Rectified Bloch oscillations in dynamically modulated waveguide arrays.

We study the dynamics of excitations in dynamically modulated waveguide arrays with an external spatial linear potential. Longitudinally periodic modulation may cause a significant change in the width of the quasi-energy band and leads to the dynamical band suppression with a linear dispersion relation. This substantially affects the Bloch oscillation dynamics. Novel dynamical phenomena with no analogue in ordinary discrete waveguides, named rectified Bloch oscillations, are highlighted. Due to the interplay between directional coupling between adjacent waveguides and diffraction suppression by the introduced onsite energy difference, at odd times of half Bloch oscillations period, the new submodes are continuously excited along two opposite rectification directions and experience same oscillation evolution, and eventually lead to the formation of a diamondlike intensity network. Both the amplitude and direction of the rectified Bloch oscillations strongly depend on the coupling strength. When coupling strength passes the critical value at which dynamical band suppression with a linear dispersion relation occurs, the direction of Bloch oscillations is inverted.