TY - JOUR
T1 - Symmetric and asymmetric solitons in dual-core couplers with competing quadratic and cubic nonlinearities
AU - Gubeskys, Lazar
AU - Malomed, Boris A.
PY - 2013/7/1
Y1 - 2013/7/1
N2 - We consider the model of a dual-core spatial-domain coupler with ?-2- and ?-3- nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing ?-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. Namely, a pair of stable asymmetric branches emerges 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 X(2) interaction, which takes into regard the cross-phase modulation part of the ?-3- interaction. When the intercore 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 ?-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.
AB - We consider the model of a dual-core spatial-domain coupler with ?-2- and ?-3- nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing ?-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. Namely, a pair of stable asymmetric branches emerges 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 X(2) interaction, which takes into regard the cross-phase modulation part of the ?-3- interaction. When the intercore 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 ?-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.
UR - http://www.scopus.com/inward/record.url?scp=84879982595&partnerID=8YFLogxK
U2 - 10.1364/JOSAB.30.001843
DO - 10.1364/JOSAB.30.001843
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AN - SCOPUS:84879982595
SN - 0740-3224
VL - 30
SP - 1843
EP - 1852
JO - Journal of the Optical Society of America B: Optical Physics
JF - Journal of the Optical Society of America B: Optical Physics
IS - 7
ER -