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Although optical resonators are widely used for controlling and engineeringthermal radiation, what has been lacking is a general theoretical framework toelucidate the thermal emission of optical resonators, and guide the design andapplication of thermally driven optical resonators. We developed a general andself-consistent formalism to describe the thermal radiation from arbitraryoptical resonators made by lossy and dispersive materials like metals, with theonly assumption that the resonators have a single predominant resonance mode.Our formalism demonstrates that the thermal emission of an optical resonator ismaximized when the mode losses to the emitter and the absorber (or far-fieldbackground) are matched, and meanwhile the predominant resonant modes areelectrically quasi-static. By efficiently calculating the resonant modes usingthe finite element methods, our formalism serves as a general principle ofdesigning the arbitrary optical resonator thermal emitters with perfect ormaximized emission.

Quasi-Normal Mode Theory for Thermal Radiation from Lossy and Dispersive Optical Resonators