. The solid line is the result of a fit to a slow saturable absorber model with
the coefficients indicated.
TIME-AVERAGED NONLINEAR RESPONSE
63
0.14
Saturable Loss
0.12
0.10
0.08
0.06
0.04
sbr98071301.opj
0.02
1.50
1.51
1.52
1.53
1.54
1.55
1.56
Wavelength (µm)
Figure 4.10 Predicted variation in the saturable loss as a function of wavelength for the structure of Figure
2.3. The data points are taken from Figures 4.8 and 4.9 and extrapolated from Figure 4.8, and
the solid line is a Gaussian fit.
12
2
Saturation Fluence (µJ/cm )
10
8
6
4
2
0
sbr98071301.opj
1.50
1.51
1.52
1.53
1.54
1.55
1.56
Wavelength (µm)
Figure 4.11 Predicted variation in the saturation fluence as a function of wavelength for the structure of
Figure 2.3. The data points are taken from Figures 4.8 and 4.9 and extrapolated from Figure
4.8, and the solid line is a Gaussian fit.
64
CHAPTER 4
35
30
AStruct
25
20
15
10
sbr98071301.opj
5
1.50
1.51
1.52
1.53
1.54
1.55
1.56
Wavelength (µm)
Figure 4.12 Predicted variation in the AStruct parameter as a function of wavelength for the structure of Figure 2.3. The data points are taken from Figures 4.8 and 4.9 and extrapolated from Figure 4.8,
and the solid line is a Gaussian fit.
TIME-AVERAGED NONLINEAR RESPONSE
65
66
CHAPTER 4
CHAPTER 5
STABILIZATION OF PASSIVE MODE-LOCKING
In this chapter1, the time-averaged nonlinear reflectivity of semiconductor saturable
absorber mirrors as a function of incident energy fluence is related to the time-resolved differential reflectivity. The presence of two-photon absorption in commonly used structures is
confirmed. Theoretical calculations predict that two-photon absorption will expand the continuous-wave mode-locking stability regime against Q-switched mode-locking, yet may
simultaneously induce multiple pulses in a laser cavity.
5.1
Effect of Two-Photon Absorption on Reflectivity
Semiconductor saturable absorber mirrors are important components used to modelock a wide range of both solid-state and fiber lasers [65, 16]. Therefore a more complete
characterization of the absorber structures is necessary to further enhance their applicability.
Theoretical consideration of the effect of two-photon absorption (TPA) in saturable Bragg
reflectors predicts that TPA is of limited significance [91]. However, as described in this
chapter, an experimental evaluation of other typical saturable absorber mirror structures
reveals that TPA is not always negligible. The saturation energy of semiconductor saturable
absorber structures is often characterized by varying the pulse fluence up to the peak satura1
Portions of this chapter appear in [115, 116, 97, 98]. Many of the results of this chapter were attained in
collaboration with Elisabeth M. Koontz, Thomas R. Schibli, Dr. Markus Joschko, Dr. Patrick Langlois,
Prof. Franz X. Kärtner, and Prof. Leslie Kolodziejski. Additional useful insights were provided by Prof.
Hermann A. Haus and Igor P. Bilinsky.
STABILIZATION OF PASSIVE MODE-LOCKING
67
tion but rarely far beyond that point. InGaAs saturable absorber structures used for modelocking lasers near 1.55 µm have been studied at high pulse energy densities via saturation
fluence and time-resolved pump-probe measurements. TPA is observed in the saturable
absorber structures in both aforementioned measurements and at fluence levels that are
expected to have an impact on the mode-locking stability and the threshold for multiple
pulses.
The semiconductor saturable absorber mirror structures under study are deposited by
gas source molecular beam epitaxy. An InP half-wave layer, containing InGaAs quantum
wells, was deposited on a 22 period GaAs/AlAs distributed Bragg reflector (DBR). Dielectric
coatings were added to the structures, following epitaxial deposition, to tailor the saturation
properties of the absorber mirrors to specific laser cavities [63, 73]. In structure A shown in
Figure 2.1, two InGaAs quantum wells (λ ~1.45 µm) are located ~15 nm from the surface of
the half-wave layer. A single quarter-wave Al2O3 antireflection coating for 1.55 µm was also
deposited. In structure B shown in Figure 2.3, four InGaAs quantum wells (λ ~1.53 µm) are
located in the center of the half-wave layer. A multi-layer resonant Si/Al2O3 coating with a
center wavelength of ~1.53 µm and a reflectivity of ~70% was added to enhance the absorption and lower the saturation fluence of the absorber.
Figures 5.1 and 5.2 depict the reflectivity at 1.54 microns as a function of energy density for structures A and B respectively, measured in the manner described in the previous
chapter. The significant feature in Figure 5.1 is the rapid roll-off in reflectivity at ~150 µJ/
cm2. The quantum wells in structure A are positioned near a null of the electric field and the
measurements were performed ~90 nm below the bandedge of the quantum wells, hence the
resulting saturable absorption was negligible. Measurements were performed at energy densities up to 1000 µJ/cm2 without observable damage to the sample. For structure B, Figure 5.2
reveals saturable absorption with a saturation fluence of ~1 µJ/cm2, in addition to a rapid rolloff in reflectivity, which occurred at ~20 µJ/cm2. In contrast to structure A, the quantum wells
are located near a peak of the electric field resulting in significant saturable absorption. Visible damage to both the semiconductor material and the resonant coating was observed in
structure B for pulse energy densities greater than 400 µJ/cm2, which is outside of the measurement range shown in Figure 5.2. The energy dependence of the reflectivity drop, seen in
both Figures 5.1 and 5.2, is consistent with the presence of TPA. (It should be noted that the
onset of TPA will move to substantially higher energy densities as the incident pulsewidth is
increased.) The fluence at which the reflectivity roll-off occurred was roughly 8 times lower
for structure B than for structure A, and is consistent with the calculated internal enhancement
produced by the resonant dielectric coating on structure B. A GaAs/AlAs DBR, identical to
68
CHAPTER 5
1.01
1.00
0.98
0.97
0.96
0.95
0.0
Norm. ∆R/R
Reflectivity
0.99
-0.5
-1.0
-1
0.94
0.1
0
1
1
2
3
Delay (ps)
10
4
5
100
1000
2
Energy Density (µJ/cm )
Figure 5.1
Saturation fluence measurements at 1.5 microns for the antireflection coated structure of Figure 2.1. The solid line is a fit using the model described in Section 5.3. The inset depicts the
time-resolved differential reflectivity measured at ~80 µJ/cm2.
those on which the saturable absorbers were deposited, was also measured up to energy densities of 1000 µJ/cm2 and did not exhibit any noticeable change in reflectivity. For a similar
DBR structure, the calculations of Obeidat, et al. predict no reflectivity change over the same
range of energy densities [91].
Pump-probe reflectivity measurements were performed to clarify the cause of the
reflectivity drop observed in the saturation fluence measurements; ~150 fs pulses at 1.54 µm
from an OPO were used in a cross-polarized, collinear arrangement as detailed in Chapter 3.
The inset of Figure 5.1 shows the resulting pump-probe trace at an energy density of ~80 µJ/
cm2; the dominant dynamic is the pump pulse-induced TPA observed by the probe pulse when
the two pulses overlap. Also present, on a longer time scale, is free carrier absorption of the
probe pulse as a result of carriers produced by TPA of the pump pulse. Insets (i) and (ii) of
Figure 5.2 depict the dynamic differential reflectivity for structure B. Inset (i), comprised of
both rapid and longer-lived components, is the response at an energy fluence near saturation,
STABILIZATION OF PASSIVE MODE-LOCKING
69
Norm. ∆R/R
1.05
1.00
0.5
(i)
0.0
-1
0
1
2
3
Delay (ps)
4
5
0.90
No TPA
0.85
0.80
0.75
0.70
Norm. ∆R/R
Reflectivity
0.95
1.0
0.5
0.0
-0.5
-1.0
-1
0.1
(ii)
0
1
2
3
Delay (ps)
1
4
5
10
100
2
Energy Density (µJ/cm )
Figure 5.2
Saturation fluence measurements 1.5 microns for the antireflection coated structure of Figure
2.3. The solid line and dashed lines are calculated using the model described in Section 5.3.
The insets depict the time-resolved differential reflectivity measured at (i) ~10 µJ/cm2 and (ii)
~200 µJ/cm2.
~10 µJ/cm2, where absorption bleaching occurs. (Inset (i) is qualitatively similar to pumpprobe measurements on other saturable absorber structures [65]) The pump-probe response at
~200 µJ/cm2 [see inset (ii)] is well within the high fluence regime (energy densities > ~20 µJ/
cm2) and is considerably different from a typical absorption bleaching response. Near zero
delay, the absorption bleaching is saturated and the TPA component dominates. Transient hot
electron-assisted absorption [121] is also apparent on a 1 ps time scale. Following TPA and
hot electron-assisted absorption, the quantum well bleaching recovers with a time constant
comparable to that observed in inset (i). A more detailed analysis of the high fluence pumpprobe measurements is presented in Chapter 3.
70
CHAPTER 5
5.2
Relating Time-Averaged and Time-Resolved Measurements
In the previous section Figures 5.1 and 5.2 relate, at several fluences, the time-averaged reflectivity measurements to time-resolved pump-probe measurements. However the
two techniques can be related even more directly. The time-averaged measurement detects
the change of reflectivity a pulse induces upon itself. Beginning at a low fluences, as the fluence increases the pulse bleaches the absorption, increasing its own reflectivity, and at higher
influences the pulse induces absorption, decreasing its own reflectivity. This condition of
self-induced change is identical to the condition when the pump and probe pulse in the timeresolved measurement are overlapped at zero delay. The change in reflectivity measured at
zero delay as a function of fluence in the pump-probe measurement corresponds to the reflectivity change observed in the time-averaged measurement.
This correspondence is investigated here quantitatively based on the measurements
obtained in Chapter 3. The structure under investigation was grown by gas source molecular
beam epitaxy and is shown in Figure 2.2. The mirror was a 22-pair GaAs/AlAs distributed
Bragg reflector (DBR) centered at 1.55 µm with a reflectivity >99% over a bandwidth of 100
nm. The absorption layer contained four InGaAs quantum wells (QWs) exhibiting a photoluminescence peak at 1.53 µm centered in a half-wave layer of InP. A single quarter-wave
Al2O3 antireflection coating was also deposited following epitaxial growth. Pump-probe
measurements were taken at 1.54 microns over a wide range of fluences, as illustrated in Figure 3.2. The change in reflectivity at exactly zero delay was plotted as a function of fluence in
Figure 5.3 as the open squares. As expected the typical saturable absorber response is
observed up to ~40 µJ/cm2, and then the onset of TPA and FCA occurs, reducing the reflectivity.
For quantitative comparison, the same structure was characterized using the time-averaged reflectivity measurement. The filled circles in Figure 5.4 show the measured reflectivity
as a function of fluence, and the solid line is a fit based on the slow saturable absorber model.
Quantitative comparison of the results of Figure 5.3 and 5.4 is quite favorable. The modulation depth in both cases is approximately 1.5-2 percent. The fluence at which the peak reflectivity occurs appears to be shifted to a slightly higher value in Figure 5.3 compared to Figure
5.4. This discrepancy, on the order of a factor of two, can reasonably be attributed to errors in
the determination of the fluence in the pump-probe measurement. In both cases the rollover
due to TPA is similar. Overall the two measurements compare quantitatively within error.
STABILIZATION OF PASSIVE MODE-LOCKING
71
-2
∆R/R0 (x10 )
2
0
-2
-4
-6
-8
Figure 5.3
0.1
1
10
100
2
Fluence (µJ/cm )
1000
The change in reflectivity as a function of fluence at 1.54 microns for the antireflection coated
sample of Figure 2.2 as obtained from pump-probe measurements at zero delay. (Open squares
- low fluence probe, filled circles - high fluence probe, filled triangles - subtracted)
Significantly more additional information can be obtained from pump-probe fluencedependent measurements. As discussed in Chapter 3, a high fluence probe can be used to
bleach the available states and isolate the induced absorption affects, as was illustrated in Figure 3.5. The filled circles in Figure 5.3 are the extracted change in reflection at zero delay as
a function of fluence using a high probe fluence. By adjusting the probe fluence in this manner, the bleaching contributions to the reflectivity curve are completely eliminated. The filled
circles in Figure 5.3 show the effect of only the induced absorption by TPA and FCA on the
reflectivity at zero delay. As was done in Figure 3.5, the results using the high and low probe
fluence can be subtracted to obtain a pure bleaching signal. The filled triangles in Figure 5.3
are the result of such subtraction between high and low probe fluence measurements. As
expected the filled triangles show only the effect of bleaching.
Using the pump-probe data, saturation curves for different time delays can also be
generated. Because each of the time components of the impulse response measured in the
pump-probe traces are based on different physical phenomenon, they may have different flu-
72
CHAPTER 5
1.00
λ = 1.54 µm
0.99
Reflectivity
0.98
0.97
2
Fsat ~ 4 µJ/cm
0.96
0.95
0.94
0.93
0.1
1
10
100
1000
2
Fluence (µJ/cm )
Figure 5.4
Measured reflectivity as a function of fluence at 1.54 microns for the antireflection coated
sample of Figure 2.2. The solid line is the result of a fit to a slow saturable absorber model.
ence dependence. Plotting the change in reflection at a time delay other than zero delay in the
pump-probe response illustrates the fluence dependence of the dominant component at that
time delay. For example in Figure 5.5 the open squares are the change in reflectivity as a
function of fluence plotted at 2.5 picoseconds following zero delay. Based on the data presented in Chapter 3, at this time delay carrier recombination effects are dominant. The open
squares in Figure 5.5 show a different fluence dependence than the open squares of Figure 5.3.
The modulation depth is comparable, but the saturation fluence is much higher for this component.
In Figure 5.5 the filled circles show the reflectivity change when a high probe fluence
is used. Because ~150 femtoseconds pulses were used in the measurement, any induced
absorption at 2.5 picoseconds cannot be due to TPA, as TPA is an instantaneous process that
occurs only at zero delay within the cross-correlation (~200 fs). At 2.5 picoseconds the
induced absorption corresponds to the effect of hot free-carrier absorption. The onset of
induced absorption shown by the filled circles occurs at a higher fluence in Figure 4.5 (~250
STABILIZATION OF PASSIVE MODE-LOCKING
73
Change of Reflectivity ∆R/R0
0.04
∆t = 2500 fs
0.02
0.00
-0.02
-0.04
0.1
1
10
100
1000
2
Energy Density (µJ/cm )
Figure 5.5
The change in reflectivity as a function of fluence at 1.54 microns for the antireflection coated
sample of Figure 2.2 as obtained from pump-probe measurements at a delay of 2.5 ps. (Open
squares - low fluence probe, filled circles - high fluence probe, filled triangles - subtracted)
µJ/cm2) than in Figure 5.3 (~70 µJ/cm2). This is consistent with the generation by TPA of
highly excited carriers which produce FCA, as discussed in Chapter 3. Figure 5.5 also shows
the subtracted results as the filled triangles. Again this corresponds to the pure saturable
absorption response of the sample. At higher fluences (>250 µJ/cm2) the change in reflectivity continues to increase, but this nonphysical phenomenon is believed to be due to errors in
the subtraction technique.
5.3
Mode-Locking Stabilization
With time-averaged and time-resolved measurements confirming that TPA is the dominant cause of the reflectivity drop observed in the saturation energy measurements, a fitting
function for the observed saturation response is generated in Figures 5.1 and 5.2. A number of
functions for the reflectivity as a function of fluence are described in Appendix A. Although
74
CHAPTER 5
structure B exhibits both fast and slow recovery dynamics, only a fast absorber model is used
for the purpose of illustration. The addition of a term to account for TPA in the standard fast
absorber model results in:




