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We investigate the possibility of generating pure heralded single photonsthrough spontaneous parametric down-conversion comparing thecounter-propagating geometry studied in [1] with more conventionalco-propagating configurations which enhance the purity of the heralded photonstate through the technique of group-velocity matching. We estimate the Schmidtnumber associated to the temporal modes as a function of the pump pulseduration for three particular configurations, showing how the differentphase-matching conditions influences the degree of separability that can beachieved.

Heralding pure single photons: a comparision between counter-propagating and co-propagating twin photons