Gap solitons under competing local and nonlocal nonlinearities

TL;DR

This paper investigates how competing local and nonlocal nonlinearities affect the existence, stability, and shape of one-dimensional gap solitons in periodic potentials, revealing complex bifurcation patterns and potential applications in optical signal processing.

Contribution

It introduces a detailed analysis of bifurcations and shape transformations of gap solitons influenced by local and nonlocal nonlinearities, highlighting new bifurcation behaviors and stability properties.

Findings

Unstable on-site GS modes become unstable near the bandgap edge with nonlocal self-defocusing.

Off-site GSs bifurcate into modes with single, double humps, and flat-tops.

Shape transformations and bifurcation cutoffs depend on the degree of nonlocality.

Abstract

We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite bandgap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the bandgap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.