Over saturation behavior of SiPMs at high photon exposure

Several types of Silicon Photomultipliers were exposed to short pulsed laser light (~ 30 ps FWHM) with its intensity varying from single photon to well above the number of microcells of the device. We observed a significant deviation of the output of SiPMs from the expected behavior although such response curve is considered to be rather trivial. We also noticed that the output exceeds the maximum expected pulse height, which should be defined as the total number of pixels times the single photon pulse height. At the highest light intensity (~ 500 times the number of pixels) that we tested, the signal output reached up to twice the maximum theoretical pulse height, and still did not fully saturate.