Effect of Curvature on Near-Field Radiative Transfer: The Modified Proximity Approximation

Near-field radiative transfer between two spheres can be computed using Rytov’s theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using an expansion of the dyadic Green’s function of the vector Helmholtz equation in a series of vector spherical waves. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to R_max/d when d/R_max → 0, where R_max is the radius of the larger sphere, and d is the smallest gap between the two spheres. Using this criterion, we show that the surface polariton mediated near–field thermal radiative conductance between two spheres of equal radii R scales as R/d as d/R → 0. We also propose a modified form of the proximity approximation to predict near–field radiative transfer between curved objects from simulations of radiative transfer between parallel surfaces.