Symmetric and asymmetric solitons in a nonlocal nonlinear coupler

TL;DR

This paper investigates how nonlocality in a dual-core optical waveguide affects soliton stability and symmetry-breaking, revealing that increased nonlocality can stabilize asymmetric solitons and alter bifurcation types.

Contribution

It introduces a detailed analysis of nonlocal effects on soliton symmetry-breaking, combining numerical, variational, and analytical methods to extend understanding beyond local nonlinear models.

Findings

Nonlocality changes SBB from subcritical to supercritical.

Asymmetric solitons become stable with increased nonlocality.

Antisymmetric solitons are less affected by nonlocality.

Abstract

We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveg- uide with nonlocal (thermal) nonlinearity. In comparison with the well-known coupled systems with the local nonlinearity, the present setting is affected by the competition of different spatial scales, viz., the coupling length and correlation radius of the nonlocality, $\sqrt{d}$. By means of numer- ical methods and variational approximation (VA, which is relevant for small d), we find that, with the increase of the correlation radius, the SBB changes from subcritical into supercritical, which makes all the asymmetric solitons stable. On the other hand, the nonlocality has little influence on the stability of antisymmetric solitons. Analytical results for the SBB are also obtained (actually, for antisymmetric "accessible solitons") in the opposite limit of the ultra-nonlocal nonlinearity, using a coupler based on the Snyder-Mitchell model. The results help to grasp the general picture of the symmetry breaking in nonlocal couplers.