Abstract
Extreme-value statistics have originally mostly been discussed in a metereological context, for example as ocean rogue waves. More recently, similar statistics became apparent for supercontinua in photonic crystal fibers [1]. As a third system, optical multiple filamentation has drawn attention as the first two-dimensional optical system in which extreme events were discovered [2]. While all these systems show similar long-tailed statistical distributions of events, the physics behind these statistics is completely different. In this study, we quantify the previously neglected characteristics of a sudden and unpredictable appearance of rogue events for the first time. Going one step beyond the all-linear statistical description of rogue waves, we employ nonlinear statistical methods such as the Grassberger-Procaccia algorithm [3] in a comparison of the degree of determinism in the three rogue-wave supporting systems. Quite surprisingly, we find that ocean rogue waves as well as extreme events in the multifilament scenario bear a limited amount of predictability in contrast to fiber rogue events. Figure 1(a) shows the experimental setup that we used to investigate the multifilament dynamics. The multifilament is generated by focusing an amplified 1 kHz Ti:sapphire laser into a 1.5 m long xenon cell (2 bar). A time series of more than 24,000 subsequent multifilaments is generated. For the results presented here, the laser peak power is adjusted to 30 GW, i.e., >10 times the power required for single filamentation in xenon at 2 bar. The fluence profile of each individual multifilament is recorded with a 500 kilopixel camera, which is triggered by the laser repetition rate. For comparison, we employed original data sets containing fiber supercontinuum rogue wave events [1] as well as published time series of the original Draupner event [4]
© 2015 IEEE
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