  Four-photon scattering in nonlinear waveguides is an important physical
process that allows photon-pair generation in well defined guided modes, with
high rate and reasonably low noise. Most of the experiments to date used the
scalar four-photon scattering process in which the pump photons and the
scattered photons have the same polarization. In birefringent waveguides,
vectorial four-photon scattering is also allowed: these vectorial scattering
processes involve photons with different polarizations. In this article, the
theory of four-photon scattering in nonlinear, birefringent, and dispersive
fibers is developed in the framework of the quantum theory of light. The work
focusses on the spectral properties and quantum correlations (including
entanglement) of photon-pairs generated in high-birefringence and
low-birefringence fibers.
