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Physical Review A

Quantum theory of optical-pulse propagation through an amplifying slab

M. Artoni, R. Loudon

Published Jan 1, 1998• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.57.622

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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.
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.
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.
Propagation of a light pulse through a dielectric slab is discussed theoretically in this paper. It is exhibited via a multiple-scattering approach that the slab can modify the phase of the pulse's frequency components, so that, when the frequency components are superposed, they cause the peak in the output pulse to appear to travel either faster or slower than in vacuum, depending on whether the slab is absorbing or amplifying. The expressions of the corresponding advancement and delay of the peak are derived and argued to be limited in magnitude by the pulse's duration.
The theoretical descriptions of the main varieties of non–classical light and the principal measures of their specifically quantum properties are outlined. The theories of quantum–optical propagation of the light through slabs of amplifying or attenuating materials are presented and the main features of the quantum noise effects produced by transmission are summarized. It is found that, while quantum light may have lower noise than classical coherent light, transmission through the slab generally increases the noise. Thus initial enthusiasm for practical low–noise advantages of non–classical light has been tempered by the realization that most kinds of optical propagation or processing enhance the noise to near–classical levels.
The reflection and transmission of a pulse through a slab which is doped with two-level or three-level atoms are investigated theoretically. The doped atoms can be passive (absorptive) or active (gain). We find that both the reflected and transmitted pulses can be superluminal simultaneously for the slab doped with absorptive two-level atoms at the slab thickness equal to (2m+1) lambda(0) /4 sqrt[epsilon(b)] (where lambda(0) is the center wavelength of the incident pulse, and epsilon(b) is the background dielectric constant of the slab) or with active three-level atoms at any thickness. By adjusting the thickness or background dielectric constant of the slab, the reflected pulse can be controlled from superluminal to subluminal or vice versa for the slab doped with absorptive two-level or absorptive three-level atoms. The energy percentage in the reflected pulse can also be controlled by changing the thickness of the slab, and the doped atoms.