Transverse spatial and frequency properties of two-photon states   generated by spontaneous parametric down-conversion
  We present a detailed account of the two-photon states generated by SPDC in both type I and type II phase matching, including the effects of anisotropy of the nonlinear medium and the frequency spread of the down-converted fields. Accurate as well as simplified expressions are derived for type I and type II phase matching in the context of Fourier Optics. The main results are compared with experimental data available in the literature, showing good agreement in all cases. 
A. G. da Costa Moura, W. A. T. Nogueira, S. P. Walborn, and C. H.   Monken