Optics

Cover Page ......Page 2 ABOUT THE AUTHOR......Page 4 Title Page ......Page 5 Copyright Page ......Page 6 Preface......Page 15 CONTENTS......Page 7 1. History of Optics......Page 21 References......Page 29 2.2 The Corpuscular Model......Page 31 2.3 The Wave Model......Page 33 2.4 The Particle Nature of Radiation......Page 35 2.5 Wave Nature of Matter......Page 37 2.7 The Single-Slit Diffraction Experiment......Page 38 2.8 The Probabilistic Interpretation of Matter Waves......Page 39 2.9 An Understanding of Interference Experiments......Page 41 2.10 The Polarization of a Photon......Page 43 Summary......Page 44 Solutions......Page 45 References and Suggested Readings......Page 46 Part 1 Geometrical Optics......Page 47 3.1 Introduction......Page 49 3.2 Laws of Reflection and Refraction from Fermat’s Principle......Page 51 3.3 Ray Paths in an Inhomogeneous Medium......Page 54 3.4 The Ray Equation and its Solutions......Page 59 3.5 Refraction of Rays at the Interface between an Isotropic Medium and an Anisotropic Medium......Page 64 Problems......Page 67 References and Suggested Readings......Page 71 4.1 Introduction......Page 73 4.2 Refraction at a Single Spherical Surface......Page 74 4.3 Reflection by a Single Spherical Surface......Page 75 4.4 The Thin Lens......Page 76 4.5 The Principal Foci and Focal Lengths of a Lens......Page 77 4.7 Lateral Magnification......Page 79 4.8 Aplanatic Points of a Sphere......Page 80 4.10 Geometrical Proof for the Existence of Aplanatic Points......Page 82 4.11 The Sine Condition......Page 83 Problems......Page 85 References and Suggested Readings......Page 86 5.1 Introduction......Page 87 5.2 The Matrix Method......Page 88 5.3 Unit Planes......Page 93 5.4 Nodal Planes......Page 94 5.5 A System of Two Thin Lenses......Page 95 Problems......Page 97 References and Suggested Readings......Page 98 6.2 Chromatic Aberration......Page 99 6.3 Monochromatic Aberrations......Page 102 Problems......Page 110 References and Suggested Readings......Page 111 Part 2 Vibrations and Waves......Page 113 7.2 Simple Harmonic Motion......Page 115 7.3 Damped Simple Harmonic Motion......Page 119 7.4 Forced Vibrations......Page 121 7.5 Origin of Refractive Index......Page 123 7.6 Rayleigh Scattering......Page 127 Problems......Page 128 References and Suggested Readings......Page 130 8.1 Introduction......Page 131 8.2 Transverse Vibrations of a Plucked String......Page 133 8.3 Application of Fourier Series in Forced Vibrations......Page 135 8.4 The Fourier Integral......Page 136 Problems......Page 137 References and Suggested Readings......Page 138 9.2 Representations of the Dirac Delta Function......Page 139 9.4 Delta Function as a Distribution......Page 140 9.5 Fourier Integral Theorem......Page 141 9.6 The Two- and Three-Dimensional Fourier Transform......Page 143 Problems......Page 144 10.2 Group Velocity......Page 147 10.3 Group Velocity of a Wave Packet......Page 151 10.4 Self Phase Modulation......Page 157 Summary......Page 159 Problems......Page 160 References and Suggested Readings......Page 161 11.1 Introduction......Page 163 11.2 Sinusoidal Waves: Concept of Frequency and Wavelength......Page 165 11.4 Energy Transport in Wave Motion......Page 166 11.5 The One-Dimensional Wave Equation......Page 167 11.6 Transverse Vibrations of a Stretched String......Page 168 11.7 Longitudinal Sound Waves in a Solid......Page 169 11.8 Longitudinal Waves in a Gas......Page 170 11.9 The General Solution of the One-Dimensional Wave Equation......Page 171 Problems......Page 174 References and Suggested Readings......Page 175 12.2 Huygens’ Theory......Page 177 12.3 Rectilinear Propagation......Page 178 12.4 Application of Huygens’ Principle to Study Refraction and Reflection......Page 179 References and Suggested Readings......Page 185 Part 3 Interference......Page 187 13.2 Stationary Waves on a String......Page 189 13.3 Stationary Waves on a String Whose Ends are Fixed......Page 191 13.5 Superposition of Two Sinusoidal Waves......Page 192 13.6 The Graphical Method for Studying Superposition of Sinusoidal Waves......Page 193 Problems......Page 195 References and Suggested Readings......Page 196 14.1 Introduction......Page 197 14.2 Interference Pattern Produced on the Surface of Water......Page 198 14.3 Coherence......Page 201 14.4 Interference of Light Waves......Page 202 14.5 The Interference Pattern......Page 203 14.6 The Intensity Distribution......Page 204 14.8 Fresnel Biprism......Page 209 14.9 