We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams. As an example, we set the boundary conditions to be anisotropic and demonstrate the first experimental observation of coherent elliptic solitons. Furthermore, exploiting the natural ability of such nonlinearities to eliminate azimuthal instabilities, we perform the first observation of stable vortex-ring solitons. These features of highly nonlocal nonlinearities affected by far-away boundary conditions open new directions in nonlinear science by facilitating remote control over soliton propagation. DOI: 10.1103/PhysRevLett.95.213904 PACS numbers: 42.65.Tg, 42.65.Jx, 47.27.Te Nonlocality plays an important role in many areas of nonlinear physics. Nonlocality typically arises from an underlying transport mechanism (heat [1], atoms in a gas [2], charge carriers [3,4], etc.) or from long-range forces (e.g., electrostatic interactions in liquid crystals [5]) and many-body interactions as with matter waves in BoseEinstein condensates [6] or plasma waves [7]. In nonlinear optics specifically, nonlocality was found in photorefractives [3,[8][9][10], in thermal nonlinear media [11][12][13][14], in atomic vapors [2], and in liquid crystals [5,15]. In principle, nonlocality acts to spread out the effects of localized excitations, and as such it can suppress modulation instabilities of homogeneous states [16]. However, in spite of the natural ''averaging'' tendency inherent to nonlocality, even highly nonlocal nonlinear media can support solitons [2,5,[17][18][19][20]. Moreover, it was suggested that nonlocality can prevent the catastrophic collapse of self-focused beams, allowing 2 1 D solitons in Kerr-type media [2,17,21]. In a similar vein, it was proposed that nonlocality can suppress azimuthal instabilities of vortex-ring beams [22,23], but such an experiment has thus far never been reported. Finally, nonlocality can considerably alter soliton interactions, e.g., giving rise to attraction between out of phase solitons [19,20,24] and between dark solitons [25], which without nonlocality always repel, and causing attraction between well separated solitons [26].Here we present an experimental study on solitons in a nonlinear medium with an extremely large range of nonlocality, such that far-away boundary conditions directly affect the soliton beam. We use the thermal optical nonlinearity in lead glass, which is of the self-focusing type. The nonlocal nature of this thermal nonlinearity is manifested in the heat-transfer (Poisson-type) equation, for which boundary conditions greatly influence the temperature distribution. The nonlinear index change is proportional to the temperature change; hence, the boundary conditions, even from afar, significantly affect the refractive index structure supporting solitons. We show that setting transversely anisotropic boundary conditions (e.g., rectangular boundaries in the transverse plane) f...

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.

We present the experimental observation of both on-site and off-site vortex-ring solitons of unity topological charge in a nonlinear photonic lattice, along with a theoretical study of their propagation dynamics and stability.

The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.

Quasicrystals are aperiodic structures with rotational symmetries forbidden to conventional periodic crystals; examples of quasicrystals can be found in aluminum alloys, polymers, and even ancient Islamic art. Here, we present direct experimental observation of disorder-enhanced wave transport in quasicrystals, which contrasts directly with the characteristic suppression of transport by disorder. Our experiments are carried out in photonic quasicrystals, where we find that increasing disorder leads to enhanced expansion of the beam propagating through the medium. By further increasing the disorder, we observe that the beam progresses through a regime of diffusive-like transport until it finally transitions to Anderson localization and the suppression of transport. We study this fundamental phenomenon and elucidate its origins by relating it to the basic properties of quasicrystalline media in the presence of disorder.