Prediction of Thermal Emission and Exchange Among Neighboring Wavelength-Sized Spheres

An analysis of radiative emission and radiative exchange among an ensemble of closely spaced, wavelength-sized spheres, in which each sphere in the ensemble is at a distinct and uniform temperature, is presented. We show that the rate of spectral emission from a specific sphere in the ensemble and the rate at which emission is exchanged between a pair of spheres can be deduced from the application of reciprocity and energy conservation principles to the solution of Maxwell’s time harmonic wave equations for a sphere ensemble that is exposed to a plane wave incident field of wavelength $λ$⁠. We show that in the limit of $d∕λ→0$⁠, the emissive exchange between a pair of spheres becomes inversely proportional to the gap thickness $d$⁠. We also show that when the spheres are in the mutual far-field zones of each other, the emissive exchange between the spheres can be well approximated by geometric configuration factors, with an effective area correction to account for finite wavelength effects.