Preface xvii
Acknowledgments xxi
1 The Physics of Waves 1
1.1 Introduction 1
1.2 One-Dimensional Wave Equation 2
1.3 General Solutions to the 1-D Wave Equation 5
1.4 Harmonic Traveling Waves 9
1.5 The Principle of Superposition 13
1.5.1 Periodic Traveling Waves 13
1.5.2 Linear Independence 14
1.6 Complex Numbers and the Complex Representation 15
1.6.1 Complex Algebra 17
1.6.2 The Complex Representation of Harmonic Waves 21
1.7 The Three-Dimensional Wave Equation 22
1.7.1 Spherical Coordinates 23
1.7.2 Three-Dimensional Plane Waves 25
1.7.3 Spherical Waves 28
Problems 31
2 Electromagnetic Waves and Photons 41
2.1 Introduction 41
2.2 Electromagnetism 42
2.3 Electromagnetic Wave Equations 53
2.3.1 Transverse Electromagnetic Waves 55
2.3.2 Energy Flow and the Poynting Vector 61
2.3.3 Irradiance 63
2.4 Photons 67
2.5.1 Single-Photon Interference 74
2.6 The Electromagnetic Spectrum 76
Problems 79
3 Reflection and Refraction 91
3.1 Introduction 91
3.2 Overview of Reflection and Refraction 92
3.2.1 Fermat's Principle of Least Time 97
3.3 Maxwell's Equations at an Interface 101
3.3.1 Boundary Conditions 101
3.3.2 Electromagnetic Waves at an Interface 104
3.4 The Fresnel Equations 107
3.4.1 Incident Wave Polarized Normal to the Plane of In-cidence 109
3.4.2 Incident Wave Polarized Parallel to the Plane of In-cidence 112
3.5 Interpretation of the Fresnel Equations 117
3.5.1 Normal Incidence 117
3.5.2 Brewster's Angle 118
3.6.1 Total Internal Reflection 121
3.6.2 Plots of the Fresnel Equations vs. Incident Angle 126
3.6.3 Phase Changes on Reflection 128
Summary 134
3.7 Reflectivity and Transmissivity 134
3.7.1 Plots of Reflectivity and Transmissivity vs. Incident Angle 139
3.7.2 The Evanescent Wave 141
3.8 Scattering 144
3.8.1 Atmospheric Scattering 145
3.8.2 Rainbows 146
3.8.3 Parhelia 150
3.9 Optical Materials 151
3.10 Dispersion 153
3.10.1 Dispersion in Dielectric Media 153
3.10.2 Dispersion in Conducting Media 168
Problems 177
4 Geometric Optics I 187
4.1 Introduction 187
4.2 Reflection and Refraction at Aspheric Surfaces 188
4.3 Reflection and Refraction at a Spherical Surface 196
4.3.1 Spherical Reflecting Surfaces 197
4.3.2 Spherical Refracting Surfaces 201
4.3.3 Sign Conventions and Ray Diagrams 206
4.4 Lens Combinations 212
4.4.1 Thin-Lenses in Close Combination 214
4.5 Optical Instruments 215
4.5.1 The Camera 215
4.5.2 The Eye 217
4.5.3 The Magnifying Glass 218
4.5.4 The Compound Microscope 220
4.5.5 The Telescope 223
4.5.6 The Exit Pupil 224
4.6 Optical Fibers 227
Problems 234
5 Geometric Optics II 243
5.1 Introduction 243
5.2 Aberrations 244
5.2.1 Chromatic Aberration 244
5.2.2 Spherical Aberration 250
5.2.3 Astigmatism and Coma 251
5.2.4 Field Curvature 252
5.2.5 Diffraction 252
5.3 Principal Points and Effective Focal Lengths 252
5.4 Thick Lenses 259
5.4.1 Principal Points and Effective Focal Lengths of Thick Lenses 262
5.5 Introduction to Matrix Methods in Paraxial Geometrical Optics 268
5.5.1 The Translation Matrix 270
5.5.2 The Refraction Matrix 272
5.5.3 The Reflection Matrix 274
5.5.4 The Ray Transfer Matrix 275
5.5.5 Location of Principal Points and Effective Focal Lengths for an Optical System 283
5.6 Radiometry 291
5.6.1 Extended Sources 293
5.6.2 Radiometry of Blackbody Sources 299
5.6.3 Rayleigh-Jeans Theory and the Ultraviolet Catastro-phe 301
5.6.4 Planck's Quantum Theory of Blackbody Radiation 305
Problems 311
6 Polarization 323
6.1 Introduction 323
6.2 Linear Polarization 323
6.2.1 Linear Polarizers 325
6.2.2 Linear Polarizer Design 329
6.3 Birefringence 334
6.5 Circular and Elliptical Polarization 339
6.5.1 Wave Plates and Circular Polarizers 344
6.7 Jones Vectors and Matrices 349
Jones Matrices 352
6.7.1 Birefringent Colors 358
Problems 362
7 Superposition and Interference 371
7.1 Introduction 371
7.2 Superposition of Harmonic Waves 372
7.3 Interference Between TwoMonochromatic ElectromagneticWaves 372
