One-dimensional Townes solitons in dual-core systems with localized coupling

TL;DR

This paper introduces an exactly solvable dual-core waveguide system with localized coupling that supports stable Townes solitons and exhibits spontaneous symmetry breaking, with potential applications in photonic device design.

Contribution

It presents a novel dual-core system with exact solutions for Townes solitons and symmetry breaking, including stability analysis and dynamic behavior of unstable states.

Findings

Exact solutions for Townes solitons and symmetry breaking in the system.

Identification of stability boundaries for asymmetric solitons.

Unstable solitons evolve into stable breathers or asymmetric states.

Abstract

The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers draw renewed interest to the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons. It is based on a dual-core waveguide with quintic self-focusing and fused (localized) coupling between the cores. The respective system of coupled nonlinear Schroedinger equations gives rise to exact solutions for full families of symmetric solitons and asymmetric ones, which are produced by the supercritical SSB bifurcation (i.e., the symmetry-breaking phase transition of the second kind). Stability boundaries of asymmetric solitons are identified by dint of numerical methods. Unstable solitons spontaneously transform into robust moderately asymmetric breathers or strongly asymmetric states with small intrinsic oscillations. The setup can be used in the design of photonic devices operating in coupling and switching regimes.