  We develop from first principles the coupled wave equations that describe
polarization-sensitive parametric amplification based on four-wave mixing in
standard (randomly birefringent) optical fibers. We show that in the
small-signal case these equations can be solved analytically, and permit us to
predict the gain experienced by the signal beam as well as its state of
polarization (SOP) at the fiber output. We find that, independently of its
initial value, the output SOP of a signal within the parametric gain bandwidth
is solely determined by the pump SOP. We call this effect of pulling the
polarization of the signal towards a reference SOP as polarization attraction,
and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond
the zero polarization mode dispersion (PMD) limit, and it takes into account
moderate deviations of the PMD from zero. In particular, our theory is capable
of analytically predicting the rate of degradation of the efficiency of the
parametric amplifier which is caused by the detrimental PMD effect.
