  We present a theoretical and experimental study of the generation of photon
pairs through the process of spontaneous four wave mixing (SFWM) in a few-mode,
birefringent fiber. Under these conditions, multiple SFWM processes are in fact
possible, each associated with a different combination of transverse modes for
the four waves involved. We show that in the weakly guiding regime, for which
the propagation modes may be well approximated by linearly polarized modes, the
departure from circular symmetry due to the fiber birefringence translates into
conservation rules which retain elements from azimuthal and rectangular
symmetries: both OAM and parity must be conserved for a process to be viable.
We have implemented a SFWM source based on a "bow-tie" birefringent fiber, and
have measured for a collection of pump wavelengths the SFWM spectra of each of
the signal and idler photons in coincidence with its partner photon. We have
used this information, together with knowledge of the transverse modes into
which the signal and idler photons are emitted, as input for a genetic
algorithm which accomplishes two tasks: i) the identification of the particular
SFWM processes which are present in the source, and ii) the characterization of
the fiber used.
