We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

We analyze the transport of light in the bulk and at the edge of photonic Lieb lattices, whose unique feature is the existence of a flat band representing stationary states in the middle of the band structure that can form localized bulk states. We find that transport in bulk Lieb lattices is significantly affected by the particular excitation site within the unit cell, due to overlap with the flat band states. Additionally, we demonstrate the existence of new edge states in anisotropic Lieb lattices. These states arise due to a virtual defect at the lattice edges and are not described by the standard tight-binding model.

We address the issue of mobility of localized modes in two-dimensional nonlinear Schrödinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals.We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.

We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear optical waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even modes centered at finite distances from the surface and reveal the physical mechanism of the nonlinearity-induced stabilization of surface modes.

We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya. V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006)]. We demonstrate strong self-trapping at the edge of a LiNbO3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.PACS numbers: 42.65. Tg, 42.65.Sf5, 42.65.Wi Interfaces between different physical media can support a special class of localized waves known as surface waves or surface modes. In periodic systems, staggered surface modes are often referred to as Tamm states [1], first identified as localized electronic states at the edge of a truncated periodic potential. Because of the difficulties in observing this type of surface waves in natural materials such as crystals, successful efforts were made to demonstrate their existence in nano-engineered periodic structures or superlattices [2]. An optical analog of linear Tamm states has been described theoretically and demonstrated experimentally for an interface separating periodic and homogeneous dielectric media [3,4].Nonlinear surface waves have been studied in different fields of physics and most extensively in optics where surface TE and TM modes were predicted and analyzed for the interfaces between two different homogeneous nonlinear dielectric media [5,6,7]. In addition, nonlinear effects have been shown to stabilize surface waves in discrete systems, generating different types of modes localized at and near the surface [8]. Self-trapping of light near the boundary of a self-focusing photonic lattice has recently been predicted theoretically [9] and demonstrated in experiment [10] through the formation of discrete surface solitons at the edge of a waveguide array.Recently, Kartashov et al. [11] predicted theoretically the existence of surface gap solitons at the interface between a uniform medium and a photonic lattice with defocusing nonlinearity. In such systems, light localization occurs inside a photonic bandgap in the form of staggered surface modes. This enables us to draw an analogy with the localized electronic Tamm states and extend it to the nonlinear regime, so that the surface gap solitons can be termed as nonlinear Tamm states. They posses a unique combination of properties related to both electronic and optical surface waves and discrete optical gap solitons. The ability to generate such surface gap solitons could provide novel and effective experimental tools for the study of nonlinear effects near surfaces with possible applications in optical sensing and switching.In this Letter we study experimentally self-action of a narrow beam propagating near the edge of a LiNbO 3 waveguide array with defocusing nonlinearity. For the first time to our knowledge, ...