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Light Propagation in Linear Optical Media

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

  1. Cover
  2. Half Title
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. About the Authors
  9. 1 Electromagnetic Fields and Origin of Light
    1. 1.1 Introduction
    2. 1.2 Electric Fields
    3. 1.3 Magnetic Fields
    4. 1.4 Electromagnetism
    5. 1.5 Vector and Scalar Potentials
    6. 1.6 Hertz Vector Potential
    7. 1.7 Radiation from an Orbiting Charge
    8. 1.8 Poynting Vector
    9. 1.9 Radiation from a Classical Atom
    10. 1.10 A Quantum Mechanical Interlude
      1. 1.10.1 Blackbody Radiation
      2. 1.10.2 Planck’s Theory of Light Quanta
      3. 1.10.3 Photoelectric Effect
      4. 1.10.4 Einstein's Theory of Photons
      5. 1.10.5 Wave Particle Duality of Matter
      6. 1.10.6 The Particle-Function of Classical Mechanics
      7. 1.10.7 The Wavefunction of Quantum Mechanics
      8. 1.10.8 The Schrödinger Equation
      9. 1.10.9 Wavefunctions of Electrons in a Stable Atom
      10. 1.10.10 Atomic Radiation
    11. 1.11 Units and Dimensions
    12. Bibliography
  10. 2 Electromagnetic Waves in Linear Media
    1. 2.1 Maxwell’s Equations in Linear Media
    2. 2.2 Electromagnetic Waves in Linear Source-Free Media
    3. 2.3 Maxwell’s Equations in Vacuum
    4. 2.4 Plane Waves
    5. 2.5 Polarization States of Light
      1. 2.5.1 Special Case 1: Linear Polarization
      2. 2.5.2 Special Case 2: |øx – – øy| = π/2| = π/2
      3. 2.5.3 Special Case 3: Ax = Ay
    6. 2.6 Spherical Waves
  11. 3 Light Propagation in Anisotropic Crystals
    1. 3.1 Introduction
    2. 3.2 Vectors Associated with Light Propagation
      1. 3.2.1 Plane Waves
      2. 3.2.2 Non-Plane Waves
    3. 3.3 Anisotropic Media
      1. 3.3.1 The Principal Coordinate Axes
      2. 3.3.2 Three Crystal Classes
      3. 3.3.3 The Principal Refractive Indices
    4. 3.4 Light Propagation in an Anisotropic Crystal
      1. 3.4.1 Allowed Directions of D̃ and Ẽ in an Anisotropic Medium
      2. 3.4.2 Values of n for a Given Propagation Direction
      3. 3.4.3 Directions of D and E for the Slow and Fast Waves
    5. 3.5 Characteristics of the Slow and Fast Waves in a Biaxial Crystal
      1. 3.5.1 ns and nf
      2. 3.5.2 ρs and ρf
      3. 3.5.3 The Components of d̂s and d̂f
      4. 3.5.4 The Components of ês and êf
    6. 3.6 Double Refraction and Optic Axes
      1. 3.6.1 Expressions for Components of d̂ in Terms of the Angles θ,ø and Ω and Ω
      2. 3.6.2 Relating the Angle δ to Ω to Ω θ, and ø
      3. 3.6.3 Directions of E and S
      4. 3.6.4 The Walk-Off Angles ρs and ρf
      5. 3.6.5 An Interim Summary
    7. 3.7 Propagation along the Principal Axes and along the Principal Planes
      1. 3.7.1 Introduction
      2. 3.7.2 Propagation along the Principal Axes X, Y, and Z
      3. 3.7.3 Propagation along the Principal Plane YZ
      4. 3.7.4 k along YZ Plane, Case 1: nX &lt; < nY &lt; < nZ
      5. 3.7.5 k along YZ Plane, Case 2: nX &gt; > nY &gt; > nZ
      6. 3.7.6 Propagation along the Principal Plane ZX
      7. 3.7.7 k along ZX Plane, Case 1a: nX &lt; < nY &lt; < nZ, &#952; &lt; &#937; < Ω
      8. 3.7.8 k along ZX Plane, Case 1b: nX &lt; < nY &lt; < nZ, &#952; &gt; &#937; > Ω
