Three-Dimensional Time-Harmonic Electromagnetic Scattering Problems from Bianisotropic Materials and Metamaterials: Reference Solutions Provided by Converging Finite Element Approximations

Praveen Kalarickel Ramakrishnan,Mirco Raffetto

doi:10.3390/electronics9071065

Abstract

A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three example problems are considered of which one deals with scattering from plasmonic gratings that exhibit bianisotropy while the other two deal with bianisotropic obstacles inside waveguides. The hypotheses that guarantee the reliability of the numerical results are verified, and the ranges of the constitutive parameters of the media involved for which the finite element solutions are guaranteed to be reliable are deduced. It is shown that, within these ranges, there can be significant bianisotropic effects for the practical media considered as examples. The ensured reliability of the obtained results can make them useful as benchmarks for other numerical approaches. To the best of our knowledge, no other tool can guarantee reliable solutions.

Highlights

Bianisotropic media have important applications in numerous practical problems ranging from the microwave to photonic frequency bands [1,2,3,4]
We demonstrate the application of the theory in [9] to derive the conditions on the constitutive parameters of these problems that guarantee the reliability of the results
The conditions are established on the constitutive parameters of such problems, under which the well posedness and finite element approximability can be guaranteed

Summary

Introduction

Bianisotropic media have important applications in numerous practical problems ranging from the microwave to photonic frequency bands [1,2,3,4]. The electromagnetic problems involving such media admit analytical solutions only in very specialized cases, and numerical simulators are necessary to solve the vast majority of them. In this context, the reliability of the numerical solvers is of utmost importance, and results guaranteeing the well posedness of the problems and the convergence of the numerical solutions are crucial. We demonstrate the application of the theory in [9] to derive the conditions on the constitutive parameters of these problems that guarantee the reliability of the results.

Mathematical Description of the Problem

Results and Discussion

Scattering from Plasmonic Gratings Behaving as Bianisotropic Metamaterials

Scattering from Chiral Obstacles in a Waveguide

Conclusions

Methods