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arXiv:0802.2777 · Physical Review A

Propagation of nonclassical optical radiation through a semiconductor slab

Dmytro Vasylyev, W. Vogel, K. Henneberger, Tim Schmielau, D.‐G. Welsch

Published Sep 29, 2008• 9 citations
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Abstract

Based on a microscopic derivation of the emission spectra of a bulk semiconductor, we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.

DOI
10.1103/physreva.78.033837

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Based on a microscopic derivation of the emission spectra of a bulk semiconductor, we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.
Abstract The combination of methods of micro‐ and macroscopic QED alows one to describe the influence of the absorbtion/ amplification and dispersion effects on the nonclassical radiation propagating through complex material systems. Within the framework of macroscopic QED the input‐otput formalism can be applied in order to include the arbitrary quantum state of the radiation field. On the other hand, the microscopic derivation of the emission spectra of a bulk semiconductor gives the physical interpretation of the noise current operators in the macroscopic theory. As an example, we investigate the propagation of the field being in squeezed vacuum state through a 5 μm ZnSe slab in absorbing and amplifying regimes. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We calculate the effects of perpendicular propagation through a dispersive and absorbing dielectric slab at arbitrary temperatures on specific nonclassical properties of an incident light field. The transmitted signal is assumed to be measured by a detector that receives radiation only from the direction normal to the slab surfaces. Squeezing and nonclassical counting statistics of the transmitted light are evaluated for continuous-wave squeezed states incident on both sides of the slab. The degree of second-order coherence is instead evaluated for an N-photon incident pulse, and the effects of transmission through the slab on its antibunching are calculated.
We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.
We apply a recently developed scheme for electromagnetic field quantization in dispersive and absorbing dielectrics to calculate the effects of perpendicular propagation through a finite-temperature dielectric slab on the properties of an incident pulse of light. The theory applies to incident pulses of nonclassical light and also reproduces the results for classical pulses in the appropriate limit. The transmitted pulse is assumed to be measured by a detector that receives radiation only from the direction normal to the slab surfaces. The Poynting vector of the transmitted light includes contributions from the incident pulse, whose shift in peak position and additional broadening or narrowing are determined, and from the thermal emission of the slab, which tends to a black-body form in the appropriate limits.
Classical optics describes quite successfully the propagation of laser light, both in free-space and inside a transparent medium. On the other hand, neither classical optics nor the conventional formulation of quantum optics can address adequately the propagation of nonclassical light. Nonclassical states of light are usually described by second-quantization operators acting onto the vacuum state of the radiation field, and the corresponding expectation values of the electric and magnetic fields are often zero. Clearly, the description of propagation of nonclassical light requires a direct quantum mechanical treatment of the spatial progression of the field operators. This chapter outlines the main features of propagative quantum optics, and examines more particularly the treatment of propagation through a linear (refractive) medium, and across a refractive interface. In order to facilitate the discussion of the physical ideas, a plane-wave propagation geometry, which greatly simplifies the mathematical treatment, is used.
We calculate the effects of normal transmission through an amplifying dielectric slab on the properties of an incident pulse of light. The transmitted pulse shows shifts in peak position and additional lengthening or shortening with respect to the unamplified incident pulse. The magnitudes of these effects are generally larger than those of the corresponding changes that occur in transparent or attenuating slabs. They are interpreted in terms of the interference of multiply reflected contributions to the transmitted pulse. The theory is valid for pulses of nonclassical light, but the same reshaping occurs for appropriate pulses of classical light.