Principles of Physical Optics

Charles A. Bennett, PhD, is Emeritus Professor of Physics at the University of North Carolina at Asheville and former Director of the UNCA Center for Teaching and Learning. Since 1983, he has collaborated with Oak Ridge National Laboratory. His research is focused on quantum optics, physical optics, and laser applications in environmental and fusion energy problems.

• Preface xiiiAcknowledgments xv1 The Physics of Waves 11.1 Introduction 11.2 One-Dimensional Wave Equation 11.3 General Solutions to the 1D Wave Equation 31.4 Harmonic Traveling Waves 51.5 The Principle of Superposition 71.5.1 Periodic Traveling Waves 71.5.2 Linear Independence 71.6 Complex Numbers and the Complex Representation 81.6.1 Complex Algebra 91.6.2 The Complex Representation of Harmonic Waves 111.7 The Three-Dimensional Wave Equation 121.7.1 Spherical Coordinates 131.7.2 Three-Dimensional Plane Waves 131.7.3 Spherical Waves 15Problems 162 Electromagnetic Waves and Photons 232.1 Introduction 232.2 Electromagnetism 232.3 Electromagnetic Wave Equations 292.3.1 Transverse Electromagnetic Waves 312.3.2 Energy Flow and the Poynting Vector 332.3.3 Irradiance 342.4 Photons 372.4.1 Single-Photon Interference 412.5 The Electromagnetic Spectrum 42Problems 433 Reflection and Refraction 513.1 Introduction 513.2 Overview of Reflection and Refraction 513.2.1 Fermat’s Principle of Least Time 553.3 Maxwell’s Equations at an Interface 573.3.1 Boundary Conditions 573.3.2 Electromagnetic Waves at an Interface 583.4 The Fresnel Equations 603.4.1 Incident Wave Polarized Normal to the Plane of Incidence 613.4.2 Incident Wave Polarized Parallel to the Plane of Incidence 633.5 Interpretation of the Fresnel Equations 653.5.1 Normal Incidence 663.5.2 Brewster’s Angle 663.5.3 Total Internal Reflection 683.5.4 Plots of the Fresnel Equations vs. Incident Angle 713.5.5 Phase Changes on Reflection 723.5.5.1 Summary 753.6 Reflectivity and Transmissivity 753.6.1 Plots of Reflectivity and Transmissivity vs. Incident Angle 783.6.2 The Evanescent Wave 793.7 Scattering 813.7.1 Atmospheric Scattering 823.7.2 Rainbows 823.7.3 Parhelia 853.8 Optical Materials 863.9 Dispersion 863.9.1 Dispersion in Dielectric Media 863.9.1.1 Nonconducting Gases 923.9.2 Dispersion in Conducting Media 943.9.2.1 Reflection from Conductors 97Problems 1004 Geometric Optics I 1074.1 Introduction 1074.2 Reflection and Refraction at Aspheric Surfaces 1074.3 Reflection and Refraction at a Spherical Surface 1124.3.1 The Paraxial Approximation 1124.3.2 Spherical Reflecting Surfaces 1134.3.2.1 Sign Conventions for Reflecting Surfaces 1144.3.3 Spherical Refracting Surfaces 1154.3.4 Sign Conventions and Ray Diagrams 1174.4 Lens Combinations 1214.4.1 Thin Lenses in Close Combination 1224.5 Optical Instruments 1234.5.1 The Camera 1234.5.2 The Eye 1244.5.3 The Magnifying Glass 1254.5.4 The Compound Microscope 1264.5.5 The Telescope 1274.5.6 The Exit Pupil 1284.6 Optical Fibers 129Problems 1335 Geometric Optics II 1395.1 Introduction 1395.2 Aberrations 1395.2.1 Chromatic Aberration 1395.2.2 