Standing Wave Solutions in Twisted Multicore Fibers

TL;DR

This paper investigates the existence and stability of standing wave solutions in twisted multi-core optical fibers, revealing conditions for their existence and stability through numerical experiments and spectral analysis.

Contribution

It introduces new findings on the existence, stability, and specific configurations of standing waves in twisted multi-core fibers, including the optical Aharonov-Bohm effect.

Findings

Standing waves exist for small coupling parameters.

Optical Aharonov-Bohm suppression occurs at specific twist and waveguide numbers.

Certain single-site energy concentration solutions are neutrally stable.

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 $\phi$ and the number of waveguides $N$ is related by $\phi = \pi/N$. 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.