The linearity of single-photon detectors allows accurate optical measurements at low light levels and using non-classical light in spectroscopy, biomedical imaging, optical communication, and sensing. However, in practice, the response of single-photon detectors can exhibit intriguing nonlinear effects that may influence the performed measurements. Here, we demonstrate a direct single-source measurement of the absolute nonlinearity of single-photon detectors with unprecedented accuracy. We discover a surprising supralinear behavior of single-photon avalanche diodes and show that it cannot be explained using known theoretical models. We also fully characterize sub- and supra-linear operation regimes of superconducting nanowire single-photon detectors and uncover the supralinearity under faint continuous illumination. The results identify new detector anomalies that supersede existing knowledge of nonlinear effects at the single-photon level.

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