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We develop a general and self-consistent formalism to describe the thermal radiation from arbitrary optical resonators made by lossy and dispersive materials like metals and graphene-based on quasi-normal modes (QNM). Our formalism derives the fundamental limit of the spectral thermal emission power from an optical resonator and proves that this limit can be achieved when the mode losses to the emitter and the absorber (or far-field background) are matched, and meanwhile, the predominant resonant mode is electrically quasi-static. We also extend our theory to optical resonators with higher order symmetry, where degenerate and spectrally-adjacent modes are taken into consideration.
With our formalism serving as a general principle of designing the thermal emitters with maximized emission in both near and far-fields, we propose a metamaterial-based structure consisting of patterned doped silicon nanorod emitters that exhibits tunable narrow-band thermal emission. Direct numerical simulation based on the Wiener chaos expansion (WCE) method is performed to accurately investigate the heat transfer mechanism of metamaterials in the near field.
By applying group theory to the geometry of thermal emitter, we identify the existence and the upper limit to the resonance mode degeneracy and its influence on the far-field thermal emission. The existence of the degeneracy proves to be harmful to the far-field thermal. The upper limit of far-field thermal radiation is derived in terms of the coupling strength between degenerate modes. By building up the thermal emitter with higher-order symmetry group, the far-field thermal radiation intensity at certain resonance frequencies turns out to be stronger compared to the single emitter when normalized to the emitting volume. It demonstrates great potential to design the meta-surface with perfect absorption.
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