Machine learning analysis of extreme events in optical fibre modulation instability

Mikko Närhi,Juha Toivonen,Lauri Salmela,John M Dudley,Cyril Billet,Goëry Genty

doi:10.1038/s41467-018-07355-y

Abstract

A central research area in nonlinear science is the study of instabilities that drive extreme events. Unfortunately, techniques for measuring such phenomena often provide only partial characterisation. For example, real-time studies of instabilities in nonlinear optics frequently use only spectral data, limiting knowledge of associated temporal properties. Here, we show how machine learning can overcome this restriction to study time-domain properties of optical fibre modulation instability based only on spectral intensity measurements. Specifically, a supervised neural network is trained to correlate the spectral and temporal properties of modulation instability using simulations, and then applied to analyse high dynamic range experimental spectra to yield the probability distribution for the highest temporal peaks in the instability field. We also use unsupervised learning to classify noisy modulation instability spectra into subsets associated with distinct temporal dynamic structures. These results open novel perspectives in all systems exhibiting instability where direct time-domain observations are difficult.

Highlights

A central research area in nonlinear science is the study of instabilities that drive extreme events
We aim to apply the techniques of machine learning to the study of chaotic nonlinear dynamics in optics, with the particular aim of studying the statistics of the maximum intensity of temporal peaks in noise-seeded modulation instability using only spectral measurements
For the modulation instability system studied here, we have shown that real-time measurements of only the spectral intensity can be combined with supervised machine learning to yield quantitative information about temporal characteristics using training based on accurate numerical simulations

Summary

Introduction

A central research area in nonlinear science is the study of instabilities that drive extreme events. The localised structures emerging from MI show complex dynamics and random statistics, and it has even been suggested that MI may be linked to the development of extreme events or rogue waves[4,5,6] Such studies have been of particular interest in nonlinear fibre optics because recent developments in real-time measurement techniques[7,8] have allowed the emergent dynamics to be characterised experimentally in both the temporal and spectral domains. The DFT technique is experimentally simpler because it involves only propagation in dispersive fibre, but is typically associated with a relatively low dynamic range of 20–25 dB21 This is a significant limitation to the detailed study of extreme events in MI which are associated with extension in the spectral wings below the −40 dB level[22,23]. Aside from the direct relevance of our results to optics, our approach has a far wider impact in showing how machine learning applied to only spectral data can be successfully used to study the properties of extreme events in the time domain

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