Analytical study of the nonlinear pulse dynamics in arrays of linearly coupled waveguides

The dynamics of nonlinear pulse propagation in arrays of linearly coupled optical waveguides is considered. For an array of three waveguides, a simplified model based on a variational method is able to predict the steady-state solutions and the strong coupling dynamics with a good degree of accuracy and to furnish a necessary condition for the existence of localized states, as confirmed by numerical solutions of the governing equations. The pulse-radiation interaction is also studied, revealing that additional, long-period oscillations overlap the linear coupling frequency. In the regime of initial conditions that lead to strong localization dynamics, we present a theoretical result that predicts to a good approximation the asymptotic localized state.