Rogue Waves of Light

Using a trained neural network from numerical simulations, researchers are able to predict the intensity of extreme waves of light emerging at the output of an optical fiber from unstable nonlinear propagation governed by the nonlinear Schrödinger equation. (Source: TUT)

Stories of giant ocean waves with great destruc­tive power are the stuff of legend and folklore, but today their scientific study is a critical area of multi­disciplinary research spanning oceano­graphy, physics and mathe­matics. A parti­cular problem faced by researchers is that these extreme waves arise seemingly randomly on the ocean’s surface, and it appears impos­sible to predict the condi­tions that may precede their appearance. A related practical diffi­culty is that it is not always possible to measure such waves completely, and the available instru­mentation most often captures only a portion of the wave charac­teristics.

Recent experiments studying analogous extreme waves of light and have now used the powerful tools of arti­ficial intel­ligence to study this problem and have succeeded in deter­mining a proba­bility distri­bution that preferen­tially identifies the emergence of rogue waves. The particular novelty of this work is that the researchers from Tampere Uni­versity of Tech­nology (TUT), Finland, and the Institut FEMTO-ST at the Université Bourgogne-Franche Comté, France, trained a neural network to identify the parti­cular time-domain properties of rogue waves with the highest and most extreme intensities from only partial infor­mation on the wave charac­teristics in the frequency or wavelength domain.

The experiments were performed by injecting laser pulses into an optical fibre system, which was designed to reproduce wave propa­gation described by a nonlinear Schrö­dinger equation, a model that can also apply to water waves. Using an instrument developed especially to measure optical spectra in real time with high dynamic range, the researchers compiled a data set of thousands of noisy spectral signals from a non­linear process called modu­lation insta­bility which is believed to be associated with some classes of rogue waves on the ocean.

Although optical spectra are easy to measure, they do not show the presence of rogue waves directly. But by using powerful numerical simu­lations to train a neural network, it was possible to develop an algorithm that could accu­rately pick out features in the spectra that could predict the emergence of a rogue wave, even though these features were essen­tially invisible to the eye of a researcher.

“Remarkably, the algorithm was shown to be capable of predicting the peak intensity of a rogue wave asso­ciated with any particular spectral measure­ment, even though experiments never actually measured the rogue wave intensity directly,” says Goëry Genty, who led the team at Tampere Univer­sity of Tech­nology. The results obtained yielded a proba­bility distri­bution for the appearance of the optical rogue waves and were also used to classify the spectral measure­ments into different sets associated with different types of rogue waves.

“As well as sugges­ting that similar techniques can be used to analyse real-time measure­ments on oceano­graphic wave data, the results open new perspec­tives in all fields of research where direct time domain obser­vations are difficult but where spectral data is available,” concludes John M. Dudley, who headed the team at the Univer­sité Bourgogne-Franche Comté. (Source: TUT)

Reference: M. Närhi et al.: Machine learning analysis of extreme events in optical fibre modulation instability, Nat. Commun. 9, 4923 (2018); DOI: 10.1038/s41467-018-07355-y

Link: Laboratory of Photonics, Tampere University of Technology, Tampere, Finland

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