      9. 3.7.9 k along ZX Plane, Case 2a: nX &gt; > nY &gt; > nZ, &#952; &lt; &#937; < Ω
      10. 3.7.10 k along ZX Plane, Case 2b: nX &gt; > nY &gt; > nZ, &#952; &gt; &#937; > Ω
      11. 3.7.11 Propagation along the Principal Plane XY
      12. 3.7.12 k along XY Plane, Case 1: nX &lt; < nY &lt; < nZ
      13. 3.7.13 k along XY Plane, Case 2: nX &gt; > nY &gt; > nZ
      14. 3.7.14 Summary of the Cases of Propagation along Principal Planes
    8. 3.8 Uniaxial Crystals
      1. 3.8.1 Field Directions of the D and E Vectors for Extraordinary and Ordinary Waves
      2. 3.8.2 &#961; &#8800; 0 Case (Extraordinary Wave) ≠ 0 Case (Extraordinary Wave)
      3. 3.8.3 Another Expression Relating &#961; and &#952;
      4. 3.8.4 &#961; = 0 Case (Ordinary Wave)
      5. 3.8.5 Two Special Cases: &#952; = 0 and &#952; = 90&#176; = 90°
    9. 3.9 Propagation Equation in Presence of Walk-Off
      1. 3.9.1 Transformation between Laboratory and Crystal Coordinate Systems
      2. 3.9.2 The Propagation Equation in Presence of Walk-Off
    10. Bibliography
  12. 4 Wave Propagation across the Interface of Two Homogeneous Media
    1. 4.1 Reflection and Refraction at a Planar Interface
    2. 4.2 Fresnel Reflection and Transmission Coefficients
    3. 4.3 Reflection and Refraction at an Interface Not Normal to a Cartesian Axis
  13. 5 Light Propagation in a Dielectric Waveguide
    1. 5.1 Conditions for Guided Waves
    2. 5.2 Field Amplitudes for Guided Waves
      1. 5.2.1 TE Modes
      2. 5.2.2 TM Modes
      3. 5.2.3 Evanescent Waves
    3. Bibliography
  14. 6 Paraxial Propagation of Gaussian Beams
    1. 6.1 Introduction
      1. 6.1.1 Paraxial Wave Equation
    2. 6.2 TEM00 Gaussian Beam Propagation and Parameters
    3. 6.3 ABCD Matrix Treatment of Gaussian Beam Propagation
      1. 6.3.1 ABCD Matrices
      2. 6.3.2 Propagation of a Gaussian Beam through Multiple Optical Elements
      3. 6.3.3 Focusing a Gaussian Beam by a Thin Lens
    4. 6.4 Higher-Order Gaussian Beams
      1. 6.4.1 Hermite-Gaussian Beams
      2. 6.4.2 Laguerre-Gaussian (LG) Beams
    5. 6.5 Azimuthal and Radial Polarization
    6. 6.6 M2 Parameter
      1. 6.6.1 Historical Evolution of M2
      2. 6.6.2 Current Usage of M2
    7. Bibliography
  15. 7 Scalar and Vector Diffraction Theories
    1. 7.1 Scalar Diffraction Theories
      1. 7.1.1 Rayleigh-Sommerfeld Diffraction Integral
      2. 7.1.2 Fresnel-Kirchhoff Diffraction Integral
    2. 7.2 Comparisons of Scalar Diffraction Model Calculations
    3. 7.3 Verification of Snell’s Laws Using Diffraction
    4. 7.4 Vector Diffraction Theories
    5. 7.5 Hertz Vector Diffraction Theory (HVDT)
      1. 7.5.1 Double Integral Forms for the Field Components
      2. 7.5.2 Single Integral Forms for the Field Components
    6. 7.6 Kirchhoff Vector Diffraction Theory (KVDT)
    7. 7.7 Analytical On-Axis Expressions and Calculations
      1. 7.7.1 Analytical On-Axis Expressions Using HVDT
      2. 7.7.2 Analytical On-Axis Expressions Using KVDT
    8. 7.8 Power Transmission Function
    9. Bibliography
  16. 8 Calculations for Plane Waves Incident upon Various Apertures
    1. 8.1 Beam Distributions in the Aperture Plane, Circular Aperture
    2. 8.2 Beam Distributions beyond the Aperture Plane for a Circular Aperture
      1. 8.2.1 On-Axis Calculations
