  We address the problem of efficient modelling of photon pairs generated in
spontaneous parametric down-conversion and coupled into single-mode fibers. It
is shown that when the range of relevant transverse wave vectors is restricted
by the pump and fiber modes, the computational complexity can be reduced
substantially with the help of the paraxial approximation, while retaining the
full spectral characteristics of the source. This approach can serve as a basis
for efficient numerical calculations, or can be combined with analytically
tractable approximations of the phase matching function. We introduce here a
cosine-gaussian approximation of the phase matching function which works for a
broader range of parameters than the gaussian model used previously. The
developed modelling tools are used to evaluate characteristics of the photon
pair sources such as the pair production rate and the spectral purity
quantifying frequency correlations. Strategies to generate spectrally
uncorrelated photons, necessary in multiphoton interference experiments, are
analyzed with respect to trade-offs between parameters of the source.
