Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media

TL;DR

This paper uses finite element analysis to study electromagnetic wave propagation in two-dimensional bianisotropic media, applying transformation optics to design metamaterials with cloaking and other functionalities.

Contribution

It introduces a finite element framework for bianisotropic media, deriving coupled PDEs, implementing PMLs, and designing metamaterials with effective anisotropic properties.

Findings

Finite element method effectively models wave propagation in bianisotropic media.

Transformation optics enables design of cloaks, concentrators, and rotators.

Homogenization approach allows metamaterials to mimic bianisotropic properties.

Abstract

We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.