Modeling and optimization of photon pair sources based on spontaneous parametric down-conversion

We address the problem of efficient modeling 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 that works for a broader range of parameters than the Gaussian model used previously. The developed modeling 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 tradeoffs between parameters of the source.