Extreme value statistics and the Pareto distribution in silicon photonics

TL;DR

This paper demonstrates that fluctuations in stimulated Raman scattering in silicon follow extreme value statistics, revealing a Pareto-like distribution and providing new insights into the behavior of optical rogue waves.

Contribution

It shows that extreme value statistics apply to silicon photonics phenomena, connecting optical fluctuations to Pareto distributions and offering a mathematical framework for understanding these extreme events.

Findings

16% of Stokes pulses account for 84% of pump energy transfer

Fluctuations follow Pareto distribution similar to 80/20 rule

Provides mathematical insight into optical rogue waves

Abstract

L-shape probability distributions are extremely non-Gaussian distributions that have been surprisingly successful in describing the frequency of occurrence of extreme events, ranging from stock market crashes and natural disasters, the structure of biological systems, fractals, and optical rogue waves. In this paper, we show that fluctuations in stimulated Raman scattering in silicon, as well as in coherent anti-Stokes Raman scattering, can follow extreme value statistics and provide mathematical insight into the origin of this behavior. As an example of the experimental observations, we find that 16% of the Stokes pulses account for 84% of the pump energy transfer, an uncanny resemblance to the empirical Pareto principle or the 80/20 rule that describes important observation in socioeconomics.