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Yaroslav V. Kartashov

Publications and source records attributed to Yaroslav V. Kartashov.

At least 55 records · Page 3Linked to original sources
arXiv2024

Observation of nonlinear fractal higher-order topological insulator

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by a factor of 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners that leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here we demonstrate first \textit{nonlinear photonic} HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

physics.optics↗
arXiv2023

Vortex solitons in topological disclination lattices

The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

nlin.PS↗
arXiv2023

Oscillating edge states in polariton topological insulators

We show that slow time-periodic variation of the external magnetic field applied to polariton topological insulator based on honeycomb array of microcavity pillars with pronounced TE-TM splitting results in oscillations of the edge states along the boundary of the insulator that are accompanied by slow transverse drift of the center of mass of the edge state along the boundary. The oscillations and drift are due to time-periodic variation of the sign of the instantaneous group velocity of the edge state with selected central Bloch momentum triggered by the variation of the Zeeman splitting in the external magnetic field. These oscillations are also accompanied by periodic exchange of norm between two polarization components of the edge state. Oscillating edge states survive despite the fact that magnetic field periodically vanishes resulting in closure of the topological gap in the instantaneous spectrum of the system. The direction of the drift and amplitude of oscillations of the edge state strongly and nonmonotonically depend on its initial central Bloch momentum.

physics.optics↗
arXiv2023

Topological gap solitons in Rabi Su-Schrieffer-Heeger lattices

In this work, using binary Bose-Einstein condensate we propose a new type of topological insulator that does not explicitly use specially designed potential landscape, but instead utilizes spatially inhomogeneous Rabi coupling between two components, in the form of one- or two-dimensional Su-Schrieffer-Heeger (SSH) structure, combined with Zeeman splitting. Such Rabi lattices reveal the appearance of topologically nontrivial phases (including higher-order ones) controlled by spatial shift of the domains with enhanced coupling between condensates within unit cells of the structure, where localized topological states appear at the edges or in the corners of truncated Rabi lattice. We also show that the properties of edge states, their spatial localization, and location of their chemical potential within topological gap can be controlled by interatomic interactions that lead to formation of gap topological edge solitons bifurcating from linear edge states. Such solitons in condensates with inhomogeneous Rabi coupling appear as very robust nonlinear topological objects that do not require any threshold norm for their formation even in two-dimensional geometries, and that can exist in stable form for both attractive and repulsive interactions. Our results demonstrate considerable enhancement of stability of solitons in topological Rabi lattices in comparison with trivial Rabi lattices. They open new prospects for realization of topologically nontrivial phases by spatial engineering of coupling in multicomponent systems.

nlin.PS↗
arXiv2023

Floquet edge solitons in modulated trimer waveguide arrays

We show that one-dimensional Floquet trimer arrays with periodically oscillating waveguides support two different and co-existing types of topological Floquet edge states in two different topological gaps in Floquet spectrum. In these systems nontrivial topology is introduced by longitudinal periodic oscillations of the waveguide centers, leading to the formation of Floquet edge states in certain range of oscillation amplitudes despite the fact that the structure spends half of the period in ``instantaneously'' nontopological phase, and only during other half-period it is ``instantaneously'' topological. Two co-existing Floquet edge states are characterized by different phase relations between bright spots in the unit cell -- in one mode these spots are in-phase, while in other mode they are out-of-phase. We show that in focusing nonlinear medium topological Floquet edge solitons, representing exactly periodic nonlinear localized Floquet states, can bifurcate from both these types of linear edge states. Both types of Floquet edge solitons can be stable and can be created dynamically using two-site excitations.

physics.optics↗
arXiv2023

Vortex solitons in large-scale waveguide arrays with adjustable discrete rotational symmetry

We consider vortex solitons in large-scale arrays composed of N elliptical waveguides placed on a ring, which can be fabricated using fs-laser writing technique in transparent nonlinear dielectrics. By introducing variable twist angles between longer axes of neighboring elliptical waveguides on a ring, we create circular arrays with adjustable discrete rotational symmetry ranging from C_N to C_1, when the number of waveguides N on the ring remains fixed. This allows to consider the impact of discrete rotational symmetry on the properties of available vortex solitons without changing the number of guiding channels in the structure, and to predict how exactly splitting of higher-order phase singularities into sets of charge-1 singularities occurs in vortex states, when they are forbidden by the discrete rotational symmetry of the structure that imposes the restrictions on the maximal possible vortex charge. It is found that separation between split charge-1 phase singularities in such higher-order vortex states increases with increase of the order of solution. We also study linear spectra of such arrays and show how variation of their discrete rotational symmetry affects linear eigenmodes, whose combinations can give rise to vortex modes. We also show that variation of discrete rotational symmetry in arrays with fixed number of guiding channels N has strong impact on stability of vortex solitons. Thus, only higher-charge vortex solitons are stable in such large-scale arrays and the number of stable states typically decreases with decrease of the order of discrete rotational symmetry of the structure at fixed N.

physics.optics↗
arXiv2023

Observation of $π$ solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous $π$ modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous $π$ modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological $π$ solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. $π$ solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such $π$ solitons are determined by their power.

