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FUNDAMENTALS OF PHOTONICS

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FUNDAMENTALS OF PHOTONICS SECOND EDITION

BAHAA E. A. SALEH University of Central Florida Boston University

MALVIN CARL TEICH Boston University Columbia University

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PREFACE TO THE SECOND EDITION

Since the publication of the First Edition in 1991, Fundamentals of Photonics has been reprinted some 20 times, translated into Czech and Japanese, and used worldwide as a textbook and reference. During this period, major developments in photonics have continued apace, and have enabled technologies such as telecommunications and applications in industry and medicine. The Second Edition reports some of these developments, while maintaining the size of this single-volume tome within practical limits.

In its new organization, Fundamentals of Photonics continues to serve as a self-contained and up-to-date introductory-level textbook, featuring a logical blend of the-ory and applications. Many readers of the First Edition have been pleased with its abundant and well-illustrated figures. This feature has been enhanced in the Second Edition by the introduction of full color throughout the book, offering improved clarity and readability.

While each of the 22 chapters of the First Edition has been thoroughly updated, the principal feature of the Second Edition is the addition of two new chapters: one on photonic-crystal optics and another on ultrafast optics. These deal with developments that have had a substantial and growing impact on photonics over the past decade.

The new chapter on photonic-crystal optics provides a foundation for understand-ing the optics of layered media, including Bragg gratings, with the help of a matrix approach. Propagation of light in one-dimensional periodic media is examined using Bloch modes with matrix and Fourier methods. The concept of the photonic bandgap is introduced. Light propagation in two- and three-dimensional photonic crystals, and the associated dispersion relations and bandgap structures, are developed. Sections on photonic-crystal waveguides, holey fibers, and photonic-crystal resonators have also been added at appropriate locations in other chapters.

The new chapter on ultrafast optics contains sections on picosecond and femtosec-ond optical pulses and their characterization, shaping, and compression, as well as their propagation in optical fibers, in the domain of linear optics. Sections on ultrafast non-linear optics include pulsed parametric interactions and optical solitons. Methods for the detection of ultrafast optical pulses using available detectors, which are relatively slow, are reviewed.

In addition to these two new chapters, the chapter on optical interconnects and switches has been completely rewritten and supplemented with topics such as wave-length and time routing and switching, FBGs, WGRs, SOAs, TOADs, and packet switches. The chapter on optical fiber communications has also been significantly updated and supplemented with material on WDM networks; it now offers concise descriptions of topics such as dispersion compensation and management, optical am-plifiers, and soliton optical communications.

Continuing advances in device-fabrication technology have stimulated the emer-gence of nanophotonics, which deals with optical processes that take place over subwavelength (nanometer) spatial scales. Nanophotonic devices and systems include quantum-confined structures, such as quantum dots, nanoparticles, and nanoscale periodic structures used to synthesize metamaterials with exotic optical properties such as negative refractive index. They also include configurations in which light (or its interaction with matter) is confined to nanometer-size (rather than micrometer-size) regions near boundaries, as in surface plasmon optics. Evanescent fields, such as those produced at a surface where total internal reflection occurs, also exhibit

v

VI PREFACE

such confinement. Evanescent fields are present in the immediate vicinity of sub-wavelength-size apertures, such as the open tip of a tapered optical fiber. Their use allows imaging with resolution beyond the diffraction limit and forms the basis of near-field optics. Many of these emerging areas are described at suitable locations in the Second Edition.

New sections have been added in the process of updating the various chapters. New topics introduced in the early chapters include: Laguerre-Gaussian beams; near-field imaging; the Sellmeier equation; fast and slow light; optics of conductive media and plasmonics; doubly negative metamaterials; the Poincaré sphere and Stokes parame-ters; polarization mode dispersion; whispering-gallery modes; microresonators; optical coherence tomography; and photon orbital angular momentum.

In the chapters on laser optics, new topics include: rare-earth and Raman fiber amplifiers and lasers; EUV, X-ray, and free-electron lasers; and chemical and random lasers. In the area of optoelectronics, new topics include: gallium nitride-based struc-tures and devices; superluminescent diodes; organic and white-light LEDs; quantum-confined lasers; quantum-cascade lasers; microcavity lasers; photonic-crystal lasers; array detectors; low-noise APDs; SPADs; and QWIPs.

The chapter on nonlinear optics has been supplemented with material on parametric-interaction tuning curves; quasi-phase-matching devices; two-wave mixing and cross-phase modulation; THz generation; and other nonlinear optical phenomena associated with narrow optical pulses, including chirp pulse amplification and supercontinuum light generation. The chapter on electro-optics now includes a discussion of electroab-sorption modulators.

Appendix C on modes of linear systems has been expanded and now offers an overview of the concept of modes as they appear in numerous locations within the book. Finally, additional exercises and problems have been provided, and these are now numbered disjointly to avoid confusion.

In this full-color edition, we have used the color code illustrated in the following chart for most of the illustrations. Light beams and field distributions are colored red (except when light beams of multiple colors are involved, as in nonlinear optics). Glass and glass fibers are depicted in light blue. Semiconductors are cast in green, with various shades representing different doping levels, and metal is indicated by the color of copper. Energy diagrams are marked in blue and forbidden photonic bandgaps in pink, as indicated.

