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Soviet Journal of Quantum Electronics

New method for calculation of the self-interaction and its application to an analysis of the shift of saturated absorption resonances in Gaussian beams

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

Published Dec 31, 1987• 6 citations
Publisher

Abstract

A new modification of the generalized method of moments is used to derive a system of differential equations which describe the behavior of a Gaussian beam in a nonlinear medium. This modification is used in an analysis of an asymmetry and frequency shifts of saturated absorption resonances and dispersion due to light-induced aperture and lens-like properties of the medium.

DOI
10.1070/qe1987v017n12abeh011351

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A new modification of the generalized method of moments is used to derive a system of differential equations which describe the behavior of a Gaussian beam in a nonlinear medium. This modification is used in an analysis of an asymmetry and frequency shifts of saturated absorption resonances and dispersion due to light-induced aperture and lens-like properties of the medium.
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.
A theoretical investigation is reported of the influence of self-focusing of Gaussian beams on the profile of a saturated absorption resonance in laser frequency standards. An analysis is made of systems with an external nonlinearly absorbing cell and an external interferometer containing a nonlinear absorber. Analytic relationships for the profile of an asymmetric resonance and a shift of its maximum in the course of local and integral photodetection of an optical beam are derived on the assumption of weak absorption and saturation.
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 problem of transformation of the parameters of a Gaussian light beam in a nonlinear medium with a complex susceptibility is solved. The parabolic approximation for the wave equation is employed. The results obtained can be used in the design of resonators and waveguides with nonlinear components. A study is made of the influence of the complex part of a nonlinear susceptibility of a substance on the threshold conditions for the self-focusing in the case of resonant absorption in a two-level system. It is shown that in this case it is possible to expect self-focusing of radiation on the low-frequency side of an absorption line.
An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.