A T‐Matrix Based Approach to Homogenize Artificial Materials

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 3D 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, a homogenization method based on the effective transition (T-)matrix, $T_{eff}$ is introduced. 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 $T_{eff}$ 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.