  A novel time-domain approach using the momentum operator is used to model
spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of
self- and cross-phase modulation on the photon-pair production rate and
heralded photon purity are investigated. We show that in the special case where
only one half of the photon-pair state is filtered that the generation rate and
purity of the heralded photons are unmodified by the presence of self- and
cross-phase modulation. The significance of this special case arises when we
consider heralded single-photon sources, where future schemes are likely to
only filter the herald photon to ensure a high heralding efficiency is
maintained.
