Principles of Scattering and Transport of Light

Cover
Half-title Page
Title Page
Copyright Page
Dedication
Contents
Foreword
Preface
1 Introduction
References and Additional Reading
Part I Wave Optics
2 Electromagnetic Waves
2.1 Macroscopic Maxwell's Equations
2.2 Wave Equations
2.3 Boundary Conditions
2.4 Energy Conservation
References and Additional Reading
3 Geometrical Optics
3.1 Plane Waves
3.2 Eikonal Equation
3.3 Ray Equation
3.4 Transport of Intensity
References and Additional Reading
4 Waves at Interfaces
4.1 Geometrical Theory of Refraction
4.2 Wave Theory of Reflection and Transmission
4.3 Total Internal Reflection
References and Additional Reading
5 Green's Functions and Integral Representations
5.1 Kirchhoff Integral Formula
5.2 The Green's Function in an Infinite Medium
5.3 Far-Field Radiation Pattern
References and Additional Reading
6 Plane-Wave Expansions
6.1 Plane-Wave Modes
6.2 Weyl Formula
6.3 Beam-Like Fields
References and Additional Reading
7 Diffraction
7.1 Rayleigh–Sommerfeld Formulas
7.2 Fresnel and Fraunhofer Diffraction
7.3 Circular Aperture
References and Additional Reading
8 Coherence Theory: Basic Concepts
8.1 Analytic Signal Representation
8.2 Random Fields and Coherence Functions
8.3 Interferometry
References and Additional Reading
9 Coherence Theory: Propagation of Correlations
9.1 Wolf Equations
9.2 van Cittert–Zernike Theorem
9.3 Coherent Mode Representation
References and Additional Reading
Exercises
Part II Scattering of Waves
10 Scattering Theory
10.1 Integral Equations
10.2 Born Series and Multiple Scattering
10.3 Scattering Amplitude and Cross Sections
10.4 T-matrix
References and Additional Reading
11 Optical Theorem
11.1 Extinguished Power
11.2 Generalized Optical Theorem
References and Additional Reading
12 Scattering in Model Systems
12.1 Point Scatterer
12.2 Collection of Point Scatterers
12.3 Scattering from Spheres of Arbitrary Size
References and Additional Reading
13 Renormalized Perturbation Theory
13.1 Rytov Series
13.2 Geometrical Optics and the Radon Transform
References and Additional Reading
14 Wave Reciprocity
14.1 Fundamental Relation
14.2 Local Form of the Reciprocity Theorem
14.3 Reciprocity of the Green's Function
14.4 Reciprocity of the Scattering Matrix
References and Additional Reading
Exercises
Part III Wave Transport
15 Multiple Scattering: Average Field
15.1 Gaussian Model
15.2 Average Field
15.3 Weak Scattering and Effective Medium
15.4 General Models of Disorder
References and Additional Reading
16 Multiple Scattering: Field Correlationsand Radiative Transport
16.1 Field Correlations
16.2 Wigner Transform
16.3 Radiative Transport
16.4 General Models of Disorder
16.5 Ward Identity
References and Additional Reading
17 Radiative Transport: Multiscale Theory
17.1 High-Frequency Asymptotics
17.2 Multiscale Expansion
References and Additional Reading
18 Discrete Scatterers and Spatial Correlations
18.1 T-matrix of a Discrete Set of Scatterers
18.2 Irreducible Vertex
18.3 Independent Scattering
18.4 Structure Factor
18.5 Correlations
18.6 Transport Mean Free Path
References and Additional Reading
19 Time-Dependent Radiative Transport and Energy Velocity
19.1 Two-Frequency Bethe–Salpeter Equation
19.2 Time-Dependent Radiative Transport Equation
19.3 Nonresonant Scattering
19.4 Resonant Scattering
19.5 Energy Velocity
References and Additional Reading
Exercises
Part IV Radiative Transport and Diffusion
20 Radiative Transport: Boundary Conditions and Integral Representations
20.1 Time-Independent Radiative Transport
20.2 Boundary Conditions and Uniqueness
20.3 Green's Functions and Integral Representations
20.4 Reciprocity
References and Additional Reading
21 Elementary Solutions of the Radiative Transport Equation
21.1 Ballistic Propagation
21.2 Collision Expansion
21.3 Isotropic Scattering
References and Additional Reading
22 Problems with Planar and Azimuthal Symmetry
22.1 Singular Eigenfunctions
22.2 Green's Function
22.3 Diffusion Approximation
References and Additional Reading
23 Scattering Theory for the Radiative TransportEquation
23.1 Integral Equations
23.2 Point Absorbers
References and Additional Reading
24 Diffusion Approximation
24.1 Angular Moments
24.2 Asymptotic Analysis
24.3 Bethe–Salpeter to Diffusion
References and Additional Reading
25 Diffuse Light
25.1 Boundary Conditions
25.2 Homogeneous Media
25.3 Plane-Wave Expansions
25.4 Half-Space Geometry
25.5 Slab Geometry
25.6 Time-Dependent Diffusion
References and Additional Reading
26 Diffuse Optics
26.1 Diffuse Waves
26.2 Wave Properties
26.3 Interference
26.4 Refraction
26.5 Diffraction
References and Additional Reading
27 Scattering of Diffuse Waves
27.1 Integral Equations
27.2 Small Inhomogeneities
27.3 Extinction Theorem
