Temporal coupled mode theory linking to surface-wave dispersion relations in near-field electromagnetic heat transfer

Abstract

We provide a detailed discussion of the use of coupled mode theory to describe near-field heat transfer. We consider a simple physical model system of coupled harmonic oscillators with each oscillator maintaining at a different temperature, where heat transfer between the oscillators can be analytically treated from first-principles using the Newton's equation and the fluctuation dissipation theorem. Applying a slowly varying envelope approximation to the Newton's equation, we derive a coupled mode theory formalism. We then apply this coupled mode theory formalism in the study of the near-field heat transfer between either silicon carbide plates or between two graphene sheets. The coupled mode theory provides a quantitative link between the dispersion relation of the coupled system and the heat transfer, and agrees with exact numerical results over all range of wavevectors. To obtain such complete agreement, the key observation here is that one should include the frequency shift, that is, the frequency of the individual mode used in the coupled mode theory should be different from the frequency of the mode of an isolated structure. Finally, we show that the coupled mode theory can be applied even when more than two modes are involved in the heat transfer. As an example, we extend our formalism to the near-field heat transfer in a four-layer graphene structure.