  In this work we study the spatio-temporal correlations of photons produced by
spontaneous parametric down conversion. In particular, we study how the waists
of the detection and pump beams impact on the spectral bandwidth of the
photons. Our results indicate that this parameter is greatly affected by the
spatial properties of the detection beam, while not as much by the pump beam.
This allows for a simple experimental implementation to control the bandwidth
of the biphoton spectra, which only entails modifying the optical configuration
to collect the photons. Moreover, we have performed Hong-Ou-Mandel
interferometry measurements that also provide the phase of the biphoton
wavefunction, and thereby its temporal shape. We explain all these results with
a toy model derived under certain approximations, which accurately recovers
most of the interesting experimental details.
