Journal
NATURE COMMUNICATIONS
Volume 10, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41467-019-12815-0
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Funding
- PRIN 2015 NEMO project [2015KEZNYM]
- H2020 QuantERA QUOMPLEX [731473]
- H2020 PhoQus [820392]
- PRIN 2017 PELM [20177PSCKT]
- Sapienza Ateneo (2016 program)
- Ministry of Science and Technology of Taiwan [105-2628-M-007-003-MY4]
- Sapienza Ateneo (2017 program)
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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 Schrodinger 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.
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