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Quantum Electronics

Coherent propagation of an optical pulse in a fibre waveguide containing quasiresonant impurities. Adiabatic following approximation

Andrei I. Maimistov

Published Sep 30, 1995• 5 citations
Publisher

Abstract

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.

DOI
10.1070/qe1995v025n09abeh000499

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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.
Theoretical research of propagation effect of ultrashort optical pulse under conditions of coherent interaction with two resonant transitions simultaneously is presented. One of the transitions is tuned in exact resonance with pulse carrier frequency; the other is distanced much more than spectral pulse width, thus the adiabatic following approximation may be applied. Interaction between the pulse and far-resonant transition is described by wave equation with nonlinear index of refraction in the form of Lorentz function for field amplitude. This wave equation is solved together with Bloch equations for the exact resonant transition. The solution in the form of stationary phase-modulated pulse is obtained, and 2π-pulse of self-induced - transparency is the special case of this solution. The obtained solution has a square under pulse envelope less than 2π, and with increasing of far-resonant transition absorption coefficient the pulse square decreases. The effect can be used for reducing of the transparency threshold of the resonant medium below pi.