Finite element analysis of electromagnetic waves in two-dimensional transformed bianisotropic media

Yan Liu (1) , Boris Gralak (2) , Sebastien Guenneau (2)

1 Xidian University
2 EPSILON - EPSILON

We analyze the wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). Starting from the Maxwell-Tellegen’s equations in bianisotropic media, we derive some system of coupled Partial Differential Equations (PDEs) for longitudinal electric and magnetic field components. These PDEs are implemented in FEM using a solid mechanics formulation. Perfectly Matched Layers (PMLs) are also discussed to model unbounded bianisotropic media. The PDEs and PMLs are then implemented in a finite element software, and transformation optics is further introduced to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. In addition, we propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magnetoelectric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that transformation based electromagnetic metamaterials can be extended to bianisotropic media.

Mots clés: Invisibility cloaks; Anisotropic optical materials; Computational electromagnetic methods; Metamaterials

Domaines: Mécanique des solides [physics.class-ph]; Acoustique [physics.class-ph]; Optique [physics.optics]

Yan Liu, Boris Gralak, Sebastien Guenneau. Finite element analysis of electromagnetic waves in two-dimensional transformed bianisotropic media. Optics Express, 2016, 24 (23), pp.26479. ⟨10.1364/OE.24.026479⟩. ⟨hal-01405293⟩