Electromagnetic field quantization in an anisotropic magnetodielectric medium with spatial-temporal dispersion

TL;DR

This paper develops a quantum framework for electromagnetic fields in complex anisotropic magnetodielectric media with spatial-temporal dispersion, using harmonic oscillators to model the medium's properties.

Contribution

It introduces a novel quantization method for electromagnetic fields in anisotropic, inhomogeneous media with dispersion, linking susceptibilities to medium-field coupling tensors.

Findings

Explicit electromagnetic field operators derived

Maxwell and constitutive equations obtained as Heisenberg equations

Medium susceptibilities expressed via coupling tensors

Abstract

By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent set of harmonic oscillators, electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are expressed as linear combinations of the ladder operators describing the magnetodielectric medium. The Maxwell and the constitutive equations of the medium are obtained as the Heisenberg equations of the total system. The electric and magnetic susceptibilities of the medium are obtained in terms of the tensors coupling the medium with the electromagnetic field. The explicit forms of the electromagnetic field operators are obtained in terms of the ladder operators of the medium.