Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

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

We present a method for determination of the random-orientation polarimetric scattering properties of an arbitrary, nonsymmetric cluster of spheres. The method is based on calculation of the cluster T matrix, from which the orientation-averaged scattering matrix and total cross sections can be analytically obtained. An efficient numerical method is developed for the T-matrix calculation, which is faster and requires less computer memory than the alternative approach based on matrix inversion. The method also allows calculation of the random orientation scattering properties of a cluster in a fraction of the time required for numerical quadrature. Numerical results for the random orientation scattering matrix are presented for sphere ensembles in the form of densely packed clusters and linear chains.

/pdf/calculation-of-the-t-matrix-and-the-scattering-matrix-for-3ji5tntlv0.pdf

Calculation of the T matrix and the scattering matrix for ensembles of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

Electromagnetic scattering by an aggregate of spheres

We use high-quality electrodynamics methods to study the extinction spectra of one-dimensional linear chains and two-dimensional planar arrays of spherical silver nanoparticles, placing emphasis on the variation of the plasmon resonance wavelength and width with array structure (spacing, symmetry), particle size, and polarization direction. Two levels of theory have been considered, coupled dipoles with fully retarded interactions and T-matrix theory that includes a converged multipole expansion on each particle. We find that the most important array effects for particles having a radius of 30 nm or smaller are captured by the couple dipole approach. Our calculations demonstrate several surprising effects that run counter to conventional wisdom in which the particle interactions are assumed to be governed by electrostatic dipolar interactions. In particular, we find that for planar arrays of particles with polarization parallel to the plane the plasmon resonance blue shifts as array spacing D decreases fo...

https://www.phy.duke.edu/~qelectron/group/Zhao_Journal%20of%20Physical%20Chemistry%20B_107.pdf

The Extinction Spectra of Silver Nanoparticle Arrays: Influence of Array Structure on Plasmon Resonance Wavelength and Width†

An outline is provided of the derivation of an order-of-scattering technique that we apply here for the first reported time to the study of light scattering by two or more interacting spheres. This new method provides what is to our knowledge the first complete physical description of the classical processes involved in cooperative EM scattering by an aggregate of spheres. In addition, the algorithms that it employs are often more efficient than those used in an already established method. Comparisons between selected calculations and experimental results are made for linear chains of three and five spheres, and effects of particle orientation are investigated theoretically.

Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I: Linear chains.

The order-of-scattering approach developed earlier [Opt. Lett. 13, 90 (1988)] and applied there to the case of linear chains of spheres is extended to the more difficult problem of scattering by clusters of spheres, the centers of which no longer need lie on a common axis. To help establish the validity of this most general calculation, comparisons are made between theoretical and experimental results for triangular and tetrahedral arrays of spheres. We also perform calculations based on an older method that requires the inversion of matrices, and we find that for the cases considered here the order-of-scattering method is substantially faster.

Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. II: Clusters of arbitrary configuration

Results of experimental measurements and theoretical calculations concerning the scattering of plane wave radiation by a system of two interacting spheres are presented. In particular, the complex scattering amplitude of such a system and the phenomena of specular resonances are addressed. Preliminary calculations of the two-sphere Muller matrix are also considered.

Electromagnetic scattering from two dielectric spheres: further comparisons between theory and experiment.

On aggregation, two identical spheres produce split resonant structures so broadened as to be observable even if their (single) progenitor resonances are narrow beyond detectability.

Kirk A. Fuller

Papers

Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I: Linear chains.

Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. II: Clusters of arbitrary configuration

Electromagnetic scattering from two dielectric spheres: further comparisons between theory and experiment.

Some novel features of morphology dependent resonances of bispheres