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Soviet Journal of Quantum Electronics

Soliton decay associated with the dipole–dipole interaction between resonant centers in two-level media

А. В. Смирнов

Published Nov 30, 1990• 0 citations
Publisher

Abstract

An analysis is made of the influence of an electric dipole–dipole interaction of resonant centers on the self-induced transparency of two-level solid media. The conditions under which this interaction is the main mechanism of decay of optical solitons are identified. It is shown that the main contribution to the decay process comes from pairs of closely spaced centers. In the case of such pairs the distance between the centers is much less than the average. Differential equations describing the change in the soliton duration are derived.

DOI
10.1070/qe1990v020n11abeh007566

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An analysis is made of the influence of an electric dipole–dipole interaction of resonant centers on the self-induced transparency of two-level solid media. The conditions under which this interaction is the main mechanism of decay of optical solitons are identified. It is shown that the main contribution to the decay process comes from pairs of closely spaced centers. In the case of such pairs the distance between the centers is much less than the average. Differential equations describing the change in the soliton duration are derived.
Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω 0 −1 (ω0 is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation.
The spatiotemporal dynamics of a light pulse injected into a dense, resonant medium under near-dipole–dipole interaction conditions is considered. Two regimes for soliton formation are investigated numerically and analytically. The first one occurs if the pulses are much shorter than both relaxation times. In the second, the pulse duration falls between those of the relaxation times and may be regarded as an incoherent one. In the latter case there are conditions in which the dephasing process is suppressed by dipole–dipole interatomic interaction. Not only are one-soliton solutions found but also a powerful pulse splitting into separate solitons is revealed. The regions in which solitons are found have been estimated. The possibility of finding incoherent solitons has been analyzed, with group-velocity dispersion and diffraction of tilted pulses, which are shown to make soliton formation easier, taken into account.
The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.
The modes of nonlinear propagation of the two-component electromagnetic pulses through optically uniaxial media containing resonant particles are studied. The features of their manifestation in the "dense" media and in the media with expressed positive and negative birefringences are discussed. It is shown that exponentially and rationally decreasing solutions of the system of material and wave equations allow us also to describe the propagation of the pulses of the self-induced transparency in isotropic media in the case, when the direct electric dipole-dipole interaction between the resonant particles is taken into account.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.
The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N -soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.