Degeneracy mediated thermal emission from nanoscale optical resonators with high-order symmetry

Conventional thermal emitters, such as a blackbody or the incandescent filament of a light bulb, lack the directionality or narrow linewidth required in many applications such as thermophotovoltaics and infrared sensing. Although thermal emission from bulk materials is well understood based on phenomenological heat transfer concepts like emissivity and the framework of classical electrodynamics, there still remains a significant gap in our understanding of thermal emission at the nanoscale. In this work, by leveraging the quasi-normal mode theory, we derive a general and self-consistent formalism to describe the thermal radiation from nanoscale resonant thermal emitters with high-order symmetric geometries, which are the basic building blocks of metasurfaces and metamaterials. The complex symmetrical geometries of the emitters yield degeneracy of quasi-normal modes. The introduction of the degeneracy can strongly mediate far-field thermal emission from nanoscale resonators, which is closely correlated to the number of degenerate modes and the coupling among the degenerate modes. Our formalism from the quasi-normal mode theory serves as a general guideline to design the complex metastructures with high-ordered degeneracy to achieve optimized absorption or emission capabilities.