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Quantum Electronics

Nonlinear absorption spectrum in the field of a weakly saturating standing wave

Oleg V. Belai, David A. Shapiro, S N Yakovenko

Published Nov 30, 2005• 1 citation
Publisher

Abstract

The spectrum of a probe field in a three-level system interacting with a standing wave at the adjacent transition is calculated. The expression for a nonlinear resonance profile is obtained taking into account diffusion in the velocity space in the fourth order of perturbation theory in the standing-wave amplitude.
DOI
10.1070/qe2005v035n11abeh013032

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The probe field spectrum of a three-level A scheme with a strong standing wave at the adjacent transition is calculated numerically taking into account velocity-varying collisions. It is shown that even a small population of the upper level changes the shape of the spectrum and increases the absorption in the line center. Taking into account the excitation of the level and the saturation of the adjacent transition allows a quantitative explanation of the experiment on argon ions in plasma of a high-current discharge.
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The effects of a strong standing wave field on the absorption behaviour of a weak probe field are studied. An absorptive medium is assumed to consist of stationary two-level atoms with arbitrary decay and pumping scheme. The spectrum with a resonant saturator does not exhibit emissive behaviour as in the travelling wave cases. With a detuned saturator the spectrum closely resembles the corresponding three-level spectrum. These features are explained from the standing wave induced spatial selectivity and inhomogeneity. The connections to Doppler-broadened spectra are discussed.
An important problem in saturated absorption spectroscopy is discussed: the width of a nonlinear absorption resonance in a low-pressure gas in a standing wave field. It is shown that the results reported by A.N. Titov et al. are incorrect. These authors stated that at weak saturations the resonance width is of the order of the reciprocal transit time of an atom traveling at the thermal velocity across a light beam. The specific source of the error is indicated, which is an incorrect mathematical treatment of the correct initial equations. It is also shown that the saturated absorption line profile in the transit limit is almost independent of the laser field configuration.
A theory of saturated absorption resonances is developed for the transit range of pressures of an absorbing gas with an arbitrary degree of saturation. The rate equation approximation is used to obtain expressions for the absorption coefficient in the cases of one traveling wave, weak and strong opposite waves, and a standing wave with a rectangular radial distribution of the intensity. An analytic study is made of the behavior of resonance widths when the saturating field intensities are varied and it is shown that, in particular, at relatively low densities the widths are proportional to the fourth root of the intensity.