qo
R ( t ) = 1 –  ----------------------- + βA Struct LI ( t ) + α o = 1 – q tot ( t ) ,
( t )
  1 + I-------



IA
(5.1)
where R(t) is the instantaneous reflectivity, t is a time on the scale of the pulsewidth, qo is the
saturable loss, I(t) is the instantaneous pulse intensity, IA is the saturation intensity of the
absorber, β is the TPA coefficient, AStruct is a structural factor accounting for the field distribution determined by both the dielectric coating and the DBR, L is the absorber thickness, and
αo is the non-saturable loss, all of which define the total saturable absorption, qtot(t). To
model the time-averaged reflectivity, the integral of the product of R(t) and I(t) is calculated,
assuming a Gaussian-shaped pulse. Theoretical regressions using this model match the measured data quite well and are depicted by the solid lines in Figures 5.1 and 5.2. (In contrast,
the dashed line in Figure 5.2 is the calculated reflectivity using the fast absorber model if TPA
is not present.) In fitting the data of structure A, shown in Figure 5.1, the saturable loss is set
to zero (because of both the chosen measurement wavelength and quantum well position).
The theoretical fit to the data for structure B (Figure 5.2) generates qo = 0.09, IA = 3.7 MW/
cm2, αo = 0.056, and AStructL = 8.62 µm with β set to 90 cm/GW [29].
Induced absorption stabilizes mode-locking in a laser by limiting the peak intensity. In
a saturable-absorber mode-locked laser, suppressing Q-switching or Q-switched mode-locking (QSML) is essential to obtaining the desired continuous-wave mode-locked state
(CWML). As shown by the dotted line in Figure 5.2, when the saturation curve of the structure without TPA present is considered, all fluences greater than ~10 µJ/cm2 would induce the
same reflectivity. Therefore in a laser such a structure would not provide a loss mechanism
which favors lower peak intensity CWML pulses over higher peak intensity QWML pulses.
On the other hand, when TPA (or other induced absorption) is present, only fluences near the
peak of the reflectivity curve (~10 µJ/cm2 in Figure 5.2) are favored. Any perturbation in the
cavity which would lead to QSML would be damped because of the higher loss for higher
peak intensities.
This optical limiting concept is illustrated in Figure 5.6, where the pulse envelope as a
function of time is plotted. On the left side of the figure a stable CWML pulse train is present
and experiences a perturbation. When TPA is present, the perturbation is damped back to the
STABILIZATION OF PASSIVE MODE-LOCKING
75
Figure 5.6
Effect of optical limiting on mode-locking stability. In the presence of TPA, following a perturbation the pulse envelope returns to a CWML state (dashed line). In the absence of TPA,
following a perturbation the pulse envelope enters a QSML state (solid line).
original CWML state, with the envelope given by the dashed line. When TPA is not present,
the perturbation leads to an undesirable QSML state, with the envelope given by the solid line.
The induced absorption in the semiconductor saturable absorber mirrors studied here works as
an optical limiter, stabilizing a laser against QSML.
To consider the effect of TPA quantitatively, the impact on mode-locking stability is
considered with the standard stability analysis [43, 87, 48]. The stability conditions derived in
Reference 60 for CWML against QSML are used, with the effect of TPA in the saturable
absorber added to the model using qtot(t) as defined in Equation 5.1. Fast saturable absorption, TPA, loss, and gain saturation are included in the stability analysis of the CWML state
against perturbations. Figure 5.7 illustrates the calculated stability regions in a logarithmic
plot of the saturation power of the absorber versus the pulse energy, both normalized to the
gain saturation [(IAAA/ILAL) versus (W/WL)], where AA is the area of the spot focussed on
76
CHAPTER 5
Figure 5.7
Calculated stability contours for a fast saturable absorber mode-locked laser. QSML is present
in the regions labeled "unstable". CWML is present in the regions labeled "stable". The area
within the solid line is the instability region without TPA included in the model. The area
within the dashed line is the instability region with TPA included in the model.
the absorber, IL is the saturation intensity of the gain, AL is the area of the beam in the gain
medium, W is the pulse energy, and WL = ILALTR where TR is round-trip time of the cavity.
[The normalized pulse energy scales with pump power (W/WL = 0 at the threshold of lasing).]
For the stability calculation the full-width half-maximum pulsewidth for a sech-shaped pulse
is 264 fs and qoTL = 4.1x104, where TL is the upperstate gain lifetime normalized to the cavity
round-trip time. The solid line in Figure 5.7 indicates the instability boundary when TPA is
not included; the inclusion of TPA reduces the instability boundary to the dashed line. Quite
clearly the region of stability is greatly increased in terms of both pulse energy and absorber
saturation when TPA is present in the absorber structure.
Several extensions of this simple model, some of which are detailed in [96, 98], are
necessary for application to specific lasers. Use of a saturable absorption model other than the
fast saturable absorption model will modify the calculated stability regions seen in Figure 5.7.
For many femtosecond lasers where strong soliton-like pulse-shaping occurs, the area theorem relates the pulsewidth to the pulse energy and has two significant consequences: first,
STABILIZATION OF PASSIVE MODE-LOCKING
77
energy increases result in spectral broadening which can be limited by filtering, and second,
energy increases produce pulse shortening which enhances TPA [87, 48]. A complete characterization of these effects requires a more detailed analysis. In general, with the addition of
TPA the stability region will increase, but the size of the improvement will depend on the
magnitude of TPA and the laser under consideration.
While TPA provides stabilization against QSML, it will also lower the threshold for
the occurrence of multiple pulses. As the peak intensity of a pulse increases, TPA-induced
loss will also increase, thus a lower-loss condition for multiple, reduced peak intensity pulses
will be favored. To predict the threshold of multiple pulses, the formalism of Reference 61
can be expanded to include the effects of TPA using qtot(t) as defined in Equation 5.1.
In summary, induced absorption has been observed in semiconductor saturable
absorber mirrors with both saturation fluence and dynamic differential reflectivity measurements. Theoretical analysis demonstrates that while TPA may limit peak power and cause
multiple pulses, it can also enable a laser to reach a stable CWML state that was not previously attainable. Appropriate use of induced absorption may lead to dramatic improvements
in stabilization against QSML for many laser systems.
78
CHAPTER 5
CHAPTER 6
ERBIUM-YTTERBIUM WAVEGUIDE LASER
In this chapter1, experiments are presented in which picosecond pulses are produced
using a semiconductor saturable absorber mirror to mode-lock an Er-Yb waveguide laser.
Continuous-wave mode-locking (CWML) is obtained with ~10 picosecond pulses at 100
MHz. The operating range of the laser illustrates the influence of two-photon absorption on
the mode locking dynamics. When an intracavity filter is added to broaden the mode-locked
spectrum, ~1 picosecond pulses are achieved.
6.1
Waveguide Laser Design
Recently, Er-Yb codoped phosphate glass planar waveguides have been developed as
an alternative to Er-doped silica fiber. Codoped waveguides offer the advantage of a significant reduction in length for equivalent gain due to the higher achievable doping concentrations of Er and Yb in phosphate glass. Such devices have been demonstrated as amplifiers for
high speed communication systems, exhibiting 11.6 dB single-pass net gain in 4.5 cm [4].
Additionally, 2 cm long waveguides have produced up to 170 mW of output power at 1540
nm as continuous-wave lasers [34], and Q-switched pulses of 200 ns with 67 W peak power
have been demonstrated with an active modulator in a cavity containing a 4.3 cm waveguide
[126]. Furthermore, passive additive pulse mode-locking (APM) has been used to generate
1
Portions of this chapter appear in [114, 118]. Many of the results of this chapter were attained in collaboration with Elisabeth M. Koontz, Dr. David J. Jones, Dr. Denis Barbier, Prof. Franz X. Kärtner, and Prof.
Leslie Kolodziejski.
ERBIUM-YTTERBIUM WAVEGUIDE LASER
79
Figure 6.1
Schematic of the laser cavity based on an Er-Yb planar waveguide. The dotted box surrounds
the filtering elements.
116 fs pulses from a fiber ring cavity based on an Er-Yb waveguide; but APM as a mode-locking mechanism becomes less effective at short cavity lengths since the amount of nonlinear
polarization rotation scales with the cavity length [54]. Thus, APM cannot be expected to
mode-lock a high fundamental repetition rate source for telecommunication applications. An
Er-Yb bulk phosphate glass laser has been mode-locked at 2.5 GHz using an active phase
modulator to generate 22 ps pulses [78], but shorter pulses are also needed at high repetition
rates. Semiconductor saturable absorbers, which have been used extensively to mode-lock a
wide range of solid state lasers [65] and fiber lasers [16], are a logical choice for ultrashort
pulse generation within short cavities.
For short pulse generation via continuous-wave mode-locking (CWML), the tendency
of a laser to Q-switch must be suppressed; this tendency increases with shorter cavities and
longer upper-state lifetimes [65]. Use of an organic dye saturable absorber has previously
been shown to produce Q-switching of a Nd-doped waveguide laser (1.054 µm) with ~25 ns
pulses at kHz repetition rates [3]. Here CWML of a laser, based on an Er-Yb planar
waveguide, is obtained by use of a semiconductor saturable absorber mirror that incorporates
intensity-limiting to suppress Q-switching. CWML pulses as short as 1 ps are obtained.
The cavity shown in Figure 6.1 contains a 5.2 cm Er-Yb waveguide, similar to that
reported in [4]. A more detailed description of the waveguide and its characteristics appears
in [55]. Fibers are butt-coupled with index matching fluid to both ends of the waveguide,
which has the intracavity facet at a 6° angle and the output facet polished flat. A 15% transmitting dielectric coating was deposited on the fiber ferule butt-coupled to the flat waveguide
facet providing an output coupler. A semiconductor Master-Oscillator Power Amplifier pump
source provides up to 450 mW at 980 nm coupled into the single-mode input fiber of the
wavelength division multiplexer (WDM). The air gap of the laser contains a lens used to
80
CHAPTER 6
focus the light from the fiber collimator onto the semiconductor saturable absorber mirror.
Initially the cavity was tested without the filtering elements depicted in the dashed box of Figure 6.1.
6.2
Operation Without Filtering
For the laser design of Figure 6.1, the intracavity losses are on the order of 30-40%, so
an absorber with a large saturable loss is required for effective mode-locking. This is in contrast to cases in which semiconductor saturable absorbers with relatively weak absorption
have been used to initiate a stronger mode-locking mechanism, such as Kerr-lens mode-locking [65]. Similarly, in fiber lasers semiconductor saturable absorbers have been used to provide a pulse starting mechanism, with polarization rotation used to optimize mode-locking
[47]. The absorbers used in the laser depicted in Figure 6.1 were designed to have saturable
losses greater than 5%.
The semiconductor saturable absorber mirror structure was deposited via gas source
molecular beam epitaxy and is illustrated in Figure 2.3. The structure consists of a half-wave
layer of InP containing four InGaAs quantum wells (QWs) deposited upon a 22 pair GaAs/
AlAs distributed Bragg reflector. The QWs (λ~1530 nm) are positioned within an InP λ/2
layer, at a peak of the standing wave pattern formed by the mirror, to obtain the lowest saturation energy and highest saturable absorption. Typically, anti-resonant coatings are added to
absorbers for use in high-power, low-loss solid-state lasers. For the laser shown in Figure 6.1
the intracavity power is less than 100 mW and the losses are quite high, so a resonant structure
is used to both increase the absorption and lower the saturation fluence. The 5-layer Si/Al2O3
dielectric coating produces a resonance centered at 1530 nm, near the peak of the Er-Yb gain
spectrum, as discussed in Chapter 4.
When the cavity configuration of Figure 6.1 is used without the filtering elements,
antireflection coated aspheric lenses with focal lengths of 6.24 and 4.5 mm are used to focus
on the absorber. CWML was self-starting at high pump powers, but at low pump powers it
required initiation by translating the saturable absorber mirror to perturb the cavity. Similar
CWML was also obtained with other absorbers having comparable absorption and saturation
fluences. At all pump powers the laser operated on the narrow Er-Yb gain peak at 1534 nm.
A typical second-harmonic autocorrelation (AC) is shown in Figure 6.2, and the corresponding optical spectrum for the CWML state is shown in Figure 6.3. For the data presented, the
output power was 1.43 mW for 125 mW of pump power, and the repetition rate was 102 MHz.
ERBIUM-YTTERBIUM WAVEGUIDE LASER
81
Intensity
1.0
sbr99050101
0.5
9.8 ps
0.0
-20
-10
0
10
20
Delay (ps)
Figure 6.2
Second harmonic generation autocorrelation of the pulses obtained with the cavity configuration of Figure 6.1 without filtering (data – solid, sech fit – dashed).
-20
sbr99050101
Power (dB)
-30
-40
-50
-60
-70
1532
1533
1534
1535
1536
Wavelength (nm)
Figure 6.3
82
Optical spectrum centered at 1534 nm of the pulses obtained with the cavity configuration of
Figure 6.1 without filtering.
CHAPTER 6
The relaxation oscillation sidemodes were suppressed by ~60 dB in the radio-frequency spectrum. The AC is fit well by a sech pulse having a width of 9.8 ps, shown as the dashed line in
Figure 6.2. The spectrum is centered at 1534.4 nm with a full-width at half-maximum
(FWHM) of 0.51 nm, which results in a time bandwidth product of 0.63, indicating the pulses
are somewhat chirped. CWML with similar pulse characteristics was obtained at 25 and 50
MHz by changing the length of fiber in the cavity.
6.3
Absorber Operation
The nonlinear reflectivity of the resonant absorber structure was measured as a function of energy density (fluence) with ~150 fs pulses at 1530 nm from an optical parametric
oscillator, using several lenses to obtain a wide range of fluences as detailed in Chapter 4. The
focussed 1/e2 intensity spot sizes were determined by scanning knife-edge measurements.
The measured reflectivity of the saturable absorber mirror is shown in Figure 6.4. (filled circles). The standard saturable absorber response is present up to ~20 µJ/cm2, at which point a
decrease in reflectivity dominated by two-photon absorption (TPA) occurs [116]. The solid
lines in Figure 6.4 depict the components of a fit using a simple model of the nonlinear reflectivity which includes non-saturable loss, absorber saturation (labeled SA), and TPA (labeled
TPA 150 fs). The details of the model are discussed in Appendix A. From the fit, the
