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Journal of Physics B Atomic and Molecular Physics

Second-order Doppler corrections to the optical susceptibility for two counter-propagating beams

Antonio Guillermo Jose Balbin Villaverde, José Antonio Roversi, J R Mohallen, J. I. Cotrim Vasconcellos

Published Mar 14, 1985• 0 citations
Publisher

Abstract

The authors consider the effect of the quadratic Doppler term on the inhomogeneous complex optical susceptibility of a two-level system for a weak beam in the presence of a saturating, counter-propagating wave, with both waves at the same frequency. There is a red shift of the resonance frequency in the absorption as well as in the dispersion. That red shift is a function of the temperature of the medium and the degree of saturation. An asymmetry of the absorption and dispersion curves is also observed which becomes stronger when the authors approach relativistic velocities of the particles. They also study for comparison purposes the effect of the quadratic Doppler term in the particular case of only one strong beam, without the weak one. They show the different behaviour of the red shift between the two cases.

DOI
10.1088/0022-3700/18/5/020

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The authors consider the effect of the quadratic Doppler term on the inhomogeneous complex optical susceptibility of a two-level system for a weak beam in the presence of a saturating, counter-propagating wave, with both waves at the same frequency. There is a red shift of the resonance frequency in the absorption as well as in the dispersion. That red shift is a function of the temperature of the medium and the degree of saturation. An asymmetry of the absorption and dispersion curves is also observed which becomes stronger when the authors approach relativistic velocities of the particles. They also study for comparison purposes the effect of the quadratic Doppler term in the particular case of only one strong beam, without the weak one. They show the different behaviour of the red shift between the two cases.
The authors consider the Doppler-broadened index of refraction of a two-level molecule of a gas for a weak travelling electromagnetic plane wave in the presence of a strong plane wave travelling in the opposite direction at the same frequency. The authors use the FVH vector model for a two-level system to calculate the real part of the non-linear susceptibility of the gas. The optical dispersion curve exhibits a wiggle at the centre line, that broadens and deepens as the gas is increasingly saturated by the strong incident wave.
It is shown that the dispersion dependence of the rotation of the plane of polarisation of weak radiation passing through a three-level atomic medium may be free of Doppler broadening, on the account of a velocity-dependent Stark-shift which is created by saturating the wave on an adjacent transition. In the case of two-photon resonance the use of opposing light beams with different frequencies gives the possibility for an essential increase of the signal on account of the resonance gain on an intermediate transition, without additional Doppler broadening.
The purpose of this work was to investigate coherence effects in the interaction of two counterpropagating electromagnetic waves with the atoms of a gas, in the case in which one of the waves is weak and frequency modulated, while the other is sufficiently intense to cause saturation. Solving the equations for the density matrix in first-order perturbation theory, the authors obtained in analytic form the real part of the susceptibility integrated over the atom's velocity, expressed in terms of the rate equation model (REM) predictions plus the coherence corrections. The relaxation constants of the levels involved in the transition were kept different in order to allow a wider range of applications of the results. Calculated line shapes related either to the frequency-modulated (FM) sideband or to the ordinary dispersion techniques are presented. The REM approximation and the coherence corrections are shown in detail for an optical line which is of interest for frequency standard investigations.
We present in this paper a calculation of the non-linear susceptibility near a Doppler-free two-photon transition. In the case of a two-level system, we find a non-perturbative solution. We deduce new effects on the non-linear refractive index which are related to the change of the linear susceptibility because of the transfer of atoms between the ground and excited levels. In the case of a more complex system, we study at the lowest order of perturbation the anisotropy induced by one beam on the other. At last, we show that it is easy to observe a bistable behaviour when atoms, inside a Pérot-Fabry cavity, interact with a beam whose wavelength is close to a two-photon resonance.
The profile of a two-photon resonant absorption line of a particle subjected to a standing optical wave is calculated allowing for the quadratic Doppler effect. It is shown that the line profile is governed entirely by the ratio of the homogeneous line width to the quadratic Doppler frequency shift. An exact expression is obtained for the line profile in the second order in ν/c and the main approximations are considered. The profiles are calculated for the 1S-2S and 1S-3S transitions in the hydrogen atom.
We show that the propagation of light in a Doppler-broadened medium can be slowed down considerably even though such medium exhibits very flat dispersion. The slowing down is achieved by the application of a saturating counter propagating beam that produces a hole in the inhomogeneous line shape. In atomic vapors, we calculate group indices of the order of 103.{10}^{3}.103. The calculations include all coherence effects.