arXiv subjects

S. K. Ivanov

Publications and source records attributed to S. K. Ivanov.

16 recordsLinked to original sources

arXiv2026

Observation of topological vortex solitons on disclinations

Vortex-carrying wave fields play a crucial role in photonics due to unusual propagation properties and interactions with matter, which enable numerous practical applications ranging from optical tweezers and imaging to information encoding and transmission. Localized vortex-carrying beams propagating in nonlinear optical media may form self-sustained excited states-vortex solitons-which are, however, usually prone to instabilities and require high powers for their stabilization in non-topological materials. Using fs-laser written aperiodic waveguide arrays, we demonstrate that photonic topological insulators with disclinations admit the formation of stable and thresholdless vortex solitons with tunable shapes. These unique materials belong to a class of higher-order topological insulators and allow the propagation of localized, topologically protected excitations at the disclination core, enabling disorder-resistant transmission of signals and energy. We show that vortex solitons bifurcate from the superposition of topologically protected linear edge states at the disclination core and remain stable in the entire forbidden topological gap. Realized topological vortex solitons with symmetries that are inaccessible in periodic lattices are the first example of excited soliton states with non-trivial phase structure in a topological insulator. Our findings shine a light on the interplay between nonlinearity, the angular momentum degree of freedom of light, and the material topology.

physics.optics↗

arXiv2025

Floquet states on disclinations

We show that periodic longitudinal modulation of waveguide arrays with disclination can result in the appearance of previously unexplored Floquet modes bound to the disclination core. Such modes arise due to oscillations of the waveguides in the array, periodically switching the structure between topological and trivial phases on each modulation period, so that on average it seems trivial. Localization of such modes depends on the amplitude of waveguide oscillations. Depending on the discrete rotational symmetry of the arrays with disclinations, these modes exhibit distinct spatial profiles unattainable in periodic lattices. Propagation in a medium with focusing cubic nonlinearity reveals that these Floquet states remain localized below a critical power threshold, indicating the possibility of the formation of disclination-bound Floquet solitons. Our results unveil a new regime of localization in photonic systems, bridging disclination topology, Floquet engineering, and nonlinearity.

physics.optics↗

arXiv2025

Observation of linear and nonlinear light trapping on topological dislocations

Topological dislocations in otherwise periodic lattices represent global structural defects that, nevertheless, typically leave the lattice periodicity intact far from the dislocation. Such dislocations arise in diverse physical systems ranging from crystalline solids, acoustic and photonic lattices and crystals to matter waves in optical lattices. Dislocations drastically affect the evolution of wave excitations in their vicinity, enabling novel mechanisms for trapping on topological defects and controlling the energy flow. Moreover, when combined with nonlinearity, such systems give rise to new types of self-sustained states of topological origin that have never been observed to date. Here we demonstrate experimentally, for the first time at optical frequencies, the waveguiding at various types of topological edge dislocations, resulting in the formation of localized photonic eigenstates with distinct and tunable shapes. Using femtosecond laser-writing techniques, we fabricated waveguide arrays with precisely tailored dislocation parameters, enabling full control over the degree of localization and internal structure of the associated modes. We further demonstrate both theoretically and experimentally that in the high-power regime, the families of thresholdless dislocation solitons bifurcate from such modes, which inherit shape diversity of their linear counterparts. Our results reveal a nontrivial interplay between nonlinearity and global lattice deformations and establish dislocation solitons as a new class of nonlinear topological states. They may stimulate the observation of new types of nonlinear states and interaction scenarios for excitations in nonlinear physical systems, where lattices with controllable global deformations can be created.

physics.optics↗

arXiv2025

Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays

Quasicrystals are unique systems that, unlike periodic structures, lack translational symmetry but exhibit long-range order dramatically enriching the system properties. While evolution of light in the bulk of photonic quasicrystals is well studied, experimental evidences of light localization near the edge of truncated photonic quasicrystal structures are practically absent. In this Letter, we observe both linear and nonlinear localization of light at the edges of radially cropped quasicrystal waveguide arrays, forming an aperiodic Penrose tiling. Our theoretical analysis reveals that for certain truncation radii, the system exhibits linear eigenstates localized at the edge of the truncated array, whereas for other radii, this localization does not occur, highlighting the significant influence of truncation on edge light localization. Using single-waveguide excitations, we experimentally confirm the presence of localized states in Penrose arrays inscribed by a femtosecond laser and investigate the effects of nonlinearity on these states. Our theoretical findings identify a family of edge solitons, and experimentally, we observe a transition from linear localized states to edge solitons as the power of the input pulse increases. Our results represent the first experimental demonstration of localization phenomena induced by the selective truncation of quasiperiodic photonic systems.

physics.optics↗

arXiv2023

Macroscopic Zeno effect in Su-Schrieffer-Heeger photonic topological insulator

The quantum Zeno effect refers to slowing down of the decay of a quantum system that is affected by frequent measurements. Nowadays, the significance of this paradigm is extended far beyond quantum systems, where it was introduced, finding physical and mathematical analogies in such phenomena as the suppression of output beam decay by sufficiently strong absorption introduced in guiding optical systems. In the latter case, the effect is often termed as macroscopic Zeno effect. Recent studies in optics, where enhanced transparency of the entire system was observed upon the increase of the absorption, were largely focused on the systems obeying parity-time symmetry, hence, the observed effect was attributed to the symmetry breaking. While manifesting certain similarities in the behavior of the transparency of the system with the mentioned studies, the macroscopic Zeno phenomenon reported here in topological photonic system is far more general in nature. In particular, we show that it does not require the existence of exceptional points, and that it is based on the suppression of decay for only a subspace of modes that can propagate in the system, alike the quantum Zeno dynamics. By introducing controlled losses in one of the arms of a topological insulator comprising two closely positioned Su-Schrieffer-Heeger arrays, we demonstrate the macroscopic Zeno effect, which manifests itself in an increase of the transparency of the system with respect to the topological modes created at the interface between two arrays. The phenomenon remains robust against disorder in the non-Hermitian topological regime. In contrast, coupling a topological array with a non-topological one results in a monotonic decrease in output power with increasing absorption.