Spherical Aberration 1435.2.3 Astigmatism and Coma 1435.2.4 Field Curvature 1435.2.5 Diffraction 1445.3 Principal Points and Effective Focal Lengths in Paraxial Optics 1445.4 Thick Paraxial Lenses 1485.4.1 Principal Points and Effective Focal Lengths of Thick Paraxial Lenses 1495.5 Introduction to Matrix Methods in Paraxial Geometrical Optics 1535.5.1 The Translation Matrix 1535.5.2 The Refraction Matrix 1555.5.3 The Reflection Matrix 1565.5.4 The Ray Transfer Matrix 1575.5.5 Location of Principal Points and Effective Focal Lengths for an Optical System 1615.6 Radiometry 1655.6.1 Extended Sources 1665.6.1.1 Spectral Distributions 1685.6.1.2 Conservation of Radiance 1685.6.2 Radiometry of Blackbody Sources 1695.6.3 Rayleigh–Jeans Theory and the Ultraviolet Catastrophe 1705.6.4 Planck’s Quantum Theory of Blackbody Radiation 173Problems 1766 Polarization 1856.1 Introduction 1856.2 Linear Polarization 1856.2.1 Linear Polarizers 1866.2.2 Linear Polarizer Design 1886.3 Birefringence 1916.4 Circular and Elliptical Polarization 1946.4.1 Wave Plates and Circular Polarizers 1966.5 Jones Vectors and Matrices 1996.5.1 Jones Matrices 2016.5.2 Birefringent Colors 204Problems 2077 Superposition and Interference 2137.1 Introduction 2137.2 Superposition of Harmonic Waves 2137.3 Interference Between Two Monochromatic Electromagnetic Waves 2147.3.1 Linear Power Detection 2157.3.2 Interference Between Beams with the Same Frequency 2167.3.2.1 Young’s Double-Slit Experiment 2167.3.3 Thin-Film Interference 2197.3.4 Quasi-Monochromatic Sources 2227.3.5 Fringe Geometry 2227.3.5.1 Lloyd’s Mirror 2237.3.5.2 Newton’s Rings 2237.3.6 Interference Between Beams with Different Frequencies 2247.3.6.1 Coherent Detection 2267.4 Fourier Analysis 2297.4.1 Fourier Transforms 2297.4.2 Position Space, k-Space Domain 2307.4.3 Frequency–Time Domain 2347.5 Properties of Fourier Transforms 2347.5.1 Symmetry Properties 2347.5.2 Linearity 2357.5.3 Transform of a Transform 2367.6 Wavepackets 2367.7 Group and Phase Velocity 2417.8 Interferometry 2437.8.1 Energy Conservation and Complementary Fringe Patterns 2487.9 Single-Photon Interference 2507.10 Multiple-Beam Interference 2517.10.1 The Scanning Fabry–Perot Interferometer 2547.11 Interference in Multilayer Films 2577.11.1 Antireflection Films 2617.11.2 High-Reflectance Films 2637.11.2.1 Fabry–Perot Interference Filters 2647.12 Coherence 2657.12.1 Temporal Coherence 2657.12.2 Spatial Coherence 2667.12.3 Michelson’s Stellar Interferometer 2697.12.4 Irradiance Interferometry 2707.12.5 Telescope Arrays 271Problems 2728 Diffraction 2818.1 Introduction 2818.2 Huygens’ Principle 2828.2.1 Babinet’s Principle 2848.3 Fraunhofer Diffraction 2848.3.1 Single Slit 2858.3.2 Rectangular Aperture 2908.3.3 Circular Aperture 2918.3.4 Optical Resolution 2948.3.5 More on Stellar Interferometry 2958.3.6 Double Slit 2958.3.7 N Slits: The Diffraction Grating 2968.3.8 The Diffraction Grating 2988.3.8.1 Chromatic Resolving Power 3028.3.9 Fraunhofer Diffraction as a Fourier Transform 3048.3.10 Apodization 3068.3.10.1 Apertures with Circular Symmetry 