Physics of Light and Optics

Transcription

1 Physics of Light and Optics Justin Peatross and Harold Stokes Brigham Young University Department of Physics and Astronomy All Publication Rights Reserved (2001) Revised April 2002 This project is supported in part by the National Science Foundation Division of Undergraduate Education (Grant number DUE ). i

2 CONTENTS Chapter 0 Chapter 1 Chapter 2 Chapter 3 Mathematical Tools 0.1 Introduction Complex Numbers Vector Calculus Fourier Theory 9 Appendix 0.A Sylvester s Theorem 14 Appendix 0.B Integrals and Formulas 15 Electromagnetic Phenomena 1.1 Introduction Coulomb s and Gauss Laws BiotSavart and Ampere s Laws Faraday s Law Continuity Equation Maxwell s Equations The Wave Equation Wave Equation in Isotropic Media 26 Plane Waves and Refractive Index 2.1 Introduction Plane Wave Solutions to the Wave Equation Dielectric Model of Refractive Index and Absorption Conductor Model of Refractive Index and Absorption Poynting s Theorem Irradiance of a Plane Wave 41 Appendix 2.A Energy Density of Electric Fields 43 Appendix 2.B Energy Density of Magnetic Fields 44 Appendix 2.C Radiometry Versus Photometry 45 Reflection and Refraction 3.1 Introduction Refraction at an Interface The Fresnel Coefficients Reflection and Transmission Brewster s Angle Total Internal Reflection 55 Appendix 3.A Boundary Conditions for Fields at an Interface 56 ii

3 Chapter 4 Chapter 5 Polarization 4.1 Introduction Linear, Circular, and Elliptical Polarization Jones Vectors for Representing Polarization Jones Matrices Jones Matrix for Polarizers at Arbitrary Angle Jones Matrices for Wave plates Polarization Effects of Reflection and Transmission Reflection from Metallic or other Absorptive Surfaces Polarization and Total Internal Reflection Ellipsometry 78 Light Propagation in Crystals 5.1 Introduction Wave Propagation in Nonisotropic Media Fresnel s Equation Uniaxial Crystal Poynting Vector in a Uniaxial Crystal 88 Appendix 5.A Rotation of Coordinates 90 Appendix 5.A Huygens' Elliptical Construct for a Uniaxial Crystal 92 Review Problems Chapters Chapter 6 Chapter 7 Multiple Boundary Problem 6.1 Introduction Double Boundary Problem Solved Using Fresnel Coefficients Double Boundary Problem at Sub Critical Angles Beyond Critical Angle: Tunneling of Evanescent Waves FabryPerot Etalon Distinguishing Nearby Wavelengths in a FabryPerot Instrument Setup of a FabryPerot Instrument Multilayer Coatings Repeated Multilayer Stacks 126 Superposition of QuasiParallel, Uniformly Polarized Plane Waves 7.1 Introduction Intensity Group Versus Phase Velocity: Superposition of Two Plane Waves Frequency Spectrum of Light Phase Delay and Group Delay Quadratic Dispersion Generalized Context for Group Delay 144 Appendix 7.A Causality and Exchange of Energy with the Medium 149 iii

4 Chapter 8 Coherence Theory 8.1 Introduction Michelson Interferometer Temporal Coherence Fringe Visibility and Coherence Length Fourier Spectroscopy Young s TwoSlit Setup and Spatial Coherence 167 Appendix 8.A Spatial Coherence with a Continuous Source 173 Appendix 8.B Non Random Phase and the van CittertZernike Theorem 174 Review Problems Chapters Chapter 9 Chapter 10 Light as Rays 9.1 Introduction The Eikonal Equation Fermat s Principle Paraxial Rays and ABCD Matrices Paraxial Reflections and Transmissions at Curved Surfaces Image Formation by a Mirrors and Lenses Image Formation by a Complex Optical Systems Stability of Laser Cavities 202 Appendix 9.A Ray Tracing To be written Diffraction 10.1 Introduction FresnelKirchhoff Diffraction Formula Babinet's principle Fresnel Approximation Fraunhofer Approximation Diffraction with Cylindrical Symmetry 218 Appendix 10.A Significance of the Scalar Wave Approximation 219 Appendix 10.B Green s Theorem 220 Chapter 11 Diffraction Applications 11.1 Introduction Diffraction of a Gaussian Field Profile Gaussian Laser Beams Fraunhofer Diffraction Through a Lens Resolving Power of a Telescope The Array Theorem Diffraction Grating Spectrometers ABCD law for Gaussian beams 249 Review Problems Chapters iv

5 Chapter 12 Chapter 13 Chapter 14 Interferograms and Holography To Be Written 12.1 Introduction 12.2 Generating Interferograms 12.3 Testing Optical Surfaces 12.4 Creating Holograms 12.5 Holographic Wave Front Reconstruction Blackbody Radiation and Lasers 13.1 Introduction Failure of Equipartition Principle Planck's Formula Einstein's A and B Coefficients 266 Appendix 13.A Thermodynamic Derivation of StefanBoltzman Law 267 Introduction to Quantum Optics To Be Written 14.1 Introduction 14.2 Photon Statistics 14.3 Coincidence Counting 14.4 Parametric Down Conversion 14.5 Interference of Correlated Photon Pairs Appendix 14.A Field Operators Appendix 14.B Analysis of Correlated Photon Pairs v

6 Preface This book is currently in a very preliminary form and will likely take several years to complete. It is used for a seniorlevel optics course for physics majors at Brigham Young University. Constructive feedback is welcome. The book is available at no cost at optics.byu.edu. In addition to completing the writing and editing of this material, we are developing a series of film clips and animations to enhance it. This curriculum benefits from a CCLI grant from the National Science Foundation Division of Undergraduate Education (DUE ). The grant has enabled the development of a number of laboratory exercises that are being integrated into the project. vi

7 Constants e o = C N m 2 Permittivity mo = 4p 10 7 T m A Permeability c = ms Speed of light in vacuum q e m e k B = C Charge of an electron = kg Mass of an electron = JK Boltzmann constant h = J s Planck s constant h = h 2p = J s s = Wm K 2 4 StefanBoltzmann constant vii