Beam cleanup via stimulated Raman scattering in multimode fibers is modeled by numerically considering the competition between the Stokes modes of graded-index and step-index fibers. The relative gain of each Stokes mode is calculated by considering the overlap the various pump and Stokes modes of the fibers. Mode competition in a graded-index fiber favors the LP01 Stokes mode while mode competition in a step-index fiber does not favor the LP01 Stokes mode. This model explains why beam cleanup has only been reported for graded-index fibers and not for step-index fibers.
Nathan B. Terry, Thomas G. Alley, and Timothy H. Russell, "An explanation of SRS beam cleanup in graded-index fibers and the absence of SRS beam cleanup in step-index fibers," Opt. Express 15, 17509-17519 (2007). https://doi.org/10.1364/OE.15.017509