Canonical quantization of electromagnetic field in the presence of nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion

TL;DR

This paper presents a canonical quantization framework for the electromagnetic field interacting with a complex nonlinear, anisotropic magnetodielectric medium exhibiting spatial-temporal dispersion, using harmonic oscillators and coupling tensors.

Contribution

It introduces a novel quantization method incorporating coupling tensors to model nonlinear anisotropic media with dispersion, extending existing electromagnetic quantization techniques.

Findings

Derived electric and magnetic susceptibility tensors from coupling tensors.

Formulated an integral equation for the electric field in frequency domain.

Solved the integral equation iteratively to arbitrary accuracy.

Abstract

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.