Asymmetric solitons in coupled second-harmonic-generating waveguides

Abstract

We report results of analytical and numerical consideration of solitons in a system of two linearly coupled second-harmonic-generating waveguides. We consider the system with arbitrary coupling constants for the fundamental and second harmonics, and with an arbitrary (but equal) mismatch inside each waveguide (in a previous work, only the limit case of equal coupling constants, and a single value of the mismatch, were considered). Two regions of existence of nontrivial asymmetric soliton states, along with bifurcation lines at which they bifurcate from obvious symmetric solitons, are identified. The analytical approach is based on the variational approximation, which is followed by direct numerical solution of the stationary ordinary differential equations. The analytical and numerical results are found to be in fairly good agreement, except for a very narrow parametric region, where the second-harmonic component of the soliton is changing its sign, having a nonmonotonous shape. We further establish the stability of the asymmetric solitons, simulating the corresponding partial differential equations, and simultaneously show that the coexisting symmetric solitons are unstable. We then analyze in detail the effects of a walkoff (spatial misalignment) between the two cores. We demonstrate that the asymmetric solitons remain stable if walkoff is small. When the walkoff becomes larger, the solitons get strongly distorted, and finally destruct when walkoff gets too large.