$T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles

TL;DR

This paper introduces a $T$-matrix computational method for accurately calculating second-harmonic generation in clusters of spherical particles with diverse optical properties, considering both surface and bulk polarization sources.

Contribution

The paper presents a novel $T$-matrix approach that incorporates both local surface and nonlocal bulk sources for SHG in spherical particle clusters, enhancing accuracy over previous methods.

Findings

Efficient numerical computation of SHG in complex spherical clusters.

Applicable to metallic, dielectric, semiconductor, and polaritonic materials.

Improved modeling accuracy by including bulk polarization sources.

Abstract

In this article, we present a $T$-matrix method for numerical computation of second-harmonic generation from clusters of arbitrarily distributed spherical particles made of centrosymmetric optical materials. The electromagnetic fields at the fundamental and second-harmonic (SH) frequencies are expanded in series of vector spherical wave functions, and the single sphere $T$-matrix entries are computed by imposing field boundary conditions at the surface of the particles. Different from previous approaches, we compute the SH fields by taking into account both local surface and nonlocal bulk polarization sources, which allows one to accurately describe the generation of SH in arbitrary clusters of spherical particles. Our numerical method can be used to efficiently analyze clusters of spherical particles made of various optical materials, including metallic, dielectric, semiconductor, and polaritonic materials.