Generalized Lorenz-mie Theories

by Gouesbet, Gerard; Grehan, Gerard

• ISBN13: 9783642171932
• ISBN10: 3642171931
• Format: Hardcover
• Copyright: 2011-02-11
• Publisher: Springer Verlag

Summary

The Lorenz-Mie theory, describing the interaction between a homogeneous sphere and an electromagnetic plane wave, is likely to be one of the most famous theories in light scattering. But, with the advent of lasers and their increasing development in various fields, it has become too old-fashioned to meet most of the modern requisites. The book deals with generalized Lorenz-Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam, relying on the method of separation of variables. A particular emphasis is stressed on the case of the homogeneous sphere but other regular particles are considered too. An extensive discussion of the methods available to the evaluation of beam shape coefficients describing the illuminating beam is provided, and several methods are discussed. Applications concern many fields such as optical particle sizing and, more generally, optical particle characterization, morphology-dependent resonances, or mechanical effects of light for optical trapping, optical tweezers and optical stretchers. Various computer programs relevant to the contents of the book are furthermore provided.

Table of Contents

Background in Maxwell's Electromagnetism and Maxwell's Equations	p. 1
General Maxwell's Equations in Cartesian Coordinates	p. 1
Maxwell's Equations in Free Space	p. 2
Maxwell's Equations in Matter	p. 3
Boundary Conditions	p. 5
Constitutive Relationships	p. 6
The Formulation in Fourier Space	p. 8
Time Harmonic Fields and Complex Representatives	p. 10
Special Maxwell's Equations for 1.1.h.i Media	p. 11
Special Maxwell's Equations in Cartesian Coordinate Systems	p. 12
Special Maxwell's Equations in Orthogonal Curvilinear Coordinate Systems	p. 12
Special Maxwell's Equations in Spherical Coordinate Systems013
Boundary Conditions	p. 14
Energy Propagation and Poynting Theorem	p. 15
Momentum Propagation	p. 17
Wave-Vector, Refractive Index and Impedance	p. 18
Potentials	p. 21
Resolution of Special Maxwell's Equations	p. 23
Special Orthogonal Curvilinear Coordinate Systems and Separability	p. 23
Bromwich Potentials	p. 24
Generalities	p. 24
Transverse Magnetic Wave	p. 25
Transverse Electric Wave	p. 28
Explicit Time Harmonic Dependence	p. 29
Use of Spherical Coordinate Systems	p. 30
BSP-Solutions	p. 31
Reduction to Ordinary Differential Equation	p. 31
Harmonic Equation	p. 32
Associated Legendre Equation	p. 33
Spherical Bessel Equation	p. 34
General Expressions for BSPs	p. 35
Generalized Lorenz-Mie Theory in the Strict Sense, and Other GLMTs	p. 37
The Scattering Problem and Global Strategy	p. 37
BSPs for the Incident Wave	p. 39
Quadratures to Evaluate BSCs gmn	p. 40
The First Method to Derive Quadrature Expressions	p. 40
The Second Method to Derive Quadrature Expressions	p. 45
Other Approaches	p. 46
BSPs for Scattered and Sphere Waves	p. 50
Expansions of Field Components	p. 51
Boundary Conditions and Generalized Scattering Coefficients	p. 55
Scattered Field Components	p. 57
Scattered Field Components in the Far Field Region	p. 58
Scattered Intensities	p. 59
Phase Angle	p. 60
Radiative Energy Balance and Associated Cross-Sections	p. 61
Generalities	p. 61
Incident Field Balance	p. 62
Scattering Cross-Section Csca	p. 64
Extinction Cross-Section Cext	p. 64
Momentum Balance and Radiation Pressure	p. 66
Generalities	p. 66
Longitudinal Radiation Pressure (z-Direction)	p. 67
Transverse Radiation Pressure (x and y Directions)	p. 70
Efficiency Factors	p. 75
Complement, Other GLMTs	p. 76
Gaussian Beams and Other Beams	p. 89
	p. 90
The Solving Paradox	p. 90
Elementary Description	p. 92
Historical	p. 93
Davis Formulation	p. 94
The Order L of Approximation	p. 96
The Order L- of Approximation	p. 96
Kogelnik's Model	p. 98
Inaccuracies at Orders L and L-	p. 99
GLMT at Orders L and L-	p. 102
Radial Field Components Er and Hr	p. 102
Beam Shape Coefficients	p. 105
Numerical Computations of Beam Shape Coefficients by Using Quadratures	p. 108
Other Beams	p. 108
Finite Series	p. 117
The General Procedure	p. 117
The NET Procedure for Gaussian Beams	p. 120
Basic Relations	p. 120
BSCs gmn™, n and m Even	p. 124
Other BSCs gmn™	p. 130
BSCs gmn™	p. 135
Numerical Computations of BSCs by Using Finite Series	p. 136
Dimensionless Formulation	p. 136
Formulae Modifications for Programming	p. 137
Special Cases of Axisymmetric and Gaussian Beams	p. 139
Axisymmetric Beams	p. 139
The LSC-Decomposition and Gaussian-Like Beams	p. 141
Axis Location in a Gaussian Beam	p. 145
Lorenz-Mie Theory	p. 150
A Theorem for the Special BSCs	p. 153
Numerical Computations of Special BSCs by Using Quadratures	p. 155
Computer Programs	p. 155
More on the Plane Wave Case	p. 156
Numerical Behaviour of Quadratures	p. 157
Computations of Special BSCs by Using Finite Series	p. 161
The Formulation	p. 161
Routines	p. 165
The Localized Approximation and Localized Beam Models	p. 169
Generalities	p. 169
The Waist Center Location Case	p. 171
The Principle of Localization	p. 171
Special BSCs	p. 171
Numerical Evidence of Validity	p. 172
Physical Evidence of Validity	p. 174
Difference of Behaviour between Rigorous Methods and Localized Approximation	p. 175
Axis Location Case	p. 176
Arbitrary Location	p. 181
A Well Posed Problem	p. 181
BSCs 9+1n and g-1n for Axis Location	p. 182
BSCs gmn for Arbitrary Location: First Attempt	p. 185
Final Generalization	p. 189
Improved Formulation and Routines	p. 190
Examples of Results	p. 191
Complement on the Localized Approximation	p. 191
Complement on the Evaluation of Beam Shape Coefficients	p. 195
Applications, and Miscellaneous Issues	p. 199
Measurement Techniques	p. 199
Internal Fields and Morphology-Dependent-Resonances	p. 211
Mechanical Effects	p. 214
Multiple Scattering	p. 227
Miscellaneous Topics	p. 228
Conclusion	p. 231
Evaluation of Quadratures, Rels (III.130) and (III.131)	p. 233
Evaluation of Quadradures, Rels (III. 151) and (III.152)	p. 235
Evaluation of Quadratures, Rels (III. 169) and (III.170)	p. 237
To Reduce the Double Summations of Chapter IV to Single Summations	p. 241
Useful Relations to Derive the BSCs of Chapter IV	p. 245
Computer Programs	p. 247
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