Guiding, Diffraction, and Confinement of Optical Radiation

Guiding, Diffraction, and Confinement of Optical Radiation presents a wide array of research studies on optics and electromagnetism. This book is organized into eight chapters that cover the problems related to optical radiation propagation and confinement. Chapter I examines the general features of electromagnetic propagation and introduces the basic concepts pertaining to the description of the electromagnetic field and its interaction with matter. Chapter II is devoted to asymptotic methods of solution of the wave equation, with particular emphasis on the asymptotic representation of the field in the form of the Luneburg-Kline series. This chapter also looks into a number of optical systems characterized by different refractive index distributions relying on the eikonal equation. Chapter III deals with stratified media, such as the multilayered thin films, metallic and dielectric reflectors, and interference filters. Chapters IV and V discuss the problem of propagation and diffraction integrals. Chapter VI describes the scattering from obstacles and the metallic and dielectric gratings. Chapters VII considers the passive and active resonators employed in connection with laser sources for producing a confinement near the axis of an optical cavity and Fabry-Perot interferometers and mainly relies on the use of diffraction theory. Chapter VIII presents the analytic approach to the study of transverse confinement near the axis of a dielectric waveguide hinges on the introduction of modal solutions of the wave equation. This book will be of value to quantum electronics engineers, physicists, researchers, and optics and electromagnetism graduate students.

Table of Contents:
Preface Chapter I General Features of Electromagnetic Propagation 1 Maxwell's Equations 2 Propagation in Time-Dispersive Media 3 State of Polarization of the Electromagnetic Field 4 Propagation in Anisotropie Media 5 Propagation in Spatially Dispersive Media 6 Energy Relations 7 Propagation in Moving Media 8 Coherence Properties of the Electromagnetic Field Problems References BibliographyChapter II Ray Optics 1 Approximate Representation of the Electromagnetic Field 2 Asymptotic Solution of the Scalar Wave Equation 3 The Eikonal Equation 4 The Ray Equation 5 Field-Transport Equation for Ao 6 Field-Transport Equations for the Higher-Order Terms Am 7 Evanescent Waves and Complex Eikonals 8 Ray Optics of Maxwell Vector Fields 9 Differential Properties of Wave Fronts 10 Caustics and Wave Fronts 11 Reflection and Refraction of a Wave Front at the Curved Interface of Two Media 12 Solution of the Eikonal Equation by the Method of Separation of Variables 13 Ray Paths Obtained by the Method of Separation of Variables 14 Scalar Ray Equations in Curvilinear Coordinates: the Principle of Fermat 15 Elements of Hamiltonian Optics Problems References Bibliography Chapter III Plane-Stratified Media 1 Introduction 2 Ray Optics for Stratified Media 3 Matched Asymptotic Expansion: Langer's Method 4 Reflection and Transmission for Arbitrarily Inhomogeneous Media 5 Exact Solution for the Linearly Increasing Transition Profile 6 Stratified Media with Piecewise-Constant Refractive Index Profiles 7 Electric Network Formalism 8 Fresnel Formulas 9 Characteristic Matrix Formalism 10 Bloch Waves 11 Passbands and Stopbands of Quarter-Wave Stacks 12 Reflection Coefficient of a Multilayer 13 Metallic and Dielectric Reflectors 14 Antireflection (AR) Coatings 15 Interference Filters 16 Anisotropie Stratified Media 17 Propagation through Periodic Media 18 Analytical Properties of the Reflection Coefficient 19 Propagation of Surface and Leaky Waves through a Thin Film 20 Illumination at an Angle Exceeding the Critical One 21 Reflection and Refraction at a Dielectric-Lossy Medium Interface 22 Surface Waves at the Interface