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

Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling

We consider Bose-Einstein condensate (BEC) subject to the action of spin-orbit-coupling (SOC) periodically modulated in the radial direction. In contrast to the commonly known principle that periodic potentials do not create bound states, the binary BEC maintains multiple localized modes in the linear limit, with their chemical potential falling into spectral gaps of the (numerically found) radial band structure induced by the spatial modulation of the SOC. In the presence of the repulsive nonlinearity, the SOC modulation supports fundamental gap solitons of the semi-vortex types, as well as higher-order vortex gap solitons. The localization degree and stability of the gap solitons strongly depend on the location of their chemical potential in the gap. Stability intervals for vortex gap solitons in a broad range of the intrinsic vorticity, from -2 to 3, are identified. Thus, the analysis reveals the previously unexplored mechanism of linear and nonlinear localization provided by the spatially periodic modulation of SOC, which may be extended to other settings, such as those for optical beams and polaritons. Unlike the commonly known quartets of eigenvalues for small perturbations, in the present system the instability is accounted for by shifted complex eigenvalue pairs.

cond-mat.quant-gas↗
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

Photonic Snake States in Two-Dimensional Frequency Combs

Taming the instabilities inherent to many nonlinear optical phenomena is of paramount importance for modern photonics. In particular, the so-called snake instability is universally known to severely distort localized wave stripes, leading to the occurrence of transient, short-lived dynamical states that eventually decay. The phenomenon is ubiquitous in nonlinear science, from river meandering to superfluids, and to date it remains apparently uncontrollable. However, here we show that optical snake instabilities can be harnessed by a process that leads to the formation of stationary and robust two-dimensional zigzag states. We find that such new type of nonlinear waves exists in the hyperbolic regime of cylindrical micro-resonators and it naturally corresponds to two-dimensional frequency combs featuring spectral heterogeneity and intrinsic synchronization. We uncover the conditions of the existence of such spatiotemporal photonic snakes and confirm their remarkable robustness against perturbations. Our findings represent a new paradigm for frequency comb generation, thus opening the door to a whole range of applications in communications, metrology, and spectroscopy.

physics.optics↗
arXiv2023

Observation of rotation-induced light localization in waveguide arrays

We study both, experimentally and theoretically, propagation of light in the fs-laser written rotating square waveguide arrays and present the first experimental evidence of light localization induced by the rotation of periodic structure in the direction of light propagation. Such linear light localization occurs either in the corners of truncated square array, where it results from the interplay between the centrifugal effect and total internal reflection at the borders of truncated array, or in the center of array, where rotation creates effective attractive optical potential. The degree of localization of linear bulk and corner modes emerging due to the rotation increases with the increase of rotation frequency. Consequently, corner and bulk solitons in rotating wave-guide arrays become thresholdless for sufficiently large rotation frequencies, in contrast to solitons in non-rotating arrays that exist only above power threshold. Focusing nonlinearity enhances localization degree of corner modes, but surprising initially it leads to broadening of bulk nonlinear states, followed by their re-localization at high input powers. Our results open new prospects for control of evolution of nonlinear multidimensional excitations by dynamically varying potentials.

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↗
arXiv2022

Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization

We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light-bullets, are the only existing and stable states for a given set of parameters. This property is extremely rare, if not unknown, in passive nonlinear physical systems. As a result, the excitation of the cavity with any input field leads to the deterministic formation of a target soliton or breather, with a spatiotemporal profile that unambiguously corresponds to the given cavity and pumping conditions. In addition, the tuning of the potential width along the temporal direction results in the existence of a plethora of stable asymmetric solitons. Our results may provide a solid route towards the observation of dissipative light bullets and three-dimensional breathers.

physics.optics↗
arXiv2022

Floquet topological insulators with hybrid edges

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological edge states may exist in Floquet insulators based on arrays of helical waveguides with hybrid edges involving alternating zigzag and armchair segments, even if the latter are long. Such edge states appear in the largest part of the first Brillouin zone and show topological protection upon passage through the defects. Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. Our results can be extended to other lattice types and physical systems, they lift some of the constraints connected with lattice terminations that may not support edge states in the absence of effects breaking time-reversal symmetry of the system and expand the variety of geometrical shapes in which topological insulators can be constructed.

physics.optics↗
arXiv2022

Nonlinear photonic disclination states

Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such states are zero-dimensional corner modes existing in two-dimensional higher-order insulators. In contrast to corner states, recently discovered disclination states also belong to the class of higher-order topological states, but are bound to the boundary of the disclination defect of the higher-order topological insulator and can be predicted using the bulk-disclination correspondence principle. Here, we present the first example of the nonlinear photonic disclination state bifurcating from its linear counterpart in the disclination lattice with a pentagonal or heptagonal core. We show that nonlinearity allows to tune location of the disclination states in the bandgap and notably affects their shapes. The structure of the disclination lattice is crucial for stability of these nonlinear topological states: for example, disclination states are stable in the heptagonal lattice and are unstable nearly in the entire gap of the pentagonal lattice. Nonlinear disclination states reported here are thresholdless and can be excited even at low powers. Nonlinear zero-energy states coexisting in these structures with disclination states are also studied. Our results suggest that disclination lattices can be used in the design of various nonlinear topological functional devices, while disclination states supported by them may play an important role in applications, where strong field confinement together with topological protection are important, such as the design of topological lasers and enhancement of generation of high harmonics.

physics.optics↗
arXiv2022

Two-dimensional Thouless pumping of light in photonic moiré lattices

Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. \rev{Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice.} Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries.

physics.optics↗