A Polychromatic Theory of Emission

The control of thermal radiation by means of micro-structured materials is an active area of research with applications such as thermophotovoltaics and radiative cooling. The original theories of thermal radiation, derived for electromagnetically large objects, predict unpolarized, omnidirectional and uncorrelated radiation. Microstructures, however, exhibit thermal emissions that can be polarized, highly directional, and spatially and temporally correlated. The original theories are also restricted to thermal equilibrium situations. In particular, they do not apply to steady-state emissions of electromagnetically small objects under a stationary illumination, where one expects significant differences in the shape and number of photons of the illuminating and emitted spectra, much as what happens when an object is under the sun. In here, we establish a polychromatic framework to predict thermal radiation in the stationary regime, which includes thermal equilibrium. After identifying an object-dependent set of independent polychromatic absorption modes, we assume that the emission also occurs independently through the outgoing versions of each polychromatic mode. Energy conservation leads then to a Kirchhoff-like law for each polychromatic mode. The salient properties of the polychromatic theory are: Emission in frequencies absent in the illumination, change in the number of photons, and applicability to both thermal radiation and luminescence upon illumination with a continuous wave laser, as long as the emitted power depends linearly on the input intensity. These properties are independent of the chosen set of polychromatic modes. In this work, we chose the absorption modes derived from the scattering operator of a given object. Some counter-intuitive results motivate the future search for a different set of modes.