Topological control of extreme waves

Giulia Marcucci (), Davide Pierangeli, Aharon J. Agranat, Ray-Kuang Lee, Eugenio DelRe and Claudio Conti
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Giulia Marcucci: University Sapienza
Davide Pierangeli: University Sapienza
Aharon J. Agranat: Hebrew University of Jerusalem
Ray-Kuang Lee: National Tsing Hua University
Eugenio DelRe: University Sapienza
Claudio Conti: University Sapienza

Nature Communications, 2019, vol. 10, issue 1, 1-8

Abstract: Abstract From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of topological control based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions through Riemann theta functions. We demonstrate the concept experimentally by reporting observations of supervised transitions between waves with different genera. Considering the box problem in a focusing photorefractive medium, we tailor the time-dependent nonlinearity and dispersion to explore each region in the state diagram of the nonlinear wave propagation. Our result is the first realization of topological control of nonlinear waves. This new technique casts light on shock and rogue waves generation and can be extended to other nonlinear phenomena.

Date: 2019
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DOI: 10.1038/s41467-019-12815-0

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