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Extreme-value statistics in nonlinear optics.

Aleksei M Zheltikov

|May 15, 2024

Summary

This summary is machine-generated.

All nonlinear optics statistics converge to universal extreme-value statistics. Polynomial nonlinearities follow Gumbel distribution, while exponentially growing signals exhibit Fréchet statistics, leading to extreme events and rogue waves.

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Area of Science:

Nonlinear optics
Statistical physics
Extreme value theory

Background:

Nonlinear optical processes generate diverse output statistics.
Understanding these statistics is crucial for predicting extreme events.

Purpose of the Study:

To identify universal statistical behaviors in nonlinear optics.
To classify extreme-value distributions (EVDs) for different nonlinearities.

Main Methods:

Analysis of statistical convergence in the extreme-value limit.
Classification of nonlinear optical phenomena based on their growth dynamics.

Main Results:

Identified convergence of various nonlinear optics statistics to universal EVDs.
Polynomial nonlinearities (Kerr effect, harmonic generation) converge to Gumbel distribution.
Exponentially growing signals (parametric instabilities, stimulated scattering) converge to Fréchet statistics, favoring extreme events.

Conclusions:

Extreme-value statistics in nonlinear optics are universal and depend on nonlinearity type.
Fréchet statistics in exponentially growing signals contribute to rogue wave phenomena.