Optics PDF

 OPTICS Bruhatsamhita-chapter 35 (6th century CE) The multi coloured rays of the Sun, being dispersed...

 OPTICS Bruhatsamhita-chapter 35 (6th century CE) The multi coloured rays of the Sun, being dispersed in a cloudy sky, are seen in the form of a bow, which is called the Rainbow. gha80482_fm_i-xviii.PMD 1 2/3/2009, 10:32 PM  ABOUT THE AUTHOR Ajoy Ghatak has recently retired as Professor of Physics from Indian Institute of Technology, Delhi. He obtained his M.Sc. from Delhi University and Ph.D. from Cornell University. His area of research is fiber optics. He has several books in this area including Introduction to Fiber Optics and Optical Electronics (both books coauthored with Prof. K. Thyagarajan and published by Cambridge University Press, United Kingdom). Professor Ghatak is a recipient of several awards including the 2008 SPIE Educator award and the 2003 Optical Society of America Esther Hoffman Beller award in recognition of his outstanding contributions to optical science and engineering education. He is also a recipient of the CSIR S. S. Bhatnagar award, the Khwarizmi International award and the International Commission for Optics Galileo Galilei award. He received DSc (Honoris Causa) from University of Burdwan in 2007. gha80482_fm_i-xviii.PMD 2 2/3/2009, 10:32 PM  OPTICS Ajoy Ghatak Emeritus Professor Department of Physics Indian Institute of Technology Delhi gha80482_fm_i-xviii.PMD 3 2/13/2009, 5:12 PM  OPTICS Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 QPD/QPD 0 9 ISBN 978–0–07–338048–3 MHID 0–07–338048–2 Global Publisher: Raghothaman Srinivasan Director of Development: Kristine Tibbetts Developmental Editor: Lorraine K. Buczek Senior Marketing Manager: Curt Reynolds Senior Project Manager: Jane Mohr Senior Production Supervisor: Laura Fuller Associate Design Coordinator: Brenda A. Rolwes Cover Designer: Studio Montage, St. Louis, Missouri Lead Photo Research Coordinator: Carrie K. Burger Compositor: Aptara®, Inc. Typeface: 10/12.5 Times Roman Printer: Quebecor World Dubuque, IA All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Cover: Laser pulses of 80 fs duration having a wavelength 800 nm (and total energy of 1.6 nJ) are incident on a special optical fiber known as a holey fiber, in which a silica core is surrounded by a periodic lattice of air holes; holey fibers are characterized by very small mode field diameters, which lead to very high intensities. Because of the high intensities, SPM (self phase modulation) and other nonlinear effects can be observed; these nonlinear effects result in the generation of new frequencies. In this experiment, the entire visible spectrum gets generated, which can be observed by passing the light coming out of the optical fiber through a prism. The repetition rate of the laser pulses is 82 MHz. The special fibers were fabricated by Dr. Shyamal Bhadra and Dr. Kamal Dasgupta and their group at CGCRI, Kolkata, and the supercontinuum generation was observed by Prof. Ajoy Kar and Dr. Henry Bookey at Heriot Watt University, Edinburgh. Photograph courtesy Prof. Ajoy Kar. Library of Congress Cataloging-in-Publication Data Ghatak, A. K. (Ajoy K.), 1939- Optics / Ajoy Ghatak. — 1st ed. p. cm. Includes index. ISBN 978–0–07–338048–3—ISBN 0–07–338048–2 (hard copy : alk. paper) 1. Optics. I. Title. QC355.3.G43 2010 535—dc22 2008054008 www.mhhe.com gha80482_fm_i-xviii.PMD 4 2/13/2009, 5:58 PM  CONTENTS Preface xiii 1. History of Optics 1 References 9 2. What Is Light? 11 2.1 Introduction 11 2.2 The Corpuscular Model 11 2.3 The Wave Model 13 2.4 The Particle Nature of Radiation 15 2.5 Wave Nature of Matter 17 2.6 The Uncertainty Principle 18 2.7 The Single-Slit Diffraction Experiment 18 2.8 The Probabilistic Interpretation of Matter Waves 19 2.9 An Understanding of Interference Experiments 21 2.10 The Polarization of a Photon 23 2.11 The Time-Energy Uncertainty Relation 24 Summary 24 Problems 25 Solutions 25 References and Suggested Readings 26 Part 1 Geometrical Optics 3. Fermat’s Principle and Its Applications 29 3.1 Introduction 29 3.2 Laws of Reflection and Refraction from Fermat’s Principle 31 3.3 Ray Paths in an Inhomogeneous Medium 34 3.4 The Ray Equation and its Solutions 39 3.5 Refraction of Rays at the Interface between an Isotropic Medium and an Anisotropic Medium 44 Summary 47 Problems 47 References and Suggested Readings 51 4. Refraction and Reflection by Spherical Surfaces 53 4.1 Introduction 53 4.2 Refraction at a Single Spherical Surface 54 4.3 Reflection by a Single Spherical Surface 55 4.4 The Thin Lens 56 4.5 The Principal Foci and Focal Lengths of a Lens 57 gha80482_fm_i-xviii.PMD 5 2/3/2009, 10:32 PM  vi Contents u 4.6 The Newton Formula 59 4.7 Lateral Magnification 59 4.8 Aplanatic Points of a Sphere 60 4.9 The Cartesian Oval 62 4.10 Geometrical Proof for the Existence of Aplanatic Points 62 4.11 The Sine Condition 63 Summary 65 Problems 65 References and Suggested Readings 66 5. The Matrix Method in Paraxial Optics 67 5.1 Introduction 67 5.2 The Matrix Method 68 5.3 Unit Planes 73 5.4 Nodal Planes 74 5.5 A System of Two Thin Lenses 75 Summary 77 Problems 77 References and Suggested Readings 78 6. Aberrations 79 6.1 Introduction 79 6.2 Chromatic Aberration 79 6.3 Monochromatic Aberrations 83 Summary 90 Problems 90 References and Suggested Readings 91 Part 2 Vibrations and Waves 7. Simple Harmonic Motion, Forced Vibrations, and Origin of Refractive Index 95 7.1 Introduction 95 7.2 Simple Harmonic Motion 95 7.3 Damped Simple Harmonic Motion 99 7.4 Forced Vibrations 101 7.5 Origin of Refractive Index 103 7.6 Rayleigh Scattering 107 Summary 108 Problems 108 References and Suggested Readings 110 8. Fourier Series and Applications 111 8.1 Introduction 111 8.2 Transverse Vibrations of a Plucked String 113 8.3 Application of Fourier Series in Forced Vibrations 115 8.4 The Fourier Integral 116 Summary 117 Problems 117 References and Suggested Readings 118 9. The Dirac Delta Function and Fourier Transforms 119 9.1 Introduction 119 9.2 Representations of the Dirac Delta Function 119 gha80482_fm_i-xviii.PMD 6 2/3/2009, 10:32 PM  Contents vii u 9.3 Integral Representation of the Delta Function 120 9.4 Delta Function as a Distribution 120 9.5 Fourier Integral Theorem 121 9.6 The Two- and Three-Dimensional Fourier Transform 123 Summary 124 Problems 124 10. Group Velocity and Pulse Dispersion 127 10.1 Introduction 127 10.2 Group Velocity 127 10.3 Group Velocity of a Wave Packet 131 10.4 Self Phase Modulation 137 Summary 139 Problems 140 References and Suggested Readings 141 11. Wave Propagation and the Wave Equation 143 11.1 Introduction 143 11.2 Sinusoidal Waves: Concept of Frequency and Wavelength 145 11.3 Types of Waves 146 11.4 Energy Transport in Wave Motion 146 11.5 The One-Dimensional Wave Equation 147 11.6 Transverse Vibrations of a Stretched String 148 11.7 Longitudinal Sound Waves in a Solid 149 11.8 Longitudinal Waves in a Gas 150 11.9 The General Solution of the One-Dimensional Wave Equation 151 Summary 154 Problems 154 References and Suggested Readings 155 12. Huygens’ Principle and Its Applications 157 12.1 Introduction 157 12.2 Huygens’ Theory 157 12.3 Rectilinear Propagation 158 12.4 Application of Huygens’ Principle to Study Refraction and Reflection 159 Summary 165 Problems 165 References and Suggested Readings 165 Part 3 Interference 13. Superposition of Waves 169 13.1 Introduction 169 13.2 Stationary Waves on a String 169 13.3 Stationary Waves on a String Whose Ends are Fixed 171 13.4 Stationary Light Waves: Ives’ and Wiener’s Experiments 172 13.5 Superposition of Two Sinusoidal Waves 172 13.6 The Graphical Method for Studying Superposition of Sinusoidal