Efficient Numerical Computation of Second-Harmonic Scattering by Clusters of Nanoparticles

In this paper, we introduce a transfer matrix method (TMM) for efficient calculation of second-harmonic generation (SHG) from clusters of nanospheres made of centrosymmetric materials. Different from current TMM formulations, our approach goes beyond the single particle configuration, thus greatly expanding its practical relevance. In addition, we incorporate in our method the contributions of both the surface and bulk nonlinear polarizations. This is especially valuable for the accurate analysis of purely dielectric systems, such as clusters of silicon or silica nanospheres, which are widely used in nanophotonics.