Abstract
I investigate the properties of spontaneous parametric down-conversion (SPDC)
involving co-linear Gaussian spatial modes for the pump and the photon
collection optics. Approximate analytical and numerical results are obtained
for the peak spectral density, photon bandwidth, pair collection probability,
heralding ratio, and spectral purity, as a function of crystal length and beam
focusing parameters. I address the optimization of these properties
individually as well as jointly, and find focusing conditions that
simultaneously bring the pair collection probability, heralding ratio, and
spectral purity to near-optimal values. These properties are also found to
be nearly scale invariant, that is, ultimately independent of crystal length.
The results obtained here are expected to be useful for designing SPDC
sources with high performance in multiple categories for the next generation
of SPDC applications.
