The art of finding the optimal scattering center(s)

TL;DR

This paper introduces a method to find optimal scattering centers in multipole expansions, ensuring unique and efficient spectral representations for modeling optical responses of various scatterers.

Contribution

It derives a novel approach to determine the optimal positions for electric and magnetic scattering centers, improving the efficiency and uniqueness of multipolar decompositions.

Findings

Optimal scattering centers are not co-located with centers of mass.

The approach reduces the complexity of multipolar spectra.

Application to various scatterers enhances numerical modeling efficiency.

Abstract

The efficient use of a multipole expansion of the far field for rapid numerical modeling and optimization of the optical response from ordered and disordered arrays of various structural elements is complicated by the ambiguity in choosing the ultimate expansion centers for individual scatterers. Since the multipolar decomposition depends on the position of the expansion center, the sets of multipoles are not unique. They may require constrained optimization to get the compact and most efficient spatial spectrum for each scatterer. We address this problem by finding {\em the optimal scattering centers} for which the spatial multipolar spectra become unique. We separately derive these optimal positions for the electric and magnetic parts by minimizing the norm of the poloidal electric and magnetic quadrupoles. Employing the long-wave approximation (LWA) ansatz, we verify the approach with the theoretical discrete models and realistic scatterers. We show that the optimal electric and magnetic scattering centers, in all cases, are not co-local with the centers of mass. The optimal multipoles, including the toroidal terms, are calculated for several structurally distinct scattering cases, and their utility for low-cost numerical schemes, including the generalized T-matrix approach, is discussed. Expansion of the work beyond the LWA is possible, with a promise for faster and universal numerical schemes.