We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanied by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

An overview is given over some of the most widely used numerical techniques for solving the electromagnetic scattering problem that start from rigorous electromagnetic theory. In particular, the theoretical foundations of the separation of variables method, the finite-difference time-domain method, the finite-element method, the method of lines, the point matching method, the method of moments, the discrete dipole approximation, and the null-field method (or extended boundary condition method) are reviewed, and the advantages and disadvantages of the different methods are discussed. Aspects concerning the T matrix formulation and the surface Green's function formulation of the electromagnetic scattering problem are addressed.

Numerical methods in electromagnetic scattering theory

Electromagnetic fluctuation-induced interactions known as van der Waals, Casimir, and Casimir-Polder forces are an active and exciting area of research. This review summarizes recent progress in this field with emphasis on theoretical and computational developments and their applications to materials including molecular structures, Dirac-like systems, optical metamaterials, composites with nontrivial boundary conditions, and biological matter.

Materials perspective on Casimir and van der Waals interactions

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.

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Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

Preface Acknowledgements 1. Introduction 2. The macroscopic Maxwell equations and monochromatic fields 3. Fundamental homogeneous-medium solutions of the macroscopic Maxwell equations 4. Basic theory of frequency-domain electromagnetic scattering by a fixed finite object 5. Far-field scattering 6. The Foldy equations 7. The Stokes parameters 8. Poynting-Stokes tensor 9. Polychromatic electromagnetic fields 10. Polychromatic scattering by fixed and randomly changing objects 11. Measurement of electromagnetic energy flow 12. Measurement of the Stokes parameters 13. Description of far-field scattering in terms of actual optical observables 14. Electromagnetic scattering by a small random group of sparsely distributed particles 15. Statistically isotropic and mirror-symmetric random particles 16. Numerical computations and laboratory measurements of electromagnetic scattering 17. Far-field observables: qualitative and quantitative traits 18. Electromagnetic scattering by discrete random media: far field 19. Near-field scattering by a sparse discrete random medium: microphysical radiative transfer theory 20. Radiative transfer in plane-parallel particulate media 21. Weak localization 22. Epilogue Appendix A. Dyads and dyadics Appendix B. Free-space dyadic Green's function Appendix C. Euler rotation angles Appendix D. Spherical-wave expansion of a plane wave in the far zone Appendix E. Integration quadrature formulas Appendix F. Wigner d-functions Appendix G. Stationary phase evolution of a double integral Appendix H. Hints and answers to selected problems Appendix I. List of acronyms References Index.

Electromagnetic Scattering by Particles and Particle Groups: An Introduction

T-matrix formulation of electromagnetic scattering from multilayered scatterers

We consider monochromatic electromagnetic scattering from a fixed configuration of an arbitrary number of separate scatteres which are immersed in a medium with constant electric and magnetic properties. Within the scatterers the electric and magnetic properties are assumed to vary smoothly. By considering the integral equations for the scattering we show that the total $T$ matrix for the configuration of the scatterers can be expressed in terms of the $T$ matrices for the individual scatterers in the same way as was previously found for a similar configuration of scatterers, each having a discontinuity in the electric and magnetic properties at the surface and constant electric and magnetic properties in its interior.

T matrix for electromagnetic scattering from an arbitrary number of scatterers with continuously varying electromagnetic properties

Quantum-mechanical elastic scattering from an assembly of nonoverlapping potentials is treated in a $T$-matrix formalism in configuration space. For potentials satisfying a certain fairly weak separation condition, the total $T$ matrix for the assembly of potentials is expressed in terms of the $T$ matrices for the individual potentials. The relation to the equations in $N$-body theory is briefly discussed.

Quantum-mechanical scattering from an assembly of nonoverlapping potentials

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T-matrix formulation of electromagnetic scattering from multilayered scatterers

T matrix for electromagnetic scattering from an arbitrary number of scatterers with continuously varying electromagnetic properties

Quantum-mechanical scattering from an assembly of nonoverlapping potentials