Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple
degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial
entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing
collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the
pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in
the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is
configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement.
Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is
monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walkoff)
of the two polarizations, along with a strong correlation between wavelength and emission direction. We also
examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized
when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be
accomplished by properly focusing the pump.