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Soviet Journal of Quantum Electronics

Asymmetry of saturation resonances due to lens and aperture effects during propagation of off-axial Gaussian beams in a nonlinear medium

Vladimir Leonardovich Derbov, Leonid A. Melnikov, A. D. Novikov

Published Aug 31, 1989• 3 citations
Publisher

Abstract

A new modification of the generalized method of moments is applied to off-axial Gaussian beams in nonlinear inhomogeneous media. Numerical estimates of the induced astigmatism, deformation of the spot, and bending of the beam are obtained for a traditional saturation spectroscopy scheme with a probe counterpropagating beam tilted slightly from the axis of a saturating beam. It is shown that this tilt results in an asymmetry of the radial dependence of the frequency shift of a saturation resonance, which is in good qualitative agreement with the experimental results.

DOI
10.1070/qe1989v019n08abeh008779

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A new modification of the generalized method of moments is applied to off-axial Gaussian beams in nonlinear inhomogeneous media. Numerical estimates of the induced astigmatism, deformation of the spot, and bending of the beam are obtained for a traditional saturation spectroscopy scheme with a probe counterpropagating beam tilted slightly from the axis of a saturating beam. It is shown that this tilt results in an asymmetry of the radial dependence of the frequency shift of a saturation resonance, which is in good qualitative agreement with the experimental results.
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.
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.
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.
The effects of possibly truncated Gaussian-beam variations in probe and saturator-wave intensities are studied analytically and numerically for saturation spectroscopy of homogeneously and inhomogeneously broadened systems. The measured saturation intensity is shown to be about 2.5 times greater for Gaussian beams than for uniform saturation. Systems characterized by the short dipole lifetime limit (T2≪T1) are treated, revealing sizeable modifications to the depths of coherent pulsation dips and Bennet holes. The equal lifetime case (T2=T1) is studied as well, showing substantial influence on the dynamic Stark effect.
We suggest an improved numerical algorithm for nonlinear paraxial optics that makes use of the modified quasi-fast-Fourier–Bessel transform and the special high-harmonic correction technique. The algorithm is applied to an initially cw near-resonance Gaussian beam propagating through a strongly saturated two-level medium. The spatial behavior is in good agreement with experiments and simulations by other authors. The spectral characteristics, which to our knowledge have not been previously studied, are shown to be drastically affected by the transverse pattern formation. The semianalytical approach of our earlier research is shown to provide a sufficient approximation of the beam, requiring only a few of the lowest-order dressed Laguerre–Gaussian modes.