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Soviet Journal of Quantum Electronics

Soliton propagation of light under conditions of adiabatic tracking and of a one-photon resistance

Dariusz Gora

Published Jun 30, 1990• 1 citation
Publisher

Abstract

A theoretical investigation is reported of the behavior of optical pulses under quasiresonant adiabatic tracking conditions. It is shown that dispersion of the group velocity and saturation of the populations of the resonant levels may give rise to soliton propagation of light. The exact solution for the envelope of a soliton is obtained for the first time subject to the saturation effect. Expressions are derived for the critical energy density in a soliton and for its duration. A study is made of the influence of the resonant saturation on the shape of a soliton envelope and its parameters. An analysis is reported of the behavior of light pulses of energies higher and lower than the critical value. It is shown that these pulses exhibit three types of quasisoliton propagation: weak, strong, and steady-state. The results for the pulses are generalized to two-dimensional light beams in a nonlinear waveguide.

DOI
10.1070/qe1990v020n06abeh006684

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A theoretical investigation is reported of the behavior of optical pulses under quasiresonant adiabatic tracking conditions. It is shown that dispersion of the group velocity and saturation of the populations of the resonant levels may give rise to soliton propagation of light. The exact solution for the envelope of a soliton is obtained for the first time subject to the saturation effect. Expressions are derived for the critical energy density in a soliton and for its duration. A study is made of the influence of the resonant saturation on the shape of a soliton envelope and its parameters. An analysis is reported of the behavior of light pulses of energies higher and lower than the critical value. It is shown that these pulses exhibit three types of quasisoliton propagation: weak, strong, and steady-state. The results for the pulses are generalized to two-dimensional light beams in a nonlinear waveguide.
An analysis is made of the propagation of ultrashort pulses in a fibre waveguide doped with resonant impurities. Equations describing the evolution of a pulse in the case of one-photon and two-photon resonances are derived on condition that the Rabi frequency is considerably less than the detuning from an exact resonance. The influence of impurity atoms on the parameters of a pulse and on the characteristics of its evolution (ultrashort pulse duration, 'soliton threshold', and ultrashort pulse collapse threshold) is determined. The corrections to these quantities have different signs for different types of resonance.
The propagation of short light pulses in a three-level medium with reverse saturable absorption taking into account relaxation is considered. It is shown that in such a medium soliton-like pulses of constant duration can propagate. The areas in the five-dimensional parameter space in which such pulses can exist are determined by numerical methods. The parameters of the problem are the characteristics of the medium – the relaxation time, the ratio of the absorption cross sections of the first excited and ground states and the initial transmittance, as well as the characteristics of the pulse – the duration and intensity.
A numerical and analytic investigation is made of the self-interaction of Gaussian beams under two-photon resonance conditions when the pulse duration is shorter than the relaxation times and the frequency detuning from resonance exceeds appreciably the spectral width of the radiation (adiabatic model). An analysis is made of defocusing (up-detuning) and self-focusing processes (down-detuning) in two-photon resonance. Three characteristic adiabatic self-focusing regimes are identified: a steady-state waveguide and weak and strong quasiwaveguide propagation. Expressions are derived for the critical powers and minimal self-focusing length.
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we find the two modes of shape-preserving pulse propagation. The pulse propagation velocity of the fast mode is equal to the speed of light in vacuum, whereas the group velocity of the other (slow) mode is significantly slowed down. These two modes represent a general asymptotic solution of the problem of adiabatic pulse propagation, i.e., a pulse of any shape, which is consistent with the adiabaticity conditions, and a finite duration evolves at large propagation distances (and, correspondingly, at large times of interaction with the medium) to a well-separated pair of fast and slow pulses. The experimental requirements for adiabatic pulse propagation in a tripod medium are similar to that needed for observation of slow light propagation in a medium with the $\ensuremath{\Lambda}$ configuration of levels. However, the tripod scheme offers a different possibility, which is absent in the $\ensuremath{\Lambda}$-medium case: collisions of fast and slow pulses. It is found numerically that after such a collision the shapes of the pulses change, so these pulses do not match the classical definition of a soliton.
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg--de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.
The amplification of intense light pulses in resonance active media with an optical Stark effect and coherence effects is examined theoretically. In the course of the amplification, the pulse may go through a stage of an incoherent Stark quasisoliton. The envelope of this quasisoliton has an approximately constant, highly asymmetric shape. The energy of the quasisoliton is approximately constant. Upon further amplification, the Stark quasisoliton "breaks up" into a train of shorter pulses. Over a sufficiently long amplification distance, a true soliton may form in the active medium. In general, this true soliton is not the same as a standard π pulse in a medium without a Stark effect.