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Single photon detectors have dark count rates that depend strongly on thebias level for detector operation. In the case of weak light sources such asnovel lasers or single-photon emitters, the rate of counts due to the lightsource can be comparable to that of the detector dark counts. In such cases, acharacterization of the statistical properties of the dark counts is necessary.The dark counts are often assumed to follow a Poisson process that isstatistically independent of the incident photon counts. This assumption mustbe validated for specific types of photodetectors. In this work, we focus onsingle-photon avalanche photodiodes (SPADs) made for 1550nm. For the InGaAsdetectors used, we find the measured distributions often differ significantlyfrom Poisson due to the presence of dead time and afterpulsing with thedifference increasing with the bias level. When the dead time is increased toremove the effects of afterpulsing, it is necessary to correct the measureddistributions for the effects of the dead time. To this end, we apply aniterative algorithm to remove dead time effects from the probabilitydistribution for dark counts as well as for the case where light from anexternal weak laser source (known to be Poisson) is detected together with thedark counts. We believe this to be the first instance of the comprehensiveapplication of this algorithm to real data and find that the correctedprobability distributions are Poisson distributions in both cases. Weadditionally use the Grassberger-Procaccia algorithm to estimate the entropyproduction rates of the dark count processes, which provides a single metricthat characterizes the temporal correlations between dark counts as well as theshape of the distribution. We have thus developed a systematic procedure fortaking data with 1550nm SPADs and obtaining accurate photocount statistics toexamine novel light sources.

Dark Current and Single Photon Detection by 1550nm Avalanche Photodiodes: Dead Time Corrected Probability Distributions and Entropy Rates