Bistable and tristable soliton switching in collinear arrays of linearly coupled waveguides

The soliton switching in an array of three, linearly coupled waveguides is investigated. Supported by a variational model, we show that a novel nonlinear switching among stable localized states is possible in long couplers. The numerical integrations of the governing equations confirm this interesting phenomenon. These results can be extended to asymmetrical nonlinear directional couplers, where the asymmetry is in the nonlinear coefficients. The tristable operational mode is investigated too and the model furnishes valuable indications in order to realize it. The model also allows a physical insight into the more general problem of steering in arrays with a large number of waveguides. Finally, an exact, antisymmetric solution of the governing equations of the three-waveguide array is also investigated, because it shows dynamical properties that might be useful in all-optical switching.