A T-matrix Based Approach to Homogenize Artificial Materials

TL;DR

This paper introduces a T-matrix based homogenization method that accurately approximates the electromagnetic response of complex artificial materials, enabling efficient analysis of arbitrarily-shaped structures made from structured molecular and metamaterials.

Contribution

The paper presents a novel homogenization approach using an effective T-matrix that captures the response of discrete artificial materials without spatial dispersion, facilitating easier computation.

Findings

Effective T-matrix captures exact response of discrete materials.

Homogenization method is free of spatial dispersion.

Enables response computation of arbitrarily-shaped structured materials.

Abstract

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as three-dimensional lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, we introduce a homogenization method based on the effective T-matrix. Such a matrix captures the exact response of the discrete material, is determined by the T-matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of the effective T-matrix to dipolar order determines the common bi-anisotropic constitutive relations. When combined with quantum-chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily-shaped volumetric patchworks of structured molecular materials and metamaterials.