Surface waves in two-dimensional modulated photonic lattices

Applying an external driving to a periodic potential drastically modifies both propagation and localization of waves. One important example is dynamic localization (DL), the suppression of broadening of a wave packet during its motion in a periodic potential under the action of an externally applied periodic field [1]. The same effect can occur for optical beams in curved waveguide arrays, where the waveguide bending [see Fig. 1(a)] mimics the effects of the driving field, leading to the cancellation of diffraction [2,3]. Importantly, DL was predicted to occur in multi-dimensional systems, and it was observed in both one- [2] and two-dimensional [3] modulated waveguide arrays. DL was also studied at the boundaries of one-dimensional lattices, where lattice modulation was shown to facilitate the formation of families of new type of defect-free linear surface modes [4,5]. Therefore, an important question is whether such surface modes can also be supported by two-dimensional modulated lattices.