SOLITONS IN COUPLED WAVE-GUIDES WITH QUADRATIC NONLINEARITY

We consider a model of two linearly coupled second-harmonic-generating waveguides. The analysis is focused on the case of no walkoff and ful l matching. We demonstrate existence of a bifurcation that transforms obvious symmetric soliton states into nontrivial asymmetric ones. The bifurcation point is found exactly, while a full analytical descriptio n of the asymmetric solutions is obtained by means of the variational approximation. Comparing this with numerical results generated by the shooting method, we conclude that, in a part of the range where the as ymmetric states are predicted, the analytical approximation provides v ery good accuracy, while in another part, the asymmetric solitons disa ppear. Whenever they exist, however, direct partial differential equat ion simulations demonstrate that they are stable, while the symmetric ones are not. We also demonstrate that the asymmetric solitons remain stable if walkoff is added. The soliton states found here can be used for optical switching.