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Physical Review A

Nonlinear absorption of monochromatic radiation near a gas-medium resonance

J. I. Cotrim Vasconcellos

Published Jan 1, 1979• 1 citation
Publisher

Abstract

Using the exact solution for a sine-driven two-level system we have calculated the nonlinear absorption coefficient of a gas of two-level molecules with homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms. We have studied the dependence of the form of the absorption lines on relaxation parameters, on the strength of the electric field, and for various ratios between the homogeneous and inhomogeneous linewidths. We include considerations about saturation of the medium caused by the external field that gives rise to the so-called power broadening of the spectral lines. The dependence of the linewidth on the saturation parameters and on the relaxation parameters is determined. These parameters appear in the ratio of the purely homogeneous and purely inhomogeneous linewidths. Asymptotic behaviors of this linewidth for the homogeneous limit and for the inhomogeneous limit are also determined.

DOI
10.1103/physreva.19.280

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Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jun 30, 1978•12 citations
Using the exact solution for a sine-driven two-level system we have calculated the nonlinear absorption coefficient of a gas of two-level molecules with homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms. We have studied the dependence of the form of the absorption lines on relaxation parameters, on the strength of the electric field, and for various ratios between the homogeneous and inhomogeneous linewidths. We include considerations about saturation of the medium caused by the external field that gives rise to the so-called power broadening of the spectral lines. The dependence of the linewidth on the saturation parameters and on the relaxation parameters is determined. These parameters appear in the ratio of the purely homogeneous and purely inhomogeneous linewidths. Asymptotic behaviors of this linewidth for the homogeneous limit and for the inhomogeneous limit are also determined.
Using the exact solution for a sine-driven two-level atom we have calculated the nonexponential attenuation experienced by a monochromatic electromagnetic beam nearly resonant with a gas of two-level atoms. The atoms are assumed to undergo collision, spontaneous decay plus inhomogeneous (Doppler, etc.) broadening. Resulting intensity-vs-distance plots for a plane wave are given for various degrees of relative homogeneous and inhomogeneous linewidths, for several saturation conditions and for several detuning frequencies. A comparison is also made with collision-broadened and linear attenuation regimes.
We have calculated t he nonlinear real index of refraction variations of a gas medium due to a strong monochromatic radiation causing saturation effects. The gas is supposed to be composed of two-leve1 molecules with which the externa1 field is nearly resonant. We assume homogeneous (hard collisions, sponfaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms acting on the real index of refraction of the medium. The nonlinear dispersion of the medium is studied as a function of the detuning f requencies, saturation c onditions and for various ratios between the homogeneous and inhomogeneous linewidths. In particular, the modification of the index of refraction due to saturation effects are emphasized. Calculamos as v ariacoes do ind ice de refracao real nao-l inear de um meio gasoso devidas a uma radiacao monocromatica intensa que causa efeitos de saturacao. Supoe-se que o gas seja composto de moleculas de dois n iveis com as quais o campo externo e quase ressonante. Supomos mecan i smos de alargamento homogeneos (c01 isoes duras, deca imento espontâneo) e inomogeneas (efeito Doppler) a gindo sobre o ind ice de refracao real do meio. A dispersao nao - linear do meio e estudada como uma funcao das frequencias de detuningl', das condicoes de saturacao e para varias razoes entre as larguras de l inha homogeneas e inomogeneas. Em part icular, sao enfat izadas as mod if icacoes do ind ice de refracao dev idas a ef e i tos de saturacao.
We consider in this paper the Doppler-broadened absorption by two-level molecules of a gas from a weak traveling electromagnetic plane wave in the presence of an oppositely traveling strong plane wave at the same frequency. Here the absorption spectrum exhibits a dip that broadens and deepens as the gas is increasingly saturated by the strong wave. This saturation effect has been employed in the recent experiments on the fine structure of atomic hydrogen performed by H\"ansch, Shahin, and Schawlow (HSS). The form, linewidth, and strength of saturation dips in the fine-structure lines are studied for experimental parameters appropriate to the hydrogen experiment. In addition, saturation line-shape curves are calculated for experimental situations in which the strengths of the stronger field give rise to stronger or weaker saturation of the gas medium and varying degrees of Doppler broadening exist. The calculation of shape of the saturation dip and absorption curves for a Doppler-broadened gas of two-level atoms is made exactly; in effect, the strong field is treated as arbitrarily strong by avoiding a perturbation-theory treatment in favor of the exact solutions for a driven two-level system. The general behavior found is in accord with intuition and experimental observations by HSS. There is an optimum saturation power which gives a prominent dip and beyond which the dip suffers "power broadening."
A previously developed diagrammatic method for calculating the nonlinear response of a dilute gas at near resonance with strong classical radiation fields is extended to include velocity-dependent homogeneous and inhomogeneous broadening phenomena. The method is applied to two-level saturated-absorption (Lamb-dip) spectroscopy. Expressions are obtained for the collision-broadened Lamb dip probed by a weak field in the presence of an arbitrarily strong saturating field and are compared to the usual infinite-Doppler-width, weak-saturation expression. We study the effects of velocity and momentum transfer on the line-shape parameters and discuss the effect of phase-changing and strong inelastic collisions on the intensity.
Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly inhomogeneous line broadening due to such causes as doppler shift arising from translational velocity. The ratio of the number of molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width ∆, where E0 is the amplitude of the electric field in the incident radiation and is the dipole moment matrix element for the transition. Excitation functions obtained in a previous paper (I) for various values of the ratio γ/β, where γ is the half line-width in the absence of inhomo­geneous broadening, are used to obtain the variation of N2/N with time under conditions of mixed broadening for various values of the ratio γ/∆ and γ/β, when the exciting radiation is in exact resonance with the central frequency of the transition.