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Optical Data Processing and Storage

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Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities

F. Maucher
  • Corresponding author
  • Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom of Great Britain and Northern Ireland
  • Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom of Great Britain and Northern Ireland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ T. Pohl / W. Krolikowski
  • Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia
  • Science Program, Texas A&M University at Qatar, Doha, Qatar
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ S. Skupin
  • Univ. Bordeaux - CNRS - CEA, Centre Lasers Intenses et Applications, UMR 5107, 33405 Talence, France
  • Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, VILLEURBANNE, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-07-05 | DOI: https://doi.org/10.1515/odps-2017-0003


We study beam propagation in the framework of the nonlinear Schrödinger equation with competing Gaussian nonlocal nonlinearities. We demonstrate that such system can give rise to self-organization of light into stable states of trains or hexagonal arrays of filaments, depending on the transverse dimensionality. This long-range ordering can be achieved by mere unidirectional beam propagation. We discuss the dynamics of long-range ordering and the crucial role which the phase of the wavefunction plays for this phenomenon. Furthermore we discuss how transverse dimensionality affects the order of the phasetransition.

This article offers supplementary material which is provided at the end of the article.

Keywords: nonlinear Schrödinger equation; selforganization; competing nonlocal nonlinearities


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About the article

Received: 2017-02-13

Revised: 2017-04-09

Published Online: 2017-07-05

Published in Print: 2017-06-27

Citation Information: Optical Data Processing and Storage, ISSN (Online) 2084-8862, DOI: https://doi.org/10.1515/odps-2017-0003.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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