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

Abstract

The T-matrix framework offers accurate and efficient modelling of electromagnetic scattering by nonspherical particles in a wide variety of applications ranging from nano-optics to atmospheric science. Its analytical setting, in contrast to purely numerical methods, also provides a fertile ground for further theoretical developments. Perhaps the main purported limitation of the method, when extended to systems of multiple particles, is the often-stated requirement that the smallest circumscribed spheres of neighbouring scatterers not overlap. We consider here such a scenario with two adjacent spheroids whose aspect ratio we vary to control the overlap of the smallest circumscribed spheres, and compute far-field cross-sections and near-field intensities using the superposition T-matrix method. The results correctly converge far beyond the no-overlap condition, and although numerical instabilities appear for the most extreme cases of overlap, requiring high multipole orders, convergence can still be obtained by switching to quadruple precision. Local fields converge wherever the Rayleigh hypothesis is valid for each single scatterer and, remarkably, even in parts of the overlap region. Our results are validated against finite-element calculations, and the agreement demonstrates that the superposition T-matrix method is more robust and broadly applicable than generally assumed.

Analytical solutions for the surface‐ and orientation‐averaged SERS enhancement factor of small plasmonic particles

“…[37] For this, it will be necessary to derive low-order approximations of the superposition T-matrix method. [38,39]…”

Orientation Averaging of Optical Chirality Near Nanoparticles and Aggregates

“…Our custom-built computer program for the scatterer-centred superposition T -matrix method is based on the algorithms described in Refs. [46,58] and has been tested against FEM simulations [48]. The validity of Eqs.…”

“…These results illustrate the power of analytical results enabled by the T -matrix method, which can provide rapid, accurate, and physically-insightful simulations of a vast range of nanostructures. We hope to encourage more researchers to adopt this method in their comparisons to experiments, but also to further improve the method beyond its current limitations [48,49].…”

Orientation dependence of optical activity in light scattering by nanoparticle clusters

“…Our simulations are performed using a rigorous solution of Maxwell's equations for multi-particle clusters, the superposition T-matrix method. 40,[44][45][46] In this framework, incident and scattered fields are expressed in bases of vector spherical waves; the scattering properties of the cluster are thereby captured in a way that is independent of the incident field, leading to efficient calculations for multiple independent incident fields, and to analytical formulas for orientation-averaged properties. These provide accurate benchmark results against which the performance of numerical methods can be tested.…”