ASYMMETRIC SOLITONS IN COUPLED 2ND-HARMONIC-GENERATING WAVE-GUIDES

We report results of analytical and numerical consideration of soliton s in a system of two linearly coupled second-harmonic-generating waveg uides. We consider the system with arbitrary coupling constants for th e fundamental and second harmonics, and with an arbitrary (but equal) mismatch inside each waveguide (in a previous work, only the limit cas e of equal coupling constants, and a single value of the mismatch, wer e considered). Two regions of existence of nontrivial asymmetric solit on states, along with bifurcation lines at which they bifurcate from o bvious symmetric solitons, are identified. The analytical approach is based on the variational approximation, which is followed by direct nu merical solution of the stationary ordinary differential equations. Th e analytical and numerical results are found to be in fairly good agre ement, except for a very narrow parametric region, where the second-ha rmonic component of the soliton is changing its sign, having a nonmono tonous shape. We further establish the stability of the asymmetric sol itons, simulating the corresponding partial differential equations, an d simultaneously show that the coexisting symmetric solitons are unsta ble. We then analyze in detail the effects of a walkoff (spatial misal ignment) between the two cores. We demonstrate that the asymmetric sol itons remain stable if walkoff is small. When the walkoff becomes larg er, the solitons get strongly distorted, and finally destruct when wal koff gets too large.