Nonlinear index effects due to pump laser bandwidth in Raman conversion

In the Raman process, the finite pump bandwidth and the medium bandwidth can result in a nonlinear index effect depending on the pump intensity. This can result in spectral dispersion and, more importantly, introduce Stokes wavefront errors due to nonuniform pump intensities. In this work, we derive an analytical expression for the nonlinear index as a function of wavelength for a flat top pump spectrum. The results indicate that the effect is most pronounced for a pump spectral bandwidth comparable to the Raman medium linewidth and becomes small in the limits of narrow and broad-band lasers. Implications on obtaining good beam quality in a Raman conversion process are discussed. In addition, the averaged gain versus laser bandwidth is derived.