k-space theory and convective gains of stimulated Raman side scattering

We have developed a k-space theory for stimulated Raman scattering. The theory is used to calculate the convective gain of stimulated Raman side scattering (SRSS) in order to clarify the discrepancies found between previous gain formulas proposed in the literature. The gains are dramatically modified by the eigenvalue of SRSS, and the maximum gain occurs not at the perfect wave-number matching condition but instead at a wave number having a small deviation that is associated with the eigenvalue. Numerical solutions of the k-space theory equations are compared with, and used to verify, analytically derived gains. We demonstrate connections to the existing path integral theories, and we derive a similar path integral formula in k space.