arXiv subjects

Sergey K. Ivanov

Publications and source records attributed to Sergey K. Ivanov.

At least 19 recordsLinked to original sources

arXiv2026

Exceptional light propagation via generalized bulk-edge correspondence

In topological photonics, the bulk-edge correspondence is conventionally imported by direct analogy with electronic systems, overlooking the fundamentally distinct spacetime symmetries of Maxwell's and Schrödinger's equations. In this work, we challenge this prevailing paradigm by demonstrating that non-trivial bulk topology alone is insufficient to guarantee localized edge states in photonic platforms. Using a Su-Schrieffer-Heeger-inspired photonic crystal, we unveil a generalized bulk-edge correspondence intrinsically shaped by the relativistic nature of electromagnetic waves. This constraint imposes a strict frequency cutoff, a feature fundamentally absent in electronic topological insulators, which enables a new regime of frequency-controlled spatial localization near the cutoff. Furthermore, we demonstrate that this generalized correspondence is polarization-dependent: transverse electric (TE) and transverse magnetic (TM) edge modes exist in different parameter regimes and exhibit distinct dispersion relations, including distinct zero-dispersion points. Our framework redefines the theoretical boundaries of topological photonics, unlocking new opportunities for polarization-selective dispersion engineering and robust pulse propagation in topological photonic platforms.

physics.optics↗

arXiv2025

Bloch-Landau-Zener Oscillations in Moiré Lattices

We develop a theory of two-dimensional Bloch-Landau-Zener (BLZ) oscillations of wavepackets in incommensurate moiré lattices under the influence of a weak linear gradient. Unlike periodic systems, aperiodic lattices lack translational symmetry and therefore do not exhibit a conventional band-gap structure. Instead, they feature a mobility edge, above which (in the optical context) all modes become localized. When a linear gradient is applied to a moiré lattice, it enables energy transfer between two or several localized modes, leading to the oscillatory behavior referred to as BLZ oscillations. This phenomenon represents simultaneous tunneling in real space and propagation constant (energy) space, and it arises when quasi-resonance condition for propagation constants and spatial proximity of interacting modes (together constituting a selection rule) are met. The selection rule is controlled by the linear gradient, whose amplitude and direction play a crucial role in determining the coupling pathways and the resulting dynamics. We derive a multimode model describing BLZ oscillations in the linear regime and analyze how both attractive and repulsive nonlinearities affect their dynamics. The proposed framework can be readily extended to other physical systems, including cold atoms and Bose-Einstein condensates in aperiodic potentials.

physics.optics↗

arXiv2024

Floquet valley Hall edge solitons

We introduce traveling Floquet valley Hall edge solitons in a genuinely continuous system consisting of a waveguide array with a dynamically varying domain wall between two honeycomb structures exhibiting broken inversion symmetry. Inversion symmetry in our system is broken due to periodic and out-of-phase longitudinal modulation of the refractive index applied to the constituent sublattices of the honeycomb structure. By combining two honeycomb arrays with different initial phases of refractive index modulation we create a dynamically changing domain wall that supports localized linear Floquet edge states despite the fact that on average two sublattices in each honeycomb structure forming the domain wall have the same refractive index. In the presence of focusing nonlinearity, bright or dark Floquet edge solitons may bifurcate from such linear Floquet edge states. We numerically identified a family of these solitons and compared them with the results obtained from the analytical approach, which involved averaging over one longitudinal period in the evolution coordinate. These solitons exhibit localization in both spatial directions - along the interface due to nonlinear self-action and across the interface as the edge states - that allows them to travel along the domain wall over long distances without noticeable shape variations.

physics.optics↗

arXiv2023

$π$-solitons on a ring of waveguides

We study the existence and stability of $π$-solitons on a ring of periodically oscillating waveguides. The array is arranged into Su-Schrieffer-Heeger structure placed on a ring, with additional spacing between two ends of the array. Due to longitudinal oscillations of waveguides, this Floquet structure spends half of the longitudinal period in topological phase, while on the other half it is nontopological. Nevertheless, waveguide oscillations lead to the emergence of anomalous topological $π$-modes at both ends of the structure that strongly couple in our ring geometry, leading to the formation of previously unexplored in-phase and out-of-phase $π$-modes. We study topological solitons bifurcating from such linear $π$-modes and demonstrate how their properties and stability depend on the size of the ring and on spacing between two ends of the array.

