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The objective is to explain the cause of the nonlinear phenomenon named "extreme value event" (EE, often called "optical rogue wave") observed in the chaotic regime of self-pulsing all solid state lasers (SPSSL). Here, EEs have the form of giant light pulses appearing sporadically and apparently at random, but more often than a statistical fluctuation. It is pertinent to recall here that EEs are spontaneously observed in the customary design of SPSSL, i.e., EEs do not require here a unusual cavity design or operation regime to be formed, as it is required in other types of optical systems instead. The main tools for this research are laser prototypes to observe EEs. Time series of the pulses and images of the laser spots are recorded and studied with techniques of nonlinear analysis, to obtain statistical properties and dynamical indices, as the distribution of oscillating modes, the values of the dimension of embedding and the Lyapunov exponents, as functions of the control parameters. The results guide the development of theoretical descriptions aimed to predict and control the formation of EEs. Regarding application interest: SPSSL are customary as miniaturized laser sources in some applications of interest for the USAF, mostly as rangefinders. Let suppose that the emission of a laser pulse of higher intensity (than the one obtained in normal regime operation) is desirable at some particular occasion. Say, to measure the distance of an object that is just beyond the limit of the rangefinder.