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

Abstract : 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.
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Submitted on : Wednesday, May 10, 2017 - 10:25:56 AM
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Yan Liu, Boris Gralak, Sebastien Guenneau. Finite element analysis of electromagnetic waves in two-dimensional transformed bianisotropic media. Optics Express, Optical Society of America, 2016, 24 (23), pp.26479. ⟨10.1364/OE.24.026479⟩. ⟨hal-01405293⟩

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