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Physica Scripta

Propagation of quantized light through bounded dispersive and absorptive media

Dmytro Vasylyev, W. Vogel, Klaus Henneberger, Felix Richter

Published Sep 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/2010/t140/014039

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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.
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.
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 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.
We show that using the properties of the photon Green's function one can successfully describe the propagation of arbitrary nonclassical optical radiation through structured materials. In contrast to the similar input-output approach, our method is not restricted neither to the spatial homogeneous matter nor to the specific direction of light beam incidence or outcoupling. Several quantum states of light are addressed in detail, such as Fock, Glauber, and different squeezed light states, and their Green functions are given. Furthermore, it is demonstrated how scattering of light at a slab can be described with Poynting's energy flow vector, and how experimental setups can be modeled.
We present a one-dimensional quantization scheme for the electromagnetic field in arbitrary planar absorbing and dispersive dielectrics, taking into account explicitly the finite extent of media. The complete form of the electric field operator includes a part that corresponds to the free fields incident from the vacuum towards the medium and a particular solution which can be expressed by using the classical Green-function integral representation of the electromagnetic field. By expressing the classical Green function in terms of the light modes of the dielectric structure, we obtain a natural generalization to absorbing media of the familiar method of mode expansion which strictly applies to non-absorbing media. As an application of our mode expansion, we obtain general quantum-optical input-output relations relating the output photon operators in vacuum to the input photon operators and to the reservoir noise operators. The input-output relations obtained are uniquely determined by the knowledge of the classical light modes of the planar system. We finally show that our quantization scheme for arbitrary planar dielectrics satisfies the prescribed equal-time commutation relations of QED.