3078.4 Fresnel Diffraction 3098.4.1 Fresnel Zones 3108.4.1.1 Circular Apertures 3138.4.1.2 Circular Obstacles 3138.4.1.3 Fresnel Zone Plate 3168.4.2 Holography 3208.4.3 Numerical Analysis of Fresnel Diffraction with Circular Symmetry 3218.4.4 Fresnel Diffraction from Apertures with Cartesian Symmetry 3238.4.4.1 Semi-Infinite Straightedge 3268.4.4.2 Single Slit 3278.4.4.3 Rectangular Aperture 3298.5 Introduction to Quantum Electrodynamics 3308.5.1 Feynman’s Interpretation 333Problems 3349 Lasers 3439.1 Introduction 3439.2 Energy Levels in Atoms, Molecules, and Solids 3439.2.1 Atomic Energy Levels 3439.2.2 Molecular Energy Levels 3469.2.3 Solid-State Energy Bands 3489.2.4 Semiconductor Devices 3529.3 Stimulated Emission and Light Amplification 3549.4 Laser Systems 3579.4.1 Atomic Gas Lasers 3589.4.1.1 Helium–Neon Laser 3599.4.2 Molecular Gas Lasers 3609.4.2.1 Carbon Dioxide Laser 3609.4.3 Solid-State Lasers 3629.4.3.1 Diode Lasers 3639.4.4 Other Laser Systems 3649.5 Longitudinal Cavity Modes 3659.6 Frequency Stability 3669.7 Introduction to Gaussian Beams 3679.7.1 Overview of Gaussian Beam Properties 3679.8 Gaussian Beam Properties 3699.8.1 Approximate Solutions to the Wave Equation 3709.8.2 Paraxial Spherical Gaussian Beams 3729.8.3 Gaussian Beam Focusing 3739.8.4 Matrix Methods and the ABCD Law 3769.9 Laser Cavities 3779.9.1 Laser Cavity with Equal Mirror Curvatures 3779.9.2 Laser Cavity with Unequal Mirror Curvatures 3799.9.3 Stable Resonators 3819.9.4 Traveling Wave Resonators 3859.9.5 Unstable Resonators 3859.9.6 Transverse Cavity Modes 3869.10 Electro-optics and Nonlinear Optics 3879.10.1 The Electro-optic Effect 3889.10.1.1 Pockels Cells 3889.10.1.2 Kerr Cells 3909.10.2 Optical Activity 3909.10.2.1 Faraday Rotation 3929.10.3 Acousto-optic Effect 3939.10.4 Nonlinear Optics 3979.10.4.1 Harmonic Generation 3989.10.4.2 Phase Conjugation Reflection by Degenerate Four-Wave Mixing 4029.10.5 Frequency Mixing 404Problems 40510 Optical Imaging 41910.1 Introduction 41910.2 Abbe Theory of Image Formation 41910.2.1 Phase Contrast Microscope 42410.3 The Point Spread Function 42510.3.1 Coherent vs. Incoherent Images 42610.3.2 Speckle 43010.4 Resolving Power of Optical Instruments 43110.5 Image Recording 43210.5.1 Photographic Film 43310.5.2 Digital Detector Arrays 43410.6 Contrast Transfer Function 43610.7 Spatial Filtering 43710.8 Adaptive Optics 441Problems 443Appendix A Chapter 1 Appendix: Transverse Traveling Waves on a String 449Appendix B Chapter 2 Appendix: Electromagnetic Wave Equations 451B. 1 Maxwell’s Equations in Differential Form and Wave Equations for ⃗E and ⃗B 451B. 2 Method 1: Cartesian Coordinates 451B.2. 1 Wave Equations for ⃗E and ⃗B 455B. 3 Method 2: Vector Calculus 456B.3. 1 Wave Equations for ⃗E and ⃗B 457Appendix C Chapter 5 Appendix: Calculation of the Jeans Number 459Appendix D Chapter 7 Appendix: Fourier Series 461D.1 Real Fourier Series 461D.2 Complex Fourier Series 467D.3 Nonperiodic Functions and Fourier Transforms 468Problems 470Appendix E Solutions to Selected Problems 473Bibliography 553Index 555