Optical ray

Optical beam

Optical wave

Glass

Dielectric wavegu

0 Fiber

■ Semiconductor

y^iy Metal

-1%::.^-

Energy levels

Photonic bandgap

Color chart

Organization In its new incarnation, Fundamentals of Photonics comprises 24 chapters compart-mentalized into six parts, as depicted in the diagram below. The form of the book is modular so that it can be used by readers with different needs; it also provides

PREFACE VII

instructors an opportunity to select topics for different courses. Essential material from one chapter is often briefly summarized in another to make each chapter as self-contained as possible. For example, at the beginning of Chapter 24 (Optical Fiber Communications), relevant material from earlier chapters that describe fibers, light sources, detectors, and amplifiers is briefly reviewed. This places the important features of the various components at the disposal of the reader before the chapter proceeds with a discussion of the design and performance of the overall communication system that makes use of these components.

f Fundamentals

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics

5. Electromagnetic Optics

6. Polarization Optics

""\ f Wave Propagation \ f Ujser Optics "\ C Lightwave Devices

7. Photonic-Crystal Optics

8. Guided-Wave Optics

9. Fiber Optics

10. Resonator Optics

11. Statistical Optics

12. Photon Optics

13. Photons and Atoms

14. Laser Amplifiers

15.1

16. Semiconductor Optics

17. Semiconductor Sources

18. Semiconductor Detectors

19. Acousto-Optics

20. Electro-Optics

21. Nonlinear Optics

22. Ultrafast Optics

23. Interconnects/Switches

24. Optical Communications

\ Optoelectronics f \ Lightwave Systems

Recognizing the different degrees of mathematical sophistication of the intended readership, we have endeavored to present difficult concepts in two steps: at an intro-ductory level providing physical insight and motivation, followed by a more advanced analysis. This approach is exemplified by the treatment in Chapter 20 (Electro-Optics), in which the subject is first presented using scalar notation and then treated again using tensor notation.

Commonly accepted notation and symbols have been used wherever possible. Be-cause of the broad spectrum of topics covered, however, there are a good number of symbols that have multiple meanings; a list of symbols and units is provided at the end of the book to clarify symbol usage. Throughout the book, important equations are highlighted by boxes to facilitate future retrieval. Sections dealing with material of a more advanced nature are indicated by asterisks and may be omitted if desired. Summaries are provided throughout at points where a recapitulation is deemed useful because of the involved nature of the material.

Each chapter also contains exercises, problem sets, and updated selected reading lists. Examples of real systems are included to emphasize the concepts governing appli-cations of current interest, and appendixes summarize the properties of one- and two-dimensional Fourier transforms, linear-systems theory, and modes of linear systems.

Representative Courses The chapters of this book may be combined in various ways for use in semester or quarter courses. Representative examples of such courses are provided below. Some of these courses may be offered as part of a sequence. Other selections may be made to suit the particular objectives of instructors and students.

- Optics/fhotonics

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics



t, PhotonteCtystal»

-■i'G<^E*Wata-öiöW.

Ifc Resonator Optics


12. Photon Optics

13, Photons and-Atoms

tt. Laser Amputera

15. Users

< IS.SwnlGonductor Optics

17. Sources

. 18.. Detectors

19. Acousto-Optics

20. Electro-Optics





VÜi PREFACE

The first six chapters of the book are suitable for an introductory course on Optics or Photonics. These may be supplemented by Chapter 11, Statistical Optics, to introduce incoherent and partially coherent light, or by the introductory sections of Chapters 8 and 9, Guided-Wave Optics and Fiber Optics, which offer applications.

Optical Information Processing

1. Ray Optics •

2. Wave Optics

3. Beam Optics

4. Fourier Optics



7. PhotonicCrystals


9. Fiber Optics



12. Photon Optics



15. Lasers


17. Sources

18. Detectors

19. Acousto-Optics

20. Electro-Optics





A course on Optical Information Processing may begin with a background of wave and beam optics, and cover Fourier Optics (including coherent image formation and processing), along with incoherent and partially coherent imaging in Statistical Optics. This may be followed by material on devices used for analog data processing, such as Acousto-Optics, and end with switches and gates (Chapter 23), which are used for digital data processing.

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics

7. Photonic Crystals


9. Fiber Optics


5. ElectromagnëttoOptiçs 11 ■ Statistical Optics

6. Polarization Optics 12. Photon Optics



15. Lasers


17. Sources

18. Detectors

Guided-Wave Optics

19. Acousto-Optics

20. Electro-Optics





A course on Guided-Wave Optics may begin with an introduction to wave propagation in layered and periodic media (Chapter 7, Photonic-Crystal Optics) and follow with the chapters on Guided-Wave Optics, Fiber Optics, and Resonator Optics. Additional topics may include Electro-Optics and Optical Interconnects and Switches.

Lasers

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics





9. Fiber Optics



12. Photon Optics



15. Lasers


17. Sources

18. Detectors

19. Acousto-Optics

20. Electro-Optics





A course on Lasers could begin with Beam Optics and Resonator Optics, and follow with the theory of interaction of light with matter (Chapter 13) and laser amplification and oscillation (Chapters 14 and 15), and include semiconductor LEDs and lasers (Chapters 16 and 17). An introduction to femtosecond lasers can be provided by including appropriate sections from Ultrafast Optics.

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics



Optoelectronics 7. Photonic Crystals 13. Photons and Atoms


9. Fiber Optics



12. Photon Optics


15. Lasers


17. Sources

18. Detectors

The three chapters covering semiconductor optics, sources/amplifiers, and detectors form a suitable basis for a course on Optoelectronics. This material may be supplemented with optics background from earlier chapters, and extended to include topics such as liquid-crystal devices (Sees. 6.5 and

19. Acousto-Optics

20. Electro-Optics





PREFACE IX

20.3), semiconductor electroabsorption modulators (Sec. 20.5), and an introduction to the use of photonic devices for switching and/or communications (Chapters 23 and 24, respectively).

