Related papers: Nonlinear compact localized modes in flux-dressed …
We propose and investigate a novel two-dimensional (2D) tight-binding model defined on a diamond-dodecagon lattice geometry that hosts multiple flat bands (FBs) and supports topological phase transitions driven by a magnetic flux. This…
We generate compact localized states in an electrical diamond lattice, comprised of only capacitors and inductors, via local driving near its flatband frequency. We compare experimental results to numerical simulations and find very good…
We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schr\"odinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site…
We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields.…
We drive periodically a two-dimensional diamond-octagon lattice model by switching between two Hamiltonian corresponding two different magnetic flux piercing through diamond plaquette to investigate the generation of topological flat bands.…
The exploration of flatband in photonics is fundamentally important, aiming to control the localization of light for potential applications in optical communications. We study the flatband physics in a synthetic space including the…
Systems with engineered flatband spectra are a postulate of high-capacity transmission links and a candidate for high-temperature superconductivity. However, their operation relies on the edge or surface modes susceptible to fluctuations…
We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear…
We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field.…
Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly…
We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in…
We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear…
The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their…
Photonic lattices have emerged as a promising approach to localize light in space, for example, through topologically protected edge states and Aharonov-Bohm caging. They are of particular importance in the study of flat band systems via…
We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…
We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain…
We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal…
We investigate the influence of quasiperiodic modulations on one-dimensional non-Hermitian diamond lattices with an artificial magnetic flux $\theta$ that possess flat bands. Our study shows that the symmetry of these modulations and the…