Stimulated Brillouin scattering in a multimode step-index fiber can be used to generate a counter-propagating, phase-conjugate beam that would prove useful in many applications, such as near diffraction limited, double-pass high-power amplifiers or coherent beam combination. Relatively little modeling of such a fiber-based phase conjugator has been done, making design decisions regarding type and length of fiber largely guesswork. A numerical model was constructed with the aim of providing educated predictions about the phase conjugate fidelity that could be expected from a given pump intensity input coupled into a specific fiber. A numerical perturbation algorithm was constructed to search for the Stokes modal arrangement with the highest gain for a given pump input. The gain was calculated from the differential equation for the Stokes power under the assumption that all pump/Stokes modes decay/grow at the same rate, and that the fiber was lossless. The model proves to be much more accurate in predicting experimentally observed phase conjugate fidelities than previous efforts. In addition, the phenomenon of beam cleanup to higher order fiber modes is predicted and explained