absorber exhibits an effective saturable loss of 14%, a non-saturable loss of 10.5%, and a saturation fluence of 0.8 µJ/cm2 at λ~1530 nm (the peak of the resonant coating). The TPA component of the fit is consistent with the TPA coefficient for InP, β=90 cm/GW [29]. Since TPA
scales with peak intensity, the calculated curves in Figure 6.4 [dashed (TPA for 1 ps pulses)
and dotted (TPA for 9 ps pulses)] depict the expected shift of the onset of TPA-induced loss to
higher fluences as the pulse width is broadened.
In Figure 6.4 the shaded region depicts the fluence incident on the absorber when the
laser is operated in the CWML state having the characteristics illustrated in Figures 6.2 and
6.3. With the nonlinear reflectivity shown in Figure 6.4 for 150 fs pulses, operation at fluences greater than 100 µJ/cm2 would not seem possible. For longer pulse durations however,
the onset of TPA will occur at higher energy densities. The curve for 9 ps pulses indicates that
the CWML operating regime of the laser occurs at fluences near the peak of the net reflectivity, as expected. Since the CWML range coincides well with the SA and TPA (9 ps) curves,
the presence of TPA apparently influences the limits of the operating regime. As discussed in
Chapter 5, mode-locking stability theory predicts that the minimum fluence required for
CWML is decreased because TPA stabilizes against QWML by limiting the peak intensity
ERBIUM-YTTERBIUM WAVEGUIDE LASER
83
SA
Reflectivity
0.90
0.85
TPA
150 fs
0.80
TPA
1 ps
0.75
0.01
Figure 6.4
0.1
1
10
100
1000
2
Energy Density (µJ/cm )
TPA
9 ps
10000
The semiconductor saturable absorber mirror reflectivity measured as a function of incident
energy fluence with 150 fs pulses at 1530 nm (dots). The solid lines are the saturable absorption (SA) and two-photon absorption (TPA 150 fs) components fit to the measured data. The
dotted (TPA 9 ps) and dashed (TPA 1 ps) lines are calculated TPA components. The shaded
region depicts the range of fluences where CWML was obtained with 9.8 ps pulses.
[116]. Furthermore, although additional pump power is available, for fluences beyond 1000
µJ/cm2 the laser output breaks up into bursts of pulses at the fundamental repetition rate, consistent with peak power limiting by TPA.
6.4
Operation With Filtering
When the laser was CWML in the configuration of Figure 6.1 without filtering, neither
pulses shorter than 9 ps nor a spectrum broader than 0.73 nm were obtained. In comparison to
the gain spectrum of Er-doped fiber, the gain spectrum of the Er-Yb waveguide is much less
smooth. The fluorescence spectrum of Er-doped fiber is shown in Figure 6.5 as a function of
pump power. The spectrum was measured from the end of the fiber where the pump was
injected. For comparison, Figure 6.6 shows the measured fluorescence spectrum of the Er-Yb
84
CHAPTER 6
Er Fluorescence
Power (dB)
80
Increasing
Pump
40
0
-40
sbr98110902.opj
1500
1520
1540
1560
1580
1600
Wavelength (nm)
Figure 6.5
Fluorescence of erbium-doped fiber as a function of pump power.
Er/Yb Fluorescence
Power (dB)
80
Increasing
Pump
40
0
-40
-80
sbr98110902.opj
1500
Figure 6.6
1520
1540 1560 1580
Wavelength (nm)
1600
Fluorescence of the erbium-ytterbium waveguide as a function of pump power.
ERBIUM-YTTERBIUM WAVEGUIDE LASER
85
waveguide as a function of pump power. The spectrum was measured from the end of the
waveguide opposite of where the pump was injected. As a function of pump power, the fluorescence of the waveguide changes considerably. For low pump powers, the spectrum is relatively smooth and broad because of re-absorption of the fluorescence in the un-pumped
portion of the waveguide. Operation at low pump power in such a re-absorption regime has
been demonstrated to broaden the mode-locked spectrum and shorten the pulse width of an
Er-Yb fiber laser [16]. In Figure 6.6 as the fluorescence saturates with pump power, the sharp
peak of the Er-Yb fluorescence at 1534 nm is clear. Because of cavity losses, mode-locking in
the configuration of Figure 6.1 was only obtained when the waveguide was pumped sufficiently to invert the entire length of the device. Because the laser is operated at high pump
levels, the fluorescence spectrum at the highest pump power in Figure 6.6 estimates the available gain, which is sharply peaked in a way similar to the mode-locked output spectrum of
Figure 6.3.
To produce a broader effective gain spectrum the additional filtering elements indicated in the dotted box of Figure 6.1 were introduced, consisting of a high reflector for normal
incidence at 1550 nm tilted to produce a tunable edge filter and a λ/4 waveplate to control the
polarization. An additional absorber was also fabricated in which the four QWs were replaced
with a single ~100 nm layer of InGaAs (with a band edge of ~1570 nm) as shown in Figure
2.4. The increase in absorbing material at longer wavelengths provided sufficient saturable
absorption to permit use of a broadband AR coating, enabling tuning of the laser where it was
not previously possible with the highly resonant coating. The reflectivity as a function of fluence is shown in Figure 4.4 of the Chapter 4. The saturation fluence was measured to be 4.7
µJ/cm2, the saturable loss was 6.2%, and the non-saturable loss was 5.9% at 1540 nm.
With careful adjustment of the angle of the filter, the laser could also be mode-locked
at wavelengths other than 1534 nm. The shortest pulses were obtained at 25 MHz and 1545
nm with 0.63 mW of output power for 150 mW of pump power. In Figure 6.7 the filled circles are the second harmonic generation autocorrelation, and the solid line is the best fit provided by a 1.07 ps sech pulse. Figure 6.8 shows the optical spectrum, exhibiting a FWHM of
2.61 nm. The resulting time-bandwidth product is 0.35, nearly transform-limited. Similar 1
ps pulses were obtained at 50 MHz at 1545 nm as well, after fiber was removed to shorten the
cavity. Laser operation with 1 ps pulses was difficult to obtain, and CWML was not achieved
over a wide range of fluences. For the 1 ps pulses at both 25 and 50 MHz, the fluences on the
absorber were ~80 and ~55 µJ/cm2, respectively; these fluences are also consistent with operation near the peak reflectivity for 1 ps pulses (See Figure 6.4), as determined by bleaching of
the absorber and pulse limiting by TPA.
86
CHAPTER 6
Intensity
1.0
0.5
0.0
Figure 6.7
1.07 ps
sbr98111201.opj
-3
-2
-1
0
1
Delay (ps)
2
3
Second harmonic generation autocorrelation of the pulses obtained with the cavity configuration of Figure 6.1 with filtering (data – filled circles, sech fit – solid line).
Output Power (dBm)
-30
-40
-50
-60
-70
-80
Figure 6.8
sbr98111201.opj
1530
1540
1550
Wavelength (nm)
1560
Optical spectrum centered at 1545 nm of the pulses obtained with the cavity configuration of
Figure 6.1 with filtering.
ERBIUM-YTTERBIUM WAVEGUIDE LASER
87
-10
Spectrum (dBm)
-20
-30
-40
-50
-60
sbr98111401
-70
1525 1530 1535 1540 1545 1550 1555 1560 1565
Wavelength (nm)
Figure 6.9
Optical spectrum of tunable pulses obtained at 100 MHz in the cavity configuration of Figure
6.1 by adjusting the bandedge filter.
Wavelength tuning of the laser was attained at both 50 and 100 MHz. When the mirror
was tilted at various angles, the gain was sufficient to produce pulses at 100 MHz at a variety
of wavelengths as shown in Figure 6.9. The figure shows operation at 1542, 1549, and 1553
nm with respective bandwidths of 0.85, 0.82, and 0.5 nm. However, the gain peak at 1534 nm
was not strongly suppressed in this configuration, as can be observed in Figure 6.9 when the
center wavelength approached the sharp gain peak. The significantly narrower spectrum
obtained in this state led to broader pulses of ~3 ps.
In summary, a laser based on an Er-Yb planar waveguide has been mode-locked with a
semiconductor saturable absorber mirror in a cavity potentially scalable to high repetition
rates. Using an absorber with a resonant coating and in the absence of gain filtering, the laser
produced 9.8 ps chirped pulses at 1534 nm with repetition rates up to 100 MHz. The fluence
range over which CWML was attained is consistent with the effects of TPA on stability and
pulse break-up. The addition of a filtering element to suppress the narrow Er-Yb gain peak
88
CHAPTER 6
and shift the laser operation to 1545 nm shortened the pulses to 1 ps at both 25 MHz and 50
MHz. With the filter, 3 ps pulses were generated from 1542-1553 nm at 50 and 100 MHz.
ERBIUM-YTTERBIUM WAVEGUIDE LASER
89
90
CHAPTER 6
CHAPTER 7
STABILIZATION OF HARMONIC MODE-LOCKING
In this chapter1, results are presented of experiments in which two-photon absorption
provided by a semiconductor mirror structure is shown to significantly reduce amplitude fluctuations in a harmonically mode-locked fiber ring laser. Pulse dropouts are eliminated in a
laser producing picosecond pulses at a repetition rate of 2 GHz.
7.1
Stabilizing Harmonically Mode-Locked Lasers
Active harmonically mode-locked fiber lasers are attractive ultrashort pulse sources at
GHz repetition rates. The available gain per meter in erbium-doped silica fiber is small,
requiring laser lengths of several meters. Therefore, fundamental repetition rates are typically
on the scale of MHz. Achieving GHz repetition rates requires that the laser operate at a
harmonic, N, of the fundamental repetition rate, creating N pulses per round trip. However
because the gain lifetime of Er is very slow (milliseconds), the fiber laser cannot equalize the
pulse energies, so the output may contain unequal-amplitude pulses or even pulse dropouts.
Several techniques have been developed to stabilize the pulse train of harmonically modelocked lasers. By controlling the cavity length with a phase-locking circuit, a stable output
stream of 22-ps pulses was produced [100]. A high-finesse Fabry-Perot étalon matched to the
repetition rate of the laser also stabilized the output [42]. Several techniques utilizing peak
1
Portions of this chapter appear in [37, 120]. Many of the results of this chapter were attained in collaboration with Matthew E. Grein, Elisabeth M. Koontz, Prof. Hermann A. Haus, and Prof. Leslie Kolodziejski. Dr. Gale S. Petrich provided additional assistance with deposition.
STABILIZATION OF HARMONIC MODE-LOCKING
91
intensity limiting have been demonstrated in which the loss for high intensity pulses is greater
than that for low intensity pulses, encouraging the formation of a train of equal-intensity
pulses. Proper biasing of nonlinear polarization rotation in the presence of a polarizer
provides a nonlinear stabilization mechanism through additive-pulse limiting (APL); while
effective, this technique suffers from environmental instability [26]. Spectral broadening due
to self-phase modulation (SPM) in the presence of filtering stabilizes against pulse
fluctuations [86]. However, hundreds of meters of fiber are typically required to generate the
necessary SPM to stabilize the pulse train. Recently, others have demonstrated that the
regime of stability can be extended using dispersion management in a sigma laser [12].
Peak intensity limiting in the form of two photon absorption (TPA) by a GaAs wafer in
transmission has been shown to prevent Q-switching in a fundamentally mode-locked
Nd:YAG laser [23]. Recently, TPA in a semiconductor saturable absorber mirror has been
used to stabilize pulses against Q-switched mode-locking [53, 116]. Here a semiconductor
mirror is used to stabilize a train of picosecond pulses and prevent pulse dropouts in a 2 GHz
harmonically mode-locked fiber laser.
7.2
Laser Design
The TPA semiconductor mirror is shown in Figure 7.1 and consists of a ~5.2 µm InP
layer deposited via gas source molecular beam epitaxy onto a 22 period GaAs/AlAs
distributed Bragg reflector (>99% reflectivity over 100 nm, centered at 1.55 µm). A dielectric
antireflection coating was deposited on the structure to enhance the field in the InP. The
structure exhibits only TPA and free-carrier absorption (FCA) in the InP layer, similar to the
structure discussed in Section 3.6. The TPA mirror is incorporated into the cavity at normal
incidence. The spot size on the TPA mirror is adjusted with focusing to control the incident
fluence and correspondingly the amount of TPA-induced loss.
To test the effect of TPA in a harmonically mode-locked fiber laser, the laser of Figure
7.2 was designed to eliminate the stabilizing effect of APL or SPM and filtering. The cavity is
similar to that described in Reference 36 and consists entirely of polarization maintaining
fiber to eliminate APL. To prevent the stabilization effects of SPM and filtering, the total
cavity length is only ~47 m, and a wide, 20 nm interference filter is used to shift the operating
wavelength away from the sharp gain peak near 1530 nm. The cavity includes a circulator
with a collimator to allow insertion of a normal incidence mirror. Aspheric lenses with various
focal lengths are added following the collimator to control the spot size on the mirror. The
92
CHAPTER 7
Figure 7.1
Schematic of an anti-reflection coated two-photon absorption mirror containing an ~5.2
micron thick InP layer. The refractive index and magnitude squared of the electric field
(λ=1.54 µm) are plotted as a function of distance from the GaAs substrate-DBR interface.
Focusing Lens
Dielectric Mirror
or TPA Mirror
Collimator
10 % Output
Circulator
LiNbO3 Amplitude
Modulator
2 GHz
Synthesizer
Figure 7.2
WDM
coupler
20 nm Bandpass
Isolator
Filter
980 nm
pump
EDF
Schematic of actively mode-locked fiber laser. Wavelength division multiplexer (WDM),
Erbium-doped fiber (EDF).
average group velocity dispersion of the cavity is ~6 ps/nm/km (anomalous). The laser is
operated at a harmonic of the round-trip time near 2 GHz with a LiNbO3 amplitude modulator
driven by a radio-frequency (rf) synthesizer.
STABILIZATION OF HARMONIC MODE-LOCKING
93
SHG Intensity, a.u.
1.0
0.8
τ = 980 fs
0.6
0.4
0.2
0.0
-8000
-4000
00012905
Figure 7.3
7.3
0
4000
8000
Delay, fs
Second harmonic generation autocorrelation of the pulses obtained without focusing on TPA
mirror.
Operation Without TPA
Initially, the TPA mirror was placed in the laser cavity without a focusing lens. This
produced a large spot size (~9.5x10-3 cm2) and a fluence << 1 µJ/cm2. Based on the nonlinear
reflectivity measurement shown in Figure 5.1 of the structure of Figure 2.1, the fluence
obtained without focusing in this cavity is well below the level where any significant TPA
could occur [116]. The filter was adjusted so the laser operated at ~1555 nm, and 164 µW
output power was obtained from the 10% output coupler; the laser produced clean ~1 ps
solitons with a spectral full-width-at-half-maximum (FWHM) of 2.65 nm. The second
harmonic-generated (SHG) autocorrelation is shown in Figure 7.3, with the corresponding
spectrum shown in Figure 7.4. Although the spectrum and autocorrelation appear clean, the rf
spectrum exhibits a supermode suppression of only ~27 dB, as shown in Figure 7.5. Such
poor supermode suppression is indicative of amplitude fluctuations or pulse dropouts. A
digitizing oscilloscope measurement is shown in Figure 7.6. The 5 Gsamples/s sampling rate
of the oscilloscope is unable to resolve individual pulses (separated by 500 ps), but groups of
pulse dropouts are easily observed in the resulting trace.
94
CHAPTER 7
0
-5
Intensity, dB
-10
-15
-20
-25
-30
-35
1545
1550
00012902
Figure 7.4
1555
1560
1565
Wavelength, nm
Optical spectrum of the pulses obtained without focusing on TPA mirror.
0
-10
Intensity, dB
-20
-30
