Casimir forces in multilayer magnetodielectrics with both gain and loss

TL;DR

This paper develops a path-integral quantization method for electromagnetic fields in amplifying magnetodielectric media, calculating Casimir forces in multilayer structures with gain and loss, revealing differences from passive media and bounds on force magnitude.

Contribution

It introduces a novel path-integral approach to quantize fields in amplifying media and computes Casimir forces considering both gain and loss, highlighting key differences from passive systems.

Findings

Casimir force remains attractive in amplifying media.

Different bounds on Casimir force for amplifying versus lossy media.

Identifies essential differences between active and passive layered media.

Abstract

A path-integral approach to the quantization of the electromagnetic field in a linearly amplifying magnetodielectric medium is presented. Two continua of inverted harmonic oscillators are used to describe the polarizability and magnetizability of the amplifying medium. The causal susceptibilities of the amplifying medium, with negative imaginary parts in finite frequency intervals, are identified and their relation to microscopic coupling functions are determined. By carefully relating the two-point functions of the field theory to the optical Green functions, we calculate the Casimir energy and Casimir forces for a multilayer magnetodielectric medium with both gain and loss. We point out the essential differences with a purely passive layered medium. For a single layer, we find different bounds on the Casimir force for fully amplifying and for lossy media. The force is attractive in both cases, also if the medium exhibits negative refraction. From our Lagrangian we also derive by canonical quantization the postulates of the phenomenological theory of amplifying magnetodielectrics.