Surface waves in two-dimensional modulated photonic lattices

In this work, we reveal substantial differences between the dynamic localization at surfaces of one- and two-dimensional modulated lattices. We study the generation of surface waves in two-dimensional periodically-curved hexagonal waveguide arrays. We find that no localized surface modes exist in two dimensional modulated lattices, in a sharp contrast to one-dimensional lattices. Numerical simulations of beam propagation are shown for hexagonal arrays exhibiting hexagonal-shaped boundaries with 5 waveguides at each facet. In the straight array, the beam experiences strong diffraction broadening. In the curved array with modulation parameters tuned to the DL regime light beam remains localized and diffraction is completely suppressed after each bending period when the light beam is launched into the central waveguide.