Symmetric and asymmetric solitons in dual-core couplers with competing quadratic and cubic nonlinearities (1305.4793v1)
Abstract: We consider the model of a dual-core spatial-domain coupler with chi2 and chi3 nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi3 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 chi2 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 chi3 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.