Fluctuational electrodynamics for nonlinear media

TL;DR

This paper extends fluctuational electrodynamics to nonlinear media by developing a perturbative approach that incorporates nonlinear optical responses into the fluctuation-dissipation framework, enabling analysis of Casimir forces in nonlinear systems.

Contribution

It introduces a perturbative method to include nonlinear optical effects in fluctuational electrodynamics, linking local fluctuations to the linear response of objects.

Findings

Casimir force calculations for nonlinear objects show deviations from linear predictions at small distances.

The developed theory aligns with the fluctuation dissipation theorem in nonlinear media.

Large separation Casimir forces approach linear optics results.

Abstract

We develop fluctuational electrodynamics for media with nonlinear optical response. In a perturbative manner, we amend the stochastic Helmholtz equation to describe fluctuations in a nonlinear setting, in agreement with the fluctuation dissipation theorem, and identify the local (Rytov) current fluctuations. We show how the linear response (the solution of the scattering problem) of a collection of objects is found from the individual responses, as measured in isolation. As an example, we compute the Casimir force acting between nonlinear objects which approaches the result for linear optics for large separations, and deviates for small distances.