Symmetric and asymmetric solitons in dual-core couplers with competing quadratic and cubic nonlinearities

TL;DR

This paper investigates the existence, stability, and bifurcation behavior of symmetric and asymmetric solitons in a dual-core coupler with competing quadratic and cubic nonlinearities, revealing complex bifurcation loops and stability properties.

Contribution

It introduces a comprehensive analysis of soliton bifurcations in dual-core systems with chi^(2) and chi^(3) nonlinearities, including the extended cascading approximation and stability of various soliton types.

Findings

Stable asymmetric solitons emerge via supercritical bifurcation.

Bifurcation loops can be concave when inter-core coupling is weak.

Single-color symmetric solitons are stable; asymmetric ones are unstable.

Abstract

We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms, and test their stability. The transition from symmetric to asymmetric soliton branches, and back to the symmetric ones proceeds via a bifurcation loop. A pair of stable asymmetric branches emerge from the symmetric family via a supercritical bifurcation; eventually, the asymmetric branches merge back into the symmetric one through a reverse bifurcation. The existence of the loop is explained by means of an extended version of the cascading approximation for the chi^(2) interaction, which takes into regard the XPM part of the chi(3) interaction. When the inter-core coupling is weak, the bifurcation loop features a concave shape, with the asymmetric branches losing their stability at the turning points. In addition to the two-color solitons, which are built of the fundamental-frequency (FF) and second-harmonic (SH) components, in the case of the self-focusing chi^(3) nonlinearity we also consider single-color solitons, which contain only the SH component, but may be subject to the instability against FF perturbations. Asymmetric single-color solitons are always unstable, whereas the symmetric ones are stable, provided that they do not coexist with two-color counterparts. Collisions between tilted solitons are studied too.