Generalized Lorenz-Mie Theories (eBook)

Contents 5
Preface 14
Background in Maxwell’s Electromagnetism and Maxwell’s Equations 36
General Maxwell’s Equations in Cartesian Coordinates 36
Maxwell’s Equations in Free Space 37
Maxwell’s Equations in Matter 38
Boundary Conditions 40
Constitutive Relationships 41
The Formulation in Fourier Space 43
Time Harmonic Fields and Complex Representatives 45
Special Maxwell’s Equations for l.l.h.i Media 46
Special Maxwell’s Equations in Cartesian Coordinate Systems 47
Special Maxwell’s Equations in Orthogonal Curvilinear Coordinate Systems 47
Special Maxwell’s Equations in Spherical Coordinate Systems 48
Boundary Conditions 49
Energy Propagation and Poynting Theorem 50
Momentum Propagation 52
Wave-Vector, Refractive Index and Impedance 53
Potentials 56
Resolution of Special Maxwell’s Equations 58
Special Orthogonal Curvilinear Coordinate Systems and Separability 58
Bromwich Potentials 59
Generalities 59
Transverse Magnetic Wave 60
Transverse Electric Wave 63
Explicit Time Harmonic Dependence 64
Use of Spherical Coordinate Systems 65
BSP-Solutions 66
Reduction to Ordinary Differential Equations 66
Harmonic Equation 67
Associated Legendre Equation 68
Spherical Bessel Equation 69
General Expressions for BSPs 70
Generalized Lorenz-Mie Theory in the Strict Sense, and Other GLMTs 72
The Scattering Problem and Global Strategy 72
BSPs for the Incident Wave 74
Quadratures to Evaluate BSCs g_nm 75
The First Method to Derive Quadrature Expressions 75
The Second Method to Derive Quadrature Expressions 80
Other Approaches 81
BSPs for Scattered and Sphere Waves 85
Expansions of Field Components 86
Boundary Conditions and Generalized Scattering Coefficients 90
Scattered Field Components 92
Scattered Field Components in the Far Field Region 93
Scattered Intensities 94
Phase Angle 95
Radiative Energy Balance and Associated Cross-Sections 96
Generalities 96
Incident Field Balance 97
Scattering Cross-Section C_sca 99
Extinction Cross-Section C_ext 99
Momentum Balance and Radiation Pressure 101
Generalities 101
Longitudinal Radiation Pressure (z-Direction) 102
Transverse Radiation Pressure (x and y Directions) 105
Efficiency Factors 110
Complement, Other GLMTs 111
Gaussian Beams and Other Beams 124
Gaussian Beam Description 125
The Solving Paradox 125
Elementary Description 127
Historical 128
Davis Formulation 129
The Order L of Approximation 131
The Order L of Approximation 131
Kogelnik’s Model 133
Inaccuracies at Orders L and L 134
GLMT at Orders L and L 137
Radial Field Components Er and Hr 137
Beam Shape Coefficients 140
Numerical Computations of Beam Shape Coefficients by Using Quadratures 143
Other Beams 143
Finite Series 152
The General Procedure 152
The NET Procedure for Gaussian Beams 155
Basic Relations 155
BSCs gmn,TM, n and m Even 159
Other BSCs gmn,TM 165
BSCs gmn,TE 170
Numerical Computations of BSCs by Using Finite Series 171
Dimensionless Formulation 171
Formulae Modifications for Programming 172
Special Cases of Axisymmetric and Gaussian Beams 173
Axisymmetric Beams 173
The LSC-Decomposition and Gaussian-Like Beams 175
Axis Location in a Gaussian Beam 179
Lorenz-Mie Theory 184
A Theorem for the Special BSCs 187
Numerical Computations of Special BSCs by Using Quadratures 189
Computer Programs 189
More on the Plane Wave Case 190
Numerical Behaviour of Quadratures 191
Computations of Special BSCs by Using Finite Series 195
The Formulation 195
Routines 199
The Localized Approximation and Localized Beam Models 203
Generalities 203
The Waist Center Location Case 205
The Principle of Localization 205
Special BSCs 205
Numerical Evidence of Validity 206
Physical Evidence of Validity 208
Difference of Behaviour between Rigorous Methods and Localized Approximation 209
Axis Location Case 210
Arbitrary Location 215
A Well Posed Problem 215
BSCs g+1n and g 1n for Axis Location 216
BSCs gmn for Arbitrary Location: FirstAttempt 219
Final Generalization 223
Improved Formulation and Routines 224
Examples of Results 225
Complement on the Localized Approximation 225
Complement on the Evaluation of Beam Shape Coefficients 229
Applications, and Miscellaneous Issues 232
Measurement Techniques 232
Internal Fields and Morphology-Dependent-Resonances 244
Mechanical Effects 247
Multiple Scattering 260
Miscellaneous Topics 261
Conclusion 264
Appendix A 266
Appendix B 268
Appendix C 270
Appendix D 273
Appendix E 276
Appendix F 277
References 288