Waves 173 13.7 The Complex Representation 175 Summary 175 Problems 175 References and Suggested Readings 176 gha80482_fm_i-xviii.PMD 7 2/3/2009, 10:32 PM  viii Contents u 14. Two-Beam Interference by Division of Wave Front 177 14.1 Introduction 177 14.2 Interference Pattern Produced on the Surface of Water 178 14.3 Coherence 181 14.4 Interference of Light Waves 182 14.5 The Interference Pattern 183 14.6 The Intensity Distribution 184 14.7 Fresnel’s Two-Mirror Arrangement 189 14.8 Fresnel Biprism 189 14.9 Interference with White Light 190 14.10 Displacement of Fringes 191 14.11 Lloyd’s Mirror Arrangement 192 14.12 Phase Change on Reflection 192 Summary 193 Problems 193 References and Suggested Readings 194 15. Interference by Division of Amplitude 195 15.1 Introduction 195 15.2 Interference by a Plane Parallel Film When Illuminated by a Plane Wave 196 15.3 The Cosine Law 197 15.4 Nonreflecting Films 198 15.5 High Reflectivity by Thin Film Deposition 201 15.6 Reflection by a Periodic Structure 202 15.7 Interference by a Plane Parallel Film When Illuminated by a Point Source 206 15.8 Interference by a Film with Two Nonparallel Reflecting Surfaces 208 15.9 Colors of Thin Films 211 15.10 Newton’s Rings 212 15.11 The Michelson Interferometer 216 Summary 219 Problems 219 References and Suggested Readings 220 16. Multiple-Beam Interferometry 221 16.1 Introduction 221 16.2 Multiple Reflections from a Plane Parallel Film 221 16.3 The Fabry–Perot Etalon 223 16.4 The Fabry–Perot Interferometer 225 16.5 Resolving Power 226 16.6 The Lummer–Gehrcke Plate 229 16.7 Interference Filters 230 Summary 231 Problems 231 References and Suggested Readings 231 17. Coherence 233 17.1 Introduction 233 17.2 The Line Width 235 17.3 The Spatial Coherence 236 17.4 Michelson Stellar Interferometer 238 17.5 Optical Beats 239 17.6 Coherence Time and Line Width via Fourier Analysis 241 17.7 Complex Degree of Coherence and Fringe Visibility in Young’s Double-Hole Experiment 243 gha80482_fm_i-xviii.PMD 8 2/3/2009, 10:32 PM  Contents ix u 17.8 Fourier Transform Spectroscopy 244 Summary 249 Problems 249 References and Suggested Readings 250 Part 4 Diffraction 18. Fraunhofer Diffraction I 253 18.1 Introduction 253 18.2 Single-Slit Diffraction Pattern 254 18.3 Diffraction by a Circular Aperture 258 18.4 Directionality of Laser Beams 260 18.5 Limit of Resolution 264 18.6 Two-Slit Fraunhofer Diffraction Pattern 267 18.7 N-Slit Fraunhofer Diffraction Pattern 269 18.8 The Diffraction Grating 272 18.9 Oblique Incidence 275 18.10 X-ray Diffraction 276 18.11 The Self-Focusing Phenomenon 280 18.12 Optical Media Technology—An Essay 282 Summary 285 Problems 285 References and Suggested Readings 287 19. Fraunhofer Diffraction II and Fourier Optics 289 19.1 Introduction 289 19.2 The Fresnel Diffraction Integral 289 19.3 Uniform Amplitude and Phase Distribution 291 19.4 The Fraunhofer Approximation 291 19.5 Fraunhofer Diffraction by a Long Narrow Slit 291 19.6 Fraunhofer Diffraction by a Rectangular Aperture 292 19.7 Fraunhofer Diffraction by a Circular Aperture 293 19.8 Array of Identical Apertures 294 19.9 Spatial Frequency Filtering 296 19.10 The Fourier Transforming Property of a Thin Lens 298 Summary 300 Problems 300 References and Suggested Readings 301 20. Fresnel Diffraction 303 20.1 Introduction 303 20.2 Fresnel Half-Period Zones 304 20.3 The Zone Plate 306 20.4 Fresnel Diffraction—A More Rigorous Approach 308 20.5 Gaussian Beam Propagation 310 20.6 Diffraction by a Straight edge 312 20.7 Diffraction of a Plane Wave by a Long Narrow Slit and Transition to the Fraunhofer Region 318 Summary 320 Problems 321 References and Suggested Readings 323 21. Holography 325 21.1 Introduction 325 21.2 Theory 327 gha80482_fm_i-xviii.PMD 9 2/3/2009, 10:32 PM  x Contents u 21.3 Requirements 330 21.4 Some Applications 330 Summary 332 Problems 332 References and Suggested Readings 333 Part 5 Electromagnetic Character of Light 22. Polarization and Double Refraction 337 22.1 Introduction 337 22.2 Production of Polarized Light 340 22.3 Malus’ Law 343 22.4 Superposition of Two Disturbances 344 22.5 The Phenomenon of Double Refraction 347 22.6 Interference of Polarized Light: Quarter Wave Plates and Half Wave Plates 351 22.7 Analysis of Polarized Light 354 22.8 Optical Activity 354 22.9 Change in the SOP (State of Polarization) of a Light Beam Propagating Through an Elliptic Core Single-Mode Optical Fiber 356 22.10 Wollaston Prism 358 22.11 Rochon Prism 359 22.12 Plane Wave Propagation in Anisotropic Media 359 22.13 Ray Velocity and Ray Refractive Index 363 22.14 Jones’ Calculus 365 22.15 Faraday Rotation 367 22.16 Theory of Optical Activity 369 Summary 371 Problems 372 References and Suggested Readings 374 23. Electromagnetic Waves 375 23.1 Maxwell’s Equations 375 23.2 Plane Waves in a Dielectric 375 23.3 The Three-Dimensional Wave Equation in a Dielectric 378 23.4 The Poynting Vector 379 23.5 Energy Density and Intensity of an Electromagnetic Wave 382 23.6 Radiation Pressure 382 23.7 The Wave Equation in a Conducting Medium 384 23.8 The Continuity Conditions 385 23.9 Physical Significance of Maxwell’s Equations 386 Summary 388 Problems 388 References and Suggested Readings 389 24. Reflection and Refraction of Electromagnetic Waves 391 24.1 Introduction 391 24.2 Reflection and Defraction at an Interface of Two Dielectrics 391 24.3 Reflection by a Conducting Medium 404 24.4 Reflectivity of a Dielectric Film 406 Summary 407 Problems 408 References and Suggested Readings 408 gha80482_fm_i-xviii.PMD 10 2/3/2009, 10:32 PM  Contents xi u Part 6 Photons 25. The Particle Nature of Radiation 411 25.1 Introduction 412 25.2 The Photoelectric Effect 412 25.3 The Compton Effect 414 25.4 The Photon Mass 418 25.5 Angular Momentum of a Photon 418 Summary 420 Problems 421 References and Suggested Readings 421 Part 7 Lasers and Fiber Optics 26. Lasers: An Introduction 425 26.1 Introduction 426 26.2 The Fiber Laser 431 26.3 The Ruby Laser 432 26.4 The He-Ne Laser 434 26.5 Optical Resonators 436 26.6 Einstein Coefficients and Optical Amplification 440 26.7 The Line Shape Function 446 26.8 Typical Parameters for a Ruby Laser 447 26.9 Monochromaticity of the Laser Beam 448 26.10 Raman Amplification and Raman Laser 449 Summary 452 Problems 453 References and Suggested Readings 454 27. Optical Waveguides I: Optical Fiber Basics Using Ray Optics 455 27.1 Introduction 456 27.2 Some Historical Remarks 456 27.3 Total Internal Reflection 459 27.4 The Optical Fiber 460 27.5 Why Glass Fibers? 461 27.6 The Coherent Bundle 462 27.7 The Numerical Aperture 462 27.8 Attenuation in Optical Fibers 463 27.9 Multimode Fibers 465 27.10 Pulse Dispersion in Multimode Optical Fibers 466 27.11 Dispersion and Maximum Bit Rates 469 27.12 General Expression for Ray Dispersion Corresponding to a Power Law Profile 470 27.13 Plastic Optical Fibers 471 27.14 Fiber-Optic Sensors 471 Problems 472 References and Suggested Readings 473 28. Optical Waveguides II: Basic Waveguide Theory and Concept of Modes 475 28.1 Introduction 475 28.2 TE Modes of a Symmetric Step Index Planar Waveguide 476 28.3 Physical Understanding of Modes 480 28.4 TM Modes of a Symmetric Step Index Planar Waveguide 481 gha80482_fm_i-xviii.PMD 11 2/3/2009, 10:32 PM  xii Contents u 28.5 TE Modes of a Parabolic Index Planar Waveguide 482 28.6 Waveguide Theory and Quantum Mechanics 483 Problems 485 References and Suggested Readings 485 29. Optical Waveguides III: Single-Mode Fibers 487 29.1 Introduction 487 29.2 Basic Equations 487 29.3 Guided Modes of a Step Index Fiber 489 29.4 Single-Mode Fiber 491 29.5 Pulse Dispersion in Single-Mode Fibers 493 29.6 Dispersion Compensating Fibers 495 Problems 