The thick-crystal regime in photon pair sources

We present comprehensive measurement data on the pump and collection beam parameters necessary to achieve high collection efficiency ($89.0 \pm 1.7 \%$) together with high brightness when a single $\beta$-Barium Borate crystal is operated in the thick-crystal regime and pumped with a narrow linewidth laser source. Spectral analysis of the collinear, non-degenerate photons suggest that the effective interaction length within the crystal is dominated by the collection beam mode and the use of longer crystals with increased spatial walk-off does not necessarily lead to a reduced collection efficiency. This result is an important consideration for optical designers who seek to develop practical photon pair sources.