PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction 1 1.2 One-Dimensional Wave Equation 2 1.2.1 Transverse Traveling Waves On A String 3 1.3 General Solutions to the 1-D Wave Equation 5 1.4 Harmonic Traveling Waves 8 1.5 The Principle of Superposition 11 1.5.1 Periodic Traveling Waves 11 1.5.2 Linear Independence 12 1.6 Complex Numbers and the Complex Representation 12 1.6.1 Complex Algebra 13 1.6.2 The Complex Representation of Harmonic Waves 16 1.7 The Three-Dimensional Wave Equation 17 1.7.1 Three-Dimensional Plane Waves 19 1.7.2 Spherical Waves 20 2 Electromagnetic Waves and Photons 25 2.1 Introduction 25 2.2 Electromagnetism 26 ix
X CONTENTS 2.3 Electromagnetic Wave Equations 32 2.3.1 Transverse Electromagnetic Waves 34 2.3.2 Energy Flow and the Poynting Vector 38 2.3.3 Irradiance 39 2.4 Photons 42 2.4.1 Single-Photon Interference 47 2.5 The Electromagnetic Spectrum 48 Appendix: Maxwell's Equations in Differential Form 53 3 Reflection and Refraction 59 3.1 Introduction 59 3.2 Overview of Reflection and Refraction 60 3.2.1 Fermat' s Principle of Least Time 63 3.3 Maxwell's Equations at an Interface 66 3.3.1 Boundary Conditions 66 3.3.2 Electromagnetic Waves at an Interface 67 3.4 The Fresnel Equations 69 3.4.1 Incident Wave Polarized Normal to the Plane of Incidence 70 3.4.2 Incident Wave Polarized Parallel to the Plane of Incidence 72 3.5 Interpretation of the Fresnel Equations 76 3.5.1 Normal Incidence 76 3.5.2 Brewster's Angle 76 3.5.3 Total Internal Reflection 78 3.5.4 Plots of the Fresnel Equations vs. Incident Angle 81 3.5.5 Phase Changes on Reflection 83 3.6 Reflectivity and Transmissivity 87 3.6.1 Plots of Reflectivity and Transmissivity vs. Incident Angle 90 3.6.2 The Evanescent Wave 92 3.7 * Dispersion 95 3.7.1 Dispersion in Dielectric Media 95 3.7.2 Dispersion in Conducting Media 104 3.8 Scattering 110 3.8.1 Atmospheric Scattering 110 3.8.2 Optical Materials 115 4 Geometric Optics 119 4.1 Introduction 120 4.2 Reflection and Refraction at Aspheric Surfaces 120 4.3 Reflection and Refraction at a Spherical Surface 125 4.3.1 Spherical Reflecting Surfaces 125 4.3.2 Spherical Refracting Surfaces 128
CONTENTS XI 4.3.3 Sign Conventions and Ray Diagrams 131 4.4 Lens Combinations 136 4.4.1 Thin-Lenses in Close Combination 137 4.5 * Principal Points and Effective Focal Lengths 138 4.6 Aberrations 143 4.6.1 Chromatic Aberration 143 4.6.2 Spherical Aberration 146 4.6.3 Astigmatism and Coma 147 4.6.4 Field Curvature 147 4.6.5 Diffraction 148 4.7 Optical Instruments 148 4.7.1 The Camera 148 4.7.2 The Eye 150 4.7.3 The Magnifying Glass 151 4.7.4 The Compound Microscope 152 4.7.5 The Telescope 153 4.7.6 The Exit Pupil 154 4.8 *Radiometry 156 4.8.1 Extended Sources 159 4.8.2 Radiometry of Blackbody Sources 161 4.8.3 Rayleigh-Jeans Theory and the Ultraviolet Catastrophe 163 4.8.4 Planck's Quantum Theory of Blackbody Radiation 165 4.9 * Optical Fibers 169 4.10 * Thick Lenses 174 4.10.1 *Principal Points and Effective Focal Lengths of Thick Lenses 176 4.11 ""Introduction to Matrix Methods in Paraxial Geometrical Optics 180 4.11.1 The Translation Matrix 180 4.11.2 The Refraction Matrix 182 4.11.3 The Reflection Matrix 184 4.11.4 The Ray Transfer Matrix 185 4.11.5 Location of Cardinal Points for an Optical System 189 Appendix: Calculation of the Jeans Number 197 Superposition and Interference 199 5.1 Introduction 200 5.2 Superposition of Harmonic Waves 200 5.3 Interference Between Two Monochromatic Electromagnetic Waves 201 5.3.1 Linear Power Detection 202 5.3.2 Interference Between Beams with the Same Frequency 203 5.3.3 Thin-Film Interference 206 5.3.4 Quasi-Monochromatic Sources 210 5.3.5 Fringe Geometry 211
