The effect of weak dispersion on stimulated Raman scattering

The Raman gain of an undepleted plane-wave multimode pump laser is calculated. The Stokes and pump fields are represented as vector states in a Hilbert space, and the Dirac bracket notation is introduced to simplify the form of the equations. It is shown that in the absence of dispersion the Stokes vector component correlated with the pump grows exponentially with the monochromatic-pump gain, while all other Stokes components experience zero growth. Perturbation theory is used to second order to determine the gain decrease resulting from relative dispersion between pump and Stokes, and the results are compared with previous works.