497 References and Suggested Readings 498 Part 8 Special Theory of Relativity 30. Special Theory of Relativity I: Time Dilation and Length Contraction 501 30.1 Introduction 501 30.2 Speed of Light for a Moving Source 502 30.3 Time Dilation 503 30.4 The Mu Meson Experiment 504 30.5 The Length Contraction 505 30.6 Understanding the Mu Meson Experiment via Length Contraction 506 30.7 Length Contraction of a Moving Train 506 30.8 Simultaneity of Two Events 407 30.9 The Twin Paradox 508 30.10 The Michelson–Morley Experiment 509 30.11 Brief Historical Remarks 511 Problems 512 References and Suggested Readings 512 31. Special Theory of Relativity II: Mass-Energy Relationship and Lorentz Transformations 513 31.1 Introduction 513 31.2 The Mass-Energy Relationship 513 31.3 The Doppler Shift 515 31.4 The Lorentz Transformation 516 31.5 Addition of Velocities 518 References and Suggested Readings 518 Appendix A: Gamma Functions and Integrals Involving Gaussian Functions 519 Appendix B: Evaluation of the Integral 521 Appendix C: The Reflectivity of a Fiber Bragg Grating 522 Appendix D: Diffraction of a Gaussian Beam 523 Appendix E: TE and TM Modes in Planar Waveguides 524 Appendix F: Solution for the Parabolic Index Waveguide 526 Appendix G: Invariance of the Wave Equation Under Lorentz Transformation 528 Name Index 000 Subject Index 000 gha80482_fm_i-xviii.PMD 12 2/3/2009, 10:32 PM  PREFACE The first laser was fabricated in 1960, and since then there has been a renaissance in the field of optics. From optical amplifiers to laser physics, fiber optics to optical communications, optical data processing to holography, optical sensors to DVD technology, ultrashort pulse generation to super continuum generation, optics now finds important applications in almost all branches of science and engineering. In addition to numerous practical applications of optics, it is said that it was the quest to understand the “nature of light” that brought about the two revolutions in science: the development of quantum mechanics started with an attempt to understand the “light quanta,” and the starting point of the special theory of relativity was Maxwell’s equations which synthesized the laws of electricity and magnetism with those of light. Because of all this, an undergraduate course in optics has become a “must” not only for students of physics but also for students of engineering. Although it is impossible to cover all areas in a single book, this book attempts to give a comprehensive account of a large number of important topics in this exciting field and should meet the requirements of a course on optics meant for undergraduate students of science and engineering. Organization of the Book The book attempts to give a balanced account of traditional optics as well as some of the recent developments in this field. The plan of the book is as follows: Chapter 1 gives a brief history of the development of optics. I have always felt that one must have a perspective of the evolution of the subject that she or he wants to learn. Optics is such a vast field that it is extremely difficult to give a historical perspective of all the areas. My own interests lie in fiber optics, and hence there is a bias toward the evolution of fiber optics and related areas. In the process, I must have omitted the names of many individuals who made important contributions to the growth of optics. Fortunately, there is now a wealth of information available through the Internet; I have also included a number of references to various books and websites. Chapter 2 gives a brief historical evolution of different models describing the nature of light. It starts with the corpuscular model of light and then discusses the evolution of the wave model and the electromagnetic character of light waves. Next we discuss the early twentieth-century experiments, which could only be explained by assuming a particle nature of light, and we end with a discussion on “wave-particle duality.” Chapters 3 to 6 cover geometrical optics. Chapter 3 starts with Fermat’s principle and discusses ray tracing through graded index media, explaining in detail the phenomena of mirage and looming, ray propagation through graded index optical waveguides, and reflection from the ionosphere. Chapter 4 covers ray tracing in lens systems, and Chap. 5 discusses the matrix method in paraxial optics, which is used in the industry. Chapter 6 gives a brief account of aberrations. Chapters 7 to 12 discuss the origin of refractive index and the basic physics of wave propagation including Huygens’ principle. Many interesting experiments (such as the redness of the setting Sun, water waves, etc.) are discussed. The concept of group velocity and the dispersion of an optical pulse as it propagates through a dispersive medium are discussed in detail. Self phase modulation, which is one of the phenomena leading to the super continuum generation (see photograph on the cover), is also explained. Chapters 13 to 16 cover the very important and fascinating area of interference and many beautiful experiments associated with it—the underlying principle is the superposition principle, which is discussed in Chap. 13. Chapter 14 discusses interference by division of the wave front including the famous Young double-hole interference experiment. gha80482_fm_i-xviii.PMD 13 2/3/2009, 10:32 PM  xiv Perface u In Chap. 15, interference by division of amplitude is discussed which allows us to understand the colors of thin films and applications such as antireflection films. The basic working principle of the fiber Bragg gratings (usually abbreviated as FBG) is discussed along with some of their important applications in the industry. In the same chapter, the Michelson interferometer is discussed which is perhaps one of the most ingenious and sensational optical instruments ever, and for which Michelson received the Nobel Prize in Physics in 1907. Chapter 16 discusses the Fabry– Perot interferometer that is based on multiple-beam interference and is characterized by a high resolving power and hence finds applications in high-resolution spectroscopy. Chapter 17 discusses the basic concept of temporal and spatial coherence. The ingenious experiment of Michelson, which used the concept of spatial coherence to determine the angular diameter of stars, is discussed in detail. Topics such as optical beats and Fourier transform spectroscopy are also discussed. Chapters 18, 19, and 20 cover the very important area of diffraction and discuss the principle behind topics such as the diffraction divergence of laser beams, resolving power of telescopes, laser focusing, X-ray diffraction, optical media technology, Fourier optics, and spatial frequency filtering. Chapter 21 discusses the underlying principle of holography and some of its applications. Dennis Gabor received the 1971 Nobel Prize in Physics for discovering the principle of holography. Chapters 22 to 24 cover are on the electromagnetic character of light waves. Chapter 22 discusses the polarization phenomenon and propagation of electromagnetic waves in anisotropic media including first-principle derivations of wave and ray velocities. Phenomena such as optical activity and Faraday rotation (and its applications to measuring large currents) are explained from first principles. In Chap. 23, starting with Maxwell’s equations, the wave equation is derived which led Maxwell to predict the existence of electromagnetic waves and to propound that light is an electromagnetic wave. Reflection and refraction of electromagnetic waves by a dielectric interface are discussed in Chap. 24. Results derived in this chapter directly explain