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Technical Physics Letters

A two-component phase-modulated soliton in a medium with a two-photon resonant transition

Guram T. Adamashvili, Nugzar T. Adamashvili, M. D. Peikrishvili, R. R. Koplatadze

Published Mar 1, 2014• 0 citations
Publisher

Abstract

A theory of optical self-induced transparency for a two-component phase-modulated soliton in a medium with a two-photon resonant transition has been developed. It is shown that a two-photon two-component soliton oscillating at the sum and difference frequencies in the vicinity of the carrier frequency can be formed under these conditions. Explicit analytical expressions are given for the form and parameters of non-linear wave under experimental conditions.

DOI
10.1134/s106378501403002x

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A theory of optical self-induced transparency for a two-component phase-modulated soliton in a medium with a two-photon resonant transition has been developed. It is shown that a two-photon two-component soliton oscillating at the sum and difference frequencies in the vicinity of the carrier frequency can be formed under these conditions. Explicit analytical expressions are given for the form and parameters of non-linear wave under experimental conditions.
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Abstract 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.
Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency ω0 and that of combination of ω0 and the trigger-field frequency ω1(2ω0 + ω1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable.