Temporal coupled-mode theory for thermal emission from multiple arbitrarily coupled resonators

Controlling the spectral response of thermal emitters has become increasingly important for a range of energy and sensing applications. Conventional approaches to achieving arbitrary spectrum selectivity in photonic systems have entailed combining multiple resonantly emissive elements together to achieve a range of spectral profiles through numerical optimization, with a universal theoretical framework lacking. Here, we develop a temporal coupled mode theory for thermal emission from multiple, arbtirarily-coupled resonators. We validate our theory against numerical simulations of complex two- and three-dimensional nanophotonic thermal emitters, highlighting the anomalous thermal emission spectra that can emerge when multiple resonators with arbitrary properties couple to each other with varying strengths.