phenomena such as Brewster’s law, total internal reflection, evanescent waves, and Fabry–Perot transmission resonances. Chapter 25 covers the particle nature of radiation, for which Einstein received the 1921 Nobel Prize. The chapter also discusses the Compton effect (for which Compton received the 1927 Nobel Prize in Physics), which established that the photon has a momentum equal to hn/c. Chapter 26 is on lasers—a subject of tremendous technological importance. The basic physics of optical amplifiers and of lasers along with their special characteristics is also discussed. Chapters 27 to 29 discuss waveguide theory and fiber optics, an area that has revolutionized communications and has found important applications in sensor technology. Chapter 27 discusses the light guidance property of the optical fiber (using ray optics) with applications in fiber-optic communication systems; the chapter also gives a very brief account of fiber-optic sensors. Chapter 28 discusses basic waveguide theory and concept of modes with Maxwell’s equations as the starting point. Chapter 29 discusses the propagation characteristics of single-mode optical fibers, which are now extensively used in optical communication systems. In 1905 Einstein put forward the special theory of relativity which is considered one of the revolutions of the last century. The starting point of the special theory of relativity was Maxwell’s equations, which synthesized the laws of electricity and magnetism with those of light. Chapters 30 and 31 describe briefly the important consequences of the special theory of relativity, i.e., time dilation, length contraction, the mass-energy relation, and Lorentz transformations. Very often a good photograph clarifies an important concept and also makes the student interested in the subject. It is with this intention that we have given a few colored photographs (in the insert at the end of the book) that describe important concepts in optics. In summary, the book discusses some of the important topics that have had a tremendous impact in the growth of science and technology. Other Important Features of the Book A large number of figures correspond to actual numerical calculations which were generated using software such as GNUPLOT and Mathematica. There are also some diagrams which give a three-dimensional perspective of the phenomenon. Most chapters start with important milestones in the area. This gives a historical perspective of the topic. gha80482_fm_i-xviii.PMD 14 2/3/2009, 10:32 PM  Preface xv u All important formulae have been derived from first principles so that the book can also be used for self-study. Numerous worked out examples are scattered throughout the book to help clarify difficult concepts. Each chapter ends with a summary of important results derived in the chapter. Experiments in Fiber Optics My own research interests are in the general area of fiber optics. I have found that there are many beautiful experiments in fiber optics, which are not very difficult to set up, that allow us not only to understand difficult concepts but also to find very important applications. For example, Optical fibers with parabolic index variation are used in optical communication systems. Ray paths in such fibers and their dispersion characteristics are of great importance. This is discussed from first principles in Chaps. 3 and 27. Chapter 10 discusses in great detail the dispersion of an optical pulse as it propagates through a dispersive medium. This is an extremely important concept. The chapter also discusses self phase modulation (usually abbreviated as SPM) that is probably the simplest nonlinear optical phenomenon which can be easily understood from first principles. Indeed, when a monochromatic laser pulse propagates through a special optical fiber, SPM (along with other phenomena) can lead to the awesome super continuum generation; we discuss this in Chap. 10. The working of a fiber Bragg grating (usually abbreviated as FBG) is a beautiful application of the interference phenomenon, and FBGs find very important applications in sensors and other optical devices. In Chap. 15, the basic physics of an FBG is discussed along with its very important application in temperature sensing at places where no other device would work. The experiment on Faraday rotation in optical fibers (discussed in Chap. 22) allows one to understand the concept of rotation of plane of polarization in the presence of a longitudinal magnetic field. This experiment finds important application in the industry for measuring very large currents (about 10,000 A or more). The theory of Faraday rotation is also given from first principles. In Chap. 22, the change in the state of polarization (usually abbreviated as SOP) of a light beam as it propagates through an elliptic core single-mode optical fiber has been discussed; the experiment not only allows one to understand the changing SOP of a beam propagating through a birefringent fiber, but also helps one to understand the radiation pattern of an oscillating dipole. Erbium-doped fiber amplifier (usually abbreviated as EDFA) and fiber lasers are discussed in Chap. 26. The working of an EDFA allows one to easily understand the concept of optical amplification. Chapters 27 through 29 are on waveguide theory and fiber optics, an area that has revolutionized communications and finds important applications in sensor technology. Optical fibers are now widely used in endoscopy, display illumination, and sensors, and of course the most important application is in the field of fiber-optic communication systems. We discuss all this in Chap. 27. Chapter 28 discusses basic waveguide theory (and concept of modes) with Maxwell’s equations as the starting point. The chapter allows one to understand the transition from geometrical optics to wave optics, which happens to be similar to the transition from classical mechanics to quantum mechanics. Chapter 29 discusses the waveguiding properties of single-mode optical fibers, which are now extensively used in optical communication systems. The prism film coupling experiment (discussed in Chap. 28) allows one to understand the concept of quantization, an extremely important concept in physics and electrical engineering. There are many such examples scattered throughout the book, and each example is unique and not usually found in other textbooks. Online Resources for Instructors Various resources are available to instructors for this text, including solutions to end-of-chapter problems, lecture PowerPoints and the text images in PowerPoint form. All these can be found at the text's website: www.mhhe.com/ghatak Acknowledgments At IIT Delhi, I was very fortunate to have the opportunity to interact with outstanding colleagues and with outstanding students, so it was always a pleasure and challenge to teach any course there. We had the opportunity and freedom to modify and develop any course and present it in a form, that would make the subject more interesting. That is how the gha80482_fm_i-xviii.PMD 15 2/3/2009, 10:32 PM  xvi Perface u present book evolved. In this evolution, many persons have helped me and have made important suggestions. First I would like to mention the name of my very close friend and colleague Prof. Ishwar Goyal, who used earlier Indian editions of this book many times while teaching Optics at IIT Delhi and offered numerous suggestions and many constructive criticisms; I am sure he would have been very happy to see this edition of the book, but unfortunately, he is no longer with us—I greatly miss my interactions with him. I am very grateful to Prof. M. S. Sodha for his constant