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Physical Review A

Quantum theory of optical pulse propagation through an absorbing and dispersive slab

M. Artoni, R. Loudon

Published Feb 1, 1997• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.55.1347

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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 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 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.
The use of instruments in optical experiments needs careful examination with regard to their action on the quantum statistics of radiation. Instruments that respond linearly to radiation may be regarded as spatially structured dielectrics whose presence can be taken into consideration by quantizing the phenomenological Maxwell theory. Since radiation in dielectric matter undergoes dispersion and absorption, the losses must necessarily be included in a quantization scheme. This central problem can be solved by using a novel approach that is based on a Green’s function expansion of the radiation field in place of a mode expansion, which fails when the losses are taken into account. The theory is applied to calculate quantum-theoretically consistent inputoutput relations for dispersive and absorptive multi-slab dielectric plates. Assuming that the polarization field and the electric field are locally related to each other, the phenomenological Maxwell equations governing the propagation of radiation in linear dielectrics, without external sources, can be quantized by supplementing them by an appropriately chosen noise source associated with the losses in the dielectric matter. For the sake of transparency, let us consider a multi-slab dielectric plate with permittivity ε(x, ω) and restrict attention to radiation that propagates along the x axis and is polarized in z direction.
We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.
The problem of quantizing the radiation field inside a nonlinear dielectric is studied. Based on the quantization of radiation in a linear dielectric which includes absorption and dispersion, we extend the theory in order to treat also nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field including the effects of linear absorption and dispersion as well as nonlinear optical effects. As a special case we derive the propagation equation of a narrow-frequency band light pulse in a Kerr medium.