-40
-50
-60
-70
00012903
1.990
1.995
2.000
2.005
Frequency, GHz
Figure 7.5
Rf spectrum of output pulses obtained without focusing on TPA mirror. Resolution bandwidth
of 30 kHz.
STABILIZATION OF HARMONIC MODE-LOCKING
95
8
Voltage, mV
6
4
2
0
-150
-100
00012910
Figure 7.6
7.4
-50
0
50
100
150
Time, ns
Digitizing oscilloscope trace obtained without focusing on TPA mirror exhibiting dropouts of
output pulses.
Operation With TPA
To test the influence of TPA on the laser, a lens was added to focus on the TPA mirror,
producing a small spot size (~5x10-8 cm2). Incorporating a lens in the cavity changes the
round-trip time slightly, but all other parameters were held constant, including filtering and
average power. The fundamental repetition rate was ~4.35 MHz, the pulse energy incident
upon the absorber was ~2.8 pJ, and the fluence indicent upon the absorber structure was ~56
µJ/cm2. An autocorrelation of the pulses obtained in this state is shown in Figure 7.7, and the
corresponding spectrum is shown in Figure 7.8. Although the average power is the same as
the previous case, longer ~2 ps pulses are produced with a narrower 1.4 nm FWHM spectrum.
In Figure 7.9 the radio frequency spectrum exhibits a supermode suppression of ~55 dB,
demonstrating a nearly 30 dB improvement. Furthermore, the upper digital oscilloscope trace
of Figure 7.10 verifies the absence of pulse dropouts. The lower trace of Figure 7.10, near 0
mV, is the background noise of the detection system in the absence of optical input.
Comparing the results with and without focusing on the TPA mirror illustrates the
influence of TPA on the system. Supermode suppression is enhanced considerably with TPA.
96
CHAPTER 7
SHG Intensity, a.u.
1.0
0.8
τ = 2.4 ps
0.6
0.4
0.2
0.0
-8000
-4000
0
00012809
spline connected
Figure 7.7
4000
8000
Delay, fs
Second harmonic generation autocorrelation of the pulses obtained with focusing on TPA mirror.
0
Intensity, dB
-10
-20
-30
1545
00012808
Figure 7.8
1550
1555
1560
1565
Wavelength, nm
Optical spectrum of the pulses obtained with focusing on TPA mirror.
STABILIZATION OF HARMONIC MODE-LOCKING
97
0
-10
Intensity, dB
-20
-30
-40
-50
-60
-70
1.985
00012807
Figure 7.9
1.990
1.995
2.000
2.005
Frequency, GHz
Rf spectrum of output pulses obtained with focusing on TPA mirror. Resolution bandwidth of
30 kHz.
The digital oscilloscope traces reveal that enhancement occurs because pulse dropouts are
eliminated. Comparing the voltages measured in the two cases, with TPA present the peak
level drops from ~7.5 mV in Figure 7.6 to ~6.5 mV in Figure 7.10, indicating that with all the
time slots filled there is less energy per pulse. Correspondingly by the soliton area theorem,
longer pulses are expected when TPA is present, as evidenced by the longer autocorrelation in
Figure 7.7 compared to Figure 7.3. However the pulsewidth increases by an amount that is
more (from 0.98 ps to 2.4 ps) than that expected from soliton theory alone, given the energy
difference in the pulses. One possible explanation is clamping of the peak intensity by TPA.
Further verification of the TPA effect was obtained by placing a standard commercial
dielectric mirror in the cavity. Nonlinear reflectivity measurements across a wide range of
fluences show that this mirror does not exhibit TPA. In the cavity, the dielectric mirror
produced results quantitatively similar to those obtained when the TPA mirror was used
without focusing [37].
The results from Figure 5.1 were used to estimate the nonlinear loss in the cavity due
to the TPA mirror. The results from the regression in Figure 5.1 were scaled by the thickness
of the InP layer in the TPA mirror shown in Figure 7.1 and by the longer pulse width incident
on the TPA mirror (2.4 ps) compared to that used in the measurement of Figure 5.1 (150
98
CHAPTER 7
8
7
Voltage, mV
6
5
4
3
2
1
0
-1
-150
-100
00012810
00012912
-50
0
50
100
150
Time, ns
Figure 7.10 Digitizing oscilloscope trace obtained with focusing on TPA mirror exhibiting no pulse dropouts is shown in the upper trace. The detector and instrument noise background in the absence
of the optical input is shown in the lower trace.
femtoseconds). With these assumptions the nonlinear loss induced in the cavity was
calculated to be 0.5-1%. This also agreed with a theoretical calculation of the nonlinear loss
due to TPA estimated by integrating over the standing-wave field present in the TPA mirror.
As shown in Chapter 3, pump-probe measurements on similar structures have shown both
TPA and FCA (from TPA-generated carriers) to be present [72]. The recovery time of FCA in
this structure is faster than the 500 picoseconds between pulses of the laser operated at 2 GHz.
However at higher repetition rates carrier accumulation leading to FCA could have an effect.
7.5
Advantages of TPA
TPA-assisted harmonic mode-locking potentially offers advantages over other
stabilization mechanisms. Because the nonlinearity required for peak intensity limiting is
contained in a thin semiconductor layer, stabilization of very short cavities is possible. The
small size of the TPA mirror compared to hundreds of meters of fiber, provides much less
sensitivity to environmental changes, and the mirror can be easily incorporated into
STABILIZATION OF HARMONIC MODE-LOCKING
99
polarization-maintaining or sigma-type cavities. TPA depends on the peak intensity, thus is
effective regardless of the dispersion of the laser; hence lasers in a non-soliton regime could
also be stabilized. Most semiconductors exhibit TPA over a very broad wavelength range,
allowing application to a variety of laser systems.
In conclusion, a TPA mirror has been demonstrated as a new device for stabilizing a
harmonically mode-locked laser. Supermode suppression in a 2 GHz harmonically modelocked fiber laser was improved by nearly 30 dB, and pulse dropouts were eliminated. TPA
offers a number of advantages over other stabilization techniques and can be applied to a wide
range of laser systems.
100
CHAPTER 7
CHAPTER 8
CONCLUSIONS AND FUTURE WORK
8.1
Conclusions
This thesis has described several significant advances in the application of semiconductor structures to passively and actively mode-locked fiber and waveguide lasers. Timeresolved pump-probe measurements were performed to characterize the nonlinear response of
semiconductor saturable absorber mirrors at high fluences and as a function of wavelength.
The effects of carrier cooling, two-photon absorption, free-carrier absorption, hot free-carrier
absorption, and carrier diffusion on the nonlinear response of semiconductor saturable
absorber mirrors has been detailed. A high probe fluence technique was used to separate
induced absorption dynamics from bleaching dynamics, and a two-color technique was used
to clarify the dynamics of hot free-carriers.
Time-averaged reflectivity measurements have been performed to develop accurate
models of laser mode-locking and to the determine the impact of various structural designs.
Time-resolved and time-averaged measurements have been related quantitatively to determine
the impact of high-fluence dynamics on mode-locking. Induced absorption present at high
intensity in semiconductor saturable absorbers has been predicted to stabilize continuouswave mode-locking against Q-switched mode-locking.
An erbium-ytterbium waveguide laser has been mode-locked with a semiconductor
saturable absorber mirror. Without intracavity filtering, the laser produced ten picosecond
pulses at 100 MHz. In this regime the effect of two-photon absorption on the stability of
CONCLUSIONS AND FUTURE WORK
101
mode-locking was observed. When intracavity filtering was added to the laser, one picosecond pulses were produced at 100 MHz and could be tuned from 1530 to 1555 nm.
A novel InP semiconductor mirror exhibiting only induced absorption was used to
enhance the stability of an active harmonically mode-locked fiber laser operating at 2 GHz.
The fiber laser was carefully designed to eliminate other mechanisms which could suppress
supermodes, to isolate the role of the semiconductor mirror. The addition of the TPA mirror
improved supermode suppression by nearly 30 dB and eliminated pulse dropouts.
Although significant progress has been made in applying semiconductor structures to
fiber and waveguide lasers, several areas remain for further investigation, some of which are
detailed in the following section.
8.2
Future Work
Reducing the saturable absorber recovery time would have a number of beneficial
effects, such as shorter pulses generated by saturable-absorber mode-locking and the possibility of mode-locking at high fundamental repetition rates. As discussed in Appendix B,
because the lifetime of the saturable absorber appears to limit the possibility of passive harmonic mode-locking, reducing the recombination time of the absorber should also allow harmonic operation with a larger number of pulses. One simple post-growth technique to reduce
the recombination time is proton bombardment [119], which produces defects in the material,
reducing the carrier lifetime. Careful characterization of the post-bombardment ultrafast
dynamics and testing the resulting saturable absorbers in various lasers should clarify the
importance of lifetime reduction.
The motivation in developing the erbium-ytterbium waveguide laser was to produce a
source fundamentally mode-locked at a high repetition rate. In this thesis a demonstration
only up to 100 MHz was attained. The cavity length could be reduced by moving the pump
multiplexer external to the laser cavity and passing the pump through a dichroic output coupler. Another possibility would be to use pump multiplexers integrated on a waveguide chip,
which have recently been developed by Teem Photonics. Finally the free space portion of the
cavity could be eliminated, by directly contacting the saturable absorber mirror to the
waveguide. However several obstacles will also have to be overcome to obtain high repetition
rates. First, the absorber recovery time will likely limit the attainable repetition rate, as discussed above. If proton bombardment can be used to sufficiently reduce the lifetime, then
mode-locking a waveguide laser at high repetition rates should be possible. Second, if the
102
CHAPTER 8
free-space focusing on the absorber is removed, the saturation fluence of the absorber must be
designed to match the mode-field diameter of the waveguide. Third, obtaining the proper
starting conditions for the laser was always difficult, so without an air gap, adjustments to the
cavity will be even more challenging. This difficultly may be reduced if an absorber with a
larger modulation depth could be developed.
Although significant supermode suppression was demonstrated for an active harmonically mode-locked fiber laser, semiconductor structures could be applied to greater advantage.
Demonstrating the stabilizing effect of two-photon absorption in lasers where other stabilization mechanisms are not available would illustrate the unique advantages of semiconductorbased stabilization. For instance, stabilization of a very short cavity or operating in a nonsoliton regime should be possible. The effect of the recovery time of the semiconductor
should be investigated. As in the case of the saturable absorber, the lifetime of the carriers in
a TPA mirror will likely dictate the repetition rate at which such a mirror could be used. In the
same way, proton bombardment may also provide a solution. Demonstrating a way to scale
the amount of induced absorption to an arbitrary level would also broaden the usefulness of
the technique. Incorporating such structures into the linear harmonically mode-locked fiber
laser demonstrated in Appendix C should be possible. Finally semiconductor saturable
absorbers could be added to active harmonically mode-locked lasers to attain shorter pulses
than would be possible otherwise.
A number of studies of mode-locking with semiconductor saturable absorber mirrors
could be undertaken with the linear fiber laser detailed in Appendix B. Significantly clearer
demonstrations of the role of TPA in stabilizing mode-locking could be performed with picosecond pulses or in a non-soliton regime where the spectral width is no longer energy dependent. Investigating the dependence of the output characteristics on the saturable absorber
properties and cavity dispersion maps are possible. Finally, providing a detailed physical
explanation for polarization sideband generation should be possible with further study.
CONCLUSIONS AND FUTURE WORK
103
104
CHAPTER 8
APPENDIX A
MODELS FOR NONLINEAR REFLECTIVITY
In this appendix1, several different models for the reflectivity of a saturable absorber
as a function of fluence are presented. The cases of the slow and fast absorber models with
and without spatial effects are derived. A simple model of two photon absorption is also
given.
A.1
Slow Saturable Absorber
Chapter 3 illustrates that the time response of semiconductor saturable absorbers can
be quite complicated, involving multiple time constants, several different physical processes,
and various saturation fluences. However simple approximations of the absorber response
can be quite useful in modeling mode-locking dynamics in lasers. A rudimentary model of a
saturable absorber exhibiting a single time constant and saturation energy is given by the differential equation
2
q – qo
A
dq
------ = – -------------- – q --------- ,
EA
dt
τA
1
(A.1)
Portions of this appendix appear in [115, 116, 96, 97, 98]. Many of the results of this appendix were
attained in collaboration with Thomas R. Schibli, Elisabeth M. Koontz, Dr. Markus Joschko, Dr. Patrick
Langlois, Prof. Franz X. Kärtner, and Prof. Leslie Kolodziejski. Additional useful insights were provided
by Prof. Hermann A. Haus and Igor P. Bilinsky.
MODELS FOR NONLINEAR REFLECTIVITY
105
where q is the round-trip (saturated) loss, t is a time on the scale of the pulse duration, qo is the
unsaturated but saturable loss, τA is the recovery time of the absorber, A is the normalized
slowly varying electric field envelope, and EA is the saturation energy of the absorber. For
analytic manipulation, Equation A.1 for the response of the absorber is often even further simplified in the slow or fast saturable absorber limits. The slow absorber model describes the
case in which
τ A » τ Pulse ,
(A.2)
where τPulse is the pulse width incident on the absorber. In such a limit
2
q – qo
A
-------------- « q --------- ,
EA
τA
(A.3)
and Equation A.1 simplifies to
2
A
dq
------ = – q --------- .
EA
dt
(A.4)
q
W- ,
ln  ----- = ----- q o
EA
(A.5)
Integrating Equation A.4 gives
where W is defined as
t
2
∫
W =
A dt .
(A.6)
–∞
Equation A.5 may be solved for the instantaneous loss
q = qo e
– W ⁄ EA
.
(A.7)
dt ,
(A.8)
The time-averaged loss for the pulse is given by
1
q̃ = -------Wo
106
∞
∫qA
2
–∞
APPENDIX A
where W o = W ( t = ∞ ) is the pulse energy. This equation may be solved by noting, based on
Equation A.6, that
2
dW
--------- = A .
dt
(A.9)
Substituting Equations A.7 and A.9 into Equation A.8 and considering the resulting change in
variable gives
1
q̃ slow = -------Wo
Wo
∫ qo e
– W′ ⁄ EA
dW′ ,
(A.10)
0
which is easily integrated to produce
–W ⁄ E
q̃ slow
qo ( 1 – e o A )
= --------------------------------------- ,
Wo ⁄ EA
(A.11)
the time-averaged loss for the pulse as a function of pulse energy in a slow saturable absorber.
For small Wo/EA, Equation A.11 simplifies to
W
q̃ slow ≅ q o  1 – ---------o- .

