Spatiotemporal dynamics in a twisted, circular waveguide array

TL;DR

This paper analyzes the existence and stability of localized light pulses in twisted multi-core optical fibers, deriving asymptotic solutions and identifying conditions for optical suppression and stability thresholds.

Contribution

It introduces asymptotic expressions for localized solutions in twisted waveguide arrays and explores their stability and suppression phenomena, extending understanding of nonlinear optical waveguides.

Findings

Localized solutions are well approximated by asymptotic expressions.

Optical suppression occurs at specific twist parameters, notably when  = /N.

Solutions are stable below a critical coupling value, which peaks at  = /N.

Abstract

We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By considering an even number, $N$, of waveguides, we derive asymptotic expressions for solutions in which the bulk of the light intensity is concentrated as a soliton-like pulses confined to a single waveguide. The leading order terms obtained are in very good agreement with results of numerical computations. Furthermore, as in the model without temporal dispersion, when the twist parameter, $\phi$, is given by $\phi = \pi/N$, these standing waves exhibit optical suppression, in which a single waveguide remains unexcited, to leading order. Spectral computations and numerical evolution experiments suggest that these standing wave solutions are stable for values of the coupling parameter less than a critical value, at which point a spectral instability results from the collision of an internal eigenvalue with the eigenvalues at the origin. This critical value has a maximum when $\phi = \pi/N$.