encouragement and support. My sincere thanks to Prof. K. Thyagarajan for continuous collaboration and for letting me use some of his unpublished notes. My grateful thanks to Prof. Arun Kumar, Prof. Lalit Malhotra, Prof. Bishnu Pal, Prof. Anurag Sharma, Prof. K. Thyagarajan (from IIT Delhi); Dr. Kamal Dasgupta and Dr. Mrinmay Pal (from CGCRI, Kolkata); Dr. Rajeev Jindal, Subrata Dutta, and Giriraj Nyati (from Moser Baer in Noida); Prof. Vengu Lakshminarayanan (from University of Waterloo, Canada) and Prof. Enakshi Sharma (now at University of Delhi South Campus) for their help in writing some portions of the book. I sincerely thank Dr. Gouranga Bose, Dr. Parthasarathi Palai (now at Tejas Networks in Bangalore), Prof. Chandra Sakher, Prof. R. S. Sirohi, Prof. K. Thyagarajan, and Dr. Ravi Varshney (from IIT Delhi); Prof. Govind Swarup (from GMRT, Pune); Dr. Somnath Bandyopadhyay, Dr. Shyamal Bhadra, Dr. Kamal Dasgupta, Dr. Tarun Gangopadhyay, Atasi Pal, and Dr. Mrinmay Pal (from CGCRI, Kolkata); Dr. Suresh Nair (from NeST, Cochin); Avinash Pasricha (from the U.S. Information Service at New Delhi); Prof. Ajoy Kar and Dr. Henry Bookey (from Heriot Watt University, Edinburgh); Dr. R. W. Terhune, Prof. R. A. Phillips, and Dr. A. G. Chynoweth (from the United States) and Dr. R. E. Bailey (from Australia) for providing me important photographs that I have used in this book. I also thank V. V. Bhat for providing me very important literature on the scientific contributions made in ancient India. I would also like to thank my other colleagues, Prof. B. D. Gupta, Dr. Sunil Khijwania, Prof. Ajit Kumar, Dr. Vipul Rastogi, Prof. M. R. Shenoy, and Prof. Kehar Singh for collaboration in research and stimulating discussions. I also thank all the authors and their publishers for allowing me to use many diagrams from their published work. I thank Prof. G. I. Opat of University of Melbourne for his invitation to attend the 1989 conference on teaching of optics which gave me many ideas on how to make difficult concepts in optics easy to understand. I am grateful to Dr. Sunil Khijwania, Monish Das, and Debasish Roy for their help in the preparation of the manuscript and in the drawing of some difficult diagrams. A part of the present writing was carried out with support from Department of Science and Technology, Government of India, which I gratefully acknowledge. I would also like to thank the following individuals who completed reviews that were instrumental in the development of this first edition: Alan Cheville Alfonso D'Alessio Oklahoma State University New Jersey Institute of Technology Dennis Derickson California Polytechnic State University–San Luis Obispo Michael Du Vernois Thomas Plant University of Minnesota Oregon State University Finally, I owe a lot to my family—particularly to my wife, Gopa—for allowing me to spend long hours in preparing this difficult manuscript and for her support all along. I will be very grateful for suggestions for further improvement of the book. My e-mail addresses are [email protected] and [email protected]. gha80482_fm_i-xviii.PMD 16 2/3/2009, 10:32 PM  DEDICATION I dedicate this book to my students; my continuous interactions with them have led to a deeper understanding of optics. I end with the quotation (which I found in a book by G. L. Squires): “ I have learnt much from my teachers, but more from my pupils.” To all my pupils, I owe a very special debt. gha80482_fm_i-xviii.PMD 17 2/3/2009, 10:32 PM gha80482_fm_i-xviii.PMD 18 2/3/2009, 10:32 PM  Chapter One HISTORY OF OPTICS The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth".... There are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce and guess. — Richard Feynman, Feynman Lectures on Physics Optics is the study of light that has always fascinated physics, and mechanics at the University of Alexandria. He humans. In his famous book On The Nature of Light Vasco wrote Catoptrica, which described the propagation of light, Ronchi wrote: reflection, and the use of mirrors. Today we tend to remember only Newton and Claudius Ptolemaeus (ca. 90 – ca. 168 AD) known in English Huygens and consider them as the two great men who as Ptolemy, was a mathematician and astronomer who lived laid the foundations of physical optics. This is not in Roman Egypt. Ptolemy’s Optics is a work that survives really true and perhaps this tendency is due to the only in a poor Arabic translation and in Latin translation of distance in time which as it increases tends to the Arabic. In it, he wrote about properties of light, includ- strengthen the contrast and to reduce the background. ing reflection, refraction, and color. He also measured the In reality, the discussion on the nature of light was fully angle of refraction in water for different angles of incidence developed even before these two men were born... and made a table of it. – Aryabhatta (AD 476 – 550) is the first of the great mathematician- It is with this perspective that I thought it would be astronomers of the classical age of Indian mathematics and appropriate to give a very brief history of the development Indian astronomy. According to the ancient Greeks, the eye was of optics. For those who want to know more of the history, assumed to be a source of light; this was also assumed by the fortunately, there is a wealth of information that is now early Indian philosophers. In the fifth century, Aryabhatta reiter- available through the Internet. ated that it was light arriving from an external source at the retina Archytas (428 – 347 BC) was a Greek philosopher, mathema- that illuminated the world around us. tician, astronomer, and statesman. It is said that he had Ibn al-Haytham (965–1039), often called as Alhazen, was propounded the idea that vision arises as the effect of an born in Basra, Iraq (Mesopotamia). Alhazen is considered invisible “fire” emitted from the eyes so that on encounter- the father of optics because of the tremendous influence of ing objects it may reveal their shapes and colors. his Book of Optics (Arabic: Kitab al-Manazir, Latin: De Aspectibus or Perspectiva). Robert S. Elliot wrote the Euclid, also known as Euclid of Alexandria, was a Greek following about the book: mathematician who was born between the years of 320 and 324 BC. In his Optica (about 300 BC) he noted that light Alhazen was one of the ablest students of optics of travels in straight lines and described the law of reflection. all times and published a seven-volume treatise on He believed that vision involves rays going from the eyes optics which had great celebrity throughout the to the object seen, and he studied the relationship between medieval period and strongly influenced Western the apparent sizes of objects and the angles that they thought, notably that of Roger Bacon and Kepler. subtend at the eye. It seems that Euclid’s work on optics This treatise discussed concave and convex mirrors came to the West mainly through medieval Arabic texts. in both cylindrical and spherical geometries, Hero (or Heron) of Alexandria (c. 10 – 70 AD) lived in anticipated Fermat’s law of least time, and Alexandria, Roman Egypt, and was a teacher of mathematics, considered refraction and the magnifying power of gha80482_ch01_001-010.PMD 1 1/14/2009, 7:17 PM  2 Optics u lenses. It contained a remarkably lucid description recently been published as of the optical system of the eye, which study led Johannes Kepler Optics. The Alhazen to the belief that light consists of rays announcement (see Ref. 5) which originate in the object seen, and not in the says, “Optics was a product © Pixtal/ageFotostock RF eye, a view contrary to that of Euclid and Ptolemy. of Kepler’s most creative pe- riod. It began as an attempt Alhazen had also studied the reverse image formed by to give astronomical optics a a tiny hole and indicated the rectilinear propagation of light. solid foundation, but soon To quote Nobel Prize–winning physicist Abdus Salam: transcended this narrow goal to become a complete recon- Ibn-al-Haitham was one of the greatest physicists of struction of the theory of light, the physiology of vision, and all time. He made experimental contributions of the the mathematics of refraction. The result is a work of extraor- highest order in optics. He enunciated that a ray of dinary breadth whose significance transcends most light, in passing through a medium, takes the path categories into which it might be placed.” Reviewing the which is easier and ‘quicker.’ In this he was book, David Lindberg writes: anticipating Fermat’s Principle of Least Time by In this book Donahue has performed service of many centuries.... Part V of Roger Bacon’s “Opus enormous value to Kepler scholars and historians of Majus” is practically an annotation to Ibn al early optics. His lucid translation of the difficult Latin Haitham’s Optics. of Kepler’s great optical treatise not only affords ready access to Kepler’s optical achievement, but There are many books written on the work of Alhazen; also reveals the clarity, rigor, and persuasive power some discussion on Alhazen’s work can be found in Ref. 1. of Kepler’s arguments. Erazmus Ciolek Witelo (born ca. 1230 and died around 1275) Hans Lippershey (1570 – September 1619) was a Dutch was a theologian, physicist, natural philosopher, and math- eyeglass maker. Many historians believe that in 1608, ematician. Witelo called himself, in Latin, Turingorum et Lippershey saw two children playing with lenses in his Polonorum filius, meaning “a son of Poland and Thuringia.” shop and discovered that images were clearer when seen Witelo wrote an exhaustive 10-volume work on optics en- through two lenses. This inspired Lippershey to the cre- titled Perspectiva, which was largely based on the work of ation of the first telescope. Some historians credit Galileo Ibn al-Haytham and served as the standard text on the sub- Galilei for the invention of the first telescope. Many histo- ject until the seventeenth century (Refs. 2–4). rians believe that Lippershey also invented the compound Leonardo da Vinci (April 15, microscope; however, there is controversy on that. See 1452 – May 2, 1519), some Ref. 6. people believed, was the first Galileo Galilei (February 15, person to observe diffraction. 1564 – January 8, 1642) is Although Alhazen had often referred to as the father studied the reverse image formed of modern physics. In 1609, © Pixtal/ageFotostock RF by a tiny hole, the first detailed Galileo was among the first description of the pinhole camera to use a refracting telescope © Library of Congress (camera obscura) was given in as an instrument to observe the manuscript Codex atlanticus stars and planets. In 1610, (c. 1485) by Leonardo da Vinci, he used a telescope as a who used it to study perspective. compound microscope, and he made improved micro- Johannes Kepler (December 27, 1571 – November 15, 1630) scopes in 1623 and after. This appears to be the first clearly was a German mathematician, astronomer, and astrologer, documented use of the compound microscope. and a key figure in the seventeenth-century astronomical revolution. In 1604, he published the book Ad Vitellionem Willebrord Snel van Royen (1580–1626) was a Dutch as- Paralipomena, Quibus Astronomiae pars Optica Traditur. tronomer and mathematician. In 1621, he discovered the law An English translation (by William H. Donahue) has of refraction that is referred to as Snell’s law. gha80482_ch01_001-010.PMD 2 1/14/2009, 7:17 PM  History of Optics 3 u Pierre de Fermat (August 17, 1601 – January 12, 1665) was a Christiaan Huygens (April 14, French mathematician and never went to college. In a letter 1629 – July 8, 1695) was a Dutch to Cureau de la Chambre (dated January 1, 1662), Fermat mathematician, astronomer, and showed that the law of refraction can be deduced by physicist. In 1678, in a communi- © Pixtal/ageFotostock RF assuming that the path of a refracted ray of light was that cation to the Academie des which takes the least time! Fermat’s principle met with Sciences in Paris, he proposed objections. In May 1662, Clerselier, an expert in optics, the wave theory of light and wrote, “The principle you take as a basis for your proof, to in particular demonstrated how wit, that nature always acts by the shortest and simplest waves might interfere to form a path, is only a moral principle, not a physical one—it is not wave front, propagating in a and can not be the cause of any effect in nature.” straight line. In 1672, Huygens gave the theory of double refraction which was discovered by Bartholinus in 1669. In René Descartes (March 31, 1596 – February 11, 1650) was 1690, he produced his famous book on optics Traite de la a highly influential French philosopher, mathematician, Lumiere; the English translation of the book is now scientist, and writer. Descartes, in his book entitled available as a Dover reprint (Ref. 11), and the entire book Dioptrique (1638), gave the fundamental laws of propaga- can be read at the website given in Ref. 12. tion of light, the laws of reflection and refraction. He also put forward the corpuscular model, regarding lumen as a Ole Christensen Rømer (September 25, 1644 – September 19, swarm of spherical corpuscles (see Refs. 7–8). In Ref. 8, 1710) was a Danish astronomer who in 1676 made the first it has been shown that “Descartes’ insightful derivation quantitative measurements of the speed of light. of Snell’s law is seen to be largely equivalent to the Sir Isaac Newton (January 4, mechanical-particle or corpuscular derivation often attrib- 1643 – March 31, 1727) is con- uted to Newton (who was seven years old at Descartes’ sidered one of the greatest death).” figures in the history of science. Francesco Maria Grimaldi (April 2, 1618 – December 28, In addition to his numerous © Pixtal/ageFotostock RF 1663). Around 1660, Grimaldi discovered the diffraction of contributions to science and light and gave it the name diffraction, which means mathematics, he made a system- “breaking up.” He interpreted the phenomenon by stating atic study of light and published that light had to consist of a very fine fluid of some sort in it in the form of a book in 1704. a state of constant vibration. He laid the groundwork for The fourth edition of the book the later invention of diffraction grating. He formulated a is available as a Dover reprint geometrical basis for a wave theory of light in his Physico- (Ref. 13) and also in the website mathesis de lumine (1666). It was this treatise which given in Ref. 14. attracted Isaac Newton to the study of optics. Newton In this book, Newton describes his experiments, first re- discussed the diffraction problems of Grimaldi in Part III of ported in 1672, on dispersion, or the separation of light into his Opticks (1704); Robert Hooke observed diffraction in a spectrum of its component colors. Grimaldi had earlier 1672. For more details see Ref. 9. observed light entering the shadow of a needle—Newton Robert Hooke, FRS (July 18, 1635 – March 3, 1703). In his explained this by saying that the needle exerts a force that 1664 book Micrographia, Robert Hooke was the first to de- “pulled” the light from the straight-line path. Hooke had scribe “Newton’s rings.” The rings are named after Newton earlier observed the colors from thin sheets of mica— because Newton explained it (incorrectly) in a communica- Newton explained this by “fits of easy transmission and tion to the Royal Society in December 1675 and presented it reflection” of the light rays. in detail in his book Opticks (1704). Hooke had also ob- Thomas Young (June 13, 1773 – May 10, 1829) was an served the colors from thin sheets of mica much later were English scientist. In 1801, Young demonstrated the wave explained through interference of light. nature of light through a simple two-hole interference Rasmus Bartholin (Latinized Erasmus Bartholinus; experiment; this experiment is considered one of 10 most August 13, 1625 – November 4, 1698) was a Danish scientist. beautiful experiments in physics (Refs. 15 and 16). Thomas In 1669, he discovered double refraction of a light ray by Young used his wave theory to explain the colors of thin calcite and wrote a 60-page memoir about the results; the films (such as soap bubbles); and relating color to explanation came later. See Ref. 10. wavelength, he calculated the approximate wavelengths of gha80482_ch01_001-010.PMD 3 1/14/2009, 7:17 PM  4 Optics u the seven colors recognized by Newton. In 1817, he the Faraday rotation. In proposed that light waves were transverse and thus this experiment, the plane explained polarization; for more details see Refs. 17–18. of polarization of linearly polarized light (propagating François Jean Dominique Arago (February 26, 1786 – through a material medium) October 2, 1853) was a French mathematician, physicist, gets rotated by the applica- astronomer, and politician; he became the twenty-fifth tion of an external magnetic © Pixtal/ageFotostock RF Prime Minister of France. In 1811, Arago observed the field aligned in the direction rotation of the plane of polarization in quartz. In 1818, of propagation. The experi- Poisson deduced from Fresnel’s theory the necessity of ment established that mag- a bright spot at the center of the shadow of a circular netic force and light were opaque obstacle. With this result, Poisson had hoped related. Faraday wrote in to disprove the wave theory; however, Arago experi- his notebook, “I have at mentally verified the prediction. Although this spot is last succeeded in... magnetising a ray of light.” usually referred to as the Poisson spot, many people call it Arago’s spot. Etienne-Louis Malus (July 23, 1775 – February 24, 1812) Joseph von Fraunhofer (March 6, 1787 – June 7, 1826) was a was a French engineer, physicist, and mathematician. German optician. In 1814, Fraunhofer invented the spectro- David Brewster, FRS (December 11, 1781 – February 10, scope and discovered 574 dark lines appearing in the solar 1868) was a Scottish scientist. spectrum; these lines are referred to as Fraunhofer lines. In In 1809, Malus had published his discovery of the 1859, Kirchhoff and Bunsen explained these lines as atomic polarization of light by reflection; however, he was unable absorption lines. In 1823, Fraunhofer published his theory to obtain the relationship between the polarizing angle and of diffraction. He also invented the diffraction grating and refractive index. In 1811, David Brewster repeated the demonstrated the accurate measurement of the wavelength. experiments of Malus for many materials and realized that when a ray is polarized by reflection, the reflected ray Augustin-Jean Fresnel (May 10, 1788 – July 14, 1827) was makes an angle of 90° with the refracted ray; he promptly a French physicist. Fresnel contributed significantly to the called this Brewster’s law! Malus is best known for the law establishment of the wave theory of light. In 1818, he wrote named after him which states that the intensity of light a memoir on diffraction for which in the following year he transmitted through two polarizers is proportional to the received the prize of the Académie des Sciences at Paris. In square of the cosine of the angle between the polarization 1819, he was nominated axes of the polarizers. In 1810, Malus published his theory Commissioner of Lighthouses, of double refraction of light in crystals. for which he was the first to construct a special type James Clerk Maxwell (June 13, © Pixtal/ageFotostock RF of lens, now called a Fresnel 1831 – November 5, 1879) lens, as substitutes for mir- was an outstanding Scottish rors. By the year 1821, he mathematician and theoretical showed that polarization physicist. Around 1865, Max- © Pixtal/ageFotostock RF could be explained only if well showed that the laws light was entirely transverse. of electricity of magnetism can be described by four Joseph Nicephore Niepce (March 7, 1765 – July 5, 1833) was partial differential equations; a French inventor and a pioneer in photography. these equations are known as Michael Faraday (September 22, 1791 – August 25, 1867) Maxwell’s equations and ap- contributed significantly to the fields of electromagnetism peared in his book A Treatise on Electricity and and electrochemistry. Faraday had established that a Magnetism, published in 1873. Maxwell also predicted the changing magnetic field produces an electric field. This existence of electromagnetic waves (which were later ob- relation subsequently was one of the four equations of served by Hertz) and showed that the speed of propagation Maxwell and is referred to as Faraday’s law. In 1845, of electromagnetic waves is approximately equal to the Faraday discovered the phenomenon that is now called (then) measured value of the speed of light; this made him gha80482_ch01_001-010.PMD 4 1/14/2009, 7:17 PM  History of Optics 5 u predict that light must be an electromagnetic wave. In 1864, contained a metal rod that had a small gap at its mid- he wrote: point, and when sparks crossed this gap violent oscillations of high frequency were set up in the rod. This velocity is so nearly that of light that it seems Hertz proved that these waves were transmitted we have strong reason to conclude that light itself through air by detecting them with another similar cir- (including radiant heat and other radiations) is an cuit some distance away. He also showed that like electromagnetic disturbance in the form of waves light waves they were reflected and refracted and, propagated through the electromagnetic field most important, that they traveled at the same speed according to electromagnetic laws. as light but had a much longer wavelength. These This synthesis represents one of the great scientific waves, originally called Hertzian waves but now achievements of the nineteenth century. In 1931 (during the known as radio waves, conclusively confirmed birth centenary celebration of Maxwell), Max Planck had Maxwell’s prediction on the existence of electromag- said, “(Maxwell’s theory)... remains for all time one of the netic waves, both in the form of light and radio waves. greatest triumphs of human intellectual endeavor.” Albert Hertz was a very modest person; after the discovery he Einstein had said, “(The work of Maxwell was)... the most said, “This is just an experiment that proves Maestro profound and the most fruitful that physics has experienced Maxwell was right, we just have these mysterious since the time of Newton.” For more details about Maxwell, electromagnetic waves that we cannot see with the naked see Ref. 19. Some of the original papers of Maxwell can be eye. But they are there.” “So, what next?” asked one of his seen in the website in Ref. 20. students at the University of Bonn. “Nothing, I guess.” John William Strutt usually referred to as Lord Rayleigh Hertz later said, “I do not think that the wireless waves I (November 12, 1842 – June 30, 1919) and John Tyndall have discovered will have any practical application.” (August 