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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Ultrashort optical pulse propagation in Kerr medium with quasi-resonant impurities

Ashat M. Basharov, Andrei I. Maimistov

Published Mar 12, 2001• 0 citations
Publisher

Abstract

A nonlinear evolution equation describing an ultrashort optical pulse propagation under quasi-resonant condition is derived by the unitary transformation method. This method allowed us to obtain the terms which are not taken into account within the framework of the adiabatic following approximation. The analysis of the nonlinear evolution equation and example of its application are given.

DOI
10.1117/12.418807

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A nonlinear evolution equation describing an ultrashort optical pulse propagation under quasi-resonant condition is derived by the unitary transformation method. This method allowed us to obtain the terms which are not taken into account within the framework of the adiabatic following approximation. The analysis of the nonlinear evolution equation and example of its application are given.
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.
A theory of quasi-resonance for the model of atoms with an arbitrary number of levels is developed by the method of unitary transformation without recourse to Bloch’s equations. Corrections to the results known from the theory of adiabatic following, which refine these results and take into account dispersion of the nonlinear response of the resonant system, are obtained. The condition for quasi-resonance with a single atomic transition is shown to impose stringent limitations on the form of the nonlinear evolution equation for the electric field envelope of the pulse with dispersion of the nonlinear response taken into account, which prohibit the reduction of the equation indicated to familiar, fully integrable systems.
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The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.