Fluctuational electrodynamics for nonlinear materials in and out of equilibrium

Abstract

Fluctuational electrodynamics (FE) is a successful and well established theory. By making use of the fluctuation dissipation-theorem (FDT), it ties together the linear response (Green's function) and the strength of thermal and quantum fluctuations in a general formalism. This is applied to diverse problems such as calculating the fluctuational forces (e.g. the Casimir force) or near-field heat transfer for bodies of arbitrary shapes and materials. One major restriction, however, is that the optical response of these materials needs to be linear. Our work seeks to extend FE for optically nonlinear materials. We make use of the facts that, in equilibrium, the FDT itself remains valid even for nonlinear systems and the nonlinearities themselves are small. This allows us to take a perturbative approach. Starting from the stochastic Helmholtz equation in equilibrium, we obtain an effective description of the system, which yields the average electric field, the physical linear response, and the fluctuations. This framework is then applied to obtain the Casimir force in equilibrium, as well as problems out of equilibrium such as radiative heat transfer and the effect of external fields.