Discrete nonlinear Schrödinger equations for periodic optical systems : pattern formation in \chi(3) coupled waveguide arrays

Christian, JM ORCID: https://orcid.org/0000-0003-2742-0569 and Fox, R 2019, Discrete nonlinear Schrödinger equations for periodic optical systems : pattern formation in \chi(3) coupled waveguide arrays , in: 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), 25th – 30th August 2019, Vienna University of Technology, Austria.

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Abstract

Discrete nonlinear Schrödinger equations have been used for many years to model the propagation of light in optical architectures whose refractive index profile is modulated periodically in the transverse direction. Typically, one considers a modal decomposition of the electric field where the complex amplitudes satisfy a coupled system that accommodates nearest neighbour linear interactions and a local intensity dependent term whose origin lies in the χ (3) contribution to the medium's dielectric response. In this presentation, two classic continuum configurations are discretized in ways that have received little attention in the literature: the ring cavity and counterpropagating waves. Both of these systems are defined by distinct types of boundary condition. Moreover, they are susceptible to spatial instabilities that are ultimately responsible for generating spontaneous patterns from arbitrarily small background disturbances. Good agreement between analytical predictions and simulations will be demonstrated.

Item Type: Conference or Workshop Item (Lecture)
Schools: Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre
Journal or Publication Title: The 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation Book of Abstracts
Publisher: Institute of Mechanics and Mechatronics, Faculty of Mechanical and Industrial Engineering Institute of Analysis and Scientific Computing, Faculty of Mathematics and Geoinformation TU Wien
ISBN: 9783200065116
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Depositing User: JM Christian
Date Deposited: 02 Mar 2020 13:21
Last Modified: 14 Jul 2020 14:45
URI: http://usir.salford.ac.uk/id/eprint/56538

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