Generalized radiation law for excited media in a nonequilibrium steady state

We consider the interacting system of light and matter and present quantum-kinetically exact relations for the propagation of light through arbitrarily absorbing and dispersive steadily excited media in a specified geometry. We arrive at an energy flow law which may be regarded as a generalization of the Kirchhoff and Planck radiation laws to nonequilibrium. The field fluctuations are shown to generally split up into medium- and vacuum-induced contributions, of which only the latter governs the energy transport between the medium and the environment. A thorough derivation of the law is given and it is discussed together with interesting details in the underlying relations and physics. Especially, in the context of excited semiconductors, quasiequilibrium emission and lasing, as well as spectral features in the presence of quantum condensation are addressed.