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Physical Review B

Generalized radiation law for excited media in a nonequilibrium steady state

F. Richter, Matthias Florian, K. Henneberger

Published Nov 20, 2008• 29 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.78.205114

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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.
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. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The presence of a medium boundary has been a major obstacle for the theoretical description of the propagation, emission and absorption of light due to the loss of translational invariance. We present a nonequilibrium photon Green's function theory that is valid for bounded (i.e., spatially inhomogeneous) media systems and also yields an energy flow law which can be seen as a generalization of the Kirchhoff and Planck laws to nonequilibrium. With the help of this law, we discuss mechanisms of emission and optical signatures of quantum condensates. An important finding is that the components of the photon GF, which describe field-field fluctuations, decompose universally into two parts related to medium kinetics and external light sources. Thanks to their specific structure, the propagation of arbitrary (even nonclassical) light can be analyzed straightforwardly. These properties are used to demonstrate the energy flux and scattering of squeezed light incident on the medium.
We present a quantum-kinetically exact theoretical framework for the propagation, emission and scattering of light in bounded media in the context of semiconductor optics. The theory is based on the nonequilibrium photon Green's functions. Its advantage is that the spatial inhomogeneity inherent to bounded media and, hence, to many semiconductor optics problems, is fully and exactly considered. The electromagnetic properties of media are treated microscopically rather than in an effective approximation, and media may be arbitrarily dispersive and absorptive. Relations for the propagation of quantized (squeezed) light as well as for the energy transport of incident and emitted light are given and discussed.
The nonequilibrium photon Green function for a bounded medium surrounded by vacuum is analyzed on the basis of the Dyson equation. As its components, the field-field fluctuations as well as the spectral function split up into parts related to medium and vacuum. Particularly, it is shown that the vacuum-induced fluctuations describe propagation of arbitrary, even nonclassical light in terms of solutions of the classical wave propagation problem. The results generalize previously obtained ones for steadily excited media in slab geometry.
The photon Green function for a system consisting of a bounded medium surrounded by vacuum is analyzed on the basis of the Dyson equation. It is found that the fluctuations of the light field decompose universally into contributions arising from generation and recombination processes in the medium, and those arising from an external electromagnetic stimulation, i.e., light incident from the vacuum. This proves to be advantageous for further quantum-kinetically exact analysis of the interplay in the coupled system of light and matter. Particularly, it is shown that arbitrary (even nonclassical) externally induced light always propagates according to the classical wave propagation problem. These results are valid for arbitrary nonequilibrium situations, regardless of specific optical properties or geometrical shapes of the matter. For demonstration, exact relations for the scattering of squeezed light by a steady-state semiconductor slab are derived on this footing.
Here, we present a new method for description of the propagation of light in bounded media. Our approach is based on the property of photon Green functions to split up into parts corresponding to medium- and vacuum-induced contributions to the field–field fluctuations. Our results apply independently of specific optical properties or geometrical shapes of the matter for arbitrary nonequilibrium situations. As an example, the transmission of an optical field in a squeezed vacuum through a semiconductor slab is discussed and a comparison of the present approach with the input–output formalism is given.