We present a theoretical and experimental study of the generation of photonpairs through the process of spontaneous four wave mixing (SFWM) in a few-mode,birefringent fiber. Under these conditions, multiple SFWM processes are in factpossible, each associated with a different combination of transverse modes forthe four waves involved. We show that in the weakly guiding regime, for whichthe propagation modes may be well approximated by linearly polarized modes, thedeparture from circular symmetry due to the fiber birefringence translates intoconservation rules which retain elements from azimuthal and rectangularsymmetries: 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, andhave measured for a collection of pump wavelengths the SFWM spectra of each ofthe signal and idler photons in coincidence with its partner photon. We haveused this information, together with knowledge of the transverse modes intowhich the signal and idler photons are emitted, as input for a geneticalgorithm which accomplishes two tasks: i) the identification of the particularSFWM processes which are present in the source, and ii) the characterization ofthe fiber used.
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