《UltraFast Optics》课程教学资源（学习资料）超快光学 Ultrafast Optics（ANDREW M.WEINER）.pdf_大学文库

viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect,57 2.4.1 Nonlinear Refractive Index Changes,57 2.4.2 Self-Amplitude Modulation,Self-Phase Modulation,and Group Velocity Dispersion,58 2.4.3 Additive Pulse Mode-Locking,60 2.4.4 Kerr Lens Mode-Locking,64 2.4.5 Mode-Locking Solutions,75 2.4.6 Initiation of Mode-Locking,81 Problems,83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions,85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum,88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry,91 3.3.1 Electric Field Cross-Correlation.92 3.3.2 Spectral Interferometry,93 3.3.3 Application:Optical Coherence Tomography,96 3.4 Intensity Correlation Measurements,99 3.4.1 Correlation Measurements Using Second-Harmonic Generation,99 3.4.2 Experimental Procedures,108 3.4.3 Correlation Measurements Using Two-Photon absorption,110 3.4.4 Higher-Order Correlation Techniques,111 3.5 Chirped Pulses and Measurements in the Time-Frequency Domain,112 3.6 Frequency-Resolved Optical Gating,118 3.6.1 Polarization-Gating FROG.119 3.6.2 Self-Diffraction FROG.122 3.6.3 Second-Harmonic-Generation FROG,124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation,125 3.6.5 Signal Recovery from FROG Traces,126 3.7 Pulse Measurements Based on Frequency Filtering.130 3.7.1 Single-Slit Approaches,131 3.7.2 Double-Slit Approach,134 3.8 Self-Referencing Interferometry,135 3.8.1 Time-Domain Interferometry of Chirped Pulses,135 3.8.2 Self-Referencing Spectral Interferometry,137 3.9 Characterization of Noise and Jitter,139 Problems,144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion,147 4.1.1 Group Velocity Definition and General Dispersion Relations,147 4.1.2 General Aspects of Material Dispersion,151 4.2 Temporal Dispersion Based on Angular Dispersion,155 4.2.1 Relation Between Angular and Temporal Dispersion,155 4.2.2 Angular Dispersion and Tilted Intensity Fronts,159 4.3 Dispersion of Grating Pairs,161

viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect, 57 2.4.1 Nonlinear Refractive Index Changes, 57 2.4.2 Self-Amplitude Modulation, Self-Phase Modulation, and Group Velocity Dispersion, 58 2.4.3 Additive Pulse Mode-Locking, 60 2.4.4 Kerr Lens Mode-Locking, 64 2.4.5 Mode-Locking Solutions, 75 2.4.6 Initiation of Mode-Locking, 81 Problems, 83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions, 85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum, 88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry, 91 3.3.1 Electric Field Cross-Correlation, 92 3.3.2 Spectral Interferometry, 93 3.3.3 Application: Optical Coherence Tomography, 96 3.4 Intensity Correlation Measurements, 99 3.4.1 Correlation Measurements Using Second-Harmonic Generation, 99 3.4.2 Experimental Procedures, 108 3.4.3 Correlation Measurements Using Two-Photon absorption, 110 3.4.4 Higher-Order Correlation Techniques, 111 3.5 Chirped Pulses and Measurements in the Time–Frequency Domain, 112 3.6 Frequency-Resolved Optical Gating, 118 3.6.1 Polarization-Gating FROG, 119 3.6.2 Self-Diffraction FROG, 122 3.6.3 Second-Harmonic-Generation FROG, 124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation, 125 3.6.5 Signal Recovery from FROG Traces, 126 3.7 Pulse Measurements Based on Frequency Filtering, 130 3.7.1 Single-Slit Approaches, 131 3.7.2 Double-Slit Approach, 134 3.8 Self-Referencing Interferometry, 135 3.8.1 Time-Domain Interferometry of Chirped Pulses, 135 3.8.2 Self-Referencing Spectral Interferometry, 137 3.9 Characterization of Noise and Jitter, 139 Problems, 144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion, 147 4.1.1 Group Velocity Definition and General Dispersion Relations, 147 4.1.2 General Aspects of Material Dispersion, 151 4.2 Temporal Dispersion Based on Angular Dispersion, 155 4.2.1 Relation Between Angular and Temporal Dispersion, 155 4.2.2 Angular Dispersion and Tilted Intensity Fronts, 159 4.3 Dispersion of Grating Pairs, 161

PREFACE This book deals with the optics of picosecond and femtosecond light pulses,primarily at wavelengths in the visible range and longer.Research in ultrafast optics started roughly forty years ago,and although this field is now tremendously active,in many aspects it has also reached a level of maturity.However,relatively few broad treatments of ultrafast optics are available.It is hoped that this book,which is both detailed and comprehensive,will be a valuable resource not only for graduate students and researchers seeking to enter ultrafast optics but also for colleagues already engaged in this fascinating field. I would like to mention a few pertinent points about my perspective in this book.First, in keeping with my training as an electrical engineer,the signals aspect of ultrafast optics is emphasized.That is,I often attempt to capture the detailed form of ultrashort pulses as they are transformed in various optical systems or evolve inside mode-locked lasers.Similarly, the detailed form of measurement data,as in ultrashort pulse characterization and ultrafast spectroscopy,is analyzed when possible. Second,although adetailed theoretical treatment is often presented,I strive to balance this with an experimental perspective.Accordingly,many