Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magneto-electric medium

TL;DR

This paper develops a rigorous canonical quantization framework for macroscopic electrodynamics in complex, inhomogeneous magneto-electric media, enabling advanced quantum optical studies in metamaterials with strong dispersion and loss.

Contribution

It introduces a mode expansion-based canonical quantization method applicable to broad classes of inhomogeneous magneto-electric media, extending previous dielectric models.

Findings

Provides a consistent quantum theory for inhomogeneous magneto-electric media.

Enables modeling of quantum optical processes in metamaterials with dispersion and loss.

Offers a foundation for guided wave and cavity quantum optics applications.

Abstract

We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field operators in either a Green function or mode expansion representation. Here we present our results in the mode expansion picture with a view to applications in guided wave and cavity quantum optics.