Photonic Devices

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics





9. Fiber Optics



12. Photon Optics



15. Lasers


17. Sources

18. Detectors

Photonic Devices is another possible topic for a course that combines photonic-crystal and guided-wave devices with electro-optic, acousto-optic, and nonlinear optical devices, and includes ultrafast optics and optical interconnects/switches.

19. Acousto-Optics

20. Electro-Optics





Fiber-Optic Communications

1. Ray Optics

2. Wave Optics

3. Beam Optics

4. Fourier Optics





9. Fiber Optics



12. Photon Optics



15. Lasers


17. Sources

18. Detectors

19. Acousto-Optics

20. Electro-Optics





A course on Fiber-Optic Communications could include optical waveguides and fibers, semiconduc-tor sources and amplifiers (possibly also Secs. 14.3C and 14.3D on optical-fiber and Raman-fiber amplifiers), as background material for the chapter on Optical Fiber Communications (Chapter 24). If fiber-optic networks are to be emphasized, Sec. 23.3 on photonic switches may also be included.

Acknowledgments We are grateful to many colleagues for providing us with valuable comments about draft chapters for the Second Edition and for drawing our attention to errors in the First Edition: Mete Atatüre, Michael Bär, Robert Balahura, Silvia Carrasco, Stephen Chinn, Thomas Daly, Gianni Di Giuseppe, Adel El-Nadi, John Fourkas, Majeed Hayat, Tony Heinz, Erich Ippen, Martin Jaspan, Gerd Keiser, Jonathan Kane, Paul Kelley, Ted Moustakas, Allen Mullins, Magued Nasr, Roy Olivier, Roberto Paiella, Peter W. E. Smith, Stephen P. Smith, Kenneth Suslick, Anna Swan, Tristan Tayag, Tommaso Toffoli, and Brad Tousley.

We extend our special thanks to those colleagues who graciously provided us with in-depth critiques of various chapters: Ayman Abouraddy, Luca Dal Negro, and Paul Prucnal.

We are indebted to the legions of students and postdoctoral associates who have posed so many excellent questions that helped us hone our presentation. In particular, many improvements were initiated by suggestions from Mark Booth, Jasper Cabalu, Michael Cunha, Darryl Goode, Chris LaFratta, Rui Li, Eric Lynch, Nan Ma, Nishant Mohan, Julie Praino, Yunjie Tong, and Ranjith Zachariah. We are especially grateful to Mohammed Saleh, who diligently read much of the manuscript and provided us with excellent suggestions for improvement throughout.

Wai Yan (Eliza) Wong provided logistical support and a great deal of assistance in crafting diagrams and figures. Many at Wiley, including George Telecki, our Editor, and Rachel Witmer have been most helpful, patient, and encouraging. We appreciate the attentiveness and thoroughness that Melissa Yanuzzi brought to the production pro-cess. Don DeLand of the Integre Technical Publishing Company provided invaluable assistance in setting up the Latex style files.

X PREFACE

We are most appreciative of the financial support provided by the National Sci-ence Foundation (NSF), in particular the Center for Subsurface Sensing and Imaging Systems (CenSSIS), an NSF-supported Engineering Research Center; the Defense Advanced Research Projects Agency (DARPA); the National Reconnaissance Office (NRO); the U.S. Army Research Office (ARO); the David & Lucile Packard Founda-tion; the Boston University College of Engineering; and the Boston University Photon-ics Center.

Photo Credits. Most of the portraits were carried forward from the First Edi-tion with the benefit of permissions provided for all editions. Additional credits are: Godfrey Kneller 1689 portrait (Newton); Siegfried Bendixen 1828 lithograph (Gauss); Engraving in the Small Portraits Collection, History of Science Collections, University of Oklahoma Libraries (Fraunhofer); Stanford University, Courtesy AIP Emilio Segrè Visual Archives (Bloch); Eli Yablonovitch (Yablonovitch); Sajeev John (John); Charles Kao (Kao); Philip St John Russell (Russell); Ecole Polytechnique (Fabry); Observa-toire des Sciences de l'Univers (Perot); AIP Emilio Segrè Visual Archives (Born); Lagrelius & Westphal 1920 portrait (Bohr); AIP Emilio Segrè Visual Archives, Weber Collection (W. L. Bragg); Linn F. Mollenauer (Mollenauer); Roger H. Stolen (Stolen); and James P. Gordon (Gordon). In Chapter 23, the Bell Symbol was reproduced with the permission of BellSouth Intellectual Property Marketing Corporation, the AT&T logo is displayed with the permission of AT&T, and Lucent Technologies permitted us use of their logo. Stephen G. Eick kindly provided the image used at the beginning of Chapter 24. The photographs of Saleh and Teich were provided courtesy of Boston University.

BAHAA E. A. SALEH

M A L V I N C A R L T E I C H

Boston, Massachusetts December 19, 2006

Third Printing Errors that appeared in the First and Second Printings of the Second Edition have been corrected in the Third Printing. A number of other improvements have also been made and the Reading Lists have been updated.

BAHAA E. A. SALEH Orlando, Florida

M A L V I N C A R L T E I C H

Boston, Massachusetts January 20, 2009

PREFACE TO THE FIRST EDITION

Optics is an old and venerable subject involving the generation, propagation, and de-tection of light. Three major developments, which have been achieved in the last thirty years, are responsible for the rejuvenation of optics and for its increasing importance in modern technology: the invention of the laser, the fabrication of low-loss optical fibers, and the introduction of semiconductor optical devices. As a result of these de-velopments, new disciplines have emerged and new terms describing these disciplines have come into use: electro-optics, optoelectronics, quantum electronics, quantum optics, and lightwave technology. Although there is a lack of complete agreement about the precise usages of these terms, there is a general consensus regarding their meanings.

