Dynamic Eigenstates of Parametric Interactions in Randomly Birefringent Fibers

In parametric devices based on nondegenerate four-wave mixing, there exist dynamic eigenstates for the signal and idler, for which there is no change of polarization as the waves propagate. For the case of parametric amplifiers with two pumps of arbitrary polarization, the eigenstates are the sum of the Stokes vectors of the pumps. 

For Bragg scattering, the eigenstate polarizations are determined by the sum of two Stokes vectors of one pump plus one of the other pump. Separated coupled-wave solutions for the evolution of the signal and idler are obtained for each eigenstate.