Numerically stable eigenmode extraction in 3D periodic metamaterials

TL;DR

This paper introduces a numerically stable and efficient eigenmode extraction method for 3D metamaterials using the Method of Moments, involving a parabolic formulation and iterative linearization to improve accuracy and computational stability.

Contribution

The paper presents a novel eigenmode extraction technique for 3D metamaterials that combines a parabolic formulation with an iterative linearization, enhancing stability and accuracy over existing methods.

Findings

Error decreases doubly exponentially with iteration time

Eigenmodes characterized by transmission coefficients and interstitial currents

Method distinguishes itself from transfer-matrix approaches

Abstract

A numerical method is presented to compute the eigenmodes supported by three dimensional (3D) metamaterials using the Method of Moments (MoM). The method relies on interstitial equivalent currents between layers. First, a parabolic formulation is presented. Then, we present an iterative technique that can be used to linearize the problem. In this way, all the eigenmodes characterized by their transmission coefficients and equivalent interstitial currents can be found using a simple eigenvalue decomposition of a matrix. The accuracy that can be achieved is only limited by the quality of simulation, and we demonstrate that the error introduced when linearizing the problem decreases doubly exponentially with respect to the time devoted to the iterative process. We also draw a mathematical link and distinguish the proposed method from other transfer-matrix based methods available in the literature.