Photonics Electro-optics is generally reserved for optical devices in which electrical effects play a role (lasers, and electro-optic modulators and switches, for example). Optoelectronics, on the other hand, typically refers to devices and systems that are essentially electronic in nature but involve light (examples are light-emitting diodes, liquid-crystal display devices, and array photodetectors). The term quantum electronics is used in connection with devices and systems that rely principally on the interaction of light with matter (lasers and nonlinear optical devices used for optical amplification and wave mixing serve as examples). Studies of the quantum and coherence properties of light lie within the realm of quantum optics. The term lightwave technology has been used to describe devices and systems that are used in optical communications and optical signal pro-cessing..

In recent years, the term photonics has come into use. This term, which was coined in analogy with electronics, reflects the growing tie between optics and electronics forged by the increasing role that semiconductor materials and devices play in optical systems. Electronics involves the control of electric-charge flow (in vacuum or in matter); photonics involves the control of photons (in free space or in matter). The two disciplines clearly overlap since electrons often control the flow of photons and, conversely, photons control the flow of electrons. The term photonics also reflects the importance of the photon nature of light in describing the operation of many optical devices.

Scope This book provides an introduction to the fundamentals of photonics. The term pho-tonics is used broadly to encompass all of the aforementioned areas, including the following:

■ The generation of coherent light by lasers, and incoherent light by luminescence sources such as light-emitting diodes.

■ The transmission of light in free space, through conventional optical components such as lenses, apertures, and imaging systems, and through waveguides such as optical fibers.

■ The modulation, switching, and scanning of light by the use of electrically, acous-tically, or optically controlled devices.

■ The amplification and frequency conversion of light by the use of wave interac-tions in nonlinear materials.

■ The detection of light. xi

XM PREFACE

These areas have found ever-increasing applications in optical communications, signal processing, computing, sensing, display, printing, and energy transport.

Approach and Presentation The underpinnings of photonics are provided in a number of chapters that offer concise introductions to:

■ The four theories of light (each successively more advanced than the preceding): ray optics, wave optics, electromagnetic optics, and photon optics.

■ The theory of interaction of light with matter. ■ The theory of semiconductor materials and their optical properties.

These chapters serve as basic building blocks that are used in other chapters to describe the generation of light (by lasers and light-emitting diodes); the transmission of light (by optical beams, diffraction, imaging, optical waveguides, and optical fibers); the modulation and switching of light (by the use of electro-optic, acousto-optic, and nonlinear-optic devices); and the detection of light (by means of photodetectors). Many applications and examples of real systems are provided so that the book is a blend theory and practice. The final chapter is devoted to the study of fiber-optic communica-tions, which provides an especially rich example in which the generation, transmission, modulation, and detection of light are all part of a single photonic system used for the transmission of information.

The theories of light are presented at progressively increasing levels of difficulty. Thus light is described first as rays, then scalar waves, then electromagnetic waves, and finally, photons. Each of these descriptions has its domain of applicability. Our approach is to draw from the simplest theory that adequately describes the phenomenon or intended application. Ray optics is therefore used to describe imaging systems and the confinement of light in waveguides and optical resonators. Scalar wave theory provides a description of optical beams, which are essential for the understanding of lasers, and of Fourier optics, which is useful for describing coherent optical systems and holography. Electromagnetic theory provides the basis for the polarization and dispersion of light, and the optics of guided waves, fibers, and resonators. Photon optics serves to describe the interactions of light with matter, explaining such processes as light generation and detection, and light mixing in nonlinear media.

Intended Audience Fundamentals of Photonics is meant to serve as:

■ An introductory textbook for students in electrical engineering or applied physics at the senior or first-year graduate level.

■ A self-contained work for self-study. ■ A text for programs of continuing professional development offered by industry,

universities, and professional societies.

The reader is assumed to have a background in engineering or applied physics, including courses in modern physics, electricity and magnetism, and wave motion. Some knowledge of linear systems and elementary quantum mechanics is helpful but not essential. Our intent has been to provide an introduction to photonics that emphasizes the concepts governing applications of current interest. The book should, therefore, not be considered as a compendium that encompasses all photonic devices and systems. Indeed, some areas of photonics are not included at all, and many of the individual chapters could easily have been expanded into separate monographs.

PREFACE XIII

Problems, Reading Lists, and Appendices A set of problems is provided at the end of each chapter. Problems are numbered in accordance with the chapter sections to which they apply. Quite often, problems deal with ideas or applications not mentioned in the text, analytical derivations, and numerical computations designed to illustrate the magnitudes of important quantities. Problems marked with asterisks are of a more advanced nature. A number of exer-cises also appear within the text of each chapter to help the reader develop a better understanding of (or to introduce an extension of) the material.

Appendices summarize the properties of one- and two-dimensional Fourier trans-forms, linear-systems theory, and modes of linear systems (which are important in polarization devices, optical waveguides, and resonators); these are called upon at appropriate points throughout the book. Each chapter ends with a reading list that includes a selection of important books, review articles, and a few classic papers of special significance.

