Solitons in Stimulated Raman Scattering

Abstract

A b s t r a c t . The semiclassical equations of SRS are derived by the following method: The manylevel molecule is described by the Schrodinger equation and subsequently all amplitudes but those of the essential two levels are eliminated by approximate integration.Especially the ttase of equal group velocities for pump and Stokes wave is considered. Terms describing a frequency shift due to dynamical Stark effect and a change of refraction index by vibrational excitation can be removed by a suitable transformation.Under various, physically different, assumptions the system of molecular and field equations is reduced to the equ'ttions describing a quasimonochromatic pulse propagating in a resonant two-level system, and in this way we can find a rich manifold of solutions. E.g., the '2n-pulse of self-induced transparency can be transferred to SRS. By other assumptions we are led to equations defining the Backlund transformation for tho sine-Gordon equation. For this case also soliton type solutions can be constructed. Solitonen bei der stimulierten RamanstreuungI n h a l t s u b e r s icht. Die halbklassischen Gleichungen der SRS werden abgeleitet, wobei von der Schrodingergleichung des Vielniveaumolekiils ausgegangen wird und die Amplituden aller bis auf die der wesentlichen zwei Niveaus durch naherungsweise Integration eliminiert werden.Insbesondere wird der Fall gleicher Gruppengeschwindigkeiten der Pump-und der Stokeswelle behandelt. Terrne, welche Frequenzverschiebung durch dynamischen Starkeffekt sowie BrechzahlLnderung durch Umbesetzung beschreiben, lassen sich durch eine geeignete Transformation beseitigen.Unter verschiedenen physikalischen Voraussetzungen gewinnt man die Gleichungen fiir einen quasimonochromatischen Impuls im resonanten Zweiniveausystem zuriick, wofiir eine grode Mannigfaltigkeit von Losungen bekannt ist. Zuni Beispiel lassen sich die 2n-Impulse der selbstinduzierten Transparenz auf die SRS ubertragen. Unter anderen Voraussetzungen gelangt man zu Differentialgleichungen, die als Backlundtransformation (beziiglich der Sinus-Gordon-Gleichung) bekannt sind und wofiir sich ebenfalls Losungen vom Solitontyp finden lassen.

Completely integrable models of nonlinear optics

“…This process is similar to SIT and it is referred to as two-photon self-induced transparency (TPSIT). This phenomenon can be described in the framework of the generalised Maxwell-Bloch equations [65,66]. These equations are converted into a new system of equation for new variables, which are quadratic functions of initial slowly varying envelopes of the electromagnetic fields [66,67].…”

Stimulated Raman Scattering: The Nonlinear Theory

“…The usual experimential situation is where only a very small fiaction of the available molecules can be excited. This is the case originally studied by Scott and Chu 1 and is the only case that we shall consider here. where we have allowed for a phenomenological molecular damping factor, Y.…”

“…We shall need to do this when we discuss the soliton solutions but for now, we shall retain this term. This damping factor will be used only in the first part of ou 1 ; discussions, after which we shall set it equal to zero. In (1), A 1 (A 2 ) is the envelope of the pump (Stokes) wave and X is the material excitation.…”

Wave Equation for Dark Coherence in Three-Level Media

“…Despite its connections to the McCall-Hahn case, and a wealth of data from many lambda experiments for guidance, the theory of two-pulse propagation [10][11][12][13][14][15] in lambda systems has many gaps. Although one link between theory and experiment in coupled-pulse propagation dynamics has been noted, in which observation [21] of predicted adiabaton pulses [22] was reported, no theoretical approach has been found, apart from purely numerical solution methods, that (a) deals nonperturbatively with the nonlinearities of the equations, (b) permits both pulses to change their shapes significantly while propagating, 3.…”

“…Here m and m 0 are the coupling coefficients for the a-g and a-g 0 transitions. The five partial differential equations governing propagation of V g and V g 0 and evolution of coherence in threelevel systems have been long known [10][11][12][13][14][15]. In addition to (3)-(5) one has the propagation equations…”