The scattering of electromagnetic radiation by nonspherical particles has become an increasingly important research topic over the past 20 years. Instead of handling anisotropic particles of arbitrary shape, the authors consider the more amenable problem of aggregates of spherical particles. This is often a very satisfactory approach as the optical response of nonspherical particles depends more on their general symmetry and the quantity of refractive material than on the precise details of their shape. The book addresses a wide spectrum of applications, ranging from scattering properties of water droplets containing pollutants, atmospheric aerosols and ice crystals to the modeling of cosmic dust grains as aggregates. In this extended second edition the authors have encompassed all the new topics arising from their recent studies of cosmic dust grains. Thus many chapters were deeply revised and new chapters were added. The new material spans The description of the state of polarization of electromagnetic waves of general form The conservation theorems of combined systems of fields and particles The appropriate multipole expansion for waves of general wave vector and of general state of polarization A number of new applications The effects of radiation pressure and radiation torque on cosmic dust grains A study of the morphology of cosmic dust grains and of the distribution and polarization of the electromagnetic field in the interior of aggregated dust grains
Author(s): F. Borghese
Series: Physics of Earth and Space Environments
Edition: 2
Publisher: Springer
Year: 2006
Language: English
Pages: 357
Tags: Физика;Периодика по физике;Physics of Earth and Space Environments;
3540374132......Page 1
Contents......Page 13
1.1 Introduction......Page 18
1.2 Field Equations......Page 19
1.3 Vector Helmholtz Equation......Page 21
1.4.1 Cartesian Vectors......Page 22
1.4.2 Spin of a Vector Field......Page 23
1.5.1 Representations of the Rotation Operators......Page 25
1.5.2 Spherical Harmonics......Page 28
1.5.3 Spin Eigenvectors......Page 30
1.6.1 Coupling of Angular Momenta......Page 31
1.6.2 Clebsch–Gordan Series......Page 33
1.6.3 Irreducible Spherical Tensors......Page 35
1.6.4 Vector Solutions to the Helmholtz Equation......Page 37
1.6.5 Divergence and Curl of the Vector Helmholtz Harmonics......Page 38
1.7 Multipole Fields......Page 39
1.7.1 Hansen's Vectors......Page 40
1.7.2 Vector Spherical Harmonics......Page 41
1.7.3 Spherical Multipole Fields......Page 43
1.8.1 Nozawa's Theorem......Page 44
1.8.3 Application to Hansen's Vectors......Page 46
2.1 Scattering Amplitude......Page 49
2.2 Cross Sections......Page 51
2.3.1 Nonabsorbing Host Medium......Page 53
2.3.2 Absorbing Host Medium......Page 55
2.4 Scattering by an Ensemble of Particles......Page 56
2.5 Refractive Index of a Dispersion of Particles......Page 58
2.6.1 Incident Plane Wave......Page 60
2.6.2 Scattered Wave and Scattering Amplitude Matrix......Page 62
2.6.3 Polarization of Light and Refractive Index of a Dispersion......Page 63
2.7 Kinematics of a Scattering Process......Page 64
2.7.1 Plane of Scattering......Page 65
2.7.2 The Meridional Plane......Page 66
2.8 Stokes Parameters......Page 68
2.8.1 Phase Matrix, Scattering Matrix and Extinction Matrix......Page 70
2.9 Polarization of Waves of General Form......Page 72
2.9.1 Spectral Density Tensor......Page 74
2.9.2 Spectral Density Stokes Parameters......Page 75
3.1.1 Poynting Theorem......Page 78
3.1.2 Conservation of Linear Momentum......Page 79
3.1.3 Conservation of Angular Momentum......Page 80
3.1.4 Monochromatic Fields......Page 81
3.2.1 Radiation Force......Page 82
3.3 Thermal Emission......Page 84
4.1.1 Plane Waves with Real Propagation Vector......Page 87
4.1.2 Plane Waves with Complex Propagation Vector......Page 90
4.2 Multipole Expansion of the Scattered Field......Page 91
4.2.1 Amplitudes of the Multipole Fields and Cross Sections......Page 92
4.3 Transition Matrix......Page 94
4.3.1 Transformation Properties of the Transition Matrix......Page 95
4.4 Refractive Index of a Polydispersion of Particles......Page 97
4.5 Orientational Averages......Page 98
4.6 Effect of an Electrostatic Field......Page 102
4.6.1 Polarizability of a Particle of Arbitrary Shape......Page 104
4.7 Effect of the Diffusive Motion......Page 106
4.8 Radiation Force on Nonspherical Particles......Page 109
4.8.1 Orientational Averages of Asymmetry Parameters......Page 111
4.9 Radiation Torque on Nonspherical Particles......Page 113
4.9.1 Axial Average of Radiation Torque......Page 118
