Molding Light in Two-Dimensional Photonic Lattices

Abstract

F abricated dielectric periodic structures such as photonic crystals are attracting increasing attention, opening new possibilities for engineering transmission and refl ection of light and developing novel applications of photonic-crystal devices for all-optical signal processing and switching.1 Conventional approaches to guiding light in such periodic structures are based on wave transport through permanent waveguides, combined with resonant Bragg refl ection and total internal refl ection. However, these approaches may only allow limited fl exibility in the light molding and routing that is inherently restricted by the fabricated geometry. Recently, we demonstrated, both theoretically and experimentally, that increased fl exibility can be achieved when the light itself induces its own waveguide through the nonlinear response of the material.2 Th e internal structure and symmetry of the generated nonlinear selftrapped state selects itself the propagation direction in defect-free periodic structures. Th e symmetry of such localized optical waves is intrinsically defi ned by the physical mechanisms responsible for light localization—i.e., by total internal refl ection and Bragg scattering. In particular, we demonstrated that, in two-dimensional periodic optically induced photonic lattices created in biased photorefractive crystals, it is possible to use both localization mechanisms to obtain self-trapped states with diff erent mobility properties along the two principal directions in a square lattice. We described theoretically the families of such highly anisotropic gap solitons and studied them experimentally. An example of such a localized mode generated experimentally is shown in the fi gure (left). It originates from the x-symmetry point of the lattice bandgap spectrum, and possesses a reduced symmetry with highly anisotropic diff raction properties. Because of this anisotropy, such modes exhibit high mobility along the direction of their spatial modulation, and they are trapped by the lattice in the other transverse direction, enabling directional wave transport with possible applications for optical routing and switching in nonlinear periodic photonic structures. We predicted and verifi ed experimentally the unique mobility of these nonlinear modes and a novel mechanism for directional nonlinear wave transport in symmetric lattices. Th e fi gure summarizes our results. We imposed an initial tilt of the input beam along the diff erent directions and studied the beam displacement at the output. In simulations, an initial tilt of 20 mrad (15 percent of the Bragg angle) along x moves the output by two lattice sites (b), whereas the same tilt in y leads to no motion of the output state (c). Even with both tilts superimposed, the soliton moves the same two lattice sites along the x-axis only (d). Two examples of the corresponding experimental results O P T IC A L B E A M S