arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 289 records · Page 16Linked to original sources

arXiv2017

Spin-orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

We consider a model of the exciton-polariton condensate based on a system of two Gross-Pitaevskii equations coupled by the second-order differential operator, which represents the spin-orbit coupling (SOC) in the system. Also included are the linear gain, effective diffusion, nonlinear loss, and the standard harmonic-oscillator trapping potential, as well as the Zeeman splitting. By means of combined analytical and numerical methods, we identify stable two-dimensional modes supported by the nonlinear system. In the absence of the Zeeman splitting, these are mixed modes, which combine zero and nonzero vorticities in each of the two spinor components, and vortex-antivortex complexes. We have also found a range of parameters where the mixed-mode and vortex-antivortex states coexist and are simultaneously stable. Sufficiently strong Zeeman splitting creates stable semi-vortex states, with vorticities 0 in one component and 2 in the other.

physics.optics↗

arXiv2017

Modulational Instability in Linearly Coupled Asymmetric Dual-Core Fibers

We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD). In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.

nlin.PS↗

arXiv2017

Two-dimensional dipolar gap solitons in free space with spin-orbit coupling

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size $a_{\perp }$, in the third direction. For quasi-2D patterns, with lateral sizes $l\gg a_{\perp }$, the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a bandgap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons(GSs), with vorticities $0$ and $1$ in the two components, are found, in quasi-analytical and numerical forms, under the action of dipole-dipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as \textit{embedded solitons} (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively.

cond-mat.quant-gas↗

arXiv2017

Single and double linear and nonlinear flatband chains: spectra and modes

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. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are studied too, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.

nlin.PS↗

arXiv2017

The interaction of Airy waves and solitons in the three-wave system

We employ the generic three-wave system, with the $χ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave solitons in a setting which is not available in other nonlinear systems. The advantage is that the single-wave TAWs, carried by either one of the FF component, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transforms them into a set of solitons, the number of which decreases with the increase of the total power. The TAW absorbs an incident small-power soliton, and a high-power soliton absorbs the TAW. Between these limits, the collision with an incident soliton converts the TAW into two solitons, with a remnant of the TAW attached to one of them, or leads to formation of a complex TAW-soliton bound state. At large velocities, the collisions become quasi-elastic.

physics.optics↗

arXiv2017

Ultrafast Optical Signal Processing with Bragg Structures

The phase, amplitude, speed, and polarization, in addition to many other properties of light, can be modulated by photonic Bragg structures. In conjunction with nonlinearity and quantum effects, a variety of ensuing micro- or nano-photonic applications can be realized. This paper reviews various optical phenomena in several exemplary 1D Bragg gratings. Important examples are resonantly absorbing photonic structures, chirped Bragg grating, and cholesteric liquid crystals; their unique operation capabilities and key issues are considered in detail. These Bragg structures are expected to be used in wide-spread applications involving light field modulations, especially in the rapidly advancing field of ultrafast optical signal processing.

physics.optics↗

arXiv2017

Solitons under spatially localized cubic-quintic-septimal nonlinearities

We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign. This setting can be implemented in optical waveguides based on colloids of nanoparticles. The solitons stability is identified by solving linearized equations for small perturbations, and is found to fully comply with the Vakhitov-Kolokolov criterion. In the limit case of tight confinement of the nonlinearity, results are obtained in an analytical form, approximating the confinement profile by a delta-function. It is found that the confinement greatly increases the largest total power of stable solitons, in the case when the quintic term is defocusing, which suggests a possibility to create tightly confined high-power light beams guided by the spatial modulation of the local nonlinearity strength.

cond-mat.quant-gas↗

arXiv2017

Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity

Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than $r^{D}$, in space of dimension $D$ with radial coordinate $r$, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate, $\sim r^{α}$ with $α\leq D$, we here test the possibility to create stable\textit{\ localized continuous waves} (LCWs) in one- and two-dimensional (1D and 2D) geometries, \textit{% localized dark solitons} (LDSs) in 1D, and \textit{localized dark vortices} (LDVs) in 2D, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a \textquotedblleft deformed-tanh" expression, which is suggested by the usual 1D dark-soliton solution. In addition to the 1D fundamental LDSs with the single notch, and 2D vortices with $S=1$, higher-order LDSs with multiple notches are found too, as well as double LDVs, with $S=2$. Stability regions for the modes under the consideration are identified by means of systematic simulations, the LCWs being completely stable in 1D and 2D, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices which are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.

