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Optics and Spectroscopy

Self-focusing and defocusing of self-similar π pulses in an amplifying two-level medium

M. B. Krylov, С. В. Сазонов

Published Feb 1, 2006• 0 citations
Publisher

Abstract

The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.

DOI
10.1134/s0030400x06020172

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The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.
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Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.
The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces σ transitions, while the extraordinary component induces the π transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.
Propagation of broad-band ultimately short light pulses in a partially absorbing medium is analyzed in the framework of the three-level model. Nonlinear wave equations are obtained describing propagation of light pulses in media with quadratic (all three transitions are allowed) or cubic (one of the transitions is forbidden) nonlinearity in the range of optical transparency or with the sine-Gordon-type nonlinearity in the region of absorption. Using the averaged variational principle, the approximate solutions of equations in the form of unipolar soliton-like signals are found and conditions of their transverse stability are determined. A stable propagation of a broad-band pulse is shown to be possible under conditions when monochromatic signals exhibit self-focusing.