Influence of Polarization Transformation in Phase Conjugation of Polarization Multiplexed Data using Bragg-Scattering FWM in nonlinear SOAs

We theoretically investigate the suitability of the selection of pump frequency ($\omega_p$) with respect to the signal frequency ($\omega_s$) for the best polarization insensitive phase conjugate generation through Bragg-scattering based four-wave mixing in nonlinear SOAs. We study the positive detuning ($\omega_s>\omega_p$) and negative detuning ($\omega_s<\omega_p)$ scenario for the inherent polarization transformation of conjugate generation at both the ports of SOA. Conjugate generation is desired to be through a unitary transformation for its utility in further digital signal processing, and we prove that only positive detuning conditions result in unitary transformation.