Acknowledgments We are grateful to many colleagues for reading portions of the text and providing helpful comments: Govind P. Agrawal, David H. Auston, Rasheed Azzam, Nikolai G. Basov, Franco Cerrina, Emmanuel Desurvire, Paul Diament, Eric Fossum, Robert J. Keyes, Robert H. Kingston, Rodney Loudon, Leonard Mandel, Leon McCaughan, Richard M. Osgood, Jan Pefina, Robert H. Rediker, Arthur L. Schawlow, S. R. Se-shadri, Henry Stark, Ferrel G. Stremler, John A. Tataronis, Charles H. Townes, Patrick R. Trischitta, Wen I. Wang, and Edward S. Yang.

We are especially indebted to John Whinnery and Emil Wolf for providing us with many suggestions that greatly improved the presentation.

Several colleagues used portions of the notes in their classes and provided us with invaluable feedback. These include Etan Bourkoff at Johns Hopkins University (now at the University of South Carolina), Mark O. Freeman at the University of Colorado, George C. Papen at the University of Illinois, and Paul R. Prucnal at Princeton Univer-sity.

Many of our students and former students contributed to this material in various ways over the years and we owe them a great debt of thanks: Gaetano L. Aiello, Mohamad Asi, Richard Campos, Buddy Christyono, Andrew H. Cordes, Andrew David, Ernesto Fontenla, Evan Goldstein, Matthew E. Hansen, Dean U. Hekel, Conor Heneghan, Adam Heyman, Bradley M. Jost, David A. Landgraf, Kanghua Lu, Ben Nathanson, Winslow L. Sargeant, Michael T. Schmidt, Raul E. Sequeira, David Small, Kraisin Songwatana, Nikola S. Subotic, Jeffrey A. Tobin, and Emily M. True. Our thanks also go to the legions of unnamed students who, through a combination of vigilance and the desire to understand the material, found countless errors.

We particularly appreciate the many contributions and help of those students who were intimately involved with the preparation of this book at its various stages of completion: Niraj Agrawal, Suzanne Keilson, Todd Larchuk, Guifang Li, and Philip Tham.

We are grateful for the assistance given to us by a number of colleagues in the course of collecting the photographs used at the beginnings of the chapters: E. Scott Barr, Nicolaas Bloembergen, Martin Carey, Marjorie Graham, Margaret Harrison, Ann Kot-tner, G. Thomas Holmes, John Howard, Theodore H. Maiman, Edward Palik, Martin Parker, Aleksandr M. Prokhorov, Jams Quinn, Lesley M. Richmond, Claudia Schüler, Patrick R. Trischitta, J. Michael Vaughan, and Emil Wolf. Specific photo credits are as follows: AIP Meggers Gallery of Nobel Laureates (Gabor, Townes, Basov, Prokhorov, W. L. Bragg); AIP Niels Bohr Library (Rayleigh, Fraunhofer, Maxwell, Planck, Bohr, Einstein in Chapter 12, W. H. Bragg); Archives de l'Académie des Sciences de Paris (Fabry); The Astrophysical Journal (Perot); AT&T Bell Laboratories (Shockley, Brat-

XiV PREFACE

tain, Bardeen); Bettmann Archives (Young, Gauss, Tyndall); Bibliothèque Nationale de Paris (Fermât, Fourier, Poisson); Burndy Library (Newton, Huygens); Deutsches Mu-seum (Hertz); ETH Bibliothek (Einstein in Chapter 11); Bruce Fritz (Saleh); Harvard University (Bloembergen); Heidelberg University (Pockels); Kelvin Museum of the University of Glasgow (Kerr); Theodore H. Maiman (Maiman); Princeton University (von Neumann); Smithsonian Institution (Fresnel); Stanford University (Schawlow); Emil Wolf (Born, Wolf). Corning Incorporated kindly provided the photograph used at the beginning of Chapter 8. We are grateful to GE for the use of their logotype, which is a registered trademark of the General Electric Company, at the beginning of Chapter 16. The IBM logo at the beginning of Chapter 16 is being used with special permission from IBM. The right-most logotype at the beginning of Chapter 16 was supplied courtesy of Lincoln Laboratory, Massachusetts Institute of Technology. AT&T Bell Laboratories kindly permitted us use of the diagram at the beginning of Chapter 22.

We greatly appreciate the continued support provided to us by the National Sci-ence Foundation, the Center for Telecommunications Research, and the Joint Services Electronics Program through the Columbia Radiation Laboratory.

Finally, we extend our sincere thanks to our editors, George Telecki and Bea Shube, for their guidance and suggestions throughout the course of preparation of this book.

BAHAA E. A. SALEH Madison, Wisconsin

MALVIN CARL TEICH

New York, New York April 3, 1991

CONTENTS

PREFACE TO THE SECOND EDITION

PREFACE TO THE FIRST EDITION xi

RAY OPTICS 1 1.1 Postulates of Ray Optics 3 1.2 Simple Optical Components 6 1.3 Graded-lndex Optics 17 1.4 Matrix Optics 24

Reading List 34 Problems 35

WAVE OPTICS 38 2.1 Postulates of Wave Optics 40 2.2 Monochromatic Waves 41

*2.3 Relation Between Wave Optics and Ray Optics 49 2.4 Simple Optical Components 50 2.5 Interference 58 2.6 Polychromatic and Pulsed Light 66


BEAM OPTICS 74 3.1 The Gaussian Beam 75 3.2 Transmission Through Optical Components 86 3.3 Hermite-Gaussian Beams 94

