Recursive Calculation of the Optical Response of Multicomponent Metamaterials

Abstract

A recursive computational procedure is developed to efficiently calculate the macroscopic dielectric function of multicomponent metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the microscopic response of the system might correspond to non‐Hermitian operators, a representation of the microscopic fields and of the response is developed, and an appropriate metric that makes all operators symmetric is introduced. This allows one to use a modified Haydock recursion, introducing complex Haydock coefficients that allow an efficient computation of the macroscopic response and the microscopic fields. The procedure is tested by comparing the results with analytical ones in simple systems and verifying whether they obey a generalized multicomponent Keller's and the Mortola and Steffe's theorems for four‐component metallic and dielectric systems.