Light scattering by oblate particles near planar interfaces: on the validity of the T-matrix approach

Abstract

We investigate the T-matrix approach for the simulation of light scattering by an oblate particle near a planar interface. Its validity has been in question if the interface intersects the particle's circumscribing sphere, where the spherical wave expansion of the scattered field can diverge. However, the plane wave expansion of the scattered field converges everywhere below the particle, and in particular at the planar interface. We demonstrate that the particle-interface scattering interaction is correctly accounted for through a plane wave expansion in combination with Fresnel reflection at the planar interface. We present an in-depth analysis of the involved convergence mechanisms, which are governed by the transformation properties between spherical and plane waves. The method is illustrated with the cases of spherical and oblate spheroidal nanoparticles near a perfectly conducting interface, and its accuracy is demonstrated for different scatterer arrangements and materials.

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

“…This is always the case for convex particles. The concept extends our recent work for the case of an oblate particle near a planar interface [16].…”

“…To account for multiple scattering of neighboring particles, the SVWF translation operator can be expressed in a plane wave expansion. In practice, one has to ensure that for a given maximal multipole order of the SWE, the in-plane wavenumber of the PWE is truncated in a regime, where the angular spectrum converges [16]. For low values of the maximal multipole order l max , the accuracy is limited by the multipole truncation error, whereas for large l max , the poor condition number of the linear system becomes prohibitive, compare [16,25].…”

“…The benefit of transforming the outgoing SWE into a PWE has been recently shown for non-spherical particles close to a layer interface [16]. In short, the intermediate transformation of the SWE into a truncated PWE acts as a regularization of the divergent part of the SWE in the near field region.…”

Extending the applicability of the T-matrix method to light scattering by flat particles on a substrate via truncation of sommerfeld integrals

“…Due to the divergence of the spherical wave expansion inside the circumscribing sphere [6], the applicability of the T -matrix method is not obvious for such geometries. Doicu et al [7] have demonstrated numerically that in fact, a surprisingly good accuracy is possible, and in a recent paper [8], we have argued that it is the convergence of the plane wave expansion and not of the spherical wave expansion that ensures a valid treatment of the reflected field from the interface. Thereby, it could be confirmed that the T -matrix method is in general valid also for flat particles on a substrate.…”

“…Thereby, it could be confirmed that the T -matrix method is in general valid also for flat particles on a substrate. However, the spectrum of the plane wave expansion converges not uniformly, but only pointwise with increasing multipole order of the scattered field's original T -matrix representation [8]. This has direct implications for the design of accurate numerical implementations.…”