This book explores generalized Lorenz–Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam relying on the method of separation of variables. Although it particularly focuses on the homogeneous sphere, the book also considers other regular particles. It discusses in detail the methods available for evaluating beam shape coefficients describing the illuminating beam. In addition it features applications used in many fields such as optical particle sizing and, more generally, optical particle characterization, morphology-dependent resonances and the mechanical effects of light for optical trapping, optical tweezers and optical stretchers. Furthermore, it provides various computer programs relevant to the content.
In the last years many new developments took place so that a new edition became necessary. This new book now incorporates solutions for many more particle shapes and morphologies, various kinds of illuminating beams, and also to mechanical effects of light, whispering-gallery modes and resonances, and optical particle characterization techniques. In addition, the new book considers localized approximations, on the renewal of the finite series technique, on a new categorization of optical forces, and the study of Bessel beams, Mathieu beams, Laguerre-Gauss beams, frozen waves
Author(s): Gérard Gouesbet, Gérard Gréhan
Edition: 3
Publisher: Springer
Year: 2023
Language: English
Pages: 410
City: Cham
Foreword to the Second Edition
Acknowledgements
Preliminaries
Introduction
Other Books Published by the Authors
Contents
List of Figures
1 Background in Maxwell's Electromagnetism and Maxwell's Equations
1.1 General Maxwell's Equations in Cartesian Coordinates
1.1.1 Maxwell's Equations in Free Space
1.1.2 Maxwell's Equations in Matter
1.1.3 Boundary Conditions
1.1.4 Constitutive Relationships
1.1.5 The Formulation in Fourier Space
1.1.6 Time Harmonic Fields and Complex Representatives
1.2 Special Maxwell's Equations for l.l.h.i Media
1.2.1 Special Maxwell's Equations in Cartesian Coordinate Systems
1.2.2 Special Maxwell's Equations in Orthogonal Curvilinear Coordinate Systems
1.2.3 Special Maxwell's Equations in Spherical Coordinate Systems
1.2.4 Boundary Conditions
1.2.5 Energy Propagation and Poynting Theorem
1.2.6 Momentum Propagation
1.2.7 Wave-Vector, Refractive Index and Impedance
1.2.8 Potentials
2 Resolution of Special Maxwell's Equations
2.1 Special Orthogonal Curvilinear Coordinate Systems and Separability
2.2 Bromwich Potentials
2.2.1 Generalities
2.2.2 Transverse Magnetic Wave
2.2.3 Transverse Electric Wave
2.3 Explicit Time Harmonic Dependence
2.4 Use of Spherical Coordinate Systems
2.5 BSP-Solutions
2.5.1 Reduction to Ordinary Differential Equations
2.5.2 Harmonic Equation
2.5.3 Associated Legendre Equation
2.5.4 Spherical Bessel Equation
2.5.5 General Expressions for BSPs
3 Generalized Lorenz–Mie Theory in the Strict Sense, and Other GLMTs
3.1 The Scattering Problem and Global Strategy
3.2 BSPs for the Incident Wave
3.3 Quadratures to Evaluate BSCs gnm
3.3.1 The First Method to Derive Quadrature Expressions
3.3.2 The Second Method to Derive Quadrature Expressions
3.3.3 Other Approaches
3.4 BSPs for Scattered and Sphere Waves
3.5 Expansions of Field Components
3.6 Boundary Conditions and Generalized Scattering Coefficients
3.7 Scattered Field Components
3.8 Scattered Field Components in the Far Field Region
3.9 Scattered Intensities
3.10 Phase Angle
3.11 Radiative Energy Balance and Associated Cross-Sections
3.11.1 Generalities
3.11.2 Incident Field Balance
3.11.3 Scattering Cross-Section Csca
3.11.4 Extinction Cross-Section Cext
3.12 Momentum Balance and Radiation Pressure
3.12.1 Generalities
3.12.2 Longitudinal Radiation Pressure (z-Direction)
3.12.3 Transverse Radiation Pressure (x and y Directions)
3.13 Efficiency Factors
3.14 Complement, Other GLMTs
4 Gaussian Beams and Other Beams
4.1 Gaussian Beam Description
4.1.1 The Solving Paradox
4.1.2 Elementary Description
4.1.3 Historical
4.1.4 Davis Formulation
4.1.5 The Order L of Approximation
4.1.6 The Order L- of Approximation
4.1.7 Kogelnik's Model
4.1.8 Inaccuracies at Orders L and L-
4.2 GLMT at Orders L and L-
4.2.1 Radial Field Components Er and Hr
4.2.2 Beam Shape Coefficients
4.3 Numerical Computations of Beam Shape Coefficients by Using Quadratures
4.4 Other Beams
5 Finite Series
5.1 The General Procedure
5.2 The NET Procedure for Gaussian Beams
5.2.1 Basic Relations
5.2.2 BSCs gn,TMm, n and m even
5.2.3 Other BSCs gn,TMm
5.2.4 BSCs gn,TEm
5.3 Numerical Computations of BSCs by Using Finite Series
5.3.1 Dimensionless Formulation
5.3.2 Formulae Modifications for Programming
6 Special Cases of Axisymmetric and Gaussian Beams
6.1 Axisymmetric Beams
6.2 The LSC-Decomposition and Gaussian-Like Beams
6.3 Axis Location in a Gaussian Beam
6.4 Lorenz–Mie Theory
6.5 A Theorem for the Special BSCs
6.6 Numerical Computations of Special BSCs by Using Quadratures
6.6.1 Computer Programs
6.6.2 More on the Plane Wave Case
6.6.3 Numerical Behaviour of Quadratures
6.7 Computations of Special BSCs by Using Finite Series
6.7.1 The Formulation
6.7.2 Routines
7 The Localized Approximation and Localized Beam Models
7.1 Generalities
7.2 The Waist Center Location Case
7.2.1 The Principle of Localization
7.2.2 Special BSCs
7.2.3 Numerical Evidence of Validity
7.2.4 Physical Evidence of Validity
7.2.5 Difference of Behaviour Between Rigorous Methods and Localized Approximation
7.3 Axis Location Case
7.4 Arbitrary Location
7.4.1 A Well Posed Problem
7.4.2 BSCs gn+1 and gn-1 for Axis Location
7.4.3 BSCs gnm for Arbitrary Location: First Attempt
7.4.4 Final Generalization
7.4.5 Improved Formulation and Routines
7.4.6 Examples of Results
7.5 Complement on the Localized Approximation
7.6 Complement on the Evaluation of Beam Shape Coefficients
8 Applications, and Miscellaneous Issues
8.1 Measurement Techniques
8.2 Internal Fields and Morphology-Dependent-Resonances
8.3 Mechanical Effects
8.4 Multiple Scattering
8.5 Miscellaneous Topics
9 Conclusion
Appendix A *2ptEvaluation of Quadratures, Rels (3.130摥映數爠eflinkspsIII.1303.1303) and (3.131摥映數爠eflinkspsIII.1313.1313)
Appendix B Evaluation of Quadradures, Rels (3.151摥映數爠eflinkspsIII.1513.1513) and (3.152摥映數爠eflinkspsIII.1523.1523)
Appendix C Evaluation of Quadratures, Rels (3.169摥映數爠eflinkspsIII.1693.1693) and (3.170摥映數爠eflinkspsIII.1703.1703)
Appendix D To Reduce the Double Summations of Chap. 4摥映數爠eflinkchap444 to Single Summations
Appendix E Useful Relations to Derive the BSCs of Chap. 4摥映數爠eflinkchap444
Appendix F Computer Programs
Appendix Supplemental Materials for the Second Edition
Appendix Supplemental Materials for the Third Edition
Appendix References
