A Framework for Formulating Polychromatic Theories of Emission

The emission of energy as electromagnetic radiation is ubiquitous, in particular because objects release thermal energy in the form of photons. Most theories of thermal radiation assume that the thermal emissions originate from a continuum of elementary monochromatic sources, uncorrelated to each other. The universality of thermal radiation motivates the consideration of theories that allow for more general kinds of elementary emissions. In here, we introduce a framework for formulating polychromatic theories of emission in the electromagnetic Hilbert space, whose computational side is based on the transition matrix, or T-matrix. Each photon is emitted as a coherent polychromatic pulse. The spectra of the different emitted pulses are derived using the natural resonance frequencies of the given finite-size object. Each resonance belongs to one of the orthogonal subspaces which decompose the absorption operator according to the symmetries of the object. Energy conservation in the steady-state is ensured by equalizing the absorption and emission of energy at each individual subspace. The framework can accommodate general illuminations, and produce emissions with frequencies that are much suppressed in or even absent from the illumination, resulting in different rates of emission and absorption of photons. This makes the framework suitable for describing other kinds of emissions, such as luminescence, in the Hilbert space.