  The theory of two counter-propagating polarized beams interacting in a
randomly birefringent fiber via the Kerr and Raman effects is developed and
applied to the quantitative description of Raman polarizers in the undepleted
regime. Here Raman polarizers, first reported by Martinelli et. al. [Opt.
Express. 17, 947 (2009)], are understood as Raman amplifiers operating in the
regime in which an initially weak unpolarized beam is converted into an
amplified fully polarized beam towards the fiber output. Three parameters are
selected for the characterization of a Raman polarizer: the degree of
polarization of the outcoming beam, its state of polarization, and its gain.
All of these parameters represent quantities that are averaged over all random
polarization states of the initially unpolarized signal beam. The presented
theory is computer friendly and applicable to virtually all practically
relevant situations, including the case of co-propagating beams, and in
particular to the undepleted as well as the depleted regimes of the Raman
polarizer.

Optics