Near-field thermal upconversion and energy transfer through a Kerr medium

We present an approach for achieving large Kerr $\chi^{(3)}$--mediated thermal energy transfer at the nanoscale that exploits a general coupled-mode description of triply resonant, four-wave mixing processes. We analyze the efficiency of thermal upconversion and energy transfer from mid- to near-infrared wavelengths in planar geometries involving two slabs supporting far-apart surface plasmon polaritons and separated by a nonlinear $\chi^{(3)}$ medium that is irradiated by externally incident light. We study multiple geometric and material configurations and different classes of interveening mediums---either bulk or nanostructured lattices of nanoparticles embedded in nonlinear materials---designed to resonantly enhance the interaction of the incident light with thermal slab resonances. We find that even when the entire system is in thermodynamic equilibrium (at room temperature) and under typical drive intensities $\sim\mathrm{W}/\mu\mathrm{m}^2$, the resulting upconversion rates can approach and even exceed thermal flux rates achieved in typical symmetric and non-equilibrium configurations of vacuum-separated slabs. The proposed nonlinear scheme could potentially be exploited to achieve thermal cooling and refrigeration at the nanoscale, and to actively control heat transfer between materials with dramatically different resonant responses.