Topological control of extreme waves

Giulia Marcucci,Ray-Kuang Lee,Aharon J Agranat,Davide Pierangeli,Eugenio Delre,Claudio Conti

doi:10.1038/s41467-019-12815-0

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.

Highlights

From optics to hydrodynamics, shock and rogue waves are widespread
We experimentally test this approach in photorefractive materials, giving evidence of an unprecedented control of nonlinear waves, which allows the first observation of the transition from focusing dispersive shock waves (DSWs) to rogue waves (RWs)
The topological classification of nonlinear beam propagation by the genera of the Riemann theta functions opens a new route to control the generation of extreme waves

Summary

Introduction

They appear as distinct phenomena, transitions between extreme waves are allowed. G represents the number of oscillating phases and evolves during light propagation: “single phase” DSWs have g 1⁄4 1, RWs have g $ 2 and SGs have g >> 2 This creates a fascinating connection between extreme waves and topology. We can change g and explore all the possible dynamic phases (see Fig. 1, where ζ is given in terms of the observation time t, detailed below) We experimentally test this approach in photorefractive materials, giving evidence of an unprecedented control of nonlinear waves, which allows the first observation of the transition from focusing DSWs to RWs

Methods

Results

Conclusion