Stokes wavefront preservation in broad-band forward raman amplification

The theory of broad-band forward Raman amplification is presented. An exact solution for the pump and Stokes fields is derived in the limit of negligible population transfer, negligible linear dispersion, an arbitrary number of axial modes with mode spacing much larger than the Raman linewidth, collimated-beam ray optics, and arbitrary Raman conversion. It is shown that if the incident pump and Stokes fields are factorable into two factors, one of which is time dependent while the other depends on transverse displacement, then the Stokes field is amplified with no alteration in its wavefront.