Generalizing Planck's Law: Nonequilibrium Emission of Excited Media

TL;DR

This paper generalizes Planck's law to nonequilibrium media by deriving explicit photon spectral functions and populations, linking emission and absorption in absorbing, dispersing systems, and discussing implications for phenomena like lasing.

Contribution

It introduces a quantum-kinetic framework that explicitly accounts for medium-induced effects, extending Planck's law to nonequilibrium steady states with arbitrary absorption and dispersion.

Findings

Photon spectral functions split into vacuum and medium contributions

Medium-induced photon populations generalize Planck's law in nonequilibrium

Bose distribution with chemical potential describes mode populations in quasi-equilibrium

Abstract

Using a quantum-kinetic many-body approach, exact results for the interacting system of field and matter in a specified geometry are presented. It is shown that both the spectral function of photons and the field fluctuations split up into vacuum- and medium-induced contributions, for which explicit expressions are derived. Using Poynting's theorem, the incoherent emission is analyzed and related to the coherent absorption as may be measured in a linear transmission-reflection experiment. Their ratio defines the medium-induced population of the modes of the transverse electromagnetic field and so generalizes Planck's law to an arbitrarily absorbing and dispersing medium in a nonequilibrium steady state. For quasi-equilibrium, this population develops into a Bose distribution whose chemical potential marks the crossover from absorption to gain and, also, characterizes the degree of excitation. Macroscopic quantum phenomena such as lasing and quantum condensation are discussed on this footing.