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Soviet Journal of Quantum Electronics

Average radius of a beam in the case of resonant steady-state self-focusing and weak nonlinearity saturation

Pavel Vojtek, A. Zh. Muradyan

Published Jun 30, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1990v020n06abeh006688

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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.
Full space-time numerical modeling of near-resonance self-action of a beam, whose frequency is harmonically modulated in time, is presented. Maxwell-Bloch equations describing the propagation of the beam through a two-level medium with saturable absorption and refraction are solved using an original stable numerical scheme for multidimensional nonlinear Schrodinger equations. Delayed redistribution of intensity over the beam cross-section due to nonlinear self-focusing and self-phase-modulation effects is shown to affect the phase and the amplitude dynamics of the output signal in a rather nontrivial way, depending on the carrier laser frequency.
The shape of the resonance of a saturated absorption is calculated at an arbitrary intensity of a probe field. It is revealed that, in the case of orthogonal polarizations of strong and probe fields, an increase in the intensity of the probe field can invert the shape of the nonlinear resonance of clearing of the medium, changing it to the resonance of absorption. The saturation of optical transitions by intrinsic spontaneous radiation increases the contrast of the inverted resonance of saturation and narrows its width. In the case of parallel polarizations of the optical fields, an absorption peak can arise in the shape of the nonlinear resonance upon splitting of the lower state.
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.
On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.