Light Propagation in Linear Optical Media

1 Electromagnetic Fields and Origin of Light
Introduction
Electric Fields
Magnetic Fields
Electromagnetism
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

2 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

3 Light Propagation in Anisotropic Crystals
Introduction
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

4 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

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

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

7 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

8 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

9 Vector Diffraction across a Curved Interface
Introduction
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

10 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

11 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
Some Commonly Used Electrodynamics and Optics Books