examples of data from the literature are included,especially in the later chapters.These examples are selected to provide concrete illustration of material that otherwise might remain abstract,to provide evidence of certain important phenomena,and sometimes to illustrate applications. Third,although the suite of applications of ultrafast optics is now very rich,this book is concerned primarily with fundamental principles.No attempt is made to cover the applications space comprehensively.Two applications are covered in some depth:ultrafast spectroscopy and ultrafast electromagnetic pulse generation and measurement.Both of these are subjects of individual chapters.Certain other applications,such as the application of optical frequency combs for precision frequency metrology,are discussed briefly within appropriate sections of related text. Fourth,the book is focused on ultrafast optics in visible and lower-frequency spectral bands,on time scales down to femtoseconds,and at intensities for which perturbative non- linear optics applies.Under these conditions the motions of bound electrons that mediate xiii

PREFACE This book deals with the optics of picosecond and femtosecond light pulses, primarily at wavelengths in the visible range and longer. Research in ultrafast optics started roughly forty years ago, and although this field is now tremendously active, in many aspects it has also reached a level of maturity. However, relatively few broad treatments of ultrafast optics are available. It is hoped that this book, which is both detailed and comprehensive, will be a valuable resource not only for graduate students and researchers seeking to enter ultrafast optics but also for colleagues already engaged in this fascinating field. I would like to mention a few pertinent points about my perspective in this book. First, in keeping with my training as an electrical engineer, the signals aspect of ultrafast optics is emphasized. That is, I often attempt to capture the detailed form of ultrashort pulses as they are transformed in various optical systems or evolve inside mode-locked lasers. Similarly, the detailed form of measurement data, as in ultrashort pulse characterization and ultrafast spectroscopy, is analyzed when possible. Second, although a detailed theoretical treatment is often presented, I strive to balance this with an experimental perspective. Accordingly, many examples of data from the literature are included, especially in the later chapters. These examples are selected to provide concrete illustration of material that otherwise might remain abstract, to provide evidence of certain important phenomena, and sometimes to illustrate applications. Third, although the suite of applications of ultrafast optics is now very rich, this book is concerned primarily with fundamental principles. No attempt is made to cover the applications space comprehensively. Two applications are covered in some depth: ultrafast spectroscopy and ultrafast electromagnetic pulse generation and measurement. Both of these are subjects of individual chapters. Certain other applications, such as the application of optical frequency combs for precision frequency metrology, are discussed briefly within appropriate sections of related text. Fourth, the book is focused on ultrafast optics in visible and lower-frequency spectral bands, on time scales down to femtoseconds, and at intensities for which perturbative nonlinear optics applies. Under these conditions the motions of bound electrons that mediate xiii

xiv PREFACE important laser-matter interactions may usually be viewed as instantaneous.Extreme nonlinear optics phenomena,arising from high-intensity laser-matter interactions for which the laser field reaches or exceeds the interatomic field,are not covered.One important ex- ample of extreme nonlinear optics is high harmonic generation,in which visible wavelength femtosecond pulses result in emission of photons in the vacuum ultraviolet(XUV)and soft x-ray bands.The use of high harmonic generation to realize attosecond pulses has become an active research topic within the last few years.Attosecond time scales and XUV and x-ray frequencies bring in entirely new physics that are beyond the scope of this book. Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future treatises. The structure of the book is as follows: Chapter 1 begins with a brief overview and motivation,discussing key attributes of ultrashort laser pulses and some application examples.Important background material, including simple electromagnetics and laser essentials,is reviewed.The chapter contin- ues with a phenomenological introduction to short pulse generation via mode-locking and concludes with a review of Fourier transforms,a mathematical tool essential to much of our treatment. Chapter 2 covers basic principles of laser mode-locking in some depth.The intent is not only to cover one of the most interesting topics at the outset,but to use the discussion on mode-locking as a physical context in which to introduce a variety of important ultrafast optical effects(e.g.,dispersion,filtering,self-phase modulation). many of which are themselves treated in detail in subsequent chapters. .Measurement of pulses