Strongly localized vectorial modes in nonlinear waveguide arrays

We report the existence of a variety of strongly localized bright vectorial modes in discrete cubic media with self-and cross-modulation. In addition to the modes familiar from the scalar limit, interesting types of solutions can be identified. These solutions are unique, to our knowledge, and have no analogs in other discrete or continuous models. The linear stability analysis of the vectorial modes discloses various instability scenarios, and permits us to draw conclusions for potential all-optical switching schemes. The analytical results obtained are confirmed by direct numerical simulations.