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Journal of Experimental and Theoretical Physics Letters

Oscillating gap 2π pulse in resonantly absorbing lattice

Boris I. Mantsyzov, R. A. Sil’nikov

Published Nov 1, 2001• 9 citations
Publisher

Abstract

The interaction of a laser pulse with resonant Bragg lattice is studied theoretically for arbitrary initial conditions on the field, inverse population, and polarization of a medium. It is shown that the oscillating 2π self-induced transparency Bragg pulse can form if the Bragg conditions are exactly met. Various regimes are described for the oscillation dynamics of the gap 2π pulse.

DOI
10.1134/1.1434285

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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 10, 1997•0 citations
The interaction of a laser pulse with resonant Bragg lattice is studied theoretically for arbitrary initial conditions on the field, inverse population, and polarization of a medium. It is shown that the oscillating 2π self-induced transparency Bragg pulse can form if the Bragg conditions are exactly met. Various regimes are described for the oscillation dynamics of the gap 2π pulse.
The gap 2\ensuremath{\pi} pulse or gap solitary wave of self-induced transparency at an inhomogeneously broadened line of a resonant Bragg periodical structure has been found theoretically as an exact solution of the coupled-mode Maxwell-Bloch equations. In the case of a slight violation of the Bragg condition at exact two-level resonance, the analytical solution for the gap 2\ensuremath{\pi} pulse with phase modulation has been obtained. Furthermore, the existence of an oscillating pulse that periodically changes in amplitude and in the sign of its velocity has been numerically shown.
Nonlinear interaction of coherent intensive optical radiation with continuous resonant photonic crystal (RPC) is analytically and numerically studied in the framework of semiclassical approach using the two-wave Maxwell–Bloch equations. The analytical solution being the gap soliton of self-induced transparency is obtained in the case of an initially unexcited continuous RPC. This solution is confirmed numerically. Influence of both initial inversion and resonant atom concentration function profile on the pulse dynamics in continuous RPC is analyzed. Suppression of the Bragg reflection and a “quasi-linear” 2π pulse propagation in the case of zero initial inversion in continuous RPC is shown. The possibility of laser pulse compression using slow spatial changing of resonant atom concentration is demonstrated.
We consider a one-dimensional photonic crystal embedded in a two-level medium with various degrees of disorder, such that the tail of localized states in the forbidden gap is resonant with self-induced transparency pulses, which can propagate in the absorbing system. We theoretically and numerically predict that the SIT pulse not only is slowed down by the disorder, but, at high scattering strengths, it is trapped by coupling with Anderson states located in proximity of the cavity surface. We develop a perturbative analysis to address the role of the random perturbation on the propagation of a 2π pulse in a two level medium.
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.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .