Two-dimensional solitons in second-harmonic-generating media with fractional diffraction

Abstract

We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov-Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single-and two-color solitons are linked by a bifurcation which takes place withthe increase of the soliton's power.