Modeling the Variance of Passive SiPMs in the Nonlinear Regime

Silicon photomultipliers (SiPMs) are widely used in high-energy physics, medical imaging, and other photon-counting applications. While their nonlinear response at high light intensities is well known, its impact on the statistical fluctuations of the detector output remains much less understood. In this work, we develop an analytical framework for the variance of the charge response of passive-quenching SiPMs in the two limiting cases of instantaneous light pulses and pulses much longer than the pixel recovery time. Based on these exact results, we propose a phenomenological model that describes the variance of the SiPM charge response for arbitrary pulse durations while accounting for pixel recovery and correlated noise. The resulting framework is then used to predict the photon-counting resolution over the full dynamic range of the detector. The model is validated through Monte Carlo simulations and experimental measurements performed with laser, LED, and scintillation light sources. The results show that the optimal photon-counting resolution is generally reached well beyond the onset of nonlinear response, since pixel saturation introduces sub-Poissonian fluctuations that partially compensate for the nonlinear compression of the SiPM response. These findings provide a practical framework for predicting photon-counting resolution and optimizing the operation of passive SiPMs over a wide dynamic range.