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We investigate the recovery of superconducting NbN-nanowire photon counters after detection of an optical pulse at a wavelength of 1550nm, and present a model that quantitatively accounts for our observations. The reset time is found to be limited by the large kinetic inductance of these nanowires, which forces a tradeoff between counting rate and either detection efficiency or active area. Devices of usable size and high detection efficiency are found to have reset times orders of magnitude longer than their intrinsic photoresponse time.
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