  We make a thorough analysis of heralded single photon sources regarding how
factors such as the detector gate-period, the photon rates, the fiber coupling
efficiencies, and the system losses affect the performance of the source. In
the course of this we give a detailed description of how to determine fiber
coupling efficiencies from experimentally measurable quantities. We show that
asynchronous sources perform, under most conditions, better than synchronous
sources with respect to multiphoton events, but only for nearly perfect
coupling efficiencies. We apply the theory to an asynchronous source of
heralded single photons based on spontaneous parametric downconversion in a
periodically poled, bulk, KTiOPO4 crystal. The source generates light with
highly non-degenerate wavelengths of 810 nm and 1550 nm, where the 810 nm
photons are used to announce the presence of the 1550 nm photons inside a
single-mode optical fiber. For our setup we find the probability of having a
1550 nm photon present in the single-mode fiber, as announced by the 810 nm
photon, to be 48%. The probability of multiphoton events is strongly suppressed
compared to a Poissonian light source, giving highly sub-Poisson photon
statistics.
