  Bragg waveguides are promising optical filters for pump suppression in
spontaneous Four-Wave Mixing (FWM) photon sources. In this work, we investigate
the generation of unwanted photon pairs in the filter itself. We do this by
taking advantage of the relation between spontaneous and classical FWM, which
allows for the precise characterisation of the nonlinear response of the
device. The pair generation rate estimated from the classical measurement is
compared with the theoretical value calculated by means of a full quantum model
of the filter, which also allows to investigate the spectral properties of the
generated pairs. We find a good agreement between theory and experiment,
confirming that stimulated FWM is a valuable approach to characterise the
nonlinear response of an integrated filter, and that the pairs generated in a
Bragg waveguide are not a serious issue for the operation of a fully integrated
nonclassical source.
