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Optics and Spectroscopy

Effect of conductivity on a self-induced transparency 0π pulse with a complicated structure

Guram T. Adamashvili, Nugzar T. Adamashvili, R. R. Koplatadze, G. N. Motsonelidze, M. D. Peikrishvili

Published Jun 8, 2004• 2 citations
Publisher

Abstract

The theory of optical self-induced transparency is developed for a 0π pulse with a complicated internal structure in an absorbing medium. It is shown that, in the process of propagation through the medium, the effects of conductivity lead to a change in the wave parameters. Explicit analytic expressions describing the double breather under these conditions are presented.

DOI
10.1134/1.1753647

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The theory of optical self-induced transparency is developed for a 0π pulse with a complicated internal structure in an absorbing medium. It is shown that, in the process of propagation through the medium, the effects of conductivity lead to a change in the wave parameters. Explicit analytic expressions describing the double breather under these conditions are presented.
Self-induced transparency effects are examined in an absorbing medium having degenerate optical transitions. Undistorted propagating light pulses exist under restrictive conditions for $j\ensuremath{\rightleftharpoons}j$ transitions (j>0j>0j>0) and for 0 \ensuremath{\rightleftharpoons} 1 and $\frac{1}{2}\ensuremath{\rightleftharpoons}\frac{3}{2}$. Pulses which propagate without energy loss for any transition ${j\ensuremath{\rightleftharpoons}j}^{\ensuremath{'}}$ also include zero-degree pulses defined as $\ensuremath{\int}\mathcal{E}(z,t)dt=0$.
A theory of optical two-component pulse of self-induced transparency in a dispersive medium has been developed. Using the generalized version of the perturbative expansion method, the system of material equations for an ensemble of two-level atoms and the wave equation in a dispersive medium are reduced to coupled nonlinear Schrödinger equations. A solution in the form of a phase-modulated two-component 0π0\pi 0π pulse is obtained. The pulse components oscillate at the sum and difference frequencies in the vicinity of the carrier-wave frequency. Explicit analytical expressions for the parameters and formation conditions of a nonlinear wave, which depend on the dispersive properties of the medium, are presented. Known results are obtained for a particular case.
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) .
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.
Resonant absorbing media having many atoms within a cubic resonance wavelength can exhibit large frequency chirps in pulse propagation due to dipole-dipole interactions among the atoms. Analytic solutions are obtained for invariant pulse propagation in such a medium consisting of interacting two-level atoms. Departures from the McCall-Hahn results include nonhyperbolic secant pulse shapes and different than 2π-area pulses. In addition, the excitation of the medium is comparatively suppressed for the same group velocity. The results are interpreted to suggest new experiments.