physics.optics↗

arXiv2023

Vortex solitons in moire optical lattices

We show that optical moire lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

physics.optics↗

arXiv2023

Light bullets in Su-Schrieffer-Heeger photonic topological insulators

We introduce a different class of thresholdless three-dimensional soliton states that form in higher-order topological insulators based on a two-dimensional Su-Schrieffer-Heeger array of coupled waveguides. The linear spectrum of such structures is characterized by the presence of a topological gap with corner states residing in them. We find that a focusing Kerr nonlinearity allows families of light bullets bifurcating from the linear corner states to exist as stable three-dimensional solitons, which inherit topological protection from their linear corner counterparts and, remarkably, survive even in the presence of considerable disorder. The light bullets exhibit a spatial localization degree that depends strongly on the array dimerization and may feature large temporal widths in the topological gap near the bifurcation point, thus drastically reducing the otherwise strong instabilities caused by higher-order effects.

physics.optics↗

arXiv2023

Rotating topological edge solitons

We address the formation of topological edge solitons in rotating Su-Schrieffer-Heeger waveguide arrays. The linear spectrum of the non-rotating topological array is characterized by the presence of topological gap with two edge states residing in it. Rotation of the array significantly modifies the spectrum and may move these edge states out of the topological gap. Defocusing nonlinearity counteracts this tendency and shifts such modes back into topological gap, where they acquire structure of tails typical for topological edge states. We present rich bifurcation structure for rotating topological solitons and show that they can be stable. Rotation of the topologically trivial array, without edge states in its spectrum, also leads to the appearance of localized edge states, but in a trivial semi-infinite gap. Families of rotating edge solitons bifurcating from the trivial linear edge states exist too and sufficiently strong defocusing nonlinearity can also drive them into the topological gap, qualitatively modifying the structure of their tails.

physics.optics↗

arXiv2021

Four-wave mixing Floquet topological soliton

We consider a topological Floquet insulator realized as a honeycomb array of helical waveguides imprinted in weakly birefringent medium. The system accounts for four-wave mixing occurring at a series of resonances arising due to Floquet phase matching. Under these resonant conditions, the system sustains stable linearly polarized and metastable elliptically polarized two-component edge solitons. Coupled nonlinear equations describing evolution of the envelopes of such solitons are derived.

physics.optics↗

arXiv2021

Floquet Edge Multicolor Solitons

Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic topological insulators can be crafted in materials that exhibit a strong nonlinear response, thus opening the door to the exploration of the interplay between nonlinearity and topological effects. Among the fascinating new phenomena arising from this interplay is the formation of topological edge solitons -- hybrid asymmetric states localized across and along the interface due to different physical mechanisms. Such solitons have so far been studied only in materials with Kerr-type, or cubic, nonlinearity. Here the first example of the topological edge soliton supported by parametric interactions in $χ^{(2)}$ nonlinear media is presented. Such solitons exist in Floquet topological insulators realized in arrays of helical waveguides made of a phase-matchable $χ^{(2)}$ material. Floquet edge solitons bifurcate from topological edge states in the spectrum of the fundamental frequency wave and remain localized over propagation distances drastically exceeding the helix period, while travelling along the edge of the structure. A theory of such states is developed. It is shown that multicolor solitons in a Floquet system exists in the vicinity of (formally infinite) set of linear resonances determined by the Floquet phase matching conditions. Away from resonance, soliton envelopes can be described by a period-averaged single nonlinear Schrödinger equation with an effective cubic nonlinear coefficient whose magnitude and sign depend on the overall phase-mismatch between the fundamental frequency and second harmonic waves.