on the femtosecond time scale is an important issue,since the speed required is considerably faster than that of existing photodetectors and oscillo- scopes.In Chapter 3 we discuss methods for characterizing ultrashort pulses.Included are historical techniques dating back to the early years of ultrafast optics (these offer only partial information but remain in widespread use)as well as more powerful tech- niques offering full waveform information.The field of ultrashort pulse characteri- zation has continued to grow,and new techniques continue to be introduced.I have not attempted to cover all the interesting measurement techniques that have been in- vented.My hope is that the discussion accompanying those methods that are included will prepare the reader to quickly grasp additional methods that may interest him or her. Dispersion is often a key limiting effect in ultrafast systems.Accordingly,in Chap- ter 4 we focus on dispersion and its compensation.After defining key concepts,the discussion covers material dispersion,then temporal dispersion arising from angular dispersion (including important grating and prism pair setups),and finally,dispersion effects in mirror structures.The effect of dispersion in the focusing of light by lenses is also discussed,as are methods for measurement of dispersion. Chapters 5 and 6 deal with ultrafast nonlinear optics.Chapter 5 emphasizes second- order nonlinear effects.After an introduction to nonlinear optics and a review of continuous-wave second-harmonic generation (SHG),new effects arising in ultra- short pulse SHG,sum and difference frequency generation,and optical parametric generation are discussed.Such effects are of primary interest in frequency conver- sion and pulse measurement applications.Chapter 6 focuses on refractive index(third- order)nonlinearities,which have seen very wide applications in ultrafast optics.Topics

xiv PREFACE important laser–matter interactions may usually be viewed as instantaneous. Extreme nonlinear optics phenomena, arising from high-intensity laser–matter interactions for which the laser field reaches or exceeds the interatomic field, are not covered. One important example of extreme nonlinear optics is high harmonic generation, in which visible wavelength femtosecond pulses result in emission of photons in the vacuum ultraviolet (XUV) and soft x-ray bands. The use of high harmonic generation to realize attosecond pulses has become an active research topic within the last few years. Attosecond time scales and XUV and x-ray frequencies bring in entirely new physics that are beyond the scope of this book. Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future treatises. The structure of the book is as follows: Chapter 1 begins with a brief overview and motivation, discussing key attributes of ultrashort laser pulses and some application examples. Important background material, including simple electromagnetics and laser essentials, is reviewed. The chapter continues with a phenomenological introduction to short pulse generation via mode-locking and concludes with a review of Fourier transforms, a mathematical tool essential to much of our treatment. Chapter 2 covers basic principles of laser mode-locking in some depth. The intent is not only to cover one of the most interesting topics at the outset, but to use the discussion on mode-locking as a physical context in which to introduce a variety of important ultrafast optical effects (e.g., dispersion, filtering, self-phase modulation), many of which are themselves treated in detail in subsequent chapters. Measurement of pulses on the femtosecond time scale is an important issue, since the speed required is considerably faster than that of existing photodetectors and oscilloscopes. In Chapter 3 we discuss methods for characterizing ultrashort pulses. Included are historical techniques dating back to the early years of ultrafast optics (these offer only partial information but remain in widespread use) as well as more powerful techniques offering full waveform information. The field of ultrashort pulse characterization has continued to grow, and new techniques continue to be introduced. I have not attempted to cover all the interesting measurement techniques that have been invented. My hope is that the discussion accompanying those methods that are included will prepare the reader to quickly grasp additional methods that may interest him or her. Dispersion is often a key limiting effect in ultrafast systems. Accordingly, in Chapter 4 we focus on dispersion and its compensation. After defining key concepts, the discussion covers material dispersion, then temporal dispersion arising from angular dispersion (including important grating and prism pair setups), and finally, dispersion effects in mirror structures. The effect of dispersion in the focusing of light by lenses is also discussed, as are methods for measurement of dispersion. Chapters 5 and 6 deal with ultrafast nonlinear optics. Chapter 5 emphasizes secondorder nonlinear effects. After an introduction to nonlinear optics and a review of continuous-wave second-harmonic generation (SHG), new effects arising in ultrashort pulse SHG, sum and difference frequency generation, and optical parametric generation are discussed. Such effects are of primary interest in frequency conversion and pulse measurement applications. Chapter 6 focuses on refractive index (thirdorder) nonlinearities, which have seen very wide applications in ultrafast optics. Topics

