Quantum theory of stimulated Raman effect in a fluctuating medium

A set of quantum-mechanical coupled Langevin equations with space-dependent variables is derived for the 1-st Stokes and Anti-Stokes, and laser field in a fluctuating two-level molecular medium pumped by an external laser source with continuous spectrum. These fundamental equations are exact within the quasi-monochromatic approximation, and applicable to wider problems which contain non-stationary cases for inhomogeneous and homogeneous broadening with continuous spectrum, spatial effects (propagation and depletion of laser field), and fluctuations. After its formulation, this theory was applied to a one-dimensional typical example for the stimulated Stokes effect. By means of quasilinearization of the fundamental equation, this theory gives not only the power spectrum of amplitude fluctuations and the mean square of phase diffusion, but also a second threshold condition for a hard mode instability as in the laser medium, and also some aspects as phase-transition-like phenomena of the stimulated Raman effect. Last, it was shown that a hard mode instability for the backward Stokes arises at a second threshold lower than that of the forward Stokes.