Standing Wave Solutions in Twisted Multicore Fibers

Abstract

In the present work, we consider the existence and spectral stability of standing wave solutions to a model for light propagation in a twisted multi-core fiber with no gain or loss of energy. Numerical parameter continuation experiments demonstrate the existence of standing wave solutions for sufficiently small values of the coupling parameter. Furthermore, standing waves exhibiting optical Aharonov-Bohm suppression, where there is a single waveguide which remains unexcited, exist when the twist parameter $\varphi$ and the number of waveguides $N$ is related by $\varphi =\pi /N$. Spectral computations and numerical timestepping simulations suggest that standing wave solutions where the energy is concentrated in a single site are neutrally stable. Solutions with asymmetric coupling and multi-pulse solutions are also briefly explored.

arXiv comment10 pages, 16 figures

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Cited by in corpus (3)

• Complex localization mechanisms in networks of coupled oscillators: two case studies
• Spatiotemporal dynamics in a twisted, circular waveguide array
• Localized synchronous patterns in weakly coupled bistable oscillators