Symmetry breakings in dual-core systems with double-spot localization of nonlinearity

TL;DR

This paper investigates symmetry breaking phenomena in a dual-core nonlinear system with localized nonlinearity spots, revealing stable asymmetric modes through numerical analysis of a more realistic model.

Contribution

It introduces a dual-core system with localized nonlinearity spots and analyzes symmetry breaking, including stable modes, extending previous idealized models.

Findings

Symmetric and asymmetric modes are analytically constructed.

All asymmetric modes are unstable in the ideal delta-function model.

Stable asymmetric modes are found in the extended model with finite spot size.

Abstract

We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries.