Bloch oscillations and resonant radiation of light propagating in arrays of nonlinear fibers with high-order dispersion

Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of the spatial Bloch oscillations on the emission of the dispersive radiation by the solitary wave is studied. It is shown that Bloch oscillations result in the generation of new frequencies. The condition of resonant emission of dispersive waves is derived and it is demonstrated that it matches very well with the results of direct numerical simulations.