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Physics of Light and Optics
Justin Peatross, Michael Ware
Brigham Young University
2011c Edition , November 14, 2012
This curriculum was originally developed for a senior-level optics course in the Department of Physics and Astronomy at Brigham Young University. Topics are addressed from a physics perspective and include the propagation of light in matter, reflection and transmission at boundaries, polarization effects, dispersion,
coherence, ray optics and imaging, diffraction, and the quantum nature of light.
Students using this book should be familiar with differentiation, integration, and standard trigonometric and algebraic manipulation. A brief review of complex numbers, vector calculus, and Fourier transforms is provided in Chapter 0, but it is helpful if students already have some experience with these concepts.
While the authors retain the copyright, we have made this book available free of charge at optics.byu.edu. This is our contribution toward a future world with free textbooks! The web site also provides a link to purchase bound copies of the book for the cost of printing. A collection of electronic material related to the text is available at the same site, including videos of students performing the lab assignments found in the book.
The development of optics has a rich history. We have included historical sketches for a selection of the ioneers in the field to help students appreciate some of this historical context. These sketches are not intended to be authoritative, the information for most individuals having been gleaned primarily from Wikipedia.
The authors may be contacted at opticsbook@byu.edu. We enjoy hearing reports from those using the book and welcome constructive feedback. We occasionally revise the text. The title page indicates the date of the last revision.
We would like to thank all those who have helped improve this material. Weespecially thank John Colton, Bret Hess, and Harold Stokes for their careful review and extensive suggestions. This curriculum benefitted from a CCLI grant from the National Science Foundation Division of Undergraduate Education (DUE-9952773).
Contents
Preface iii
Table of Contents v
Mathematical Tools 1
0.1 Vector Calculus 1
0.2 Complex Numbers 6
0.3 Linear Algebra 11
0.4 Fourier Theory 13
Appendix 0.A Table of Integrals and Sums 20
Exercises 21
1 Electromagnetic Phenomena 27
1.1 Gauss' Law 28
1.2 Gauss' Law for Magnetic Fields 29
1.3 Faraday's Law 31
1.4 Ampere's Law 32
1.5 Maxwell's Adjustment to Ampere's Law 33
1.6 Polarization of Materials 36
1.7 The Wave Equation 37
Exercises 41
2 Plane Waves and Refractive Index 45
2.1 Plane Wave Solutions to the Wave Equation 45
2.2 Index of Refraction 48
2.3 The Lorentz Model of Dielectrics 51
2.4 Index of Refraction of a Conductor 54
2.5 Poynting's Theorem 55
2.6 Irradiance of a Plane Wave 58
Appendix 2.A Radiometry, Photometry and Color 60
Appendix 2.B Clausius-Mossotti Relation 63
Appendix 2. C Energy Density of Electric Fields 66
Appendix 2.D Energy Density of Magnetic Fields 68
Exercises 69
3 Reflection and Refraction 73
3.1 Refraction at an Interface 73
3.2 The Fresnel Coefficients 77
3.3 Reflectance and Transmittance 78
3.4 Brewster's Angle 80
3.5 Total Internal Reflection 81
3.6 Reflections from Metal 83
Appendix 3. A Boundary Conditions For Fields at an Interface .... 84
Exercises 86
4 Multiple Parallel Interfaces 89
4.1 Double-Interface Problem Solved Using Fresnel Coefficients . . . 90
4.2 Two-Interface Transmittance at Sub Critical Angles 93
4.3 Beyond Critical Angle: Tunneling of Evanescent Waves 96
4.4 Fabry-Perot 98