2E 
(A.12)
A
A.2
Fast Saturable Absorber
A similar expression for the time-averaged reflectivity can be obtained for the fast saturable
absorber case. In this limit
τ A « τ Pulse .
(A.13)
Since the absorber response time is much faster than the pulse duration, the saturable loss will
follow the pulse envelope. As a consequence,
q–q
dq
------ « -------------o- ,
dt
τA
(A.14)
which reduces Equation A.1 to
MODELS FOR NONLINEAR REFLECTIVITY
107
2
q – qo
A
-------------- = – q --------- .
EA
τA
(A.15)
Solving for the saturated loss gives
qo
q = ------------------,
2
A
1 + --------IA
(A.16)
where the absorber saturation intensity, IA, is defined as
EA
I A = ------.
τA
(A.17)
For the slow saturable absorber case, the time-averaged response did not depend on a particular pulse shape. Because the fast saturable absorber follows the pulse envelope, the time-averaged response does depend on a particular pulse shape. Here the time-averaged response is
calculated for a hyperbolic secant pulse, given by
A ( t ) = A o sech -t ,
τ
(A.18)
where Ao is the peak field amplitude and τ is the hyperbolic secant pulse width. Substituting
this pulse shape into Equation A.6 gives the pulse energy:
W o = 2A o2 τ .
(A.19)
The time-averaged saturated loss can be obtained from Equation A.8 using the expression for
the instantaneous saturated loss in Equation A.16, the pulse shape in Equation A.18, and the
pulse energy in Equation A.19 to give
q̃ fast
1 = -----------2A o2 τ
∞
qo
2t
--------------------------------∫ Ao2 2 t- Ao2 sec h -τ- dt .
– ∞ 1 + ------- sec h -IA
τ
(A.20)
To solve this integral, a change of variable is performed using
x = -t- ,
τ
108
(A.21)
APPENDIX A
with the identities
d2
----tanh x = sec h x
dx
(A.22)
and
2
2
1 – tan h x = sec h x ,
(A.23)
and the introduction of the dimensionless intensity parameter
W
α = ----------- .
2I A τ
(A.24)
Equation A.20 reduces to
q̃ fast
∞
qo
= ----2
1
d
-  ------ tanh x dx .
∫ --------------------------------------2  dx

