  In an experiment reported recently [Phys. Rev. Lett. 100, 133601 (2008)], we
demonstrated that, through group velocity matched parametric downconversion,
heralded single photons can be generated in pure quantum states without
spectral filtering. The technique relies on factorable photon pair production,
initially developed theoretically in the strict collinear regime; focusing -
required in any experimental implementation - can ruin this factorability. Here
we present the numerical model used to design our single photon sources and
minimize spectral correlations in the light of such experimental
considerations. Furthermore, we show that the results of our model are in good
agreement with measurements made on the photon pairs and give a detailed
description of the exact requirements for constructing this type of source.
