Recursive Calculation of the Optical Response of Multicomponent Metamaterials

TL;DR

This paper presents a recursive computational method to efficiently determine the optical response of complex multicomponent metamaterials, accommodating arbitrary geometries and compositions within the long wavelength approximation.

Contribution

A novel recursive approach that simplifies calculating the macroscopic dielectric function of multi-component metamaterials with arbitrary structures.

Findings

Method accurately reproduces analytical results in simple systems.

Results obey generalized Keller's and Mortola-Stefé's theorems.

Efficient computation of microscopic fields and response.

Abstract

We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the microscopic response of the system might correspond to non-Hermitian operators, we develop a representation of the microscopic fields and of the response, and we introduce an appropriate metric that makes all operators symmetric. This allows us to use a modified Haydock recursion, introducing complex Haydock coefficients that allow an efficient computation of the macroscopic response and the microscopic fields. We test our procedure comparing our results to analytical ones in simple systems, and verifying they obey a generalized multicomponent Keller's theorem and the Mortola and Stef\'e's theorem for four component metalic and dielectric systems.