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Soviet Journal of Quantum Electronics

Compensation of self-focusing distortions in quasiresonant amplification of a light pulse

A. Yu. Okulov, А. Н. Ораевский

Published Feb 28, 1988• 11 citations
Publisher

Abstract

A theoretical analysis is made of the compensation of a positive nonlinear refractive index of insulators containing impurities by saturation of the refractive index in the anomalous dispersion region. The exact solutions are obtained for self-similar amplification of a laser pulse under conditions of homogeneous broadening of a resonant transition. It is shown that profiling of the time envelope of a steady-state bleaching wave of a saturable absorber together with detuning of the pulse frequency upward from resonance makes it possible to increase the threshold of small-scale self-focusing.

DOI
10.1070/qe1988v018n02abeh011482

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A theoretical analysis is made of the compensation of a positive nonlinear refractive index of insulators containing impurities by saturation of the refractive index in the anomalous dispersion region. The exact solutions are obtained for self-similar amplification of a laser pulse under conditions of homogeneous broadening of a resonant transition. It is shown that profiling of the time envelope of a steady-state bleaching wave of a saturable absorber together with detuning of the pulse frequency upward from resonance makes it possible to increase the threshold of small-scale self-focusing.
Light pulse amplification in a fiber amplifier is analyzed using a two-level model of resonant impurity atoms in a preinverted state. A steady-state ultrashort pulse propagating in such an amplifier is predicted. The dispersion broadening of this pulse is compensated by a nonlinear compression due to self-interaction, whereas an increase in the amplitude is compensated by linear losses. The dependence of the total energy of a transient pulse on the fiber wavelength is determined and a study is made of the role of the spatial inhomogeneity of the population inversion of the impurity atoms. Quasicoherent amplification is discussed.
The propagation of laser light a few wavelengths inside a saturable absorber is theoretically studied. Computed steady-state solutions of the Maxwell–Bloch equations that describe the unidimensional propagation of a plane monochromatic wave, without introducing the slowly varying envelope approximation, show how saturation effects can influence this propagation. This can even lead to the appearance of a self-reflected wave inside the absorber because of the refractive-index changes that are induced by nonlinear coupling. One finds a close relation between the failure of the slowly varying envelope approximation and the presence of the self-reflected wave.
The temporal envelope profile and the phase of a steady-state pulse propagating through a resonant medium in the presence of nonresonant nonlinearity are derived. The formation of solitonlike pulses takes place as a result of the balance of the self-phase modulation generated by nonresonant nonlinearity and the nonlinear resonant group-velocity dispersion induced by the self-induced-transparency effect in a resonant medium. Self-phase-modulation action leads to distortion of the pulse when its power and inverse duration exceed the critical values Pcr and τcr-1. We show the destructive role of self-phase modulation in the case of self-induced-transparency pulse generation in a laser with erbium-doped fiber as an intracavity coherent absorber.
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.
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.