Diffractive resonant radiation emitted by spatial solitons in waveguide arrays

We study analytically and numerically the diffractive resonant radiation emitted by spatial solitons, which is generated in waveguide arrays with Kerr nonlinearity. The phase matching condition between solitons and radiation is derived and studied for the first time and agrees well with direct pulse propagation simulations. The folded dispersion due to the Brillouin zone leads to a peculiar anomalous soliton recoil that we describe in detail. © 2013 American Physical Society.