1 + α – α tan h x
(A.25)
–∞
A further change of variable is performed using
y = tanh x ,
(A.26)
to produce
1
q̃fast
qo
1
= ----- ∫ ----------------------------2 dy .
2 1 + α – αy
(A.27)
α -,
-----------1+α
(A.28)
–1
A final change of variable using
z =
gives
qo
α q̃ fast = ----- --------------------2 α( 1 + α)
α
------------1+α
∫
α – -----------1+α
1 ------------dz ,
2
1–z
(A.29)
which can be analytically integrated to
MODELS FOR NONLINEAR REFLECTIVITY
109
1 - arc tanh  -----------α - ,
q̃fast = q o --------------------
1 + α
α( 1 + α)
(A.30)
the time-averaged loss of the pulse in a fast saturable absorber, assuming a hyperbolic secant
pulse shape.
A.3
Slow Saturable Absorber with Spatial Effects
When a beam is focused on to a saturable absorber, the intensity varies spatially. The
expressions derived in the previous two sections assumed an intensity distribution which is
constant spatially. The normalized intensity incident on a saturable absorber as a function of
time and position for a Gaussian beam can be written
Wo
2 – r2 ⁄ w2o
,
I ( r ,t ) = ------------- ( f ( t ) )  ------2- e
w

τ Pulse
o
(A.31)
where r is the radial position from the center of the beam, Wo is the total pulse energy, f(t) is
the temporal pulse shape, wo is the Gaussian beam waist, and the coefficients are such that the
equation is normalized to
∫ ∫ I ( r ,t ) dt dA
= Wo .
(A.32)
Inspection of Equation A.31 reveals that the spatial and temporal components are mathematically separable. Therefore including spatial effects into the time-averaged saturated loss only
involves the spatial integration of the previous results. The time-average saturated loss for the
slow absorber case, Equation A.11, may be rewritten in terms of fluence as
–F ⁄ F
q̃ slow
A
qo ( 1 – e
)
= ----------------------------------- ,
F ⁄ FA
(A.33)
2
where the fluence F ( r = 0 ) = 2W o ⁄ w o is given by
2W o –r 2 ⁄ w2o
-e
F = ---------,
w o2
(A.34)
and the saturation fluence of the absorber is given by
110
APPENDIX A
2E
F A = ---------A- .
w o2
(A.35)
Substituting equations A.34 and A.35 into A.33 and integrating over the normalized Gaussian
beam distribution gives
2 2
–r ⁄ w
q̃ slow, eff
o
Woe


– ----------------------
EA 
1 – e


 2 2
∞

 –r ⁄ wo 2r
------- dr .
-e
= ∫ qo ------------------------------------2
2
–r ⁄ wo
w o2
0
Woe
-----------------------EA
(A.36)
The integral is simplified with a change of variable
2
r ,
x = -----w o2
(A.37)
to
Wo
q̃ slow, eff
–x
– ------- e 
EA ∞ 
EA
------= qo
1 – e
 dx .
∫
Wo 0 

(A.38)
An additional change of variable
–x
y = e ,
(A.39)
gives
Wo
q̃ slow, eff
– ------- y

EA
1 – e

EA 0 

= q o -------- ∫ ---------------------------- dy .
Wo 1
y
(A.40)
A final change variable
Wo
z = y -------- ,
EA
(A.41)
produces the time- and spatially-averaged saturated loss for a slow saturable absorber,
MODELS FOR NONLINEAR REFLECTIVITY
111
q̃ slow, eff
E A W o ⁄ EA ( 1 – e –z )
--------------------- dz .
= q o -------- ∫
z
Wo 0
(A.42)
Although the result is not fully analytic, Equation A.42 requires the evaluation of only a single
normalized numerical integral. For small z, the equation simplifies to
W
q̃slow, eff ≅ q o  1 – ---------o- .

