The semiclassical theory of spontaneous Raman scattering is reviewed. From the semiclassical theory we identify the parameters and dynamical variables involved in Raman scattering. A classical theory of stimulated Raman scattering is constructed. It is an extension of the theory of Shen and Bloembergen. We show that the system is a weakly coupled system. Because the driving term contains dynamical variables, the linewidth of the stimulated Stokes wave should be smaller than that of the spontaneous Stokes wave. Using Riemann's method, we obtain Kroll's solution rigorously, in a more general form. The steady-state limit is also derived rigorously. The conditions for the transient and steady-state gains are discussed. It is shown that for the transient case one may have an abrupt change of the Stokes gain versus incident laser power.
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