4.10 Thermal Emission Force on Nonspherical Particles......Page 120
5.1 Homogeneous Spheres......Page 123
5.1.1 Homogeneous Spheres Sustaining Longitudinal Waves......Page 126
5.2 Radially Nonhomogeneous Spheres......Page 128
5.3 Resonances......Page 131
5.4 Aggregates of Spheres......Page 132
5.4.1 T-scheme, E-scheme and Convergence of Calculations......Page 136
5.5 Spheres Containing Spherical Inclusions......Page 139
5.6 Finite Elements Methods......Page 143
5.6.1 Discrete Dipole Approximation......Page 144
5.6.2 Finite Difference Time Domain Method......Page 146
6. Scattering from Particles on a Plane Surface......Page 149
6.1 Incident and Reflected Fields......Page 150
6.2 Perfectly Reflecting Surface......Page 152
6.2.1 Orientational Averages......Page 154
6.3.1 Reflection Rule for H-Multipole Fields......Page 157
6.3.2 Calculation of the Reflected Field......Page 161
6.4 Scattering from a Sphere on a Dielectric Substrate......Page 163
6.4.1 Reflection of the Incident and Scattered Wave......Page 164
6.4.2 Amplitudes of the Scattered Field......Page 165
6.4.3 Scattering Amplitude and Transition Matrix......Page 166
6.5.1 Multipole Expansion of the Fields......Page 168
6.5.2 Transition Matrix for an Aggregate in the Presence of a Surface......Page 171
6.6 Perfectly Reflecting vs. Dielectric Surface: Similarities and Differences......Page 173
6.7 Total Internal Reflection and Evanescent Waves......Page 174
6.7.1 Scattering of Evanescent Waves by Single and Aggregated Spheres......Page 176
7. Applications: Aggregated Spheres, Layered Spheres, and Spheres Containing Inclusions......Page 178
7.1 General Features of Scattering from Aggregated Spheres......Page 179
7.1.1 Comparison with Experimental Data......Page 182
7.1.2 Effect of the Structural Changes......Page 185
7.2 Clusters of Large Spheres......Page 192
7.2.1 Compact Clusters......Page 193
7.2.2 Linear Chains......Page 199
7.2.3 Acceptable Convergence......Page 201
7.3 Clusters in an Electrostatic Field......Page 203
7.4 Extinction from Single and Aggregated Layered Spheres......Page 209
7.4.1 Metal Spheres with a Soft Surface......Page 211
7.4.2 Metal Spheres with a Dielectric Coating......Page 213
7.4.3 Dielectric Spheres with a Metal Coating......Page 214
7.4.4 Metal Spheres with a Metallic Coating......Page 215
7.4.5 Considerations on Convergence......Page 216
7.5 Spheres Sustaining the Propagation of Longitudinal Waves......Page 218
7.6 Spheres Containing Inclusions......Page 221
7.6.1 Metallic Inclusion in a Dielectric Sphere......Page 222
7.6.2 Empty Cavity in a Dielectric Sphere......Page 225
7.6.3 Spheres Containing Two Metallic Inclusions......Page 226
7.6.4 Resonances of a Sphere Containing a Spherical Inclusion......Page 232
7.7 Spheres with Cavities and Depolarization of the Internal Field......Page 237
7.8 Correlation Spectroscopy......Page 241
7.9 Radiation Force on Aggregates of Spheres......Page 246
7.9.1 Binary Clusters......Page 247
7.9.2 Six-Spheres Clusters......Page 249
7.10 Radiation Torque on Aggregated Spheres......Page 252
7.11 Thermal Emission Force on Aggregated Spheres......Page 255
8.1 Aggregated Spheres and Hemispheres on a Metallic Surface......Page 258
8.2 Inclusion-Containing Hemispheres on a Metallic Surface......Page 265
8.3 Resonance Suppression Mechanism......Page 271
8.3.1 Single Hemispheres......Page 272
8.3.2 Binary Clusters......Page 275
8.4.1 Single Spheres......Page 277
8.4.2 Aggregates of Spheres in Fixed Orientation......Page 283
8.4.3 Randomly Oriented Aggregates......Page 287
8.5 Scattering of Evanescent Waves......Page 290
8.5.1 Single Spheres......Page 291
8.5.2 Binary Aggregates......Page 292
9.1 Properties of Atmospheric Ice Crystals in the Infrared......Page 295
9.2 Ice Crystals in the mm Wave Range......Page 301
10.1 Interstellar Dust......Page 310
10.2 Modeling Cosmic Dust Grains as Aggregates......Page 312
10.3 Fluffy Particles......Page 317
10.3.1 Optical Properties of Porous Bare Grains......Page 318
10.3.2 Coated Grains and Clustering......Page 321
10.4 Radiation Pressure on Fluffy Cosmic Dust Grains......Page 324
10.5 Ultraviolet Radiation Within Grain Cavities......Page 330
10.5.1 The Field Inside Central Cavities......Page 331
10.5.2 The Field Inside Interstitial Cavities......Page 332
10.5.3 Field Depolarization......Page 338
A.1 Bessel and Hankel Functions......Page 341
A.2 Spherical Harmonics......Page 342
A.3.2 Orientational Averages......Page 343
A.6 General Approach to the Computational Problem......Page 344
References......Page 346
I......Page 354
R......Page 355
S......Page 356
V......Page 357
