Wave-front replication versus beam cleanup by stimulated scattering

It is shown that the equations for forward/backward-stimulated scattering may, in the limit of highly aberrated beams, be expressed in the Dirac bracket notation. This compact notation illuminates the form of the solution, which states that for high gain the Stokes beam becomes spatially correlated with the pump. The formalism clarifies the distinction between three limiting regimes of seeded Raman conversion: two yield Raman beam cleanup, and the third yields Raman wave-front replication.