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We present a theoretical and experimental analysis of the joint effects ofthe transverse electric field distribution and of the nonlinear crystalcharacteristics on the properties of photon pairs generated by spontaneousparametric downconversion (SPDC). While it is known that for a sufficientlyshort crystal the pump electric field distribution fully determines the jointsignal-idler properties, for longer crystals the nonlinear crystal propertiesalso play an important role. In this paper we present experimental measurementsof the angular spectrum (AS) and of the conditional angular spectrum (CAS) ofphoton pairs produced by spontaneous parametric downconversion (SPDC), carriedout through spatially-resolved photon counting. In our experiment we controlwhether or not the source operates in the short-crystal regime through thedegree of pump focusing, and explicitly show how the AS and CAS measurementsdiffer in these two regimes. Our theory provides an understanding of theboundary between these two regimes and also predicts the correspondingdiffering behaviors.

Effects of crystal length on the angular spectrum of spontaneous parametric downconversion photon pairs