Finite element modeling of electromagnetic properties in photonic bianisotropic structures

Abstract

Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.

Graphical abstract

Keywords

bianisotropic / finite element method / adjoint

References

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Acknowledgements

The authors acknowledge the financial support from the National Key Research and Development Program of China (No. 2019YFB2203100) and the National Natural Science Foundation of China (Grant No. 11874026).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s12200-021-1213-5 and is accessible for authorized users.

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