Light Propagation in Linear Optical Media  book cover
1st Edition

Light Propagation in Linear Optical Media

ISBN 9781138076327
Published March 29, 2017 by CRC Press
388 Pages 166 B/W Illustrations

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Book Description

Light Propagation in Linear Optical Media describes light propagation in linear media by expanding on diffraction theories beyond what is available in classic optics books. In one volume, this book combines the treatment of light propagation through various media, interfaces, and apertures using scalar and vector diffraction theories.

After covering the fundamentals of light and physical optics, the authors discuss light traveling within an anisotropic crystal and present mathematical models for light propagation across planar boundaries between different media. They describe the propagation of Gaussian beams and discuss various diffraction models for the propagation of light. They also explore methods for spatially confining (trapping) cold atoms within localized light-intensity patterns.

This book can be used as a technical reference by professional scientists and engineers interested in light propagation and as a supplemental text for upper-level undergraduate or graduate courses in optics.

Table of Contents

Electromagnetic Fields and Origin of Light
Electric Fields
Magnetic Fields
Vector and Scalar Potentials
Hertz Vector Potential
Radiation from an Orbiting Charge
Poynting Vector
Radiation from a Classical Atom
A Quantum Mechanical Interlude
Units and Dimensions

Electromagnetic Waves in Linear Media
Maxwell’s Equations in Linear Media
Electromagnetic Waves in Linear Source-Free Media
Maxwell’s Equations in Vacuum
Plane Waves
Polarization States of Light
Spherical Waves

Light Propagation in Anisotropic Crystals
Vectors Associated with Light Propagation
Anisotropic Media
Light Propagation in an Anisotropic Crystal
Characteristics of the Slow and Fast Waves in a Biaxial Crystal
Double Refraction and Optic Axes
Propagation along the Principal Axes and Along the Principal Planes
Uniaxial Crystals
Propagation Equation in Presence of Walk-Off

Wave Propagation across the Interface of Two Homogeneous Media
Reflection and Refraction at a Planar Interface
Fresnel Reflection and Transmission Coefficients
Reflection and Refraction at an Interface Not Normal to a Cartesian Axis

Light Propagation in a Dielectric Waveguide
Conditions for Guided Waves
Field Amplitudes for Guided Waves

Paraxial Propagation of Gaussian Beams
TEM00 Gaussian Beam Propagation and Parameters
ABCD Matrix Treatment of Gaussian Beam Propagation
Higher-Order Gaussian Beams
Azimuthal and Radial Polarization
M2 Parameter

Scalar and Vector Diffraction Theories
Scalar Diffraction Theories
Comparison of Scalar Diffraction Model Calculations
Verification of Snell’s Laws Using Diffraction
Vector Diffraction Theories
Hertz Vector Diffraction Theory (HVDT)
Kirchhoff Vector Diffraction Theory (KVDT)
Analytical On-Axis Expressions and Calculations
Power Transmission Function

Calculations for Plane Waves Incident Upon Various Apertures
Beam Distributions in the Aperture Plane, Circular Aperture
Beam Distributions beyond the Aperture Plane for a Circular Aperture
The Longitudinal Component of the Electric Field, Ez
Beam Distributions in the Aperture Plane, Elliptical Aperture
Beam Distributions beyond the Aperture Plane for a Elliptical Aperture
Beam Distributions in the Aperture Plane for a Square Aperture
Beam Distributions beyond the Aperture Plane for a Square Aperture

Vector Diffraction across a Curved Interface
Theoretical Setup, Case 1 vs. Case 2
Vector Diffraction Theory at a Spherical Surface, Case 1
Normalization and Simplification, Case 1
Calculation of Electromagnetic Fields and Poynting Vectors, Case 1
Summary, Case 1
Introduction, Case 2
Theoretical Setup, Case 2
Theory, Case 2
Normal Incidence Calculations, Case 2
Spherical Aberration, Case 2
Off-Axis Focusing and Coma, Case 2

Diffraction of Gaussian Beams
Gaussian Hertz Vector Diffraction Theory, GHVDT
Validation of GHVDT
Calculations of Clipped Gaussian Beams Using GHVDT
Longitudinal Field Component in the Unperturbed Paraxial Approximation
Gaussian Beam Propagation Using Luneberg’s Vector Diffraction Theory
Analytical Model for Clipped Gaussian Beams
Calculations and Measurements for Clipped Gaussian Beams

Trapping Cold Atoms with Laser Light
Introduction to Trapping Atoms Using Light Fields
Optical Dipole Trapping Potential Energy
Diffracted Light Just beyond a Circular Aperture
Projection of Diffraction Patterns
Polarization-Dependent Atomic Dipole Traps

Appendix: Complex Phase Notation, Engineer’s vs. Physicist’s
Sinusoidal Waves
Complex Notation Using Euler’s Formulas
Engineer’s vs. Physicist’s Notation
Use of Engineer’s and Physicist’s Complex Notation in This Book
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"The material supplied covers a specific area of electromagnetic analysis that is not usually encountered in optics books. The thorough mathematical analysis of the diffraction process could be of great interest to researchers in the field. The book includes also specific introductory chapters on the approaches for studying light, and specifically the electromagnetic approach. The sections of the chapters regarding anisotropic media are also quite detailed. The book is written by recognized researchers in the field."
–Dr. Félix Fanjul-Vélez, Applied Optical Techniques Group Electronics Technology, Systems and Automation Engineering Department, University of Cantabria, Santander, Spain