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Marcucci G, Pierangeli D, Agranat AJ, et al. Topological control of extreme waves. Nat Commun. 2019;10(1):5090doi: 10.1038/s41467-019-12815-0.
Marcucci, G., Pierangeli, D., Agranat, A. J., Lee, R. K., DelRe, E., & Conti, C. (2019). Topological control of extreme waves. Nature communications, 10(1), 5090. https://doi.org/10.1038/s41467-019-12815-0
Marcucci, Giulia, et al. "Topological control of extreme waves." Nature communications vol. 10,1 (2019): 5090. doi: https://doi.org/10.1038/s41467-019-12815-0
Marcucci G, Pierangeli D, Agranat AJ, Lee RK, DelRe E, Conti C. Topological control of extreme waves. Nat Commun. 2019 Nov 08;10(1):5090. doi: 10.1038/s41467-019-12815-0. PMID: 31704911; PMCID: PMC6841676.
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Nat Commun. 2019 Nov 08;10(1):5090. doi: 10.1038/s41467-019-12815-0.

Topological control of extreme waves.

Nature communications

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

Affiliations

  1. Department of Physics, University Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy. [email protected].
  2. Institute for Complex Systems, Via dei Taurini 19, 00185, Rome, Italy. [email protected].
  3. Department of Physics, University Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy.
  4. Institute for Complex Systems, Via dei Taurini 19, 00185, Rome, Italy.
  5. Applied Physics Department, Hebrew University of Jerusalem, 91904, Jerusalem, Israel.
  6. Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, 300, Taiwan.

PMID: 31704911 PMCID: PMC6841676 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.

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