Stored electromagnetic energy and radiated power by spherical thermal micro/nano-emitters: Radiation Q-factor

Abstract

We examine theoretically (based on fluctuational electrodynamics) the stored electromagnetic energy and radiated power by a spherical thermal emitter. Moreover, we propose a measure for the radiation quality Q-factor for a polychromatic source such as a thermal emitter. We consider that the thermal emitter is made of tungsten and silicon carbide and we study in detail how the aforementioned radiative quantities depend on size and temperature of the antenna. Particularly, we obtain the emissivity (ratio of spectral radiated power by emitter and that by an ideal blackbody), and the spectral density of stored electromagnetic energy normalized with respect to that of a blackbody. For a SiC-emitter, the emissivity and the normalized spectral stored density energy exhibit multiple narrow peaks associated with surface phonon-polariton and whispering gallery mode resonances; while for a W-antenna, high ohmic losses yield broad spectra of the aforementioned quantities (only an interband resonance appears). These spectra depend strongly on particle size; the corresponding unnormalized spectra are perturbed by the temperature. There is an optimal size of the antenna for which the emissivity is maximal; the aforementioned materials yield an emissivity larger than one. The radiation Q-factor decreases as particle radius and temperature increase, implying that the radiation efficiency of a thermal emitter increases as these parameters grow. The Q-factor for a W-antenna is smaller than that for a SiC-antenna (same size and temperature) for nano-scale particles, whereas, for micrometric particles, the opposite happens over a certain temperature range. Our work might have implications for infrared sources and thermophotovoltaics.