4E A
(A.43)
In this limit, the saturation fluence for the pulse as a whole, with a Gaussian spatial distribution, is EA/2, not the expression given by Equation A.35.
A.4
Fast Saturable Absorber with Spatial Effects
As with the slow absorber case of the last section, spatial effects can be readily included in the
fast saturable absorber case. The dimensionless power parameter of Equation A.24 can be
redefined to include a spatial intensity distribution
2
–r ⁄ w
2
o
Io e
W
I
r
(
)
α = ----------- = --------- = --------------------- ,
2I A τ
IA
IA
(A.44)
where Io is the peak intensity and IA is the saturation intensity. After substituting Equation
A.44, the time-average saturated loss for the fast saturable absorber, Equation A.30, can be
integrated over the normalized Gaussian beam distribution to give
q̃ fast, eff =
∞
∫0 qo
I o –r 2 ⁄ w2o 

----e

 2 2
IA
2r1

 e – r ⁄ wo -----dr . (A.45)
----------------------------------------------------------arc
tanh
------------------------------
I o –r 2 ⁄ w2o
I o –r 2 ⁄ w2o
I o –r 2 ⁄ w2o 
w o2
 1 + ----- e

----- e
1 + ----- e


IA
IA
IA


A change of variable
2
r -,
x = -----w o2
(A.46)
gives
112
APPENDIX A
q̃ fast, eff =
I


----o- e –x 

I
–x
1
A
------------------------------------------ arc tanh  ---------------------- e dx .


I
I
I
 1 + ----o- e –x
----o- e –x  1 + ----o- e –x
IA 
IA 
IA 

∞
∫0 qo
(A.47)
A further change of variable
–x
y = e ,
(A.48)
produces
q̃ fast, eff =
1
∫0 qo
I


----o- y 

IA 
1
-------------------------------- arc tanh  ----------------- dy .

Io 
Io 
Io 
 1 + ----- y
----- y 1 + ----- y
IA 
IA 
IA 

(A.49)
A final change of variable
Io
z = y ----- ,
IA
(A.50)
gives the time- and spatially-averaged saturated loss for a fast saturable absorber
Is Io ⁄ Is
1
z - dz .
-------------------arc
tanh  ----------q̃ fast, eff = qo ---- ∫

