Model of transient amplification by stimulated raman scattering

Abstract

A semiclassical model for light amplification by stimulated Raman scattering is presented. The phases of the Stokes, anti-Stokes, and laser waves are assumed to be perfectly matched. Depletion of the laser pump is neglected. The corresponding system of equations for input pulses of arbitrary shape is solved analytically by the Riemann-Volterra method. Gain is suppressed for close Raman polarizations.Introduction. Stationary stimulated Raman scattering SRS [1-3] occurs when the pulse lengths are considerably longer than the dephasing time of the molecular vibrations. Otherwise, so-called transient (nonstationary) SRS takes place [4][5][6][7]. In the latter case, the system response to the external radiation is delayed and it acquires a number of new properties which differ from those of stationary SRS. When the depletion of the pump radiation is low [8], the gain for an input Stokes signal in transient SRS is independent of the width of the Raman scattering line, is lower than the gain for stationary SRS, and is determined by the total energy of the pulse, rather than its intensity [5,6]. These results are based primarily on an analytic solution of the corresponding equations with the effect of the antiStokes radiation on the kinetics of the transient SRS neglected [5]. With the anti-Stokes component taken into account, this kind of solution has been obtained only for the special case in which the SRS active medium is excited by a rectangular pulse and the dephasing time for the molecular vibrations is assumed to be infinite [9].In this paper an analytic solution is proposed for the general form of this problem. A solution is obtained for phase synchronization of the exciting, Stokes, and anti-Stokes waves. The Riemann-Volterra method of the theory of partial differential equations [10] is used to obtain the solution.Model Equations and Their Transformation. We consider SRS of laser pulses with powers I p ≤ 10 7 W/cm