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Optimizing the brightness of a spontaneous parametric down conversion (SPDC)source is an important task for many quantum information applications. Weinvestigate the optimal focusing conditions to maximize the number of photonsproduced in an SPDC process and coupled with single-mode fibers. We provide ageneral expression for the two-photon wavefunction, generalizing previous knownresults, by considering collinear and non-collinear emission. We presentanalytical expressions for our results in the thin crystal limit and clarifythe relation between different focusing conditions already existing in theliterature. Differently from what was previously reported, we show that theoptimal ratio between the pump waist and the generated photons waist depends onthe emission angle: It is $1/\sqrt2$ for collinear degenerate emission andapproaches $1/2$ for larger collection angles. The role of spectral filters isalso analyzed. We support and enrich our discussion with numerical simulations,performed for type-I SPDC in a $\beta$ barium borate crystal. For this type ofemission, we also investigate the role of the transverse walk-off outside thethin crystal regime.

Optimal focusing conditions for bright spontaneous parametric down-conversion sources