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

Christian, JM; Fox, R

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.

Citation

pattern formation in \chi(3) coupled waveguide arrays. Presented at 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), Vienna University of Technology, Austria

• Presentation Conference Type: Lecture
• Conference Name: 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019)
• Conference Location: Vienna University of Technology, Austria
• Online Publication Date: Aug 30, 2019
• Publication Date: Aug 30, 2019
• Deposit Date: Mar 2, 2020
• Publicly Available Date: Mar 2, 2020
• Book Title: The 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation Book of Abstracts
• ISBN: 9783200065116
• DOI: https://doi.org/10.34726/waves2019
• Publisher URL: https://doi.org/10.34726/waves2019
• Related Public URLs: http://waves2019.at/
• Additional Information: Event Type : Conference