PREFACE XV include self-phase modulation,pulse compression,solitons,continuum generation,and propagation equations,including propagation equations relevant for pulses down to a few optical cycles. Chapter 7 takes advantage of material developed in earlier chapters to continue the discussion of mode-locking at a more advanced level.Included are soliton nonlinear optics phenomena observed in the mode-locking of fiber lasers,stretched pulse lasers operating in the normal dispersion regime,and soliton mode-locking of solid-state lasers with slow saturable absorbers.Important aspects of sub-10-fs laser design and stabilized frequency combs important for precision frequency metrology are also discussed Chapter 8 focuses on the manipulation of ultrashort pulses.The chapter begins with de- tailed coverage of ultrafast Fourier optics methods that enable ultrashort pulse shaping and arbitrary waveform generation.It then treats various chirped pulse approaches for waveform manipulation and measurement,including interesting time lens approaches. Finally,femtosecond pulse amplification techniques,leading to realization of pulses with unparalleled peak power,are discussed. .Ultrafast time-resolved spectroscopy is possibly the most widely practiced application of ultrashort light pulses.This field is highly interdisciplinary,and the number of differ- ent physical systems probed using ultrafast techniques is large.In Chapter 9 I present and analyze selected important concepts in femtosecond time-resolved spectroscopy. No attempt is made to cover all the applications or all the experimental variations.A pedagogical challenge is that students studying ultrafast optics may have very differ- ent degrees of preparation in quantum mechanics,which is needed for a detailed microscopic understanding of many of the systems studied via ultrafast techniques. Therefore,this chapter takes a two-pronged approach.First,techniques such as pump- probe,which principally probe incoherent(phase insensitive)population relaxation processes,are treated classically,although quantum concepts such as energy levels do appear phenomenologically.Experiments on population relaxation in organic dye molecules and in direct-gap semiconductors such as GaAs are discussed for illustra- tion.Second,after a necessarily brief(and possibly inadequate)introduction to relevant quantum mechanics,spectroscopies sensitive to coherent (phase sensitive)phenomena are discussed.These subjects are treated with the help of quantum mechanics.Topics include wave packet phenomena in semiconductors and molecules,coherent polariza- tion effects,and measurement of dephasing.A final topic,impulsive stimulated Raman scattering,is treated in a largely classical framework. The final chapter deals with another important application of ultrafast optics:the gen- eration and measurement of picosecond and subpicosecond electrical and electro- magnetic transients.Both electrical signals propagating on-chip on transmission-line structures and terahertz(THz)electromagnetic radiation freely propagating in space are considered.Finally,THz time-domain spectroscopy,a technique that provides exciting capability for materials characterization and sensing in a spectral region that is difficult to access by either direct electronic or optical means,is discussed. Several problems are provided at the end ofeach chapter,ranging from simple theoretical questions to practical exercises requiring numerical computation.As an example of the latter,in the Chapter 2 problems the student is asked to simulate pulse evolution through many round trips in a mode-locked laser cavity,finally arriving at the self-consistent pulse

PREFACE xv include self-phase modulation, pulse compression, solitons, continuum generation, and propagation equations, including propagation equations relevant for pulses down to a few optical cycles. Chapter 7 takes advantage of material developed in earlier chapters to continue the discussion of mode-locking at a more advanced level. Included are soliton nonlinear optics phenomena observed in the mode-locking of fiber lasers, stretched pulse lasers operating in the normal dispersion regime, and soliton mode-locking of solid-state lasers with slow saturable absorbers. Important aspects of sub-10-fs laser design and stabilized frequency combs important for precision frequency metrology are also discussed. Chapter 8 focuses on the manipulation of ultrashort pulses. The chapter begins with detailed coverage of ultrafast Fourier optics methods that enable ultrashort pulse shaping and arbitrary waveform generation. It then treats various chirped pulse approaches for waveform manipulation and measurement, including interesting time lens approaches. Finally, femtosecond pulse amplification techniques, leading to realization of pulses with unparalleled peak power, are discussed. Ultrafast time-resolved spectroscopy is possibly the most widely practiced application of