Io 0
z(1 + z)
1 + z
(A.51)
As with the slow absorber case, the final result is a normalized numerical integral.
A.5
Two-Photon Absorption
The time-averaged loss due to two-photon absorption can be derived in a way similar to the
losses in the previous sections. The instantaneous loss due to TPA follows the equation
1 – q TPA = e
– α TPA L
,
(A.52)
where qTPA is the instantaneous loss due to TPA, αTPA is the loss coefficient for TPA, and L is
the thickness of the TPA region. For most of the cases considered here (and measured in
MODELS FOR NONLINEAR REFLECTIVITY
113
Chapter 4), the TPA-induced loss is relatively small. A perturbational approximation to the
exponential can be used to give
1 – q TPA ≅ 1 – α TPA L ,
(A.53)
q TPA ≅ α TPA L .
(A.54)
and
The TPA loss coefficients can be written in terms of physical parameters as
2
βA Struct A
q TPA ≅ ------------------------------ L ,
A Eff
(A.55)
where β is the TPA coefficient for the material, AStruct is a parameter accounting for structural
effects such as the standing wave field and intensity enhancement due to various optical coatings, and AEff is the spot size on the TPA region. The time-averaged loss due to TPA is
obtained assuming the hyperbolic secant pulse shape of Equation A.18 and by substituting
Equation A.55 into Equation A.8 to give
q̃ TPA
1 βA Struct L 4
= ----- ------------------------ A o
W A Eff
∞
∫ sec h
–∞
4t
-- dt .
τ
(A.56)
To solve in terms of the pulse energy, Equation A.19 provides the relation
2
W
4
A o = -------o- .
2
4τ
(A.57)
Substituting Equation A.57 and analytically performing the integral in Equation A.56 gives
2
q̃ TPA
1 βA Struct L W o 4τ
= -------- ------------------------ -------2- ----- ,
W o A Eff 4τ 3
(A.58)
which can be simplified to
βA Struct L W o
q̃ TPA = ------------------------ -------- ,
3A Eff τ
114
(A.59)
APPENDIX A
the final expression for the time-average loss due to TPA assuming a hyperbolic secant pulse
shape.
A.6
Time-Averaged Reflectivity
The results of the previous several sections may be combined to produce a function for
the time-averaged reflectivity, R̃ , which includes effects of saturable absorption, two-photon
absorption, and non-saturable loss. The time-averaged reflectivity is simply the subtraction of
the various loss terms from the maximum reflectivity
R̃ = 1 – q̃ – q̃ TPA – α o ,
(A.60)
where q̃ is selected from the models above depending on the absorber, q̃ TPA is taken from the
previous section, and αo is the non-saturable loss.
MODELS FOR NONLINEAR REFLECTIVITY
115
116
APPENDIX A
APPENDIX B
PASSIVELY MODE-LOCKED FIBER LASER
In this appendix1, preliminary results from a linear fiber laser mode-locked with a
semiconductor saturable absorber mirror are presented. The effects of various dispersion
maps on pulse generation were investigated. Initial studies of spectral sidebands produced by
polarization rotation in the laser were completed. Saturable absorber mirror structures
designed for stabilizing mode-locking with TPA were tested. Finally, pulse bunching in the
laser, presumably due to absorber recovery, was investigated.
B.1
Dispersion Management
Linear fiber lasers with a variety of dispersion maps were mode-locked with a semiconductor saturable absorber mirror. The semiconductor structure consisted of an anti-reflection coated half-wave InP-based absorber structure deposited by gas source molecular beam
epitaxy on a distributed Bragg reflector (DBR). The AlAs/GaAs DBR produces >99% reflectivity over ~100 nm, centered at 1550 nm. The absorber layer consists of six InGaAs quantum
wells (λ ~ 1580 nm) centered within the half-wave layer for maximum interaction with the
standing wave formed by the mirror.
1
Many of the results of this appendix were attained in collaboration with Elisabeth M. Koontz, Juliet T.
Gopinath, Thomas R. Schibli, Prof. Franz X. Kärtner, and Prof. Leslie Kolodziejski.
PASSIVELY MODE-LOCKED FIBER LASER
117
98 0 nm
Pump
L en s
W DM
E DF
x
S atu ra ble
A b so rb er
Figure B.1
λ /4
C o llim a tor
15 % Ou tp ut
C o u pler
SMF
x
SMF
Schematic of fiber laser. Wavelength Division Multiplexer (WDM), Erbium Doped Fiber
(EDF), Single-Mode Fiber (SMF).
The laser cavity shown in Figure B.1 was constructed. The net dispersion of the cavity
was controlled by changing the amount of anomalous dispersion fiber (SMF-28) relative to
the amount of normal dispersion erbium-doped fiber (EDF). The fluence incident on the
absorber was controlled by selecting the focal length of the focusing lens and the intracavity
power. When the cavity was adjusted for a round-trip dispersion of -0.133 ps2, the laser
would self-start to produce a single pulse with the spectrum shown in Figure B.2. The full
width at half maximum of the spectrum was 4.84 nm. The spectrum exhibits considerable
sideband structure. Kelly sidebands are present as well as polarization sidebands, which will
be discussed in the Section B.2. As with other soliton lasers, multiple pulses were generated
as the pump power was increased, as will be discussed in Section B.4.
The round-trip dispersion of the laser was modified to +0.007 ps2 by reducing the
amount of SMF-28 in the cavity. Again mode-locking was self-starting, and the spectrum of
Figure B.3, with a full-width-at-half-maximum of 10.95 nm, was produced by a single pulse.
At this dispersion the sideband structure is considerably reduced and the bandwidth broadened. The dependence of the spectral width on the dispersion of the cavity and the reduction
of sidebands are similar to the effects observed in stretched pulse P-APM ring lasers. Further
investigation of the dependence of the output characteristics on the saturable absorber properties and cavity dispersion maps are an area of potential study.
B.2
Polarization Sidebands
The optical spectrum of Figure B.2 exhibits the expected Kelly sidebands because the
net dispersion is anomalous [66], but other sidebands are also present. Such sidebands have
been observed in other linear saturable absorber mode-locked fiber lasers and were denoted
polarization sidebands [19]. Researchers have attributed other unusual sideband structure in
118
APPENDIX B
-30
Spectrum (dB)
-40
-50
-60
1570
Figure B.2
1580
1590
1600
Wavelength (nm)
1610
Optical spectrum obtained for anomalous dispersion operation.
APM mode-locked fiber lasers to modulation instability [113]. Here, the occurrence of the
polarization sidebands appeared to be related to the evolution of the polarization state in the
laser. Because the laser does not include a significant polarization-dependent loss, the output
polarization is free to rotate. Depending on the polarization control in the laser, the output
polarization will rotate at different frequencies. With appropriate biasing of the laser in polarization and energy, vector solitons can be formed, which by virtue of their nonlinearity maintain a specific "locked" polarization state [20]. When vector solitons are formed the
polarization sidebands are no longer present in the optical spectrum. Although such vector
solitons have been studied both theoretically and experimentally [20, 18, 104], a detailed
explanation for the polarization sidebands has not been proposed.
To investigate the dependence of the polarization sidebands on intracavity polarization
state, the optical spectrum was measured as a function of intracavity wave-plate rotation.
Figure B.4 shows the optical spectrum measured as the quarter wave-plate shown in Figure
B.1 was varied in five degree increments. A small amount of continuous-wave breakthrough
PASSIVELY MODE-LOCKED FIBER LASER
119
Spectrum (dB)
-30
-40
-50
-60
1570
Figure B.3
1580
1590
1600
Wavelength (nm)
1610
Optical spectrum obtained for slightly normal dispersion operation.
is apparent in the optical spectrum, but the autocorrelation remained clean for all states.
Clearly as a function of wave-plate rotation, the location of some of the sidebands changes.
Those sidebands which are fixed in wavelength are thought to be Kelly sidebands, and those
which move are denoted polarization sidebands. Pairs of polarization sidebands appear to
cross at approximately 1565 and 1548 nm in the bottom trace. For a very narrow range of
wave-plate settings outside of those shown in the figure, vector solitons were obtained.
To further characterize the various sidebands, the polarization state of the spectra was
measured. The output of the laser was measured on an optical spectrum analyzer after collimation into free space and passing through a quarter wave-plate, half wave-plate, and polarizing beam splitter. Initially the transmitted power through the polarizing beam splitter was
maximized by adjusting the two wave-plates external to the laser. The optical spectrum was
measured as a function of external half wave-plate rotation. Figure B.5 shows the measured
optical spectrum with the external half wave-plate varied from zero degrees in the top trace to
45 degrees in the bottom trace, moving between two orthogonal polarization states. From
120
APPENDIX B
-20
sbr98111001.opj
Spectrum (dBm)
-40
-60
-80
-100
-120
1540
1550
1560
1570
1580
Wavelength (nm)
Figure B.4
Optical spectrum for various intracavity quarter-wave-plate settings. From top to bottom the
wave-plate is varied in five degree increments.
Figure B.5 some polarization sidebands appear in one polarization state but not in the other.
This result suggests that polarization sidebands are associated with both orthogonal polarization states. At this point the physical mechanism for the sideband generation is unclear, and
more study is necessary.
B.3
Stabilization with Two-Photon Absorption
Although in Section 6.3 the operation of the erbium-ytterbium waveguide laser
appeared to illustrate the influence of two-photon absorption on mode-locking stability, the
results did not provide a quantitative measure of the impact. A quantitative study was
attempted using the soliton laser of Figure B.1 and a variety of semiconductor saturable
absorber mirrors. The mirror structure of Figure 2.4 was overgrown with additional layers of
InP. Because the InP will only add induced absorption, the additional layers lower the fluence
threshold at which induced absorption occurs without altering the saturable absorber proper-
PASSIVELY MODE-LOCKED FIBER LASER
121
-20
sbr98112401.opj
Spectrum (dBm)
-40
-60
-80
-100
-120
1540
1550
1560
1570
1580
Wavelength (nm)
Figure B.5
Optical spectrum through a polarizing beam splitter with various external-cavity half-waveplate settings. From top to bottom the wave-plate is varied from 45 to 0 degrees.
ties. Saturable absorber mirrors without InP overgrowth, 5 λ/2-layers of additional InP, and
20 λ/2-layers of additional InP were tested in the laser under identical conditions.
In Figure B.6, the spectral full-width-at-half-maximum is plotted as a function of pulse
energy in the cavity, for each of the structures over the range where a single pulses was
present. The lowest pulse energy corresponds to the continuous-wave mode-locking
(CWML) threshold. The highest pulse energy corresponds to a pulse breaking threshold,
where more than one pulse begins to exist because two pulses of lower peak intensity sense
less loss than a single pulse. From the stabilization theory, additional two-photon absorption
should lower the pulse energy threshold where CWML occurs, and this is the case in the data.
Additionally stronger intensity limiting should lower the threshold where pulses breaking
occurs. In Figure B.6, the pulse breaking threshold decreases significantly. Although these
results are quantitative, the threshold differences of less than 20% are not overly dramatic.
Such small differences are likely because the laser is operated in the soliton regime, where
122
APPENDIX B
∆λFWHM (nm)
5
4
λ/2
3
6 λ/2 InP
InP
2
21 λ/2
6 λ/2
InP
21 λ/2
1
InP
0
60
70
λ/2
InP
InP
Pulse Breaking
Threshold
CWML
Threshold
80
90
100
110
Pulse Energy (pJ)
Figure B.6
Spectral width versus pulse energy for a soliton fiber laser mode-locked with saturable
absorber mirrors having different thicknesses of InP.
intensity limiting must compete with filtering. Future work with picosecond pulses or in a
non-soliton regime where the spectral width is no longer energy dependent could provide a
significantly more clear demonstration of stabilization with TPA.
B.4
Absorber Lifetime Reduction
The laser of Figure B.1 can be pumped to reach a multiple pulse regime. In Figure B.7
the spectral full-width-at-half-maximum is plotted on the left axis as a function of pump current. In the same figure the number of pulses at each pump current is illustrated on the right
axis. The spectral width increases with pump power by the soliton area theorem, and multiple
pulses are generated because the loss is lower for multiple pulses than for a single pulse.
When multiple pulses are generated, they separate in time to become equally spaced, produc-
PASSIVELY MODE-LOCKED FIBER LASER
123
8
12.0
7
∆λFWHM (nm)
11.5
5
4
11.0
3
2
10.5
Number of Pulses
6
1
10.0
240
260
280
300
320
340
0
Current (mA)
Figure B.7
Spectral width and number of pulses versus pump current for a soliton fiber laser mode-locked
with a saturable absorber mirror.
ing a passive harmonically mode-locked pulse train. Such time equalization has been
observed previously in saturable absorber mode-locked fiber lasers and was attributed to gain
relaxation dynamics [17, 71]. The optical spectrum up to approximately 310 mA is similar to
those shown in Figures B.2, B.4, and B.5, and the high dynamic-range autocorrelation is
clean. The laser generates multiple pulses in this manner until seven pulses are generated.
When the pump current exceeds approximately 310 mA, all seven pulses collapse into
a single bunch of pulses at the fundamental repetition rate. At this point the autocorrelation
changes significantly, going from a clean sech-shaped autocorrelation to a short pulse with a
large background. Figure B.8 depicts the measured normalized autocorrelations at four different pump currents. From bottom to top in the Figure B.8 the pump current is 390, 475, 550,
and 650 mA. The pulse structure in the lowest trace suggests multiple pulses held together in
a bunch. The recovery time of the saturable absorber is one possible mechanism which acts to
pull the pulses together into a single burst. Because gain relaxation competes against absorber
recovery, the position of the pulses is not fixed in time, resulting in the smeared autocorrela-
124
APPENDIX B
Normalized AC
1
0.1
0.01
-80000
-60000
-40000
-20000
0
Delay (fs)
Figure B.8
Autocorrelations of a bunched multiple pulse state at several pump currents. From bottom to
top the pump current is 390, 475, 550, and 650 mA.
tion envelope. As the pump current is increased, more and more pulses are generated but are
not held together as strongly by the saturable absorber, producing a background with a longer
time constant.
To investigate how the bunched-pulse state is related to the saturable absorber recovery time, an autocorrelation taken at the threshold of pulse bunching is shown in Figure B.9.
At this threshold the number of pulses is the fewest, so continuous bleaching of the saturable
absorber is least likely. An exponential recovery was fit to the background portion of the
bunched pulse, shown by the solid line in Figure B.9. The regression produced a time constant of ~40 picoseconds, which matches within error the recombination time of this saturable
absorber structure measured via pump-probe. This is further evidence that the long recovery
time of the saturable absorber is the mechanism for the pulse bunching effect.
PASSIVELY MODE-LOCKED FIBER LASER
125
Normalized AC
1
0.1
0.01
-80000
-60000
-40000
-20000
0
Delay (fs)
Figure B.9
126
Autocorrelation of a bunched multiple pulse state with an exponential fit of the long background envelope.
APPENDIX B
APPENDIX C
ACTIVELY MODE-LOCKED FIBER LASER
In this appendix1, preliminary results from an actively mode-locked linear fiber laser
are presented. The effect of operating a LiNbO3 amplitude modulator in the travelling-wave
regime is studied.
Active harmonic mode-locking is particularly attractive for communication systems
which require a high bit-rate locked to an external clock. However most such lasers are
implemented in a ring geometry where pulses pass through the modulator in only one direction. A linear laser has several advantages such as the possibility of integration, the simple
incorporation of a semiconductor saturable absorber mirror, and the feasibility of environmental stability through Faraday rotation. A linear harmonically mode-locked fiber laser was
demonstrated by making use of the traveling-wave properties of a phase modulator [117]. In a
traveling-wave modulator the electrodes are designed such that at high frequencies the electrical signal travels with the optical signal. However for frequencies which are greater than
approximately the inverse of twice the transit time through the modulator, the phase modulation on the counter-propagating wave is insignificant [35, 24].
1
Portions of this appendix appear in [117]. Many of the results of this appendix were attained in collaboration with Matthew E. Grein, Elisabeth M. Koontz, and Prof. Leslie Kolodziejski.
ACTIVELY MODE-LOCKED FIBER LASER
127
Dielec tric
M irro r
P o la rization
C o n tro ller
L en s
Figure C.1
98 0 nm
Pump
Co llim a tor
W DM
P h ase
M o du lato r
E rb ium
F ib er
15 % Ou tp ut
C o u pler
P o la rization
C o n tro ller
Schematic of active harmonically mode-locked linear laser. Wavelength Division Multiplexer
(WDM).
The laser shown in Figure C.1 was constructed with an anomalous round-trip cavity
dispersion of -0.07 ps2. When the modulator was operated at low frequencies (100-500
MHz), the laser produced the optical spectrum and autocorrelation shown in Figure C.2. The
spectrum displays significant modulation, and the autocorrelation indicates a very long background pulse. These frequencies are far below the traveling-wave regime, so the modulator
imparts a significant phase shift on the counter-propagating light. When the modulator frequency is increased to 4 GHz, well above the traveling-wave frequency, the spectrum and
autocorrelation shown in Figure C.3 were produced. The modulation is absent from the spectrum, and the picosecond pulse is clean over a high dynamic range. These initial results demonstrate that linear harmonically mode-locked lasers are possible, but more work could be
done to realize their full potential.
128
APPENDIX C
-20
Power (dB)
-30
-40
-50
-60
-70
1555
1560
1565
Wavelength (nm)
1570
Normalized AC
1
0.1
0.01
-20 -15 -10
Figure C.2
-5
0
5
Delay (ps)
10
15
20
Low frequency operation. Optical spectrum (Top) and autocorrelation (Bottom).
ACTIVELY MODE-LOCKED FIBER LASER
129
-20
Power (dB)
-30
-40
-50
-60
-70
1555
1560
1565
Wavelength (nm)
1570
Normalized AC
1
0.1
0.01
-8
Figure C.3
130
-6
-4
-2
0
2
Delay (ps)
4
6
8
High frequency operation. Optical spectrum (Top) and autocorrelation (Bottom).
APPENDIX C
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