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Optics Letters

Spatial-asymmetry distribution of a saturated-absorption peak

A. Le Floch, Roger Le Naour, J. Lenormand, G. Jézéquel

Published Jan 1, 1981• 5 citations
Publisher

Abstract

The amount of asymmetry of saturated-absorption peaks observed outside a cavity with two collinearly counter-propagating Gaussian beams is analyzed at different points in the cross section of the probe beam. Although the total beam exhibits a quasi-symmetric line shape, a spatial distribution of asymmetries with different amounts and signs is obtained versus the distance to the beam axis. A simple model taking account of pure focusing and defocusing effects induced by a saturated Gaussian beam leads to agreement between experiment and theory for the 5944-A neon line in the case of saturated-absorption spectroscopy.

DOI
10.1364/ol.6.000048

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 1, 1992•0 citations
The amount of asymmetry of saturated-absorption peaks observed outside a cavity with two collinearly counter-propagating Gaussian beams is analyzed at different points in the cross section of the probe beam. Although the total beam exhibits a quasi-symmetric line shape, a spatial distribution of asymmetries with different amounts and signs is obtained versus the distance to the beam axis. A simple model taking account of pure focusing and defocusing effects induced by a saturated Gaussian beam leads to agreement between experiment and theory for the 5944-A neon line in the case of saturated-absorption spectroscopy.
A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.
A spatial dependence of the demodulated signal over the cross-section of a laser beam used for saturation spectroscopy has been observed. If the detector is not exposed to the full beam this spatial dependence causes a distortion of the line-shape. In extreme cases this distortion can lead to frequency shifts as large as 15% of the full width of the resonance. A model is presented in which the self-focusing effect acts to separate spatially the different frequency components of the modulated laser beam and thus allows for a spatial inhomogeneity of the demodulated signal. Numerical evaluation of the model agrees well with the experimental data provided a strong enhancement of the beam convergence in the absorption medium is applied.
Saturated absorption spectroscopy linewidths down to half the natural linewidth have been obtained for the sodium D1{\mathit{D}}_{1}D1​ transition in a strongly absorbing gas cell. The strong-line-narrowing effect is achieved by using an experimental ``tandem'' approach with two absorbing cells in series, where the saturated absorption output from the first cell is used as an input beam for a saturated absorption measurement in the second cell. A physical interpretation of the line-narrowing mechanism in highly absorbing media is presented, which, among other things, explains why the narrowing effects are different for crossover transitions. It is further argued that in these experiments the line-narrowing effect is caused by optical pumping and can be appropriately described by rate equations. This is different from several other recent papers on high-contrast transmission spectroscopy, where full Bloch vector models were necessary to fully describe the line shapes. Here a rate equation model, which includes two spatial dimensions, is developed, and reasonable agreement is obtained between experimental and theoretical data. \textcopyright{} 1996 The American Physical Society.
We present a theoretical analysis of the spatial shape of two symmetric signals of degenerate four-wave mixing induced by Gaussian beams in a thin sample of two-level atoms. Our calculations take into account the full spatial and spectral dependences of the relevant nonlinear susceptibilities that govern the two processes. This reveals two interesting effects. The first one is that the total power of incident beams affects the transverse profile of the four-wave-mixing signals at the medium exit and their free propagation. The second one is the influence of the spectral characteristics of the medium on the longitudinal profile of both generated signals upon free propagation. We argue that the first effect can be seen as the saturation of the medium in regions of higher intensity, while the second can be understood as the result of a nonlinear contribution to the refractive index inside the atomic medium. These effects can be symmetric between the two signals, with asymmetries induced by different detunings from the resonance of the incident fields.
Only for optically thin layers and plane waves may the intensity of a light wave be unambiguously expressed in terms of the nonlinear susceptibility of the medium. In aperture limited light beams the saturation parameter and the Stark shifts are local variables, while the output intensity of the pump and probe beams is an integral characteristic of the transmission process. The output spectrum is affected by diffraction, nonlinear refraction, and saturated absorption. The nonlinear refraction is a cause of a spectral line asymmetry which is well- known in saturation spectroscopy. In addition to usual line broadening, the saturated absorption causes specific beam effects, related to the formation of a self-induced transparency channel. The diffraction of the beam due to this self-induced aperture may result in the enhancement of the on-axis intensity, which is not a result of the self-induced lens effects. All these factors are taken into account by the mathematical model suggested in the present work. The propagation of the near-resonance saturating pump and non-saturating probe beams of various initial profiles through a homogeneously broadened two-level gas is simulated numerically. The calculations carried out make it possible to analyze the contribution of the propagation phenomena, mentioned above, to the output spectra of the beams.