QED in arbitrary linear media: amplifying media

TL;DR

This paper extends a quantum electrodynamics framework to include amplifying media within linear response theory, enabling analysis of electromagnetic phenomena like Casimir forces in such media.

Contribution

The authors generalize a previous QED approach to encompass amplifying media, clarifying its validity and connecting it with earlier quantization methods.

Findings

Derived electromagnetic-field correlation functions for amplifying media

Established conditions for the validity of the generalized theory

Connected the framework with earlier quantization schemes

Abstract

Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium--media that give rise to absorption [Phys. Rev. A \textbf{75}, (2007) 053813]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media. To illustrate the theory, we present the electromagnetic-field correlation functions that determine the Casimir force in the presence of amplifying media.