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Coherent soliton propagation through doped optical fibers: cloning, breakup, and soliton interactions

Solange Bessa Cavalcanti, E. J. S. Fonseca, Dilson P. Caetano, Jandir M. Hickmann

Published Jun 1, 2001• 0 citations
Publisher

Abstract

The simultaneous propagation of two optical pulses through a doped nonlinear dispersive medium modelled by a resonant three-level system was investigated numerically, within the framework of a pair of coupled extended nonlinear Schrödinger equations. These included the contribution of the dopant resonances whose dynamics is governed by Bloch equations. In this work, we review the interesting possibilities on the manipulation of fields such as cloning, breakup and soliton interactions, that the combination of coherent population trapping with nonlinear dispersive media offers.

DOI
10.1590/s0001-37652001000200005

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The simultaneous propagation of two optical pulses through a doped nonlinear dispersive medium modelled by a resonant three-level system was investigated numerically, within the framework of a pair of coupled extended nonlinear Schrödinger equations. These included the contribution of the dopant resonances whose dynamics is governed by Bloch equations. In this work, we review the interesting possibilities on the manipulation of fields such as cloning, breakup and soliton interactions, that the combination of coherent population trapping with nonlinear dispersive media offers.
The simultaneous propagation of two optical pulses through a nonlinear dispersive medium composed of a resonant three-level system is investigated. By choosing a soliton of area 4 pi and order N=2 at the pump frequency, together with a weaker pulse with a sech profile at the signal frequency, we show that the pump soliton breaks up into a pair of solitary waves which are cloned to the signal frequency. Due to a combination of coherent population trapping and nonlinear dispersive effects, the pair interacts in a repulsive fashion so that the taller wave travels faster than the shorter one.
Using a numerical approach we report on the cloning dynamics of simultaneous self-induced transparency (SIT) and nonlinear Schrödinger (NLS) solitons in a doped nonlinear dispersive medium. This technique involves a three-level atomic system interacting resonantly with two optical fields within a Lambda scheme. As a result, a pulse in the signal frequency is transformed into a replica of the pulse in the pump frequency. The atomic population evolution shows that the basic mechanism behind the cloning process is the coherent population trapping effect. Furthermore, it is shown that the signal clone presents characteristics of both the SIT soliton and NLS soliton.
Fiber guided optical signal propagating in a Erbium doped nonlinear resonant medium is known to produce cleaner solitonic pulse, described by the self induced transparency (SIT) coupled to nonlinear Schrödinger equation. We discover two new possibilities hidden in its integrable structure, for amplification and control of the optical pulse. Using the variable soliton width permitted by the integrability of this model, the broadening pulse can be regulated by adjusting the initial population inversion of the dopant atoms. The effect can be enhanced by another innovative application of its constrained integrable hierarchy, proposing a system of multiple SIT media. These theoretical predictions are workable analytically in details, correcting a well known result.
The coherent propagation of a pair of matched pulses in a doped two-mode nonlinear dispersive waveguide is investigated, where the dopant is modeled by a V-type three-level system. Relations involving the parameters of the pulses and the propagation medium that allow us to observe the formation of coupled bright solitons are derived. The analytical result is verified by numerically solving the propagation equations together with the evolution of the three-level system. The numerical results show a stable propagation of the pair of pulses corroborating the theoretical result.