We report on the first experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.PACS numbers: 42.65. Tg, 42.65.Jx, 42.70.Qs Periodic photonic structures and photonic crystals recently attracted a lot of interest due to the unique ways they offer for controlling light propagation. Periodic modulation of the refractive index modifies the diffraction properties and strongly affects nonlinear propagation and localization of light [1]. Recently, many nonlinear effects including the formation of lattice solitons have been demonstrated experimentally in one-and twodimensional optically-induced photonic lattices [2,3,4,5]. The concept of optically-induced lattices [6] relies on the modulation of the refractive index of a nonlinear medium with periodic optical patterns, and the use of a weaker probe beam to study scattering of light from the resulting periodic photonic structure.So far, only simple stationary structures have been described theoretically and generated experimentally in optically-induced lattices [2,3,4,5,6]. One of the most important next steps is the study of nonlinear modes with a nontrivial phase such as vortices, the fundamental localized objects appearing in many branches of physics. In optics, vortices are associated with the screw phase dislocations carried by diffracting optical beams [7]. When such vortices propagate in a defocusing nonlinear Kerrlike medium, the vortex core becomes self-trapped, and the resulting structure is known as an optical vortex soliton [1]. Such vortex solitons are usually generated experimentally on a broad background beam [8,9]. They demonstrate many similarities with the vortices observed in superfluids and Bose-Einstein condensates.In contrast, optical vortex solitons do not exist in a self-focusing nonlinear medium; a ring-like optical beam with a phase dislocation carrying a finite orbital angular momentum [10] decays into the fundamental solitons flying off the main ring [11]. This effect was first observed experimentally in saturable Kerr-like nonlinear medium [12], and then in photorefractive [9] and quadratic [13] nonlinear media in the self-focusing regime.Recent theoretical studies of the discrete [14] and continuous models of nonlinear periodic lattices [15,16] suggest that the vortex-like structures can be supported by the lattice even in the self-focusing regime. In this Letter, we report on the first experimental observation of discrete (lattice) vortex solitons and demonstrate, both theoretically and experimentally, that localized optical vortices can be generated in a self-focusing nonlinear medium, being stabilized by the two-dimensional periodic potential of a photonic lattice.To lay a background for our experiment, first we study numerically the generation of discrete vortex solitons in a two-dimensional ...

Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed-because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene-a photonic honeycomb lattice-to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems.

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.