Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium

TL;DR

This paper extends fluctuational electrodynamics to nonlinear materials, deriving a framework to analyze thermal radiation and heat flow, including novel effects like negative emissivity and heat flow reversal.

Contribution

It introduces a perturbative approach to nonlinear fluctuational electrodynamics, incorporating nonlinear optical responses into the fluctuation-dissipation framework.

Findings

Nonlinear optical effects can be incorporated via an effective dielectric function.

Kirchhoff's law requires careful application in nonlinear systems.

Negative spectral emissivity suggests heat flow reversal at certain frequencies.

Abstract

We develop fluctuational electrodynamics for media with nonlinear optical response in and out of thermal equilibrium. Starting from the stochastic nonlinear Helmholtz equation and using the fluctuation dissipation theorem, we obtain perturbatively a deterministic nonlinear Helmholtz equation for the average field, the physical linear response, as well as the fluctuations and Rytov currents. We show that the effects of nonlinear optics, in or out of thermal equilibrium, can be taken into account with an effective, system-aware dielectric function. We discuss the heat radiation of a planar, nonlinear surface, showing that Kirchhoff's must be applied carefully. We find that the spectral emissivity of a nonlinear nanosphere can in principle be negative, implying the possibility of heat flow reversal for specific frequencies.