  A systematic study of the nonlinear response of Silicon Photomultipliers
(SiPMs) has been conducted through Monte Carlo simulations. SiPMs have been
proven to show a universal nonlinear response when it is expressed in terms of
relative parameters independent of both the gain and the photon detection
efficiency (PDE). Nonlinearity has been shown to mainly depend on the balance
between the photon rate and the pixel recovery time. However, exponential-like
and finite light pulses have been found to lead to different nonlinear
behaviors, which also depend on the correlated noise, the overvoltage
dependence of the PDE, and the impedance of the readout circuit. Correlated
noise has been shown to have a minor impact on nonlinearity, but it can
significantly affect the shape of the SiPM output current.
  Considering these dependencies and previous statistical analysis of the
nonlinear response of SiPMs, two simple fitting models have been proposed for
exponential-like and finite light pulses, explaining the role of their various
terms and parameters. Even though these models have only three fitting
parameters, they provide an accurate description of the nonlinear response of
SiPMs for a wide range of situations.
