We numerically demonstrate the formation of the spatiotemporal version of theso-called diffractive resonant radiation generated in waveguide arrays withKerr nonlinearity when a long pulse is launched into the system. The phasematching condition for the diffractive resonant radiation that we have foundearlier for CW beams also works well in the spatiotemporal case. By introducinga linear potential, one can introduce a continuous shift of the centralwavenumber of a linear pulse, whereas in the nonlinear case one can demonstratethat the soliton self-wavenumber shift can be compensated by the emission ofdiffractive resonant radiation, in a very similar fashion as it is done inoptical fibers. This work paves the way for designing unique optical devicesthat generate spectrally broad supercontinua with a controllable directionalityby taking advantage of the combined physics of optical fibers and waveguidearrays.
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