We investigate the detection of an ultra-bright single-photon source using highly efficient superconducting nanowire single-photon detectors (SNSPDs) at telecom wavelengths. Both the single-photon source and the detectors are characterized in detail. At a pump power of 100 mW (400 mW), the measured coincidence counts can achieve 400 kcps (1.17 Mcps), which is the highest ever reported at telecom wavelengths to the best of our knowledge. The multi-pair contributions at different pump powers are analyzed in detail. We compare the experimental and theoretical second order coherence functions $g^{(2)}(0)$ and find that the conventional experimentally measured $g^{(2)}(0)$ values are smaller than the theoretically expected ones. We also consider the saturation property of SNSPD and find that SNSPD can be easier to saturate with a thermal state rather than with a coherent state. The experimental data and theoretical analysis should be useful for the future experiments to detect ultra-bright down-conversion sources with high-efficiency detectors.
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