Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities

Maucher, F.; Pohl, T.; Krolikowski, W.; Skupin, S.

Abstract

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.

Citation

Maucher, F., Pohl, T., Krolikowski, W., & Skupin, S. (2017). Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities. Optical Data Processing and Storage, 3(1), 13-19. https://doi.org/10.1515/odps-2017-0003

• Journal Article Type: Article
• Acceptance Date: May 1, 2017
• Online Publication Date: Jul 5, 2017
• Publication Date: Jun 27, 2017
• Deposit Date: Jul 9, 2017
• Publicly Available Date: Oct 18, 2017
• Journal: Optical Data Processing and Storage
• Electronic ISSN: 2084-8862
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 3
• Issue: 1
• Pages: 13-19
• DOI: https://doi.org/10.1515/odps-2017-0003
• Public URL: https://durham-repository.worktribe.com/output/1375006