2, 1820 – December 4, 1893) was an Irish natural We should mention here that in 1842 (when Maxwell was philosopher. In 1869, John Tyndall had discovered that when only 11 years old) the U.S. physicist Joseph Henry had light passes through a transparent liquid with small particles in magnetized needles at a distance of over 30 ft (with two suspension (such as a small amount of milk put in water), the floors, each 14 in. thick) from a single spark. Thus, though shorter blue wavelengths are scattered more strongly than the Joseph Henry was not aware of it, he had produced and red; thus from the side, the color looks blue and the light detected electromagnetic waves; for more details see e.g., coming out straight appears reddish. Many people call this the book by David Park (Ref. 25) and the original collection Tyndall scattering, but it is more often referred to as Rayleigh of Henry’s papers referenced in Park’s book. scattering because Rayleigh studied this phenomenon in Hertz was also the first scientist to observe the photoelectric great detail and showed (in 1871) that scattering is inversely effect. In 1887, while receiving the electromagnetic waves in a coil with a spark gap, he found that the maximum spark length proportional to the fourth power of the wavelength (see Ref. 21). was reduced when the apparatus was put in a black box (this is Thus the blue color is scattered 10 times more than the red so because the box absorbed the ultraviolet radiation which color (because the red color has a wavelength which is about helped the electrons to jump across the gap). Hertz reported the 1.75 times the wavelength of blue). This is the reason why the observations but did not pursue further and also did not make sky appears blue. Although violet has an even smaller any attempt to explain them. In 1897, J. J. Thomson discovered wavelength, the sky does not appear violet because there is electrons, and in 1899, he showed that electrons are emitted very little violet in the sunlight! Some of the scientific papers when light falls on a metal surface. In 1902, Philip Lenard of Lord Rayleigh can be seen at the website given in Ref. 22. observed that (1) the kinetic energy of the emitted electrons was Lord Rayleigh received the 1904 Nobel Prize in Physics. independent of the intensity of the incident light and (2) the In 1854, John Tyndall demonstrated light guidance in energy of the emitted electron increased when the frequency of water jets, duplicating but not acknowledging Babinet (see the incident light was increased. Ref. 23 for more details). Alexander Graham Bell (March 3, 1847 – August 2, 1922) Heinrich Rudolf Hertz (February 22, 1857 – January 1, was born and raised in Edinburgh, Scotland he emigrated to 1894) was a German physicist after whom the hertz, the SI Canada in 1870 and then to the United States in 1871. The unit of frequency, is named. To quote from Ref. 24: photophone was invented jointly by Alexander Graham Bell In 1888, in a corner of his physics classroom at the and his assistant Charles Sumner Tainter on February 19, Karlsruhe Polytechnic in Berlin, Hertz generated 1880. Bell believed the photophone was his most important electric waves using an electric circuit; the circuit invention. gha80482_ch01_001-010.PMD 5 1/14/2009, 7:17 PM  6 Optics u Albert Abraham Michelson (December 19, 1852 – May 9, extremely feeble light source; this led the Nobel Prize– 1931) was born in Strelno, Prussia, and moved to the United winning physicist P. A. M. Dirac to make the famous States at the age of 2. Michelson built the famous statement, “Each photon then interferes only with itself.” interferometer which was later called the Michelson Taylor has often been described as one of the great interferometer. He was awarded the 1907 Nobel Prize in physical scientists of the twentieth century. For more Physics (the first American to receive the Nobel Prize in details, see Ref. 28. Science) for his optical precision instruments and the William Henry Bragg (July 2, 1862 – March 10, 1942) and spectroscopic and metrological investigations carried out William Lawrence Bragg (March 31, 1890 – July 1, 1971). with their aid. In the presentation speech, the President of William Lawrence Bragg (the son) discovered the most the Royal Swedish Academy of Sciences said, “... Your famous Bragg’s law, which makes it possible to calculate interferometer has rendered it possible to obtain a non- the positions of the atoms within a crystal from the way in material standard of length, possessed of a degree of which an X-ray beam is diffracted by the crystal lattice. He accuracy never hitherto attained. By its means we are made this discovery in 1912, during his first year as a enabled to ensure that the prototype of the meter has research student in Cambridge. He discussed his ideas with remained unaltered in length, and to restore it with absolute his father (William Henry Bragg), who developed the X-ray infallibility, supposing it were to get lost.” In 1887, he and spectrometer in Leeds. In 1915, father and son were jointly Edward Morley carried out the famous Michelson–Morley awarded the Nobel Prize in Physics for their services in the experiment, which proved that ether did not exist. David analysis of crystal structure by means of X-rays. The Park (Ref. 25) has written: “He (Michelson) was 34 when he collaboration between father and son led many people to established that ether cannot be found; he made delicate believe that the father was the inventor of Bragg’s law, a optical measurements for 44 more years and to the end of fact that upset the son! his days did not believe there could be a wave without some material substance to do the waving.” Arthur Holly Compton (September 10, 1892 – March 15, Maurice Paul Auguste Charles Fabry (June 11, 1867 – July 9, 1962) in 1922 found that the energy of an X-ray or gamma ray 1945) and Jean-Baptiste Alfred Pérot (November 3, 1863 – photon decreases due to scattering by free electrons. This November 28, 1925) were French physicists. In 1897, Fabry discovery, known as the Compton effect, demonstrates the and Pérot published their important article on what we now corpuscular nature of light. Compton received the 1927 call the Fabry–Pérot interferometer. For more details about Nobel Prize in Physics for his discovery of the effect named them see Ref. 26. after him. The research papers of Compton can be found in the website given in Ref. 29. Albert Einstein (March 14, 1879 –April 18, 1955) was an out- Louis de Broglie (August 15, 1892 – March 19, 1987) was a standing theoretical physicist. French physicist. In 1924, de Broglie (pronounced in French Einstein is best known for his as de Broy) formulated the de Broglie hypothesis, claiming theory of relativity and specifi- that all matter, not just light, has a wavelike nature; he related wavelength to the momentum. De Broglie’s formula Library of Congress cally mass-energy equivalence E = mc2. Einstein in 1905 put was confirmed three years later for electrons with the forward that light consists of observation of electron diffraction in two independent quanta of energy; this eventually experiments. De Broglie received the 1929 Nobel Prize in led to the development of quan- Physics for his discovery of the wave nature of electrons. tum theory. In 1917, in a paper entitled “On the Quantum In the presentation speech it was mentioned: Theory of Radiation,” Einstein, while rederiving Planck’s law, Louis de Broglie had the boldness to maintain that... was able to predict the process of stimulated emission, and matter is, by its nature, a wave motion. At a time almost 40 years later, t