XII CONTENTS 5.3.6 Interference Between Beams with Different Frequencies 212 5.4 Fourier Analysis 218 5.4.1 Fourier Transforms 218 5.4.2 Position Space, k-space Domain 219 5.4.3 Frequency-Time Domain 223 5.5 Properties of Fourier Transforms 224 5.5.1 Symmetry Properties 224 5.5.2 Linearity 225 5.5.3 Transform of a Transform 225 5.6 Wavepackets 226 5.7 Group and Phase Velocity 232 5.8 Interferometry 235 5.8.1 * Energy Conservation and Complementary Fringe Patterns 240 5.9 Single-Photon Interference 243 5.10 Multiple-Beam Interference 244 5.10.1 The Scanning Fabry-Perot Interferometer 247 5.11 Interference in Multilayer Films 251 5.11.1 Antireflection Films 255 5.11.2 High-Reflectance Films 257 5.12 Coherence 259 5.12.1 Temporal Coherence 260 5.12.2 Spatial Coherence 261 5.12.3 Michelson's Stellar Interferometer 264 5.12.4 Irradiance Interferometry 265 5.12.5 Telescope Arrays 266 Appendix: Fourier Series 269 Diffraction 281 6.1 Introduction 282 6.2 Huygens' Principle 282 6.2.1 Babinet's Principle 284 6.3 Fraunhofer Diffraction 285 6.3.1 Single Slit 286 6.3.2 Rectangular Aperture 291 6.3.3 Circular Aperture 293 6.3.4 Optical Resolution 295 6.3.5 More on Stellar Interferometry 297 6.3.6 Double Slit 298 6.3.7 N Slits: The Diffraction Grating 299 6.3.8 The Diffraction Grating 301 6.3.9 Fraunhofer Diffraction as a Fourier Transform 308 6.3.10 Apodization 311
CONTENTS XIII 6.4 Fresnel Diffraction 313 6.4.1 Fresnel Zones 315 6.4.2 Holography 325 6.4.3 Numerical Analysis of Fresnel Diffraction with Circular Symmetry 327 6.4.4 Fresnel Diffraction from Apertures with Cartesian Symmetry 329 6.5 Introduction to Quantum Electrodynamics 338 6.5.1 Feynman's Interpretation 341 7 Lasers 345 7.1 Introduction 345 7.2 Energy Levels in Atoms, Molecules, and Solids 346 7.2.1 Atomic Energy Levels 346 7.2.2 Molecular Energy Levels 350 7.2.3 Solid-state Energy Bands 352 7.2.4 Semiconductor Devices 354 7.3 Stimulated Emission and Light Amplification 357 7.4 Laser Systems 361 7.4.1 Atomic Gas Lasers 363 7.4.2 Molecular Gas Lasers 364 7.4.3 Solid-State Lasers 367 7.4.4 Other Laser Systems 369 7.5 Longitudinal Cavity Modes 370 7.6 Frequency Stability 371 7.7 Introduction to Gaussian Beams 372 7.7.1 Overview of Gaussian Beam Properties 372 7.8 Derivation of Gaussian Beam Properties 375 7.8.1 Approximate Solutions to the Wave Equation 376 7.8.2 Paraxial Spherical Gaussian Beams 378 7.8.3 Gaussian Beam Focusing 380 7.8.4 Matrix Methods and the ABCD Law 384 7.9 Laser Cavities 385 7.9.1 Laser Cavity with Equal Mirror Curvatures 386 7.9.2 Laser Cavity with Unequal Mirror Curvatures 388 7.9.3 Stable Resonators 390 7.9.4 Traveling Wave Resonators 394 7.9.5 Unstable Resonators 394 7.9.6 Transverse Cavity Modes 395 8 Optical Imaging 399 8.1 Introduction 400 8.2 Abbe Theory of Image Formation 400
XIV CONTENTS 8.2.1 Phase Contrast Microscope 405 8.3 The Point Spread Function 407 8.3.1 Coherent vs. Incoherent Images 407 8.3.2 Speckle 412 8.4 Resolving Power of Optical Instruments 413 8.5 Image Recording 415 8.5.1 Photographic Film 416 8.5.2 Digital Detector Arrays 417 8.6 Contrast Transfer Function 420 8.7 Spatial Filtering 421 8.8 Adaptive Optics 425 9 Polarization and Nonlinear Optics 431 9.1 Introduction 432 9.2 Linear Polarization 432 9.2.1 Linear Polarizers 433 9.2.2 Linear Polarizer Design 436 9.3 Birefringence 439 9.4 Circular and Elliptical Polarization 443 9.4.1 Wave Plates and Circular Polarizers 444 9.5 Jones Vectors and Matrices 449 9.5.1 Birefringent Colors 455 9.6 The Electro-optic Effect 458 9.6.1 Pockels Cells 458 9.6.2 Kerr Cells 460 9.7 Optical Activity 461 9.8 Faraday Rotation 463 9.9 Acousto-optic Effect 464 9.10 Nonlinear Optics 469 9.11 Harmonic Generation 471 9.11.1 Phase Conjugation Reflection by Degenerate Four-Wave Mixing 476 9.12 Frequency Mixing 478 References 483 Index 485