Extreme-value statistics in nonlinear optics

Zheltikov, Aleksei M.

doi:10.1364/OL.510419

Title: Extreme-value statistics in nonlinear optics

Journal Article · 08 May 2024 · Optics Letters

DOI: https://doi.org/10.1364/OL.510419 · OSTI ID:2346281

We show that, although nonlinear optics may give rise to a vast multitude of statistics, all these statistics converge, in their extreme-value limit, to one of a few universal extreme-value statistics. Specifically, in the class of polynomial nonlinearities, such as those found in the Kerr effect, weak-field harmonic generation, and multiphoton ionization, the statistics of the nonlinear-optical output converges, in the extreme-value limit, to the exponentially tailed, Gumbel distribution. Exponentially growing nonlinear signals, on the other hand, such as those induced by parametric instabilities and stimulated scattering, are shown to reach their extreme-value limits in the class of the Fréchet statistics, giving rise to extreme-value distributions (EVDs) with heavy, manifestly nonexponential tails, thus favoring extreme-event outcomes and rogue-wave buildup.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024882

OSTI ID:: 2346281

Journal Information:: Optics Letters, Journal Name: Optics Letters Journal Issue: 10 Vol. 49; ISSN 0146-9592; ISSN OPLEDP

Publisher:: Optical Society of AmericaCopyright Statement

Country of Publication:: United States

Language:: English

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