*3.4 Laguerre-Gaussian and Bessel Beams 97 Reading List 100 Problems 100

FOURIER OPTICS 102 4.1 Propagation of Light in Free Space 105 4.2 Optical Fourier Transform 116 4.3 Diffraction of Light 121 4.4 Image Formation 127 4.5 Holography 138


xv

XVI CONTENTS

5 ELECTROMAGNETIC OPTICS 150 5.1 Electromagnetic Theory of Light 152 5.2 Electromagnetic Waves in Dielectric Media 156 5.3 Monochromatic Electromagnetic Waves 162 5.4 Elementary Electromagnetic Waves 164 5.5 Absorption and Dispersion 170 5.6 Pulse Propagation in Dispersive Media 184

*5.7 Optics of Magnetic Materials and Metamaterials 190 Reading List 193 Problems 195

6 POLARIZATION OPTICS 197 6.1 Polarization of Light 199 6.2 Reflection and Refraction 209 6.3 Optics of Anisotropie Media 215 6.4 Optical Activity and Magneto-Optics 228 6.5 Optics of Liquid Crystals 232 6.6 Polarization Devices 235


7 PHOTONIC-CRYSTAL OPTICS 243 7.1 Optics of Dielectric Layered Media 246 7.2 One-Dimensional Photonic Crystals 265 7.3 Two- and Three-Dimensional Photonic Crystals 279


8 GUIDED-WAVE OPTICS 289 8.1 Planar-Mirror Waveguides 291 8.2 Planar Dielectric Waveguides 299 8.3 Two-Dimensional Waveguides 308 8.4 Photonic-Crystal Waveguides 311 8.5 Optical Coupling in Waveguides 313 8.6 Sub-Wavelength Metal Waveguides (Plasmonics) 321


9 FIBER OPTICS 325 9.1 Guided Rays 327 9.2 Guided Waves 331 9.3 Attenuation and Dispersion 348 9.4 Holey and Photonic-Crystal Fibers 359


1 0 RESONATOR OPTICS 365 10.1 Planar-Mirror Resonators 367 10.2 Spherical-Mirror Resonators 378 10.3 Two- and Three-Dimensional Resonators 390 10.4 Microresonators 394


CONTENTS XVÜ

1 1 STATISTICAL OPTICS 403 11.1 Statistical Properties of Random Light 405 11.2 Interference of Partially Coherent Light 419

*11.3 Transmission of Partially Coherent Light Through Optical Systems 427 11.4 Partial Polarization 436


1 2 PHOTON OPTICS 444 12.1 The Photon 446 12.2 Photon Streams 458

* 12.3 Quantum States of Light 471 Reading List 476 Problems 478

1 3 PHOTONS AND ATOMS 482 13.1 Energy Levels 483 13.2 Occupation of Energy Levels 499 13.3 Interactions of Photons with Atoms 501 13.4 Thermal Light 517 13.5 Luminescence and Scattering 522


1 4 LASER AMPLIFIERS 532 14.1 Theory of Laser Amplification 535 14.2 Amplifier Pumping 539 14.3 Common Laser Amplifiers 547 14.4 Amplifier Nonlinearity 556

* 14.5 Amplifier Noise 562 Reading List 564 Problems 565

1 5 LASERS 567 15.1 Theory of Laser Oscillation 569 15.2 Characteristics of the Laser Output 575 15.3 Common Lasers 590 15.4 Pulsed Lasers 605


1 6 SEMICONDUCTOR OPTICS 627 16.1 Semiconductors 629 16.2 Interactions of Photons with Charge Carriers 660


xviii CONTENTS

1 7 SEMICONDUCTOR PHOTON SOURCES 680 17.1 Light-Emitting Diodes 682 17.2 Semiconductor Optical Amplifiers 702 17.3 Laser Diodes 716 17.4 Quantum-Confined and Microcavity Lasers 728


1 8 SEMICONDUCTOR PHOTON DETECTORS 748 18.1 Photodetectors 749 18.2 Photoconductors 758 18.3 Photodiodes 762 18.4 Avalanche Photodiodes 767 18.5 Array Detectors 775 18.6 Noise in Photodetectors 777


1 9 ACOUSTO-OPTICS 804 19.1 Interaction of Light and Sound 806 19.2 Acousto-Optic Devices 819

*19.3 Acousto-Optics of Anisotropie Media 828 Reading List 832 Problems 832

2 0 ELECTRO-OPTICS 834 20.1 Principles of Electro-Optics 836

*20.2 Electro-Optics of Anisotropie Media 849 20.3 Electro-Optics of Liquid Crystals 856

*20.4 Photorefractivity 863 20.5 Electroabsorption 868


2 1 NONLINEAR OPTICS 873 21.1 Nonlinear Optical Media 875 21.2 Second-Order Nonlinear Optics 879 21.3 Third-Order Nonlinear Optics 894

*21.4 Second-Order Nonlinear Optics: Coupled-Wave Theory 905 *21.5 Third-Order Nonlinear Optics: Coupled-Wave Theory 917 *21.6 Anisotropie Nonlinear Media 924 *21.7 Dispersive Nonlinear Media 927


2 2 ULTRAFAST OPTICS 936 22.1 Pulse Characteristics 937 22.2 Pulse Shaping and Compression 946 22.3 Pulse Propagation in Optical Fibers 960

CONTENTS XIX

22.4 Ultrafast Linear Optics 973 22.5 Ultrafast Nonlinear Optics 984 22.6 Pulse Detection 999


2 3 OPTICAL INTERCONNECTS AND SWITCHES 1016 23.1 Optical Interconnects 1018 23.2 Passive Optical Routers 1030 23.3 Photonic Switches 1038 23.4 Optical Gates 1058


2 4 OPTICAL FIBER COMMUNICATIONS 1072 24.1 Fiber-Optic Components 1074 24.2 Optical Fiber Communication Systems 1084 24.3 Modulation and Multiplexing 1101 24.4 Fiber-Optic Networks 1106 24.5 Coherent Optical Communications 1112


