Model for transient stimulated molecular Raman scattering

The theory of transient stimulated Raman scattering is developed for a molecule with nondegenerate initial and final states. The general coupled Maxwell-Bloch equations describing this case are presented for an arbitrary number of Stokes and anti-Stokes fields, including effects of ac Stark shift, transient refractivity, saturation, and phase mismatching. Various common cases are examined, leading to simpler equations of field propagation and molecular evolution. In the case of only pump and first Stokes fields in dispersionless medium, the Stokes will stably phase lock to the pump when Stokes is increasing, but still smaller than the pump, and Stokes is decreasing, but still larger than the pump. Inhomogeneous broadening is described by an ensemble of scattering molecules. The ensemble averaged Bloch equation is formally solved to give the Raman source as a convolution of the ensemble distribution with the homogeneously broadened density matrix. The couple scattering of an arbitrary number of Stokes and anti-Stokes fields is compactly described by a unitary transformation among suitable normalized field envelopes, with the antihermitean gain operator a function of the density matrix and the phase shift.