Interference with White Light......Page 210 14.10 Displacement of Fringes......Page 211 14.12 Phase Change on Reflection......Page 212 Problems......Page 213 References and Suggested Readings......Page 214 15.1 Introduction......Page 215 15.2 Interference by a Plane Parallel Film When Illuminated by a Plane Wave......Page 216 15.3 The Cosine Law......Page 217 15.4 Nonreflecting Films......Page 218 15.5 High Reflectivity by Thin Film Deposition......Page 221 15.6 Reflection by a Periodic Structure......Page 222 15.7 Interference by a Plane Parallel Film When Illuminated by a Point Source......Page 226 15.8 Interference by a Film with Two Nonparallel Reflecting Surfaces......Page 228 15.9 Colors of Thin Films......Page 231 15.10 Newton’s Rings......Page 232 15.11 The Michelson Interferometer......Page 236 Problems......Page 239 References and Suggested Readings......Page 240 16.2 Multiple Reflections from a Plane Parallel Film......Page 241 16.3 The Fabry–Perot Etalon......Page 243 16.4 The Fabry–Perot Interferometer......Page 245 16.5 Resolving Power......Page 246 16.6 The Lummer–Gehrcke Plate......Page 249 16.7 Interference Filters......Page 250 References and Suggested Readings......Page 251 17.1 Introduction......Page 253 17.2 The Line Width......Page 255 17.3 The Spatial Coherence......Page 256 17.4 Michelson Stellar Interferometer......Page 258 17.5 Optical Beats......Page 259 17.6 Coherence Time and Line Width via Fourier Analysis......Page 261 17.7 Complex Degree of Coherence and Fringe Visibility in Young’s Double-Hole Experiment......Page 263 17.8 Fourier Transform Spectroscopy......Page 264 Problems......Page 269 References and Suggested Readings......Page 270 Part 4 Diffraction......Page 271 18.1 Introduction......Page 273 18.2 Single-Slit Diffraction Pattern......Page 274 18.3 Diffraction by a Circular Aperture......Page 278 18.4 Directionality of Laser Beams......Page 280 18.5 Limit of Resolution......Page 284 18.6 Two-Slit Fraunhofer Diffraction Pattern......Page 287 18.7 N-Slit Fraunhofer Diffraction Pattern......Page 289 18.8 The Diffraction Grating......Page 292 18.9 Oblique Incidence......Page 295 18.10 X-ray Diffraction......Page 296 18.11 The Self-Focusing Phenomenon......Page 300 18.12 Optical Media Technology—An Essay......Page 302 Problems......Page 305 References and Suggested Readings......Page 307 19.2 The Fresnel Diffraction Integral......Page 309 19.5 Fraunhofer Diffraction by a Long Narrow Slit......Page 311 19.6 Fraunhofer Diffraction by a Rectangular Aperture......Page 312 19.7 Fraunhofer Diffraction by a Circular Aperture......Page 313 19.8 Array of Identical Apertures......Page 314 19.9 Spatial Frequency Filtering......Page 316 19.10 The Fourier Transforming Property of a Thin Lens......Page 318 Problems......Page 320 References and Suggested Readings......Page 321 20.1 Introduction......Page 323 20.2 Fresnel Half-Period Zones......Page 324 20.3 The Zone Plate......Page 326 20.4 Fresnel Diffraction—A More Rigorous Approach......Page 328 20.5 Gaussian Beam Propagation......Page 330 20.6 Diffraction by a Straight edge......Page 332 20.7 Diffraction of a Plane Wave by a Long Narrow Slit and Transition to the Fraunhofer Region......Page 338 Summary......Page 340 Problems......Page 341 References and Suggested Readings......Page 343 21.1 Introduction......Page 345 21.2 Theory......Page 347 21.4 Some Applications......Page 350 Problems......Page 352 References and Suggested Readings......Page 353 Part 5 Electromagnetic Character of Light......Page 355 22.1 Introduction......Page 357 22.2 Production of Polarized Light......Page 360 22.3 Malus’ Law......Page 363 22.4 Superposition of Two Disturbances......Page 364 22.5 The Phenomenon of Double Refraction......Page 367 22.6 Interference of Polarized Light: Quarter Wave Plates and Half Wave Plates......Page 371 22.8 Optical Activity......Page 374 22.9 Change in the SOP (State of Polarization) of a Light Beam Propagating Through an Elliptic Core Single-Mode Optical Fiber......Page 376 22.10 Wollaston Prism......Page 378 22.12 Plane Wave Propagation in Anisotropic Media......Page 379 22.13 Ray Velocity and Ray Refractive Index......Page 383 22.14 Jones’ Calculus......Page 385 22.15 Faraday Rotation......Page 387 22.16 Theory of Optical Activity......Page 389 Summary......Page 391 Problems......Page 392 References and Suggested Readings......Page 394 23.2 Plane Waves in a Dielectric......Page 395 23.3 The Three-Dimensional Wave Equation