Measurement of Coupling PDC photon sources with single-mode and   multimode optical fibers
  We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multi-mode optical fibers as a function of the pump beam diameter, crystal length and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multi-mode PDC light (defined by, for instance, multi-mode fibers or apertures, corresponding to bucket detection). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single spatial mode. We also define a multimode collection efficiency that is useful for single-photon detector calibration applications. 
Stefania Castelletto, Ivo Pietro Degiovanni, Alan Migdall, Valentina   Schettini, Michael Ware