A FOURIER TRANSFORM 1122 A.1 One-Dimensional Fourier Transform 1122 A.2 Time Duration and Spectral Width 1124 A.3 Two-Dimensional Fourier Transform 1128

Reading List 1131

B LINEAR SYSTEMS 1132 B.1 One-Dimensional Linear Systems 1132 B.2 Two-Dimensional Linear Systems 1135

Reading List 1136

C MODES OF LINEAR SYSTEMS 1137

SYMBOLS AND UNITS 1142

AUTHORS 1159

INDEX 1161

FUNDAMENTALS OF PHOTONICS

C H A P T E R

1 RAY OPTICS

1.1 1.2

1.3

1.4

POSTULATES OF RAY OPTICS SIMPLE OPTICAL COMPONENTS A. Mirrors B. Planar Boundaries C. Spherical Boundaries and Lenses D. Light Guides

GRADED-INDEX OPTICS A. The Ray Equation B. Graded-lndex Optical Components

*C. The Eikonal Equation MATRIX OPTICS A. The Ray-Transfer Matrix B. Matrices of Simple Optical Components C. Matrices of Cascaded Optical Components D. Periodic Optical Systems

3 6

17

24

Sir Isaac Newton (1642-1727) set forth a theory of optics in which light emissions con-sist of collections of corpuscles that propagate rectilinearly.

Pierre de Fermât (1601-1665) enunciated the principle that light travels along the path of least time.

1

Light can be described as an electromagnetic wave phenomenon governed by the same theoretical principles that govern all other forms of electromagnetic radiation, such as radio waves and X-rays. This conception of light is called electromagnetic optics. Electromagnetic radiation propagates in the form of two mutually coupled vector waves, an electric-field wave and a magnetic-field wave. Nevertheless, it is possible to describe many optical phenomena using a simplified scalar wave theory in which light is described by a single scalar wavefunction. This approximate way of treating light is called scalar wave optics, or simply wave optics.

When light waves propagate through and around objects whose dimensions are much greater than the wavelength of the light, the wave nature is not readily discerned and the behavior of light can be adequately described by rays obeying a set of geomet-rical rules. This model of light is called ray optics. From a mathematical perspective, ray optics is the limit of wave optics when the wavelength is infinitesimally small.

Thus, electromagnetic optics encompasses wave optics, which, in turn, encompasses ray optics, as illustrated in Fig. 1.0-1. Ray optics and wave optics are approximate theo-ries that derive their validity from their successes in producing results that approximate those based on the more rigorous electromagnetic theory.

Figure 1.0-1 The theory of quantum optics provides an explanation of virtually all optical phe-nomena. The electromagnetic theory of light (elec-tromagnetic optics) provides the most complete treatment of light within the confines of classical optics. Wave optics is a scalar approximation of electromagnetic optics. Ray optics is the limit of wave optics when the wavelength is very short.

Although electromagnetic optics provides the most complete treatment of light within the confines of classical optics, certain optical phenomena are characteristically quantum mechanical in nature and cannot be explained classically. These phenomena are described by a quantum version of electromagnetic theory known as quantum electrodynamics. For optical phenomena, this theory is also referred to as quantum optics.

Historically, the theories of optics developed roughly in the following sequence: (1) ray optics —> (2) wave optics —* (3) electromagnetic optics —> (4) quantum optics. These models are progressively more complex and sophisticated, and were devel-oped successively to provide explanations for the outcomes of increasingly subtle and precise optical experiments. The optimal choice of a model is the simplest one that satisfactorily describes a particular phenomenon, but it is sometimes difficult to know a priori which model will achieve this. Fortunately, however, experience often provides a good guide.

For pedagogical reasons, the initial chapters in this book follow the historical order indicated above. Each model of light begins with a set of postulates (provided without proof), from which a large body of results are generated. The postulates of each model are shown to arise in special cases of the next-higher-level model. In this chapter we begin with ray optics.

Quantum Optics

Electromagnetic Optics

Wave Optics

Ray Optics

2

1.1 POSTULATES OF RAY OPTICS 3

This Chapter Ray optics is the simplest theory of light. Light is described by rays that travel in different optical media in accordance with a set of geometrical rules. Ray optics is therefore also called geometrical optics. Ray optics is an approximate theory. Al-though it adequately describes most of our daily experiences with light, there are many phenomena that ray optics does not adequately describe (as amply attested to by the remaining chapters of this book).

Ray optics is concerned with the location and direction of light rays. It is therefore useful in studying image formation — the collection of rays from each point of an object and their redirection by an optical component onto a corresponding point of an image. Ray optics permits us to determine conditions under which light is guided within a given medium, such as a glass fiber. In isotropic media, optical rays point in the direction of the flow of optical energy. Ray bundles can be constructed in which the density of rays is proportional to the density of light energy. When light is generated isotropically from a point source, for example, the energy associated with the rays in a given cone is proportional to the solid angle of the cone. Rays may be traced through an optical system to determine the optical energy crossing a given area.

This chapter begins with a set of postulates from which the simple rules that govern the propagation of light rays through optical media are derived. In Sec. 1.2 these rules are applied to simple optical components such as mirrors and planar or spher-ical boundaries between different optical media. Ray propagation in inhomogeneous (graded-index) optical media is examined in Sec. 1.3. Graded-index optics is the basis of a technology that has become an important part of modern optics.