ultrashort light pulses. This field is highly interdisciplinary, and the number of different physical systems probed using ultrafast techniques is large. In Chapter 9 I present and analyze selected important concepts in femtosecond time-resolved spectroscopy. No attempt is made to cover all the applications or all the experimental variations. A pedagogical challenge is that students studying ultrafast optics may have very different degrees of preparation in quantum mechanics, which is needed for a detailed microscopic understanding of many of the systems studied via ultrafast techniques. Therefore, this chapter takes a two-pronged approach. First, techniques such as pumpprobe, which principally probe incoherent (phase insensitive) population relaxation processes, are treated classically, although quantum concepts such as energy levels do appear phenomenologically. Experiments on population relaxation in organic dye molecules and in direct-gap semiconductors such as GaAs are discussed for illustration. Second, after a necessarily brief (and possibly inadequate) introduction to relevant quantum mechanics, spectroscopies sensitive to coherent (phase sensitive) phenomena are discussed. These subjects are treated with the help of quantum mechanics. Topics include wave packet phenomena in semiconductors and molecules, coherent polarization effects, and measurement of dephasing. A final topic, impulsive stimulated Raman scattering, is treated in a largely classical framework. The final chapter deals with another important application of ultrafast optics: the generation and measurement of picosecond and subpicosecond electrical and electromagnetic transients. Both electrical signals propagating on-chip on transmission-line structures and terahertz (THz) electromagnetic radiation freely propagating in space are considered. Finally, THz time-domain spectroscopy, a technique that provides exciting capability for materials characterization and sensing in a spectral region that is difficult to access by either direct electronic or optical means, is discussed. Several problems are provided at the end of each chapter, ranging from simple theoretical questions to practical exercises requiring numerical computation. As an example of the latter, in the Chapter 2 problems the student is asked to simulate pulse evolution through many round trips in a mode-locked laser cavity, finally arriving at the self-consistent pulse

xvi PREFACE solution.I regularly assign such numerical problems in my own course on ultrafast optics at Purdue University.Although in my experience such problems require substantial effort on the part of the student,they result in a much better understanding of the phenomena involved,not to mention improved skill in applying numerical tools such as the fast Fourier transform.For homework on pulse measurement I have frequently synthesized FROG or other data on a computer;I then distribute the data file to the class with the assignment to process the data to extract the pulse shape.(I have not included such problems in the current book,as I deemed it more expedient to let instructors generate their own pulses and corresponding data files.)The numerical problems included in the book may be used as is or may simply serve to inspire instructors to invent their own numerically oriented problems. Authoring this book has been a project of nearly ten years.I began formal writing while on sabbatical during the 1999-2000 academic year at the Max Born Institute (MBI)for Nonlinear Optics and Ultrashort Pulse Spectroscopy in Berlin,Germany.Work continued for many years,but in a fragmented way,at my home institution.I made substantial progress toward completion during a second sabbatical during the 2006-2007 academic year in Boulder,Colorado,where Isplit my time at the National Institute of Standards of Technology (NIST)and at JILA,a joint enterprise of NIST and the University of Colorado.I owe great thanks to my sabbatical hosts,Prof.Thomas Elsaesser of the MBI,Dr.Leo Hollberg of NIST,and Prof.Steve Cundiff of JILA,for making these stays possible.I would also like to thank the MBI and the Alexander von Humboldt Foundation for assistance with funding during my stay in Berlin and NIST and JILA for assistance with funding during my stay in Boulder. I would like to thank many persons who generously provided input and assistance in various aspects of this project.Giullo Cerullo,Steve Cundiff,Alex Gaeta,and Franz Kaertner provided helpful comments and clarification on various technical topics(in some cases,on multiple topics).Virginia Lorenz made available a copy of her University of Colorado Ph.D.thesis,which provided a very helpful overview of dephasing.At Purdue University,DeeDee Dexter provided invaluable logistical and secretarial assistance through- out the course of this project.Dan Leaird was always willing to lend an ear when I wanted to voice ideas about the book project;Dan also deserves great thanks for his unflagging attention to our ultrafast optics and fiber communications research laboratory,even when I sometimes became distracted by the burdens of authorship.Many students deserve credit for identifying errors in preliminary versions of the manuscript,which