Schmidt decompositions of parametric processes II: Vector four-wave mixing

In vector four-wave mixing, one or two strong pump waves drive two weak signal and idler waves, each of which has two polarization components. In this report, vector four-wave mixing processes in a randomly-birefringent fiber (modulation interaction, phase conjugation and Bragg scattering) are studied in detail. For each process, the Schmidt decompositions of the coupling matrices facilitate the solution of the signal-idler equations and the Schmidt decomposition of the associated transfer matrix. The results of this report are valid for arbitrary pump polarizations.