Method of successive approximations in the theory of stimulated Raman scattering of a randomly modulated pump

Stimulated Raman scattering of a randomly modulated pump is investigated by the method of successive approximations. This involves expanding solutions in terms of small parameters, which are ratios of the correlation scales of random effects to other characteristic dynamic scales of the problem. Systems of closed equations are obtained for the moments of the amplitudes of the Stokes and pump waves and of the molecular vibrations. These describe the dynamics of the process allowing for changes in the pump intensity and statistics due to a three-wave interaction. By analyzing equations in higher-order approximations, it is possible to establish the conditions of validity of the first (Markov) and second approximations. In particular, it is found that these are valid for pump intensities $J_L$ both above and below the critical value $J_L\gtrsim J_{cr}$ near which the gain begins to increase rapidly and reproduction of the pump spectrum by the Stokes wave is initiated. Solutions are obtained for average intensities of the Stokes wave and molecular vibrations in the first approximation in a constant pump field. It is established that, for $J_L\gtrsim J_{cr}$, the Stokes wave undergoes rapid nonsteady-state amplification which is associated with an increase in the amplitude of the molecular vibrations. The results of the calculations show good agreement with known experimental data.