physics.optics↗

arXiv2021

Trigonometric shock waves for the Kaup-Boussinesq system

We consider the modulationally stable version of the Kaup-Boussinesq system which models propagation of nonlinear waves in various physical systems. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich-Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a non-zero wave excitation on one of the sides of the discontinuity. Our analytical results are confirmed by numerical calculations.

nlin.PS↗

arXiv2021

Floquet defect solitons

We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such configuration represents a line defect, in the lattice plane, which is periodically modulated along the propagation direction. In the linear limit, such a system sustains line defect modes, whose number coincides with the number of tilted layers. In the presence of nonlinearity the branches of defect solitons propagating along the defect line bifurcate from each of the linear defect modes. Depending on the effective dispersion induced by the Floquet spectrum of the underline system the bifurcating solitons can be either bright or dark. Dynamics and stability of such solitons are studied numerically.

physics.optics↗

arXiv2021

Nonlinear second-order photonic topological insulators

Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a co-dimension of at least two. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems, the flourishing field of experimental HOTI research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. In our work, we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.

physics.optics↗

arXiv2021

Topological dipole Floquet solitons

We theoretically introduce a new type of topological dipole solitons propagating in a Floquet topological insulator based on a kagome array of helical waveguides. Such solitons bifurcate from two edge states belonging to different topological gaps and have bright envelopes of different symmetries: fundamental for one component, and dipole for the other. The formation of dipole solitons is enabled by unique spectral features of the kagome array which allow the simultaneous coexistence of two topological edge states from different gaps at the same boundary. Notably, these states have equal and nearly vanishing group velocities as well as the same sign of the effective dispersion coefficients. We derive envelope equations describing components of dipole solitons and demonstrate in full continuous simulations that such states indeed can survive over hundreds of helix periods without any noticeable radiation into the bulk.

nlin.PS↗

arXiv2020

Nonlinearity-induced photonic topological insulator

The hallmark feature of topological insulators renders edge transport virtually impervious to scattering at defects and lattice disorder. In our work, we experimentally demonstrate a topological system, using a photonic platform, in which the very existence of the topological phase is brought about by nonlinearity. Whereas in the linear regime, the lattice structure remains topologically trivial, light beams launched above a certain power threshold drive the system into its transient topological regime, and thereby define a nonlinear unidirectional channel along its edge. Our work studies topological properties of matter in the nonlinear regime, and may pave the way towards compact devices that harness topological features in an on-demand fashion.

physics.optics↗

arXiv2020

Formation of dispersive shock waves in evolution of a two-temperature collisionless plasma

The nonlinear dynamics of pulses in a two-temperature collisionless plasma with formation of dispersion shock waves is studied. An analytical description is given for arbitrary form of an initial disturbance with smooth enough density profile on a uniform density background. For large time after the wave breaking moment dispersive shock waves are formed. Motion of their edges is studied in framework of Gurevich-Pitaevskii theory and Whitham theory of modulations. The analytical results are compared with numerical solution.

physics.plasm-ph↗

arXiv2020

Formation of dispersive shock waves in a saturable nonlinear medium

We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of step-like initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.

nlin.PS↗

arXiv2020

Riemann problem for the light pulses in optical fibers for the generalized Chen-Lee-Liu equation

We provide the classification of possible wave structures evolving from initially discontinuous profiles for the photon fluid propagating in a normal dispersion fiber. The dynamics of light field is described by the generalized Chen-Lee-Liu equation, which belongs to the family of the nonlinear Schrödinger equations with a self-steepening type term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. This equation is also used in investigations of the dynamics of modulated waves propagating through a single nonlinear transmission network. We describe its periodic solutions and the corresponding Whitham modulation equations. The wave patterns generated by the initial parameter profiles are composed of different building blocks which are presented in detail. It is shown that evolution dynamics in this case is much richer than that for the nonlinear Schrödinger equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity. Our analytic results are confirmed by numerical simulations.

nlin.PS↗

arXiv2020

Bragg solitons in topological Floquet insulators

We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.

physics.optics↗