Open AccessMind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids
Author(s) -
Dmitri Schebarchov,
Eric C. Le Ru,
Johan Grand,
Baptiste Auguié
Publication year - 2019
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.27.035750
Subject(s) - superposition principle , multipole expansion , physics , matrix (chemical analysis) , rayleigh scattering , optics , field (mathematics) , scattering , convergence (economics) , spheres , near and far field , statistical physics , computational physics , mathematics , quantum mechanics , materials science , astronomy , pure mathematics , economics , composite material , economic growth
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.