4.5 Setup of a Fabry-Perot Instrument 100
4.6 Distinguishing Nearby Wavelengths in a Fabry-Perot Instrument 101
4.7 Multilayer Coatings 105
4.8 Repeated Multilayer Stacks 109
Exercises 112
5 Propagation in Anisotropic Media 117
5.1 Constitutive Relation in Crystals 117
5.2 Plane Wave Propagation in Crystals 119
5.3 Biaxial and Uniaxial Crystals 123
5.4 Refraction at a Uniaxial Crystal Surface 124
5.5 Poynting Vector in a Uniaxial Crystal 125
Appendix 5.A Symmetry of Susceptibility Tensor 128
Appendix 5.B Rotation of Coordinates 129
Appendix 5. C Electric Field in Crystals 131
Appendix 5.D Huygens' Elliptical Construct for a Uniaxial Crystal . . 134
Exercises 136
Review, Chapters 1-5 139
6 Polarization of Light 145
6. 1 Linear, Circular, and Elliptical Polarization 146
6.2 Jones Vectors for Representing Polarization 147
6.3 Elliptically Polarized Light 148
6.4 Linear Polarizers and Jones Matrices 149
6.5 Jones Matrix for Polarizers at Arbitrary Angles 152
6.6 Jones Matrices for Wave Plates 153
.7 Polarization Effects of Reflection and Transmission 156
Appendix 6.A Ellipsometry 157
Appendix 6.B Partially Polarized Light 159
Exercises 166
CONTENTS
7 Superposition of Quasi-Parallel Plane Waves 171
7.1 Intensity of Superimposed Plane Waves 172
7.2 Group vs. Phase Velocity: Sum of Two Plane Waves 174
7.3 Frequency Spectrum of Light 176
7.4 Packet Propagation and Group Delay 181
7.5 Quadratic Dispersion 183
7.6 Generalized Context for Group Delay 185
Appendix 7.A Pulse Chirping in a Grating Pair 189
Appendix 7.B Causality and Exchange of Energy with the Medium . . 191
Appendix 7. C Kramers-Kronig Relations 196
Exercises 200
8 Coherence Theory 203
8.1 Michelson Interferometer 203
8.2 Coherence Time and Fringe Visibility 208
8.3 Temporal Coherence of Continuous Sources 209
8.4 Fourier Spectroscopy 210
8.5 Young's Two-Slit Setup and Spatial Coherence 211
Appendix 8.A Spatial Coherence for a Continuous Source 216
Appendix 8.B Van Cittert-Zernike Theorem 217
Exercises 219
Review, Chapters 6-8 223
9 Light as Rays 227
9.1 The Eikonal Equation 228
9.2 Fermat's Principle 231
9.3 Paraxial Rays and ABCD Matrices 235
9.4 Reflection and Refraction at Curved Surfaces 237
9.5 ABCD Matrices for Combined Optical Elements 239
9.6 Image Formation 241
9.7 Principal Planes for Complex Optical Systems 244
9.8 Stability of Laser Cavities 245
Appendix 9.A Aberrations and Ray Tracing 248
Exercises 251
10 Diffraction 257
10.1 Huygens' Principle as Formulated by Fresnel 258
10.2 Scalar Diffraction Theory 260
10.3 Fresnel Approximation 262
10.4 Fraunhofer Approximation 264
10.5 Diffraction with Cylindrical Symmetry 265
Appendix 10.A Fresnel-Kirchhoff Diffraction Formula 267
Appendix 10.B Green's Theorem 270
Exercises 272
viii
CONTENTS
11 Diffraction Applications 275
11.1 Fraunhofer Diffraction Through a Lens 275
11.2 Resolution of a Telescope 279
11.3 The Array Theorem 282
11.4 Diffraction Grating 284
11.5 Spectrometers 285
11.6 Diffraction of a Gaussian Field Profile 287
11.7 Gaussian Laser Beams 289
Appendix 11. A ABCD Law for Gaussian Beams 291
Exercises 295
12 Interferograms and Holography 301
12.1 Interferograms 301
12.2 Testing Optical Components 302
12.3 Generating Holograms 303
12.4 Holographic Wavefront Reconstruction 304
Exercises 307
Review, Chapters 9-12 309
13 Blackbody Radiation 315
13.1 Stefan-Boltzmann Law 316
13.2 Failure of the Equipartition Principle 317
13.3 Planck's Formula 319
13.4 Einstein's A and B Coefficients 322
Appendix 13.A Thermodynamic Derivation of the Stefan-Boltzmann Law 324
Appendix 13. B Boltzmann Factor 326
Exercises 328
Index 331
Physical Constants 337
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