Electromagnetic Scattering by Bianisotropic Spheres

TL;DR

This paper develops a new theoretical framework for electromagnetic scattering by bianisotropic spheres using electromagnetic orbitals, extending Mie theory to complex anisotropic media.

Contribution

Introduction of electromagnetic orbitals as linear combinations of vector spherical harmonics for bianisotropic media, enabling scattering analysis of arbitrary bianisotropic spheres.

Findings

Derived scattering theory for bianisotropic spheres with arbitrary parameters

Provided simple expressions for plane wave expansion in spherical harmonics

Confirmed polarizability results in Rayleigh limit consistent with previous models

Abstract

Electromagnetic fields in bulk bianisotropic media can be represented using plane waves whose k-vectors can be found using the index of refraction operator method and belong to the Fresnel wave surfaces that fall into one of the 5 hyperbolic classes that are used as the taxonomy of bianisotropic media [Durach et al., Appl. Sci., Opt. Comm. (2020), PIER (2022)]. It has been demonstrated that, alternatively, the linear combinations of vector spherical harmonics can be used as a set of solutions of vector Helmholtz equation in gyroelectric, gyromagnetic, and gyrotropic anisotropic media to develop Mie theory of scattering by anisotropic spheres [Lin, Chui, Phys. Rev. E (2004), Li, Ong, Zheng, Phys. Rev. E (2012)]. In this paper we introduce electromagnetic orbitals for bianisotropic media as linear combinations of vector spherical harmonics, which represent a set of solutions of Maxwells equations in bianisotropic media. Using these bianisotropic orbitals we develop a theory of scattering of electromagnetic radiation by bianisotropic spheres with arbitrary effective material parameters and sizes. As a by-product we obtain a simple expression for the expansion of a vector plane wave over vector spherical harmonics (cf. Sarkar, Halas, Phys. Rev. E (1997)). We obtain the polarizability expressions in Rayleigh limit of our theory in agreement with the previous results of the electrostatic approximation [Lakhtakia, J. Phys (1990), Sihvola, Mic. Opt. Tech. Lett. (1994)].