in a Dielectric......Page 398 23.4 The Poynting Vector......Page 399 23.6 Radiation Pressure......Page 402 23.7 The Wave Equation in a Conducting Medium......Page 404 23.8 The Continuity Conditions......Page 405 23.9 Physical Significance of Maxwell’s Equations......Page 406 Problems......Page 408 References and Suggested Readings......Page 409 24.2 Reflection and Defraction at an Interface of Two Dielectrics......Page 411 24.3 Reflection by a Conducting Medium......Page 424 24.4 Reflectivity of a Dielectric Film......Page 426 Summary......Page 427 References and Suggested Readings......Page 428 Part 6 Photons......Page 429 25. The Particle Nature of Radiation......Page 431 25.2 The Photoelectric Effect......Page 432 25.3 The Compton Effect......Page 434 25.5 Angular Momentum of a Photon......Page 438 Summary......Page 440 References and Suggested Readings......Page 441 Part 7 Lasers and Fiber Optics......Page 443 26.1 Introduction......Page 445 26.2 The Fiber Laser......Page 451 26.3 The Ruby Laser......Page 452 26.4 The He-Ne Laser......Page 454 26.5 Optical Resonators......Page 456 26.6 Einstein Coefficients and Optical Amplification......Page 460 26.7 The Line Shape Function......Page 466 26.8 Typical Parameters for a Ruby Laser......Page 467 26.9 Monochromaticity of the Laser Beam......Page 468 26.10 Raman Amplification and Raman Laser......Page 469 Summary......Page 472 Problems......Page 473 References and Suggested Readings......Page 474 27. Optical Waveguides I: Optical Fiber Basics Using Ray Optics......Page 475 27.2 Some Historical Remarks......Page 476 27.3 Total Internal Reflection......Page 479 27.4 The Optical Fiber......Page 480 27.5 Why Glass Fibers?......Page 481 27.7 The Numerical Aperture......Page 482 27.8 Attenuation in Optical Fibers......Page 483 27.9 Multimode Fibers......Page 485 27.10 Pulse Dispersion in Multimode Optical Fibers......Page 486 27.11 Dispersion and Maximum Bit Rates......Page 489 27.12 General Expression for Ray Dispersion Corresponding to a Power Law Profile......Page 490 27.14 Fiber-Optic Sensors......Page 491 Problems......Page 492 References and Suggested Readings......Page 493 28.1 Introduction......Page 495 28.2 TE Modes of a Symmetric Step Index Planar Waveguide......Page 496 28.3 Physical Understanding of Modes......Page 500 28.4 TM Modes of a Symmetric Step Index Planar Waveguide......Page 501 28.5 TE Modes of a Parabolic Index Planar Waveguide......Page 502 28.6 Waveguide Theory and Quantum Mechanics......Page 503 References and Suggested Readings......Page 505 29.2 Basic Equations......Page 507 29.3 Guided Modes of a Step Index Fiber......Page 509 29.4 Single-Mode Fiber......Page 511 29.5 Pulse Dispersion in Single-Mode Fibers......Page 513 29.6 Dispersion Compensating Fibers......Page 515 Problems......Page 517 References and Suggested Readings......Page 518 Part 8 Special Theory of Relativity......Page 519 30.1 Introduction......Page 521 30.2 Speed of Light for a Moving Source......Page 522 30.3 Time Dilation......Page 523 30.4 The Mu Meson Experiment......Page 524 30.5 The Length Contraction......Page 525 30.7 Length Contraction of a Moving Train......Page 526 30.8 Simultaneity of Two Events......Page 527 30.9 The Twin Paradox......Page 528 30.10 The Michelson–Morley Experiment......Page 529 30.11 Brief Historical Remarks......Page 531 References and Suggested Readings......Page 532 31.2 The Mass-Energy Relationship......Page 533 31.3 The Doppler Shift......Page 535 31.4 The Lorentz Transformation......Page 536 References and Suggested Readings......Page 538 Appendix A: Gamma Functions and Integrals Involving Gaussian Functions......Page 539 Appendix B: Evaluation of the Integral......Page 541 Appendix C: The Reflectivity of a Fiber Bragg Grating......Page 542 Appendix D: Diffraction of a Gaussian Beam......Page 543 Appendix E: TE and TM Modes in Planar Waveguides......Page 544 Appendix F: Solution for the Parabolic Index Waveguide......Page 546 Appendix G: Invariance of the Wave Equation Under Lorentz Transformation......Page 548 Name Index......Page 559 Subject Index......Page 549 "This text provides a comprehensive, balanced account of traditional optics, as well as some of the recent developments in the field. - Designed to meet the optics course requirements for undergraduate students of science and engineering, Optics is also an excellent reference source for practicing engineers wanting to obtain a greater understanding of optics."--Jacket