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We study analytically and numerically a kind of diffractive resonantradiation emitted by spatial solitons, which is generated in waveguide arrayswith Kerr nonlinearity. The phase matching condition between soliton andradiation is derived and agrees well with direct pulse propagation simulations.The folded dispersion due to the Brillouin zone leads to a peculiar anomaloussoliton recoil that we describe in detail. A linear potential applied acrossthe array generates the analogue of the Raman self-frequency shift in opticalfibers, only now applied to the wavenumber. We demonstrate that it is possibleto mimic closely temporal fiber-optical dynamics, unveiling the new effects ofwavenumber-supercontinuum generation and the compensation of the 'solitonself-wavenumber shift' by the emitted diffractive radiation. This work pavesthe way for designing unique optical devices that generate spectrally broadsupercontinua with a controllable directionality.

Diffractive resonant radiation emitted by spatial solitons in waveguide arrays: towards a spatiotemporal supercontinuum generation