A perturbation analysis of polarization-decoupled Brillouin-enhanced four-wave mixing

The technique of polarization-decoupled Brillouin-enhanced four-wave mixing is known for its high-reflectivity, high-quality phase conjugation. The treatment accounts for the transverse structure of the pump and signal beams within a waveguide in the paraxial approximation, assuming a steady-state acoustic wave and assuming that many transverse modes of the waveguide are excited by the four mixing waves. The zeroth-order equations are obtained for the polarization states of the signal and conjugate beams by dropping all phase-mismatch terms. Under the stated assumptions, the phase-mismatched terms are found to make only a small contribution. A first-order solution accounts for phase-mismatch terms and determines the loss of conjugation fidelity as a function of the angular spread of the pump laser beam, the pump-signal angle, the pump intensities, and the pump mutual fidelity