physics.optics↗

arXiv2023

Observation of linear and nonlinear light localization at the edges of moiré lattices

We observe linear and nonlinear light localization at the edges and in the corners of truncated moiré lattices created by the superposition of periodic mutually-twisted at Pythagorean angles square sublattices. Experimentally exciting corner linear modes in the fs-laser written moiré lattices we find drastic differences in their localization properties in comparison with the bulk excitations. We also address the impact of nonlinearity on the corner and bulk modes and experimentally observe the crossover from linear quasi-localized states to the surface solitons emerging at the higher input powers. Our results constitute the first experimental demonstration of localization phenomena induced by truncation of periodic moiré structures in photonic systems.

physics.optics↗

arXiv2022

Motion of dark solitons in a non-uniform flow of Bose-Einstein condensate

We study motion of dark solitons in a non-uniform one-dimensional flow of Bose-Einstein condensate. Our approach is based on Hamiltonian mechanics applied to the particle-like behavior of dark solitons in a slightly non-uniform and slowly changing surrounding. In one-dimensional geometry, the condensate's wave function undergoes the jump-like behavior across the soliton and this leads to generation of the counterflow in the background condensate. For correct description of soliton's dynamics, the contributions of this counterflow to the momentum and energy of the soliton are taken into account. The resulting Hamilton equations are reduced to the Newton-like equation for the soliton's path and this Newton equation is solved in several typical situations. The analytical results are confirmed by numerical calculations.

nlin.PS↗

arXiv2022

Observation of nonlinearity-controlled switching of topological edge states

We report the experimental observation of the periodic switching of topological edge states between two dimerized fs-laser written waveguide arrays. Switching occurs due to the overlap of the modal fields of the edge states from topological forbidden gap, when they are simultaneously present in two arrays brought into close proximity. We found that the phenomenon occurs for both strongly and weakly localized edge states and that switching rate increases with decreasing spacing between the topological arrays. When topological arrays are brought in contact with nontopological ones, switching in topological gap does not occur, while one observes either the formation of nearly stationary topological interface mode or strongly asymmetric diffraction into the nontopological array depending on the position of the initial excitation. Switching between topological arrays can be controlled and even completely arrested by increasing the peak power of the input signal, as we observed with different array spacings.

physics.optics↗

arXiv2020

Plasma slab expansion into vacuum

The problem of collisionless plasma slab expansion into vacuum is solved within a two-temperature hydrodynamic approximation in the dispersionless limit of zero Debye radius. In the framework of such an approach, the solution by the Riemann method provides quite accurate description of the whole process of plasma dynamics. It is shown that the dispersionless approximation agrees very well with exact numerical solution of the full system of plasma hydrodynamic equations.

nlin.PS↗

arXiv2019

Evolution of intensive light pulses in a nonlinear medium with the Raman effect

In this paper, we study the evolution of intensive light pulses in nonlinear single-mode fibers. The dynamics of light in such fibers is described by the nonlinear Schrödinger equation with the Raman term, due to stimulated Raman self-scattering. It is shown that dispersive shock waves are formed during the evolution of sufficiently intensive pulses. In this case, the situation is much richer than for the nonlinear Schrödinger equation with Kerr nonlinearity only. The Whitham equations are obtained under the assumption that the Raman term can be considered as a small perturbation. These equations describe slow evolution of dispersive shock waves. It is shown that if one takes into account the Raman effect, then dispersive shock waves can asymptotically acquire a stationary profile. The analytical theory is confirmed by numerical calculations.

nlin.PS↗

arXiv2019

Evolution of wave pulses in fully nonlinear shallow-water theory

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.

nlin.PS↗

arXiv2018

Riemann problem for the photon fluid: self-steepening effects

We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schroedinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.

nlin.PS↗

arXiv2018

Simple waves in a two-component Bose-Einstein condensate

We consider dynamics of simple waves in a two-component Bose-Einstein condensates. The evolution of the condensate is described by the Gross-Pitaevskii equations which can be reduced for simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fuid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between inter-species and intra-species nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

cond-mat.quant-gas↗

arXiv2017

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferro-magnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as to the appearance of new elements --- contact dispersive shock waves --- that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

cond-mat.quant-gas↗

arXiv2017

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

nlin.PS↗

arXiv2017

Expansion Dynamics of a Two-Component Quasi-One-Dimensional Bose-Einstein Condensate: Phase Diagram, Self-Similar Solutions, and Dispersive Shock Waves

We investigate the expansion dynamics of a Bose-Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the non-uniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, what reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas-Fermi approximation. We obtained self-similar solutions of these differential equations for several important special cases and wrote out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms can be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves was also considered. We compare the numerical solutions of the Gross-Pitaevskii equations with their approximate analytical solutions and study numerically the situations when the analytical method admits no exact solutions.

cond-mat.quant-gas↗