Strongly localized modes in discrete systems with quadratic nonlinearity

We report the existence of bright and dark families of strongly localized modes in discrete systems with a quadratic nonlinearity. It is shown analytically and confirmed numerically that the second-harmonic field may form stable bound states with fundamental fields of different topologies. Furthermore, we found different types of solutions having analogs neither in other discrete models nor in continuum models and studied the background stability of dark modes.