between Two Media 23 Impedance Boundary Conditions Problems References BibliographyChapter IV Fundamentals of Diffraction Theory 1 Introduction 2 Green's Function Formalism 3 Kirchhoff-Kottier Formulation of the Huygens Principle 4 Sommerfeld Radiation Condition 5 Rayleigh's Form of Diffraction Integrals for Plane Screens 6 Babinet's Principle 7 Diffraction Integrals for Two-Dimensional Fields 8 Plane-Wave Representation of the Field 9 Angular Spectrum Representation 10 Fresnel and Fraunhofer Diffraction Formulas 11 Field Expansion in Cylindrical Waves 12 Cylindrical Waves of Complex Order and Watson Transformation 13 Field Patterns in the Neighborhood of a Focus 14 Reduction of Diffraction Integrals to Line Integrals 15 Coherent and Incoherent Imagery Problems References Bibliography Chapter V Asymptotic Evaluation of Diffraction Integrals 1 Introduction 2 Stationary-Phase Method 3 Shadow Boundaries: Stationary Point near End Point 4 Caustics of Cylindrical Fields: Two Adjacent Stationary Points 5 Field in Proximity to a Two-Dimensional Cusp: A Model for the Impulse Response in the Presence of Defocusing and Third-Order Aberration 6 Steepest-Descent Method 7 Diffraction Effects at a Plane Interface between Two Dielectrics 8 Asymptotic Evaluation of the Diffraction Integrals in Cylindrical Coordinates 9 Asymptotic Series Derived from Comparison Integrals: Chester-Friedman-Ursell (CFU) Method 10 Asymptotic Evaluation of the Field Diffracted from an Aperture 11 Asymptotic Approximations to Plane-Wave Representation of the Field 12 Willis Formulas Problems References Bibliography Chapter VI Aperture Diffraction and Scattering from Metallic and Dielectric Obstacles 1 Introduction 2 Diffraction from a Wedge 3 Diffraction from a Slit 4 Diffraction from a Dielectric Cylinder 5 S-Matrix and Watson-Regge Representation 6 Surface Diffraction Waves 7 Generalized Fermat Principle and Geometric Theory of Diffraction 8 Scattering from a Dielectric Body 9 Physical Optics Approximation for a Perfect Conductor 10 Electromagnetic Theory of Diffraction from Perfectly Conducting and Dielectric Gratings 11 Scattering from Finite Bodies 12 Spherical Harmonics Representation of the Scattered Field 13 Scattering from Spherical Particles Problems References Bibliography Chapter VII Optical Resonators and Fabry-Perot Interferometers 1 Generalities on Electromagnetic Resonators 2 Generalities on Optical Resonators 3 Frequency Response of a Resonator 4 Ray Theory of a Closed Elliptic Resonator 5 Linear Resonators 6 Characterization of Resonators by Means of Lens Sequences and g-Parameters 7 Fields Associated with Sources Located at Complex Points 8 Hermite - Gauss and Laguerre - Gauss Beams 9 Ray-Transfer Matrix Formalism for a Lens Waveguide Equivalent to a Resonator 10 Modal Representation of the Field Inside a Stable Resonator Free of Diffraction Losses 11 Focus on Stable Resonators 12 Focus on Unstable Resonators 13 Wave Theory of Empty Resonators 14 Fox-Li Integral Equations 15 Overview of Mode Calculations 16 Stable Cavities with Rectangular Geometry 17 Rotationally Symmetric Cavities 18 Diffraction Theory of Unstable Resonators 19 Active Resonators 20 Frequency Control 21 Fabry-Perot Interferometers Problems References Bibliography Chapter VIII Propagation in Optical Fibers 1 Geometric Optics 2 Step-Index Fibers 3 Graded-Index Fibers 4 Mode Theory 5 Mode Theory for Step-Index Fibers 6 Weakly Guiding Step-Index Fibers 7 Parabolic-Index Fibers 8 Nonguided Modes 9 Single-Mode Fibers 10 The Electromagnetic Field Inside the Fiber 11 Attenuation 12 Modal Dispersion 13 Chromatic Dispersion 14 Modal Noise 15 Coupled-Mode Theory 16 Statistical Theory of Propagation in an Ensemble of Fibers 17 Polarization-Maintaining Optical Fibers 18 Nonlinear Effects in Optical Fibers 19 Self-Induced Nonlinear Effects Problems References Bibliography Appendix Index