  This study investigated the nonlinear frequency conversions between the six
polarization modes of a two-mode birefringent fiber. The aim was to demonstrate
that the selective excitation of different combinations of linearly polarized
spatial modes at the pump wavelength initiates distinct intermodal vector
four-wave mixing processes. In particular, this study shows that exciting two
orthogonally polarized LP01 and LP11 modes can result in simultaneous
generation of up to three pairs of different spatial modes of orthogonal
polarizations at different wavelengths. The role of the phase birefringence of
the spatial modes in the phase-matching of such a four-wave mixing process was
explained. Moreover, the theoretical predictions were verified through
numerical simulations based on coupled nonlinear Schrodinger equations and also
confirmed experimentally in a commercially available birefringent fiber.
