Electromagnetic field quantization in an anisotropic and inhomogeneous magnetodielectric

TL;DR

This paper develops a quantum framework for electromagnetic fields in complex media, modeling anisotropic and inhomogeneous magnetodielectrics with two quantum fields, deriving Maxwell's equations, and calculating susceptibilities.

Contribution

It introduces a novel quantization method for electromagnetic fields in anisotropic, inhomogeneous media using two quantum fields and explicit coupling tensors.

Findings

Derived Maxwell and constitutive equations for the medium

Expressed electric and magnetic polarizations via ladder operators

Calculated susceptibility tensors in terms of coupling tensors

Abstract

The electromagnetic field in an anisotropic and inhomogeneous magnetodielectric is quantized by modelling the medium with two independent quantum fields. Some coupling tensors coupling the electromagnetic field with the medium are introduced. Electric and magnetic polarizations are obtained in terms of the ladder operators of the medium and the coupling tensors explicitly. Using a minimal coupling scheme for electric and magnetic interactions, the Maxwell equations and the constitutive equations of the medium are obtained. The electric and magnetic susceptibility tensors of the medium are calculated in terms of the coupling tensors. Finally the efficiency of the approach is elucidated by some examples.