The poisson property of extreme events in optics

Abstract Statistics of extreme events in optics, defined as above-threshold counts of an optical signal, is shown to converge, in the large-sample-size limit, to a generalized Poisson distribution whose mean is found via the exponent of the respective extreme-value distribution. Specifically, extreme-event readouts from polynomial and exponential optical nonlinearities are shown to converge in their statistics to Poisson distributions whose means are, respectively, exponential and slower-than-exponential functions of the extreme-event-counter threshold. Extreme-event counts of a phase readout, on the other hand, converge to a Poisson process whose mean is a light-tailed function of the threshold. The Poisson-limit property of extreme events in optics suggests a powerful resource for a unified treatment of a vast variety of extreme-event phenomena, ranging from optical rogue waves to laser-induced damage.