Radiative heat transfer in nonlinear Kerr media

We obtain a fluctuation--dissipation theorem describing thermal electromagnetic fluctuation effects in nonlinear media that we exploit in conjunction with a stochastic Langevin framework to study thermal radiation from Kerr ($\chi^{(3)}$) photonic cavities coupled to external environments at and out of equilibrium. We show that that in addition to thermal broadening due to two-photon absorption,the emissivity of such cavities can exhibit asymmetric,non-Lorentzian lineshapes due to self-phase modulation. When the local temperature of the cavity is larger than that of the external bath, we find that the heat transfer into the bath exceeds the radiation from a corresponding linear black body at the same local temperature. We predict that these temperature-tunable thermal processes can be observed in practical, nanophotonic cavities operating at relatively small temperatures.