For 75 years it has been known that radiative heat transfer can exceed far-field blackbody rates when two bodies are separated by less than a thermal wavelength. Yet an open question has remained: what is the maximum achievable radiative transfer rate? Here we describe basic energy-conservation principles that answer this question, yielding upper bounds that depend on the temperatures, material susceptibilities, and separation distance, but which encompass all geometries. The simple structures studied to date fall far short of the bounds, offering the possibility for significant future enhancement, with ramifications for experimental studies as well as thermophotovoltaic applications.
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