Optical components are often centered about an optical axis, about which the rays travel at small inclinations. Such rays are called paraxial rays. This assumption is the basis of paraxial optics. The change in the position and inclination of a paraxial ray as it travels through an optical system can be efficiently described by the use of a 2 x 2-matrix algebra. Section 1.4 is devoted to this algebraic tool, called matrix optics.

1.1 POSTULATES OF RAY OPTICS

Postulates of Ray Optics

■ Light travels in the form of rays. The rays are emitted by light sources and can be observed when they reach ah optical detector.

■ An optical medium is characterized by a quantity n > 1, called the refractive index. The refractive index n = c0/c where c0 is the speed of light in free space and c is the speed of light in the medium. Therefore, the time taken by light to travel a distance d is d/c = nd/c0. It is proportional to the product nd, which is known as the optical pathlength.

■ In ah inhomogeneous medium the refractive index n(r) is a function of the position r = (x, y, z). The optical path length along a given path between two points A and B is therefore

Optical pathlength = / n(r)ds, (1-1-1)

where ds is the differential element of length along the path. The time taken by light to travel from A to B is proportional to the optical pathlength.

4 CHAPTER 1 RAY OPTICS

■ Fermat's Principle. Optical rays traveling between two points, A and B, fol-low a path such that the time of travel (or the optical pathlength) between the two points is an extremum relative to neighboring paths. This is expressed mathematically as

5 I n(r)ds = 0, (1.1-2) JA

where the symbol Ô, which is read "the variation of," signifies that the optical pathlength is either minimized or maximized, or is a point of inflection. It is, however, usually a minimum, in which case:

Light rays travel along the path of least time.

Sometimes the minimum time is shared by more than one path, which are then all followed simultaneously by the rays. An example in which the pathlength is maximized is provided in Prob. 1.1-2.

In this chapter we use the postulates of ray optics to determine the rules governing the propagation of light rays, their reflection and refraction at the boundaries between different media, and their transmission through various optical components. A wealth of results applicable to numerous optical systems are obtained without the need for any other assumptions or rules regarding the nature of light.

Propagation in a Homogeneous Medium Ina homogeneous medium the refractive index is the same everywhere, and so is the speed of light. The path of minimum time, required by Fermat's principle, is therefore also the path of minimum distance. The principle of the path of minimum distance is known as Hero's principle. The path of minimum distance between two points is a straight line so that in a homogeneous medium, light rays travel in straight lines (Fig. 1.1-1).

Figure 1.1-1 Light rays travel in straight lines. Shadows are perfect projections of stops.

1.1 POSTULATES OF RAY OPTICS 5

Reflection from a Mirror Mirrors are made of certain highly polished metallic surfaces, or metallic or dielectric films deposited on a substrate such as glass. Light reflects from mirrors in accordance with the law of reflection:

The reflected ray lies in the plane of incidence; the angle of reflection equals the angle of incidence.

The plane of incidence is the plane formed by the incident ray and the normal to the mirror at the point of incidence. The angles of incidence and reflection, 9 and 9', are defined in Fig. 1.1-2(a). To prove the law of reflection we simply use Hero's principle. Examine a ray that travels from point A to point C after reflection from the planar mirror in Fig. 1.1 -2(6). According to Hero's principle, for a mirror of infinitesimal thickness, the distance AB + BC must be minimum. If C is a mirror image of C, then BC — BC, so that AB + BC must be a minimum. This occurs when ABC is a straight line, i.e., when B coincides with B' so that 9 = 9'.

Plane of incidence "

Mirror Mirror

Incident ray

c

/*('•*

A

C

«y'Y

■'B

(b)

Figure 1.1-2 (a) Reflection from the surface of a curved mirror, (b) Geometrical construction to prove the law of reflection.

Reflection and Refraction at the Boundary Between Two Media At the boundary between two media of refractive indexes n\ and n2 an incident ray is split into two — a reflected ray and a refracted (or transmitted) ray (Fig. 1.1-3). The reflected ray obeys the law of reflection. The refracted ray obeys the law of refraction:

The refracted ray lies in the plane of incidence; the angle of refraction ö2 is related to the angle of incidence 9\ by Snell's law,

(1.1-3) Snell's law

The proportion in which the light is reflected and refracted is not described by ray optics.

6 CHAPTER 1 RAY OPTICS

Figure 1.1 -3 Reflection and refraction at the boundary between two media.

EXERCISE 1.1-1

Proof of Snell's Law. The proof of Snell's law is an exercise in the application of Fermat's principle. Referring to Fig. 1.1-4, we seek to minimize the optical pathlength n\AB+n2BC between points A and C. We therefore have the following optimization problem: Minimize nidi sec#i + n2d2 sec 82 with respect to the angles 9\ and 02, subject to the condition di tan 0\ + d2 tan 62 = d. Show that the solution of this constrained minimization problem yields Snell's law.

«l "2

d2 C

ex\/B

Figure 1.1 -4 Construction to prove Snell's law.

The three simple rules — propagation in straight lines and the laws of reflection and refraction — are applied in Sec. 1.2 to several geometrical configurations of mirrors and transparent optical components, without further recourse to Fermat's principle.

1.2 SIMPLE OPTICAL COMPONENTS

A. Mirrors

Planar Mirrors A planar mirror reflects the rays originating from a point Pi such that the reflected rays appear to originate from a point P2 behind the mirror, called the image (Fig. 1.2-1).

Paraboloidal Mirrors The surface of a paraboloidal mirror is a paraboloid of revolution. It has the useful property of focusing all incident rays parallel to its axis to a single point called the fo-cus. The distance PF — f defined in Fig. 1.2-2 is called the focal length. Paraboloidal

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