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Soviet Journal of Quantum Electronics

Theory of resonances of saturated absorption in low-pressure gases

N. M. Danileiko, Леонід Петрович Яценко

Published May 31, 1987• 1 citation
Publisher

Abstract

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.

DOI
10.1070/qe1987v017n05abeh009074

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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.
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 three-dimensional theory for the resonant interaction of electromagnetic waves with a gas of two-level atoms is formulated in terms of macroscopic variables. The theory is utilized to find the steady-state attenuation of a plane wave in the presence of another plane wave running in the opposite direction with different amplitude. Contributions are included from the reflection of the oppositely running wave by an induced standing-wave inhomogeneity in the population inversion of the medium. The resulting attenuation and reflection coefficients are expressed as velocity integrals of continued fractions. Correspondence is made with existing gas-laser theories, yielding the formulation of a high-intensity ring-laser theory. Analytic approximations for the coefficients are presented for the Doppler-limit cases of both waves weak, one wave weak, and negligible reflection (rate-equation approximation). More-general cases have been calculated numerically. The attenuation coefficients exhibit a Lamb-dip feature. The relative depth of the dip increases rapidly with power at low saturation levels, slowly at high saturation, and is greater in the attenuation of the weaker wave. The width of the dip is nonlinearly power broadened. The shape of the dip is very nearly Lorentzian, except for one special case at high power in which the line splits. The propagation equations for the two waves are integrated over long absorption paths. A large resulting attenuation increases the relative size of the dip while decreasing the power broadening.
The review deals with resonance phenomena resulting from saturation of low-pressure-gas absorption lines by a coherent optical field, when the spectral lines are inhomogeneously broadened by the Doppler effect. Principal attention is paid to narrow resonances of width much smaller than the Doppler widths, which are produced upon saturation of the absorption by light waves under various experimental conditions (inside and outside the laser resonator, in traveling and standing waves, in spatially separated waves, etc.), owing to different effects (absorption saturation, mode interaction in the laser). Each of the phenomena is considered from both the theoretical and the experimental points of view. The phenomena considered serve as a basis of a new branch of optical spectroscopy, namely nonlinear laser spectroscopy of ultrahigh resolution.
A theoretical analysis is made of the interaction of a spatially bounded plane standing optical wave with a molecular gas at a very low pressure. This theory applies to weak and strong (saturating) fields. Calculations are made of the profile, amplitude, and width of a Lamp dip as a function of the intensity of the saturating field and of the dimensions of the light beam. The role of slow molecules in the formation of the dip is identified. It is shown that in weak saturating fields the width of the resonance is governed by the average thermal velocity of molecules in a gas and by the transverse size of the light beam.