LIST OF TOPICS x Chapter 17 Physical Properties of Gaussian Beams 17.1 Gaussian Beam Propagation 663 17.2 Gaussian Beam Focusing 675 17.3 Lens Laws and Gaussian Mode Matching 680 17.4 Axial Phase Shift:The Guoy Effect 682 17.5 Higher-Order Gaussian Modes 685 17.6 Multimode Optical Beams 695 Chapter 18 Beam Perturbation and Diffraction 18.1 Grating Diffraction and Scattering Effects 698 18.2 Aberrated Laser Beams 706 18.3 Aperture Diffraction:Rectangular Apertures 712 18.4 Aperture Diffraction:Circular Apertures 727 Chapter 19 Stable Two-Mirror Resonators 19.1 Stable Gaussian Resonator Modes 744 19.2 Important Stable Resonator Types 750 19.3 Gaussian Transverse Mode Frequencies 761 19.4 Misalignment Effects in Stable Resonators 767 19.5 Gaussian Resonator Mode Losses 769 Chapter 20 Complex Paraxial Wave Optics 20.1 Huygens'Integral and ABCD Matrices 777 20.2 Gaussian Beams and ABCD Matrices 782 20.3 Gaussian Apertures and Complex ABCD Matrices 786 20.4 Complex Paraxial Optics 792 20.5 Complex Hermite-Gaussian Modes 798 20.6 Coordinate Scaling with Huygens'Integrals 805 20.7 Synthesis and Factorization of ABCD Matrices 811 Chapter 21 Generalized Paraxial Resonator Theory 21.1 Complex Paraxial Resonator Analysis 815 21.2 Real and Geometrically Stable Resonators 820 21.3 Real and Geometrically Unstable Resonators 822 21.4 Complex Stable and Unstable Resonators 828 21.5 Other General Properties of Paraxial Resonators 835 21.6 Multi-Element Stable Resonator Designs 841 21.7 Orthogonality Properties of Optical Resonator Modes 847 Chapter 22 Unstable Optical Resonators 22.1 Elementary Properties 858 22.2 Canonical Analysis for Unstable Resonators 867 22.3 Hard-Edged Unstable Resonators 874 22.4 Unstable Resonators:Experimental Results 884 Chapter 23 More on Unstable Resonators 23.1 Advanced Analyses of Unstable Resonators 891
LIST OF TOPICS 23.2 Other Novel Unstable Resonator Designs 899 23.3 Variable-Reflectivity Unstable Resonators 913 LASER DYNAMICS AND ADVANCED TOPICS Chapter 24 Laser Dynamics:The Laser Cavity Equations 24.1 Derivation of the Laser Cavity Equations 923 24.2 External Signal Sources 932 24.3 Coupled Cavity-Atom Equations 941 24.4 Alternative Formulations of the Laser Equations 944 24.5 Cavity and Atomic Rate Equations 949 Chapter 25 Laser Spiking and Mode Competition 25.1 Laser Spiking and Relaxation Oscillations 955 25.2 Laser Amplitude Modulation 971 25.3 Laser Frequency Modulation and Frequency Switching 980 25.4 Laser Mode Competition 992 Chapter 26 Laser Q-Switching 26.1 Laser Q-Switching:General Description 1004 26.2 Active Q-Switching:Rate-Equation Analysis 1008 26.3 Passive (Saturable Absorber)Q-Switching 1024 26.4 Repetitive Laser Q-Switching 1028 26.5 Mode Selection in Q-Switched Lasers 1034 26.6 Q-Switched Laser Applications 1039 Chapter 27 Active Laser Mode Coupling 27.1 Optical Signals:Time and Frequency Descriptions 1041 27.2 Mode-Locked Lasers:An Overview 1056 27.3 Time-Domain Analysis:Homogeneous Mode Locking 1061 274 Transient and Detuning Effects 1075 27.5 Frequency-Domain Analysis:Coupled Mode Equations 1087 27.6 The Modulator Polarization Term 1092 27.7 FM Laser Operation 1095 Chapter 28 Passive Mode Locking 28.1 Pulse Shortening in Saturable Absorbers 1104 28.2 Passive Mode Locking in Pulsed Lasers 1109 28.3 Passive Mode Locking in CW Lasers 1117 Chapter 29 Laser Injection Locking 29.1 Injection Locking of Oscillators 1130 29.2 Basic Injection Locking Analysis 1138 29.3 The Locked Oscillator Regime 1142 29.4 Solutions Outside the Locking Range 1148
LIST OF TOPICS xi 29.5 Pulsed Injection Locking:A Phasor Description 1154 29.6 Applications:The Ring Laser Gyroscope 1162 Chapter 30 Hole Burning and Saturation Spectroscopy 30.1 Inhomogeneous Saturation and "Hole Burning"Effects 1171 30.2 Elementary Analysis of Inhomogeneous Hole Burning 1177 30.3 Saturation Absorption Spectroscopy 1184 30.4 Saturated Dispersion Effects 1192 30.5 Cross-Relaxation Effects 1195 30.6 Inhomogeneous Laser Oscillation:Lamb Dips 1199 Chapter 31 Magnetic-Dipole Transitions 31.1 Basic Properties of Magnetic-Dipole Transitions 1213 31.2 The Iodine Laser:A Magnetic-Dipole Laser Transition 1223 31.3 The Classical Magnetic Top Model 1228 31.4 The Bloch Equations 1236 31.5 Transverse Response:The AC Susceptibility 1243 31.6 Longitudinal Response:Rate Equation 1249 31.7 Large-Signal and Coherent-Transient Effects 1256 Index 1267
PREFACE This book presents a detailed and comprehensive treatment of laser physics and laser theory which can serve a number of purposes for a number of different groups.It can provide,first of all,a textbook for graduate students,or even well-prepared seniors in science or engineering,describing in detail how lasers work,and a bit about the applications for which lasers can be used.Problems, references and illustrations are included throughout the book. Second,it can also provide a solid and detailed description of laser physics and the operational properties of lasers for the practicing engineer or scientist who needs to learn about lasers in order to work on or with them. Finally,the advanced sections of this text are sufficiently detailed that this book will provide a useful one-volume reference for the experienced laser engineer or laser researcher's bookshelf.The discussions of advanced laser topics,such as optical