7.3.1 Linear Power Detection 375
7.3.2 Interference Between Beams with the Same Frequency 377
7.3.3 Thin-Film Interference 382
7.4.1 Quasi-Monochromatic Sources 388
7.4.2 Fringe Geometry 389
7.4.3 Interference Between Beams with Different Frequen-cies 393
7.6 Fourier Analysis 401
7.6.1 Fourier Transforms 401
7.6.2 Position Space, k-Space Domain 403
7.6.3 Frequency-Time Domain 409
7.7 Properties of Fourier Transforms 409
7.7.1 Symmetry Properties 409
7.7.2 Linearity 411
7.7.3 Transform of a Transform 412
7.8 Wavepackets 412
7.9 Group and Phase Velocity 420
7.10 Interferometry 424
7.11.1 Energy Conservation and Complementary Fringe Pat-terns 432
7.12 Single-Photon Interference 437
7.13 Multiple-Beam Interference 437
7.13.1 The Scanning Fabry-Perot Interferometer 442
7.15 Interference in Multilayer Films 449
7.15.1 Antireflection Films 455
7.15.2 High-Reflectance Films 458
7.16 Coherence 461
7.16.1 Temporal Coherence 461
7.16.2 Spatial Coherence 464
7.16.3 Michelson's Stellar Interferometer 469
7.16.4 Irradiance Interferometry 470
7.16.5 Telescope Arrays 472
Problems 474
8 Diffraction 487
8.1 Introduction 487
8.2 Huygens' Principle 488
8.2.1 Babinet's Principle 492
8.3 Fraunhofer Diffraction 494
8.3.1 Single Slit 495
8.3.2 Rectangular Aperture 503
8.3.3 Circular Aperture 505
8.3.4 Optical Resolution 509
8.3.5 More on Stellar Interferometry 511
8.3.6 Double Slit 512
8.3.7 N Slits: The Diffraction Grating 514
8.3.8 The Diffraction Grating 517
8.5.1 Fraunhofer Diffraction as a Fourier Transform 527
8.5.2 Apodization 531
8.7 Fresnel Diffraction 535
8.7.1 Fresnel Zones 538
8.7.2 Holography 554
8.7.3 Numerical Analysis of Fresnel Diffraction with Cir-cular Symmetry 556
8.7.4 Fresnel Diffraction from Apertures with Cartesian Symmetry 559
8.8 Introduction to Quantum Electrodynamics 570
8.8.1 Feynman's Interpretation 575
Problems 577
9 Lasers 589
9.1 Introduction 589
9.2 Energy Levels in Atoms, Molecules, and Solids 590
9.2.1 Atomic Energy Levels 590
9.2.2 Molecular Energy Levels 597
9.2.3 Solid-state Energy Bands 599
9.2.4 Semiconductor Devices 603
9.4 Stimulated Emission and Light Amplification 608
9.5 Laser Systems 613
9.5.1 Atomic Gas Lasers 616
9.5.2 Molecular Gas Lasers 619
9.5.3 Solid-State Lasers 623
9.6.1 Other Laser Systems 627
9.7 Longitudinal Cavity Modes 628
9.8 Frequency Stability 630
9.9 Introduction to Gaussian Beams 631
9.9.1 Overview of Gaussian Beam Properties 632
9.10 Gaussian Beam Properties 636
9.10.1 Approximate Solutions to the Wave Equation 638
9.10.2 Paraxial Spherical Gaussian Beams 641
9.10.3 Gaussian Beam Focusing 643
9.10.4 Matrix Methods and the ABCD Law 648
9.11 Laser Cavities 650
9.11.1 Laser Cavity with Equal Mirror Curvatures 650
9.11.2 Laser Cavity with Unequal Mirror Curvatures 654
9.11.3 Stable Resonators 657
9.11.4 Traveling Wave Resonators 662
9.11.5 Unstable Resonators 663
9.11.6 Transverse Cavity Modes 664
9.12 Electro-Optics and Nonlinear Optics 667
9.12.1 The Electro-optic Effect 668
9.12.2 Optical Activity 672
9.12.3 Acousto-optic Effect 676
9.14.1 Nonlinear Optics 683
9.16.1 Frequency Mixing 697
Problems 699
10 Optical Imaging 719
10.1 Introduction 719
10.2 Abbe Theory of Image Formation 720
10.2.1 Phase Contrast Microscope 728
10.3 The Point Spread Function 730
10.3.1 Coherent vs. Incoherent Images 731
10.3.2 Speckle 738
10.4 Resolving Power of Optical Instruments 739
10.5 Image Recording 742
10.5.1 Photographic Film 742
10.5.2 Digital Detector Arrays 745
10.6 Contrast Transfer Function 748
10.7 Spatial Filtering 751
10.8 Adaptive Optics 754
Problems 759
A Chapter 1 Appendix: Transverse Traveling Waves on a String767
B Chapter 2 Appendix: Electromagnetic Wave Equations 771
C Chapter 5 Appendix: Calculation of the Jeans Number 785
D Chapter 7 Appendix: Fourier Series 787
Complex Fourier Series 797
Non-periodic Functions and Fourier Transforms 799
Problems 802
E Appendix: Solutions to selected Problems 803
Index 921
