Plane-wave coupling formalism for T -matrix simulations of light scattering by nonspherical particles

Abstract

The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of applicability of the T-matrix method by accounting for the coupling of scattered fields between highly non-spherical particles in close vicinity. This is achieved using an alternative formulation of the translation operator for spherical vector wave functions, based on a plane wave expansion of the particle's scattered electromagnetic field. The accuracy and versatility of the present approach is demonstrated by simulating arbitrarily oriented and densely packed spheroids, for both, dielectric and metallic particles.

Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

“…In this paper, we have focused on random nanocomposites that contain nanospheres at volume fractions below because this range is experimentally accessible [ 43–49 ] and offers an unprecedented control of the magnitude and dispersion of the effective refractive index. [ 19 ] However, our approach can be readily generalized: First, to other types of scatterers, including atoms, molecules, [ 22 ] as well as nanoparticles with other shapes [ 8,29–31,65,66 ] and, second, also to other kinds of particle distributions. Specifically, both random packings [ 13,67–70 ] as well as the transition regime between ordered and disordered packings [ 71–74 ] exhibit a fascinating complexity.…”

“…However, this does not limit the generality of our approach because both nanoparticles with other symmetries as well as atomic and molecular scatterers can be captured within the same framework. [ 8,22,29–35 ] For spherical nanoparticles with a radius of , the electric dipole polarizability can be determined using Mie theory [ 36 ] : where a 1 is the lowest order (electric dipole) Mie coefficient and is the size parameter. [ 2,37 ] By substituting this expression into Equation (1), the composite material's effective refractive index can be readily obtained from .…”

Controlling three-dimensional optical fields via inverse Mie scattering

“…In particular, extending the method to cylindrical scatterers would allow the method to be applied to conventional binary semiconductor manufacturing processes. Furthermore, a plane wave coupling method is needed to improve the accuracy and use of the TMM to be compatible with cylindrical scatterers and substrates as the TMM becomes unstable for the closely packed ensembles of nonspherical scatterers ubiquitous in discrete scatterer optics (34,35). In addition to the plane wave coupling method, it is also possible to use spheroidal basis functions to allow for closer scatterer packing (36).…”

Mind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids

“…The superposition T-matrix method (STM) [9][10][11] generalises the framework to collections of disjoint scatterers, such as a clump of interstellar dust [12,13], a collection of ice crystals [14] or soot particles [15,16] in air, or colloidal clusters of plasmonic nanoparticles in solution [8,[17][18][19]. The major stated restriction of STM method is the condition that the particles' smallest circumscribed spheres should not overlap [9,11,20,21], which has limited its application to either sparse clusters or spherical particles. This "no-overlap" condition can be traced back to Peterson and Ström [9], who used it to avert potential problems when translating the underlying series expansions.…”

“…While the assumption is irrelevant if all the constituent scatterers are spheres [11,32,33], it becomes increasingly more restrictive for highly anisotropic scatterers, effectively ruling out potential studies of densely packed aggregates. Recently, modifications have been proposed [21,34] to overcome this limitation, but at the expense of added complexity and computational demands.…”