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 study the propagation of non-diffracting images in kagome photonic lattices. In a weak-coupling regime (discrete approach), the linear spectrum is composed by only three bands, including a completely degenerated and flat one. The states forming this special band are well localized in space and constitute building blocks for this lattice. By linearly combining these non-diffractive fundamental modes, different shapes can be composed and, therefore, a given image will propagate without distortion. As an example, we compare the linear propagation of a particular image for kagome and rectangular lattices. At the end, we test our concept by performing numerical simulations in a continuous kagome potential.

Abstract:We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.

We demonstrate a method to experimentally calibrate the refractive index modulation in photorefractive lattices, a task rarely addressed that is crucial for quantitative comparisons of theories with experiments. We consider the linear propagation of a normally incident plane wave through simple lattices and its modulation amplitude at crystal output face. Finding no evidence of longitudinal (Talbot-like) oscillations, we discard an ideal propagation theory and construct a simple effective model that includes longitudinal relaxation. We obtain calibrations of 1D and 2D lattices consistent with standard theory in a high saturation regime. For 2D lattices, we find anisotropies χ = 1.5 − 2.5, stronger for smaller lattice period, and refractive indexes larger than for 1D lattices, also with more noise. Technol. 14, 423-428 (1996). 12. R. Magnusson and T. Gaylord, "Use of dynamic theory to describe experimental results from volume holography," J. Appl. Phys. 47, 190-199 (1976 oscillations are faster, we expect even stronger damping effects. 31. We take into account the finite resolution of our imaging system by convoluting the profiles given by the effective theory by a gaussian optical response of r.m.s width σ 0 = 0.80µm.