Wave propagation in waveguide arrays with alternating positive and negative couplings

We introduce a waveguide array model with alternating positive and negative couplings between adjacent waveguides. Two different settings where such a model can be realized are identified as arrays of defects in Bragg gratings and arrays with propagation constants that periodically vary along the propagation direction. We analyze the properties of wave propagation in such waveguide arrays and find several interesting properties that have no counterpart in the case of arrays with constant couplings. These include the beam self-splitting, self-induced Talbot oscillations, symmetric evolution of Bloch oscillations, and new families of lattice solitons.