27.4 Surface Integral Equations
References and Additional Reading
Exercises
Part V Speckle and Interference Phenomena
28 Intensity Statistics
28.1 Fully Developed Speckle
28.2 Amplitude Distribution Function
28.3 Intensity Distribution Function
28.4 Speckle Contrast
28.5 Intensity Statistics of Unpolarized Electromagnetic Waves
References and Additional Reading
29 Some Properties of Rayleigh Statistics
29.1 High-Order Moments of the Intensity
29.2 Field and Intensity Correlations
29.2.1 Factorization of the Intensity Correlation Function
29.2.2 Diagrammatic Representation
29.3 Diagrammatic View of Rayleigh Statistics
References and Additional Reading
30 Bulk Speckle Correlations
30.1 Model of Disorder
30.2 Field Correlation Function in the Ladder Approximation
30.3 Intensity Correlation Function
References and Additional Reading
31 Two-Frequency Speckle Correlations
31.1 Two-Frequency Bethe–Salpeter Equation
31.2 Two-Frequency Ladder Propagator
31.3 Field Correlation Function in an Infinite Medium
References and Additional Reading
32 Amplitude and Intensity Propagators for Multiply-Scattered Fields
32.1 Amplitude Propagator
32.1.1 The Scattering Sequences Picture
32.1.2 Rigorous Definition of a Scattering Sequence
32.2 Correlation Function of the Amplitude Propagator
32.3 Correlation Function in an Infinite Medium
32.4 Intensity Propagator
References and Additional Reading
33 Far-Field Angular Speckle Correlations
33.1 Angular Correlation Function
33.2 Field Angular Correlation Function
33.3 Intensity Propagator in the Diffusion Approximation
33.4 Intensity Correlation Function and Memory Effect
33.5 Size of a Speckle Spot
33.6 Number of Transmission Modes
References and Additional Reading
34 Coherent Backscattering
34.1 Reflected Far-Field
34.2 Reflected Intensity
34.3 Reciprocity of the Amplitude Propagator
34.4 Coherent Backscattering Enhancement
34.5 Coherent Backscattering Cone and Angular Width
References and Additional Reading
35 Dynamic Light Scattering
35.1 Single Scattering Regime
35.2 Measured Signal and Siegert Relation
35.3 Multiple-Scattering Regime and Diffusing-Wave Spectroscopy
References and Additional Reading
Exercises
Part VI Electromagnetic Waves and Near-Field Scattering
36 Vector Waves
36.1 Vector Wave Equation
36.2 Energy Conservation
36.3 Reflection and Transmission of Electromagnetic Waves
References and Additional Reading
37 Electromagnetic Green's Functions
37.1 Tensor Green's Function
37.2 Far-Field and Near-Field Asymptotics
37.3 Far-Field Radiated Power
37.4 Plane-Wave Expansion
37.5 Transverse and Longitudinal Green's Function
37.6 Half-Space Green's Function
References and Additional Reading
38 Electric Dipole Radiation
38.1 Far-Field, Near-Field and Quasi-static Limit
38.2 Radiated Power
38.3 Local Density of States
38.4 Local Density of States and Dipole Radiation
38.5 A Simple Classical to Quantum Correspondence
38.6 Purcell Factor
38.7 Cross Density of States
References and Additional Reading
39 Scattering of Electromagnetic Waves
39.1 Integral Equations
39.2 Scattering Amplitude and Cross Sections
39.3 Born Approximation and Rayleigh–Gans Scattering
References and Additional Reading
40 Electromagnetic Reciprocity and the Optical Theorem
40.1 Lorentz Reciprocity Relation
40.2 Consequences of the Reciprocity Theorem
40.3 Conservation of Energy in a Scattering Problem
40.4 Optical Theorem for Electromagnetic Waves
40.5 Integral Theorems
References and Additional Reading
41 Electromagnetic Scattering by Subwavelength Particles
41.1 Polarizability
41.2 Energy Conservation
41.3 Rayleigh and Resonant Scattering
41.4 Near-Field Scattering
41.5 Near-Field Local Density of States
41.6 Discussion
References and Additional Reading
42 Multiple Scattering of Electromagnetic Waves: Average Field
42.1 Model of Disorder
42.2 Average Green's Function
42.3 Self-Energy and the Effective Medium
References and Additional Reading
43 Multiple Scattering of Electromagnetic Waves: Radiative Transport
43.1 Bethe–Salpeter Equation
43.2 Radiative Transport
43.3 Diffusion Approximation and Depolarization
References and Additional Reading
44 Bulk Electromagnetic Speckle Correlations
44.1 Intensity Correlation Function
44.2 Field Correlation Function
44.3 Degree of Spatial Coherence
References and Additional Reading
45 Near-Field Speckle Correlations
45.1 Field Correlation Function in a Semi-Infinite Geometry
45.2 Far-Field Regime
45.3 Near-Field Regime
45.4 Extreme Near-Field
References and Additional Reading
46 Speckle Correlations Produced by a Point Source
46.1 Angular Intensity Correlation Function
46.2 Speckle Correlations and Fluctuations of the Local Density of States
46.3 Single Scattering
References and Additional Reading
Exercises
Index