Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

The validity of the Rayleigh hypothesis (RH) has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nano-optics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the RH, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments.