Stable Vortex Solitons Research Articles

Vortex light bullets in rotating Quasi-Phase-Matched photonic crystals

We present a methodology for the generation of stable vortex light bullets (LBs) in rotating Quasi-Phase-Matched (QPM) photonic crystals with quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure, which is feasible to realize by using contemporary technological advancements. Within this framework, square- and rhombus-shaped LBs are observed, both of which are constructed as four-peak vortex mode. The control parameters include the effective phase mismatch, power, rotating frequency, and the size of checkerboard cells. These parameters play key roles in determining the distribution and stability domains of vortex LBs. In contrast to the stable vortex solitons observed in two-dimensional (2D) quadratic systems, the LBs investigated in the 3D rotating system exhibit narrower stability domains within the system’s parameter space. The rotating frequency results in the transition of LBs from quadrupole to traditional vortex modes. Potential applications of this research lie in the field of optical communications and information processing.

Semivortex solitons and their excited states in spin-orbit-coupled binary bosonic condensates.

It is known that two-dimensional two-component fundamental solitons of the semivortex (SV) type, with vorticities (s_{+},s_{-})=(0,1) in their components, are stable ground states (GSs) in the spin-orbit-coupled (SOC) binary Bose-Einstein condensate with the contact self-attraction acting in both components, in spite of the possibility of the critical collapse in the system. However, excited states (ESs) of the SV solitons, with the vorticity set (s_{+},s_{-})=(S_{+},S_{+}+1) and S_{+}=1,2,3,..., are unstable in the same system. We construct ESs of SV solitons in the SOC system with opposite signs of the self-interaction in the two components. The main finding is stability of the ES-SV solitons, with the extra vorticity (at least) up to S_{+}=6. The threshold value of the norm for the onset of the critical collapse, N_{thr}, in these excited states is higher than the commonly known critical value, N_{c}≈5.85, associated with the single-component Townes solitons, N_{thr} increasing with the growth of S_{+}. A velocity interval for stable motion of the GS-SV solitons is found too. The results suggest a solution for the challenging problem of the creation of stable vortex solitons with high topological charges.

Stable Vortex Solitons Sustained by Localized Gain in a Cubic Medium

Stable Vortex Solitons Sustained by Localized Gain in a Cubic Medium

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

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 CN to C1, 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.

Stable higher-charge vortex solitons in the cubic-quintic medium with a ring potential.

We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges m. The cubic-quintic nonlinear medium with an imprinted ring-shaped modulation of the refractive index is shown to support two branches of VSs, which are controlled by the radius, width, and depth of the modulation profile. While the lower-branch VSs are unstable in their nearly whole existence domain, the upper branch is completely stable. Vortex solitons with m ≤ 12 obey the anti-Vakhitov-Kolokolov stability criterion. The results suggest possibilities for the creation of stable narrow optical VSs with a low power, carrying higher vorticities.

Vortex solitons in moiré optical lattices.

We show that optical moiré 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 a 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.

Completely Localized Stable Elliptic and Vortex Solitons in Magnetized Dusty Plasma

We numerically and theoretically investigated the elliptic and vortex solitons, and their dynamical stabilities in a magnetized dusty plasma. By using the Petviashvili method, a type of completely localized solitons, which are also confirmed analytically, is found numerically. Numerical results indicate that the amplitude is proportional to its velocity and inverse proportional to the nonlinear interaction strength. The linear stability analysis shows that these solitons are always linearly stable, which agrees well with the nonlinear dynamic evolution. Finally, we find that both elastic and inelastic collisions exist when two localized solitons collide. It is an elastic one when the collision occurs between a localized soliton and a stable line soliton. However, a series of localized solitons will be excited if a localized soliton and an unstable line soliton collide, suggesting that inelastic collisions also exist. This finding may be helpful to understand the nonlinear phenomena in magnetized dusty plasma.

Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain

We consider settings providing the existence of stable two-dimensional (2D) dissipative solitons with zero and nonzero vorticity in optical media with the quadratic ($\chi^{(2)}$) nonlinearity. To compensate the spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized amplifying region ("hot spot",HS), carrying the linear gain, is included, acting onto either the FF component or SH one. In both cases, the Gaussian radial gain profile supports stable fundamental dissipative solitons pinned to the HS. The structure of existence and stability domains for the 2D solitons is rather complex. They demonstrate noteworthy features, such as bistability and spontaneous symmetry breaking. A ring-shaped gain profile acting onto the FF component supports stable vortex solitons, with the winding number up to 5, and multipoles. Nontrivial transformation of vortex-soliton profiles upon either growth of the gain value or stretching the gain profile is observed.

Elliptic vortex beam in a fractional complex Ginzburg–Landau model

We have investigated the elliptical vortex structures in dissipative media governed by the fractional complex cubic-quintic Ginzburg–Landau model. Stable regions of generating dissipative fundamental, dipole, tripole and fourpole solitons are found for relatively small elliptical coefficient (e ) at values of (LI) , which can produce critical or supercritical collapse in free space. By adjusting the system parameters, the elliptical vortex can evolve into the circular ones and remain stable circular vortex structure with given topological charge of the vorticity S (from 1 to 4). Effects of the value of the respective LI on stability regions of generation stable circular vortex solitons have been investigated in detail. These results have potential applications in optical signal processing.

Formation and stability of vortex solitons in nematic liquid crystals

We study the propagation dynamics of bright optical vortex solitons in nematic liquid crystals with a nonlocal reorientational nonlinear response. We investigate the role of optical birefringence on the stability of these solitons. In agreement with recent experimental observations, we show that the birefringence-induced astigmatism can eventually destabilize these vortex solitons. However, for low and moderate birefringence, vortex solitons can propagate stably over experimentally relevant distances.

Spatiotemporal solitons in dispersion-managed multimode fibers

We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The DM map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal ‘light bullets’, stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstrate that stability of the 3D spatiotemporal solitons is determined by the usual DM-strength parameter, S: they are quasi-stable at , and completely stable at . Stable vortex solitons are constructed too. We also consider collisions between the 3D solitons, in both axial and transverse directions. The interactions are quasi-elastic, including periodic collisions between solitons which perform shuttle motion in the transverse plane.

Two dimensional spacial soliton in atomic gases with PT-symmetry potential.

We propose a realistic physical scheme to realize linear Gaussian optical potential with parity-time (PT) symmetry and two dimensional (2D) spacial solitons in a coherent atomic gas. It is shown that the PT-symmetric potential can be created through the spatial modulation of the control and relevant atomic parameters. We find that the Gaussian PT potential parameters, the imaginary part and the width and the position, play crucial roles in the occurrence of the PT phase transition. We demonstrate that the system supports stable 2D dipole solitons and vortex solitons, which can be managed via tuning PT potential. Furthermore, the dynamic characteristics of the symmetric scatter and collision of solitons are shown.

Stable analytical and numerical constructed vector optical vortex solitons

A Kerr-type nonlinear system of two incoherently coupled components with spatially inhomogeneous nonlinearity is discussed by means of separation of variables. The hierarchies of analytical as well as numerical constructed vector vortex solitons with higher topological charge (S ≥ 2) are generated. Some basic properties of solutions like the existence, appearance, the effective diameter are studied. The stability of obtained vector vortex solitons are predicted by small disturbance analysis and confirmed by direct simulation. Some thresholds of propagation constant supporting stable vector vortex solitons are given.

Two dimension PT symmetry spacial soliton in atomic gases with linear and nonlinear potentials

We present a physical scheme to realize combined linear and nonlinear optical potentials with parity-time (PT) symmetry and two dimensional (2D) spacial solitons in a coherent atomic gas. It is shown that the combined PT-symmetric potentials can be created through the spatial modulation of the control and relevant atomic parameters. We find that the imaginary part of the nonlinear PT potential plays a crucial role for the occurrence of the PT phase transition. We demonstrate that the system supports stable 2D dipole solitons and vortex solitons, which can be managed via tuning PT potentials.

Vortex nematicons in planar cells.

We provide experimental evidence that stable vortex-solitons in nematic liquid crystals, termed vortex nematicons, can be generated in planar cells without any external biases, neither electric nor magnetic. We report on nonlinear vortices with extraordinary-wave beams in various undoped samples, pin-pointing how material nonlocality and birefringence aid their stable propagation. Finally, we also demonstrate confinement and waveguiding of an incoherent co-polarized probe signal by the nonlinear vortex.

Vortex solitons in fractional systems with partially parity-time-symmetric azimuthal potentials

We address the propagation dynamics of topological states in the framework of nonlinear fractional Schrodinger equation modulated by a partially parity-time ( $$\mathcal {PT}$$ )-symmetric azimuthal potential. While the eigenvalue spectra in a $$\mathcal {PT}$$ system experience a symmetry breaking, the p $$\mathcal {PT}$$ system exhibits entirely real spectra. The variation of Levy index impacts the properties of nonlinear vortex states evidently, including the existence domain, power, and stability. Unlike nonlinear vortices in conservative systems, vortex solitons with opposite charges exhibit different features, due to the nonequivalence of the gain–loss distribution along the azimuthal direction. Linear-stability analysis collaborated with direct numerical propagation simulations demonstrates that stable vortex solitons are possible only when their components are connected as a whole entity. Higher-charged vortex solitons are shown to be more stable than those with lower charges. We, thus, put forward the first example of stable vortex solitons in fractional configurations.

(INVITED) Vortex solitons: Old results and new perspectives

A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to instabilities induced by the critical and supercritical collapse, respectively, in the 2D and 3D models with cubic focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses, first, two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, viz., the prediction of robust quantum droplets. Two other topics outline new schemes elaborated for the creation of stable vortical solitons. One scheme relies on the use of spin-orbit coupling (SOC) in binary BEC, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S=0 and (+/-)1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is different in the 2D and 3D geometries. In 2D, SOC helps to create a ground state (GS), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed too, such as vortex solitons in dissipative media and attempts to create vortex solitons in experiments.

Robust {bf{P}}{bf{T}} symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

The real spectrum of bound states produced by {bf{P}}{bf{T}}-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. The breakup essentially impedes the use of {bf{P}}{bf{T}}-symmetric systems for various applications. On the other hand, it is known that the {bf{P}}{bf{T}} symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) {bf{P}}{bf{T}} symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose {bf{P}}{bf{T}} symmetry remains unbroken for arbitrarily large values of the gain-loss coefficient. Further, we introduce an extended 2D model with the imaginary part of potential ~xy in the Cartesian coordinates. The latter model is not a {bf{P}}{bf{T}}-symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the {bf{P}}{bf{T}} symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable {bf{P}}{bf{T}} symmetry, while generic soliton families are found in a numerical form. The {bf{P}}{bf{T}}-symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with m = 1, 2, and 3. In the model with imaginary potential ~xy, families of single- and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.

New models for multi-dimensional stable vortex solitons

New models for multi-dimensional stable vortex solitons