Impact of imbalancing in the self-splitting of beams with nested vortices into solitons in quadratic non-linear crystals

We address the existence and instability of bright vortex solitary waves in quadratic non-linear media under conditions for Type II second-harmonic ge neration and study in detail the effects introduced by the presence of powe r imbalancing at the fundamental frequency. We fmd the families of solitary -wave solutions with different combinations of topological charges of the n ested vortices and show their spontaneous azimuthal instability. The growth rates of the azimuthal perturbations are calculated as a function of the i mbalancing. Experimental consequences are stressed and discussed. (C) 1998 Elsevier Science B.V. All rights reserved.