Two-Dimensional Surface Waves in Modulated Photonic Lattices Ivan L. Garanovich 1 *, Alexander Szameit 2 , Andrey A. Sukhorukov 1 , Matthias Heinrich 3 , Felix Dreisow 3 , Thomas Pertsch 3 , Stefan Nolte 3 , Andreas Tünnermann 3 , and Yuri S. Kivshar 1 1 Nonlinear Physics Centre and Centre for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia 2 Solid State Institute and Physics Department, Technion, 32000 Haifa, Israel 3 Institute of Applied Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany e-mail address: *E-Mail: ilg124@physics.anu.edu.au Abstract: We study surface waves in two-dimensional modulated photonic lattices and demonstrate that, in a sharp contrast to one-dimensional lattices where localized surface modes can exist, the radiation escapes along the boundaries of the two-dimensional structure. 1. Surface modes in one-dimensional lattices Applying an external driving to a periodic potential drastically modifies both propagation and localization of waves. One important example is dynamic localization, 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 [2-4]. Importantly, dynamic localization was predicted to occur in multi-dimensional systems, and it was observed in both one- [2, 3] and two-dimensional [4] modulated waveguide arrays. Dynamic localization 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 [5, 6]. The appearance of these novel surface modes is a result of nontrivial modification of the diffraction properties in the vicinity of the lattice edge, which is introduced by the lattice modulation. Therefore, an important question is whether such surface modes can also be supported by two- dimensional modulated lattices. 2. Two-dimensional surface waves 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 [see a sketch in Fig. 1(a)]. We find that no localized surface modes exist in two- dimensional modulated lattices, in a sharp contrast to one-dimensional lattices [5, 6]. Fig. 1. (a) Sketch of a periodically curved hexagonal waveguide array. The insert shows the orientation of the coordinate axes. (b-d) Numerical simulations of the beam propagation in the array with hexagonal-shaped boundaries (marked with a dashed line). The waveguide spacing is d = 22 mm. Arrows mark the waveguide which is excited at the input facet. (b) Output diffraction profile in the straight array. The propagation distance is one modulation period. (c) Output beam profile in the curved array in the regime of dynamic localization when the central waveguide is excited. The propagation distance is ten modulation periods. (d) The same as (c) when the edge waveguide is excited. In Figs. 1(b-d) 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 [Fig. 1(b)]. In the curved array with modulation parameters tuned to the dynamic localization regime [4] light beam remains localized and diffraction is completely suppressed after each bending period when the light beam is launched into the central waveguide [Fig. 1(c)]. In contrast, when the light beam is launched into the edge waveguide of the same curved array it diffracts away from the initially excited lattice site [Fig. 1(d)]. This IQEC/CLEO Pacific Rim 2011 ● 28 August - 1 September 2011 ● Sydney, Australia 978-0-9775657-7-1  2011 AOS 63