were used over sev- eral iterations of my graduate course.Prof.Dongsun Seo,a sabbatical visitor from Korea, also pointed out several items in need of correction.A number of graduate students kindly agreed to carry out numerical work,generating data that resulted in a number of figures. These students include Jung-Ho Chung,Ehsan Hamidi,Zhi Jiang,Houxun Miao,Bhaskaran Muralidharan,Ninad Pimparkar,Haifeng Wang,Mark Webster,and Shang-Da Yang.V.R Supradeepa checked several equations on my behalf.Zhi Jiang was especially helpful in proofing the typeset manuscript. This book includes well over 200 figures,many of which were composed especially for this project.Although many others were taken from the literature,almost all of these were modified or redrawn to ensure readability and to achieve consistency of appearance and notation.I am tremendously grateful to Bill Drake,Jr.,for fulfilling this responsibility with great skill from the inception of this project until it neared completion.Tragically,Bill succumbed to cancer at an early age.He continued to contribute to this book even as he struggled against the disease that ultimately killed him.Michael Black took over technical

xvi PREFACE solution. I regularly assign such numerical problems in my own course on ultrafast optics at Purdue University. Although in my experience such problems require substantial effort on the part of the student, they result in a much better understanding of the phenomena involved, not to mention improved skill in applying numerical tools such as the fast Fourier transform. For homework on pulse measurement I have frequently synthesized FROG or other data on a computer; I then distribute the data file to the class with the assignment to process the data to extract the pulse shape. (I have not included such problems in the current book, as I deemed it more expedient to let instructors generate their own pulses and corresponding data files.) The numerical problems included in the book may be used as is or may simply serve to inspire instructors to invent their own numerically oriented problems. Authoring this book has been a project of nearly ten years. I began formal writing while on sabbatical during the 1999–2000 academic year at the Max Born Institute (MBI) for Nonlinear Optics and Ultrashort Pulse Spectroscopy in Berlin, Germany. Work continued for many years, but in a fragmented way, at my home institution. I made substantial progress toward completion during a second sabbatical during the 2006–2007 academic year in Boulder, Colorado, where I split my time at the National Institute of Standards of Technology (NIST) and at JILA, a joint enterprise of NIST and the University of Colorado. I owe great thanks to my sabbatical hosts, Prof. Thomas Elsaesser of the MBI, Dr. Leo Hollberg of NIST, and Prof. Steve Cundiff of JILA, for making these stays possible. I would also like to thank the MBI and the Alexander von Humboldt Foundation for assistance with funding during my stay in Berlin and NIST and JILA for assistance with funding during my stay in Boulder. I would like to thank many persons who generously provided input and assistance in various aspects of this project. Giullo Cerullo, Steve Cundiff, Alex Gaeta, and Franz Kaertner provided helpful comments and clarification on various technical topics (in some cases, on multiple topics). Virginia Lorenz made available a copy of her University of Colorado Ph.D. thesis, which provided a very helpful overview of dephasing. At Purdue University, Dee Dee Dexter provided invaluable logistical and secretarial assistance throughout the course of this project. Dan Leaird was always willing to lend an ear when I wanted to voice ideas about the book project; Dan also deserves great thanks for his unflagging attention to our ultrafast optics and fiber communications research laboratory, even when I sometimes became distracted by the burdens of authorship. Many students deserve credit for identifying errors in preliminary versions of the manuscript, which were used over several iterations of my graduate course. Prof. Dongsun Seo, a sabbatical visitor from Korea, also pointed out several items in need of correction. A number of graduate students kindly agreed to carry out numerical work, generating data that resulted in a number of figures. These students include Jung-Ho Chung, Ehsan Hamidi, Zhi Jiang, Houxun Miao, Bhaskaran Muralidharan, Ninad Pimparkar, Haifeng Wang, Mark Webster, and Shang-Da Yang. V. R. Supradeepa checked several equations on my behalf. Zhi Jiang was especially helpful in proofing the typeset manuscript. This book includes well over 200 figures, many of which were composed especially for this project. Although many others were taken from the literature, almost all of these were modified or redrawn to ensure readability and to achieve consistency of appearance and notation. I am tremendously grateful to Bill Drake, Jr., for fulfilling this responsibility with great skill from the inception of this project until it neared completion. Tragically, Bill succumbed to cancer at an early age. He continued to contribute to this book even as he struggled against the disease that ultimately killed him. Michael Black took over technical