      2. 8.2.2 Diffracted Beam Shapes
    3. 8.3 The Longitudinal Component of the Electric Field, Ez
    4. 8.4 Beam Distributions in the Aperture Plane, Elliptical Aperture
    5. 8.5 Beam Distributions beyond the Aperture Plane for an Elliptical Aperture
    6. 8.6 Beam Distributions in the Aperture Plane for a Square Aperture
    7. 8.7 Beam Distributions beyond the Aperture Plane for a Square Aperture
    8. Bibliography
  17. 9 Vector Diffraction across a Curved Interface
    1. 9.1 Introduction
    2. 9.2 Theoretical Setup, Case 1 vs. Case 2
      1. 9.2.1 Case 1, Light Propagation across a Convex Boundary into an Optically Thicker Medium
      2. 9.2.2 Case 2, Light Propagation across a Concave Boundary into an Optically Thinner Medium
    3. 9.3 Vector Diffraction Theory at a Spherical Surface, Case 1
    4. 9.4 Normalization and Simplification, Case 1
    5. 9.5 Calculation of Electromagnetic Fields and Poynting Vectors, Case 1
    6. 9.6 Summary, Case 1
    7. 9.7 Introduction, Case 2
    8. 9.8 Theoretical Setup, Case 2
    9. 9.9 Theory, Case 2
      1. 9.9.1 Normally Incident Light, Case 2
      2. 9.9.2 Light Incident at an Angle, Case 2
    10. 9.10 Normal Incidence Calculations, Case 2
    11. 9.11 Spherical Aberration, Case 2
    12. 9.12 Off-Axis Focusing and Coma, Case 2
      1. 9.12.1 Single Beam
      2. 9.12.2 Two Beams
    13. Bibliography
  18. 10 Diffraction of Gaussian Beams
    1. 10.1 Gaussian Hertz Vector Diffraction Theory, GHVDT
    2. 10.2 Validation of GHVDT
    3. 10.3 Calculations of Clipped Gaussian Beams Using GHVDT
      1. 10.3.1 The Region between Pure-Diffraction and Unperturbed Behavior
      2. 10.3.2 Effect of Diffraction on the M2 Parameter
      3. 10.3.3 Radial and Longitudinal Intensities
      4. 10.3.4 Maximum Obtainable Irradiance for Clipped Gaussian Beams
    4. 10.4 Longitudinal Field Component in the Unperturbed Paraxial Approximation
    5. 10.5 Gaussian Beam Propagation Using Luneberg's Vector Diffraction Theory
    6. 10.6 Analytical Model for Clipped Gaussian Beams
    7. 10.7 Calculations and Measurements for Clipped Gaussian Beams
    8. Bibliography
  19. 11 Trapping Cold Atoms with Laser Light
    1. 11.1 Introduction to Trapping Atoms Using Light Fields
    2. 11.2 Optical Dipole Trapping Potential Energy
    3. 11.3 Diffracted Light Just beyond a Circular Aperture
      1. 11.3.1 Choosing a Propagation Model, HVDT
      2. 11.3.2 Calculated Light Fields and Atom Trap Potentials
    4. 11.4 Projection of Diffraction Patterns
      1. 11.4.1 Choosing a Beam Propagation Model, Fresnel Diffraction
      2. 11.4.2 Projection Calculations
    5. 11.5 Polarization-Dependent Atomic Dipole Traps
      1. 11.5.1 Theory of the Polarization Dependence of the Optical Dipole Trapping Potential Energy
      2. 11.5.2 Computational Results for Atom Traps beyond a Circular Aperture
      3. 11.5.3 Bringing Atom Traps Together and Apart for Two-Qubit Operations
    6. Bibliography
  20. A Complex Phase Notation, Engineer's vs. Physicist&#8217;s
    1. A.1 Sinusoidal Waves
    2. A.2 Complex Notation Using Euler's Formulas
    3. A.3 Engineer's vs. Physicist's Notation
    4. A.4 Use of Engineer's and Physicist's Complex Notation in This Book
    5. A.5 Some Commonly Used Electrodynamics and Optics Books
  21. Index