resonators,Q-switching,mode locking,and injection locking,extend far enough into the current state of the art to provide a working reference on these and similar topics.References for further reading in the recent literature are included in nearly every section. One unique feature of this book is that it removes much of the quantum mystique from "quantum electronics"(the generic label often applied to lasers and laser applications).Many people think of lasers as quantum devices.In fact,however,most of the basic concepts of laser physics,and virtually all the practical details,are classical in nature.Lasers(and masers)of all types and in all frequency ranges are simply electronic devices,of great interest and importance to the electronics engineer. In the analogous case of semiconductor electronics,for example,the transis- tor is not usually thought of as a quantum device.Mental images of holes and electrons as classical charged particles which accelerate,drift,diffuse and re- combine are used both by semiconductor device engineers to do practical device engineering,and by solid-state physics researchers to understand sophisticated physics experiments.These classical concepts serve to explain and make under- standable what is otherwise a complex quantum picture of energy bands,Bloch wavefunctions,Fermi-Dirac distributions,and occupied or unoccupied quantum states.The same simplification can be accomplished for lasers,and laser devices can then be very well understood from a primarily classical viewpoint,with only limited appeals to quantum terms or concepts. The approach in this book is to build primarily upon the classical electron oscillator model,appropriately extended with a descriptive picture of atomic en- ergy levels and level populations,in order to provide a fully accurate,detailed and physically meaningful understanding of lasers.This can be accomplished xi带
xiv PREFACE without requiring a previous formal background in quantum theory,and also without attempting to teach an abbreviated and inadequate course in this sub ject on the spot.A thorough understanding of laser devices is readily available through this book,in terms of classical and descriptively quantum-mechanical concepts,without a prior course in quantum theory. I have also attempted to review,at least briefly,relevant and necessary back- ground material for each successive topic in each section of this book.Students will find the material most understandable,however,if they come to the book with some background in electromagnetic theory,including Maxwell's equations; some understanding of the concept of electromagnetic polarization in an atomic medium;and some familiarity with the fundamentals of electromagnetic wave propagation.An undergraduate-level background in optics and in Fourier trans- form concepts will certainly help;and although familiarity with quantum theory is not required,the student must have at least enough introduction to atomic physics to be prepared to accept that atoms do have quantum properties,espe- cially quantum energy levels and transitions between these levels. The discussions in this book begin with simple physical descriptions and then go into considerable analytical detail on the stimulated transition process in atoms and molecules;the basic amplification and oscillation processes in laser devices;the analysis and design of laser beams and resonators;and the com- plexities of laser dynamics (including spiking,Q-switching,mode locking,and injection locking)common to all types of lasers.We illustrate the general princi- ples with specific examples from a number of important common laser systems, although this book does not attempt to provide a detailed handbook of different laser systems.Extensive references to the current literature will,however,guide the reader to this kind of information. There is obviously a large amount of material in this book.The author has taught an introductory one-quarter "breadth"course on basic laser concepts for engineering and applied physics students using most of the material from the first part of the book on "Basic Laser Physics"(see the Table of Contents), especially Chapters 1-4,6-8 and 11-13.A second-quarter "depth"course then adds more advanced material from Chapters 5,9,10,30,31 and selected sections from Chapters 24-29.A complete course on optical beams and resonators can be taught from Chapters 14 through 23. I am very much indebted to many colleagues for help during the many years while this book was being written.I wish it were possible to thank by name all the students in my classes and my research group who lived through too many years of drafts and class notes.Special thanks must go to Judy Clark,who became a TEX and computer expert and did so much of the editing and manuscript preparation;to the Air Force Office of Scientific Research for supporting my laser research activities over many years;to Stanford University,and especially to Donald Knuth,for providing the environment,and the computerized text preparation tools,in which this book could be written;and to the Alexander von Humboldt Foundation and the Max Planck Institute for Quantum Optics in Munich,who supplied the opportunity for the manuscript at last to be completed. Finally,there are my wife Jeannie,and my family,who made it all worthwhile. Anthony E.Siegman