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Topological modes (TMs) are typically localized at boundaries, interfaces and dislocations, and exponentially decay into the bulk of a large enough lattice. Recently, the non-Hermitian skin effect has been leveraged to delocalize the…

This paper presents a theoretical analysis on bulk and edge states in honeycomb lattice photonic crystals with and without time-reversal and/or space-inversion symmetries. Multiple Dirac cones are found in the photonic band structure and…

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries…

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths.…

We suggest a novel type of photonic structures where the strength of diffraction can be managed in a very broad frequency range. We introduce optimized arrays of curved waveguides where light beams experience wavelength-independent normal,…

We propose to utilize symmetry-protected zero modes of a photonic lattice to realize a single-mode, fixed-frequency, and spatially tunable laser. These properties are the consequence of the underlying non-Hermitian particle-hole symmetry,…

The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying…

Recent experimental work has demonstrated the ability to achieve reconfigurable photon localization in lossy photonic lattices by continuously driving them with lasers strategically positioned at specific locations. This localization…

We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the…

We realize fractal-like photonic lattices using cw-laser-writing technique, thereby observe distinct compact localized states (CLSs) associated with different flatbands in the same lattice setting. Such triangle-shaped lattices, akin to the…

We demonstrate the spontaneous formation of spatial patterns in a damped, ac-driven cubic Klein-Gordon lattice. These patterns are composed of arrays of intrinsic localized modes characteristic for nonlinear lattices. We analyze the…

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious…

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response…

The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…

Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable…

Artificial defects embedded in periodic structures are important foundation for creating localized states with vast range of applications in condensed matter physics, photonics and acoustics. In photonics, localized states are extensively…

We present and analyze mechanisms for the patterned deposition of particles in a spatio-temporally driven lattice. The working principle is based on the breaking of the spatio-temporal translation symmetry, which is responsible for the…

Localized states universally appear when a periodic potential is perturbed by defects or terminated at its surface. In this Letter, we theoretically and experimentally demonstrate a mechanism that generates localized states through…

We study tunable refraction of light in one-dimensional periodic lattices induced optically in a photorefractive crystal. We observe experimentally both positive and negative refraction of beams which selectively excite the first or second…