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American Journal of Physics

Absorption of a pulse by an optically dense medium: An argument for field quantization

P. R. Berman, J.-L. Le Gouët

Published Apr 15, 2011• 2 citations
Publisher

Abstract

The theory of the absorption of a weak optical pulse by an optically dense medium is shown to lead to unphysical results unless the radiation field is quantized. In contrast to the photoelectric effect, the atom-field dynamics for pulsed field absorption can be obtained using elementary quantum mechanics without imposing any assumptions on the nature of the detection process. As such, pulsed field absorption offers distinct advantages over the photoelectric effect as a proving ground for field quantization. If the classical field pulse is replaced by a quantized, multimode field state, many classical field results are recovered without the inconsistencies that arise in the classical field calculation.

DOI
10.1119/1.3549235

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The theory of the absorption of a weak optical pulse by an optically dense medium is shown to lead to unphysical results unless the radiation field is quantized. In contrast to the photoelectric effect, the atom-field dynamics for pulsed field absorption can be obtained using elementary quantum mechanics without imposing any assumptions on the nature of the detection process. As such, pulsed field absorption offers distinct advantages over the photoelectric effect as a proving ground for field quantization. If the classical field pulse is replaced by a quantized, multimode field state, many classical field results are recovered without the inconsistencies that arise in the classical field calculation.
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Abstract In the framework of the consistent microscopic theory, universal analytic expressions describing absorption of laser pulses of an arbitrary duration in an optically dense medium have been derived, and their limiting cases have been considered. For the Gaussian and Lorentzian spectral profiles, simple expressions have been obtained for the absorption coefficient as a function of dimensionless parameters (optical thickness of the medium, the pulse duration and carrier frequency). Based on the performed calculations, the effect of the optical thickness of the medium on the dependences of the absorption coefficient on the pulse parameters has been revealed.
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.
Interactions of a quantized electromagnetic field In the preceding chapters we have studied the quantum properties of the electromagnetic field, but we have treated it as a free or non-interacting quantum system until now. However, both the emission and the absorption of light imply interactions with other quantum systems, and we now turn to the treatment of such interaction problems. It is true that, to a limited extent, we have already succeeded in treating some interactions of light in previous chapters, without invoking the full apparatus of the quantum theory of interacting systems. For example, in Chapter 9 the electromagnetic field was treated as a classical potential acting on an atomic quantum system, and in Sections 12.2 and 12.9 we invoked simple heuristic arguments to describe the operation of certain optical detectors. But these are limited applications, and, in any case, the validity of results obtained in this way needs to be confirmed. To describe the state of a quantized electromagnetic field (F) in interaction with some other quantum system (A), we evidently require an enlarged, or product Hilbert space, which encompasses both F and A, of which the Hilbert spaces of F and A are subspaces. We shall find it convenient to refer to the other system A as an ‘atomic system’, simply to give a name, without restricting the nature of A. The dynamical variables of the field Ô F( t ) and of the atomic system Ô A( t ) commute at the same time t , and at the beginning, when the interaction between them is assumed to be turned on, each operator acts only on the state vectors within its respective Hilbert space.
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.