Physics of light and optics

Preface......Page 3
Table of Contents......Page 5
0.1 Vector Calculus......Page 9
0.2 Complex Numbers......Page 14
0.3 Linear Algebra......Page 19
0.4 Fourier Theory......Page 21
Appendix 0.A Table of Integrals and Sums......Page 28
Exercises......Page 29
1 Electromagnetic Phenomena......Page 35
1.1 Gauss' Law......Page 36
1.2 Gauss' Law for Magnetic Fields......Page 37
1.3 Faraday's Law......Page 39
1.4 Ampere's Law......Page 40
1.5 Maxwell's Adjustment to Ampere's Law......Page 41
1.6 Polarization of Materials......Page 44
1.7 The Wave Equation......Page 45
Exercises......Page 49
2.1 Plane Wave Solutions to the Wave Equation......Page 53
2.2 Index of Refraction......Page 56
2.3 The Lorentz Model of Dielectrics......Page 59
2.4 Index of Refraction of a Conductor......Page 62
2.5 Poynting's Theorem......Page 63
2.6 Irradiance of a Plane Wave......Page 66
Appendix 2.A Radiometry, Photometry, and Color......Page 68
Appendix 2.B Clausius-Mossotti Relation......Page 71
Appendix 2.C Energy Density of Electric Fields......Page 74
Appendix 2.D Energy Density of Magnetic Fields......Page 76
Exercises......Page 77
3.1 Refraction at an Interface......Page 81
3.2 The Fresnel Coefficients......Page 85
3.3 Reflectance and Transmittance......Page 86
3.4 Brewster's Angle......Page 88
3.5 Total Internal Reflection......Page 89
3.6 Reflections from Metal......Page 91
Appendix 3.A Boundary Conditions For Fields at an Interface......Page 92
Exercises......Page 94
4 Multiple Parallel Interfaces......Page 97
4.1 Double-Interface Problem Solved Using Fresnel Coefficients......Page 98
4.2 Two-Interface Transmittance at Sub Critical Angles......Page 101
4.3 Beyond Critical Angle: Tunneling of Evanescent Waves......Page 104
4.4 Fabry-Perot......Page 106
4.5 Setup of a Fabry-Perot Instrument......Page 108
4.6 Distinguishing Nearby Wavelengths in a Fabry-Perot Instrument......Page 109
4.7 Multilayer Coatings......Page 113
4.8 Repeated Multilayer Stacks......Page 117
Exercises......Page 120
5.1 Constitutive Relation in Crystals......Page 125
5.2 Plane Wave Propagation in Crystals......Page 127
5.3 Biaxial and Uniaxial Crystals......Page 131
5.4 Refraction at a Uniaxial Crystal Surface......Page 132
5.5 Poynting Vector in a Uniaxial Crystal......Page 133
Appendix 5.A Symmetry of Susceptibility Tensor......Page 136
Appendix 5.B Rotation of Coordinates......Page 137
Appendix 5.C Electric Field in Crystals......Page 139
Appendix 5.D Huygens' Elliptical Construct for a Uniaxial Crystal......Page 142
Exercises......Page 144
Review, Chapters 1–5......Page 147
6 Polarization of Light......Page 153
6.1 Linear, Circular, and Elliptical Polarization......Page 154
6.2 Jones Vectors for Representing Polarization......Page 155
6.3 Elliptically Polarized Light......Page 156
6.4 Linear Polarizers and Jones Matrices......Page 157
6.5 Jones Matrix for Polarizers at Arbitrary Angles......Page 160
6.6 Jones Matrices for Wave Plates......Page 161
6.7 Polarization Effects of Reflection and Transmission......Page 164
Appendix 6.A Ellipsometry......Page 165
Appendix 6.B Partially Polarized Light......Page 167
Exercises......Page 174
7 Superposition of Quasi-Parallel Plane Waves......Page 179
7.1 Intensity of Superimposed Plane Waves......Page 180
7.2 Group vs. Phase Velocity: Sum of Two Plane Waves......Page 182
7.3 Frequency Spectrum of Light......Page 184
7.4 Packet Propagation and Group Delay......Page 189
7.5 Quadratic Dispersion......Page 191
7.6 Generalized Context for Group Delay......Page 193
Appendix 7.A Pulse Chirping in a Grating Pair......Page 197
Appendix 7.B Causality and Exchange of Energy with the Medium......Page 199
Appendix 7.C Kramers-Kronig Relations......Page 204
Exercises......Page 208
8.1 Michelson Interferometer......Page 211
8.2 Coherence Time and Fringe Visibility......Page 216
8.3 Temporal Coherence of Continuous Sources......Page 217
8.4 Fourier Spectroscopy......Page 218
8.5 Young's Two-Slit Setup and Spatial Coherence......Page 219
Appendix 8.A Spatial Coherence for a Continuous Source......Page 224
Appendix 8.B Van Cittert-Zernike Theorem......Page 225
Exercises......Page 227
Review, Chapters 6–8......Page 231
9 Light as Rays......Page 235
9.1 The Eikonal Equation......Page 236
9.2 Fermat's Principle......Page 239
9.3 Paraxial Rays and ABCD Matrices......Page 243
9.4 Reflection and Refraction at Curved Surfaces......Page 245
9.5 ABCD Matrices for Combined Optical Elements......Page 247
9.6 Image Formation......Page 249
9.7 Principal Planes for Complex Optical Systems......Page 252
9.8 Stability of Laser Cavities......Page 253
Appendix 9.A Aberrations and Ray Tracing......Page 256
Exercises......Page 259
10 Diffraction......Page 265
10.1 Huygens' Principle as Formulated by Fresnel......Page 266
10.2 Scalar Diffraction Theory......Page 268
10.3 Fresnel Approximation......Page 270
10.4 Fraunhofer Approximation......Page 272
10.5 Diffraction with Cylindrical Symmetry......Page 273
Appendix 10.A Fresnel-Kirchhoff Diffraction Formula......Page 275
Appendix 10.B Green's Theorem......Page 278
Exercises......Page 280
11.1 Fraunhofer Diffraction Through a Lens......Page 283
11.2 Resolution of a Telescope......Page 287
11.3 The Array Theorem......Page 290
11.4 Diffraction Grating......Page 292
11.5 Spectrometers......Page 293
11.6 Diffraction of a Gaussian Field Profile......Page 295
11.7 Gaussian Laser Beams......Page 297
Appendix 11.A ABCD Law for Gaussian Beams......Page 299
Exercises......Page 303
12.1 Interferograms......Page 309
12.2 Testing Optical Components......Page 310
12.3 Generating Holograms......Page 311
12.4 Holographic Wavefront Reconstruction......Page 312
Exercises......Page 315
Review, Chapters 9–12......Page 317
13 Blackbody Radiation......Page 323
13.1 Stefan-Boltzmann Law......Page 324
13.2 Failure of the Equipartition Principle......Page 325
13.3 Planck's Formula......Page 327
13.4 Einstein's A and B Coefficients......Page 330
Appendix 13.A Thermodynamic Derivation of the Stefan-Boltzmann Law......Page 332
Appendix 13.B Boltzmann Factor......Page 334
Exercises......Page 336
Index......Page 339
Physical Constants......Page 345