  The photonic crystal fiber (PCF) is one of the excellent media for generating
photon pairs via spontaneous four wave mixing. Here we study how the
inhomogeneity of PCFs affect the spectral properties of photon pairs from both
the theoretical and experimental aspects. The theoretical model shows that the
photon pairs born in different place of the inhomogeneous PCF are coherently
superposed, and a modulation in the broadened spectrum of phase matching
function will appear, which prevents the realization of spectral factorable
photon pairs. In particular, the inhomogeneity induced modulation can be
examined by measuring the spectrum of individual signal or idler field when the
asymmetric group velocity matching is approximately fulfilled. Our experiments
are performed by tailoring the spectrum of pulsed pump to satisfy the specified
phase matching condition. The observed spectra of individual signal photons,
which are produced from different segments of the 1.9 m inhomogeneous PCF,
agree with the theoretical predictions. The investigations are not only useful
for fiber based quantum state engineering, but also provide a dependable method
to test the homogeneity of PCF.
