Type I parametric down conversion of highly focused Gaussian beams in finite length crystals

摘要

We study the correlations in wave vector space of photon pairs generated bytype I spontaneous parametric down conversion using a Gaussian pump beam. Weanalyze both moderate focused and highly focused regimes taking specialattention to the angular spectrum and the conditional angular spectrum. Simpleanalytic expressions are derived that allow us to study in detail thedependence of these spectra on the waist of the source and the length of thenonlinear crystal. These expressions are in good agreement with numericalexpectations and reported experimental results. They are used to make asystematic search of optimization parameters that improve the feasibility ofusing highly focused Gaussian beams to generate idler and signal photons withpredetermined mean values and spread of their transverse wave vectors.