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Soviet Journal of Quantum Electronics

Propagation of a Gaussian light beam in a nonlinear medium with a complex susceptibility

V G Kukushkin

Published Aug 31, 1985• 1 citation
Publisher

Abstract

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.

DOI
10.1070/qe1985v015n08abeh007610

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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 analysis is made of resonant self-focusing of high-intensity laser radiation in a medium consisting of two-level atoms and exhibiting a homogeneously broadened transition. An ordinary nonlinear differential equation with exponential factors is used to describe the change in the average radius of the beam. It is shown that in the absence of absorption this average radius oscillates periodically. The spatial period of the oscillations is determined. Calculations are made of the transverse and longitudinal dimensions of a caustic of nonlinear foci. It is shown that the dependence of these dimensions on the detuning from a resonance is V-shaped, whereas the dependences on the density of the medium, on the radius of curvature of the beam, and on the average radius of the beam at the entry to the medium are monotonic.
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The propagation of two-component laser radiation in a medium consisting of atoms with a Λ level scheme is investigated. The simultaneous self-focusing of two beams is considered. The main features of this phenomenon are: 1) lowering of the self-focusing threshold by several orders of magnitude in comparison with the known case of saturation of a transition in a two-level atom; 2) a strong dependence of the character of the propagation of the radiation on the difference between the detunings of the two frequency components of the field from resonance, which is associated with fulfillment of the two-photon resonance condition.
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.