  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.
