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Spontaneous parametric down-conversion (SPDC) is a widely used process toprepare entangled photon pairs. In SPDC, a second-order nonlinear crystal ispumped by a coherent laser beam to generate photon pairs. The photon pairs areusually detected by single-mode fibers (SMF), where only photons in a Gaussianmode can be collected. The collection modes possess typical Gaussianparameters, namely a beam waist and a focal plane position. The collectionefficiency of photons highly depends on the choice of both parameters. Theexact focal plane position of the pump beam relative to those of the detectionmodes is difficult to determine in a real experiment. Usually, theoretical andexperimental studies assume that the focal plane positions of the pump and thegenerated beams are positioned in the center of the crystal. The displacementof beam focal planes can lead to deviations from expected results and thecoupling efficiency into SMF can increase or decrease. In this work, weconsider variable positions of focal planes and investigate how shifts of thesefocal planes influence the spatial and temporal properties of photon pairs. Wepresent SPDC arrangements, in which the knowledge of the exact position of thefocal planes is essential, as well as scenarios, where focal planedisplacements do not contribute significantly to experimental outcomes. Thesefindings are of particular interest for achieving higher efficiency in SPDCexperiments.

Spatial and temporal characteristics of spontaneous parametric down-conversion with varying focal planes of interacting beams