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Novel Lasers and Devices - Basic Aspects

SOLITON PULSE PROPAGATION IN DENSE RESONANT MEDIA

Anatoly A. Afanas'ev, Andrey G. Cherstvy, R. A. Vlasov

Published Jan 1, 1999• 0 citations
Publisher

Abstract

In this report we consider the condition for invariant pulse propagation in dense resonant medium (DRM) by analogy with well known phenomenon of self-induced transparency deduced from the usual Maxwell- Bloch formulation [1] and investigated experimentally [2].
DOI
10.1364/nlda.1999.lmb7

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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.
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A theory based on the method of the inverse scattering problem is presented describing propagation of an ultrashort light pulse under the condition that resonant interaction with atoms of the medium is initially switched on by an additional Stark pulse. A Hamiltonian form of the Maxwell-Bloch equation is found without redefining the spatiotemporal variables. The method of the inverse scattering problem is based on a special spectral problem. Equations of the Gel’fand-Levitan-Marchenko type and a soliton solution are obtained.
A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is neglected; the equations are valid at densities less than about 10 18 atoms cm -3 . At such densities the 2 pi sech pulse of McCall and Hahn (1967, 1969) remains a good approximate well into the picosecond range. The more accurate solution is chirped by a factor proportional to the square of the ratio of the spectral width of the pulse to its carrier wave frequency. The stability of this pulse solution and other N soliton solutions of the approximate Maxwell-Bloch equations is demonstrated.