nlin.PS↗

arXiv2017

Effects of the third-order dispersion on continuous waves in complex potentials

A class of constant-amplitude (CA) solutions of the nonlinear Schrodinger equation with the third-order spatial dispersion (TOD) and complex potentials are considered. The system can be implemented in specially designed planar nonlinear optical waveguides carrying a distribution of local gain and loss elements, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting a required phase-gradient structure of the CA state. It is shown that the diffraction of truncated CA states with a correct phase structure can be strongly suppressed. The main subject of the analysis is the modulational instability (MI) of the CA states. The results show that the TOD term tends to attenuate the MI. In particular, simulations demonstrate a phenomenon of weak stability, which occurs when the linear-stability analysis predicts small values of the MI growth rate. The stability of the zero state, which is a nontrivial issue in the framework of the present model, is studied too

physics.optics↗

arXiv2017

Solitons supported by singular modulation of the cubic nonlinearity

A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a repulsive or attractive linear potential too. We find that a pair of mutually symmetric peaks readily gives rise to the spontaneous symmetry breaking (SSB) of modes pinned to individual peaks, while antisymmetric pinned modes are always unstable, transforming into robust spatially odd breathers. Three- and five-peak structures support symmetric modes, with in-phase or twisted profiles, and do not give rise to asymmetric states. A stability area is found for the twisted states pinned to the triple peaks, while the corresponding in-phase modes are unstable, unless the three modulation peaks are set very close to each other, covered by a single-peak pinned mode. All patterns pinned to five peaks are unstable too. Collisions of moving solitons with the singular-modulation peak are studied too. Slowly moving solitons bounce back from the peak, while the collisions are quasi-elastic for fast solitons. In the intermediate case, the soliton is destroyed by the collision. In a special case, the condition of a resonance of the incident soliton with a trapped mode supported by the peak leads to capture of the soliton.

physics.optics↗

arXiv2017

Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self- focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad sta- bility areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numeri- cal results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation.

nlin.PS↗

arXiv2017

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrodinger equations with position-dependent effective masses

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than PT-symmetric ones, but feature similar properties. Our results may suggest new experiments for PT-symmetric nonlinear waves in nonlinear nonuniform optical media.

nlin.PS↗

arXiv2017

Cross-symmetric dipolar-matter-wave solitons in double-well chains

We consider a dipolar Bose-Einstein condensate trapped in an array of two-well systems with an arbitrary orientations of the dipoles relative to the system's axis. The system can be built as a chain of local traps sliced into two parallel lattices by a repelling laser sheet. It is modelled by a pair of coupled discrete Gross-Pitaevskii equations, with dipole-dipole self- and cross-interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the cross-interaction is asymmetric, replacing the familiar symmetric two-component discrete solitons by two new species of cross-symmetric ones, on-site- and off-site-centered, which are strongly affected by the orientation of the dipoles and separation between the parallel lattices. A very narrow region of intermediate asymmetric discrete solitons is found at the boundary between the on- and off-site families. Two different types of solitons in the $\mathcal{PT}$%-symmetric version of the system are constructed too, and stability areas are identified for them.

cond-mat.quant-gas↗

arXiv2017

Dissipative Soliton Fiber Lasers with Higher-Order Nonlinearity, Multiphoton Absorption and Emission, and Random Dispersion

We study the generation of dissipative solitons (DSs) in the model of the fiber-laser cavities under the combined action of cubic-quintic nonlinearity, multiphoton absorption and/or multiphoton emission (nonlinear gain) and gain dispersion. A random component of the group-velocity dispersion (GVD) is included too. The DS creation and propagation is studied by means of a variational approximation and direct simulations, which are found to be in reasonable agreement. With a proper choice of the gain, robust DS operation regimes are predicted for different combinations of multiphoton absorption and emission, in spite of the presence of the perturbation in the form of the random GVD. Importantly, the zero background around the solitons remains stable in the presence of the (necessary) linear gain. The solitons are stable too against a certain (realistic) level of noise. Another essential finding is that the quintic gain in the form of three-photon emission (3PE) offers an alternative mechanism for supporting stable solitons, provided that it is not too strong. The DSs coexist in low- and high amplitude forms, for a given value of their width. The low-amplitude DS is stable, while its high-amplitude counterpart is subject to the blowup instability, in the presence of the 3PE. Interactions between DSs show various scenarios of the creation of breather states through merger of the two solitons.

physics.optics↗

arXiv2017

Long-range transverse Ising model built with dipolar condensates in two-well arrays

Dipolar Bose-Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic-antiferromagnetic phase transition, and nontrivial phases due to frustration. The considered setup as well allows the study of Kibble-Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field transverse Ising model in 1D. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and generation of local transverse fields, thus allowing the study of Anderson-like localization of imbalance perturbations in the two-well stack under controllable conditions.

cond-mat.quant-gas↗

arXiv2016

Rotating vortex clusters in media with inhomogeneous defocusing nonlinearity

We show that media with inhomogeneous defocusing cubic nonlinearity growing toward the periphery can support a variety of stable vortex clusters nested in a common localized envelope. Nonrotating symmetric clusters are built of an even number of vortices with opposite topological charges, located at equal distances from the origin. Rotation makes the clusters strongly asymmetric, as the centrifugal force shifts some vortices to the periphery, while others approach the origin, depending on the topological charge. We obtain such asymmetric clusters as stationary states in the rotating coordinate frame, identify their existence domains, and show that the rotation may stabilize some of them.

physics.optics↗

arXiv2016

Multidimensional solitons: Well-established results and novel findings

A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the same 2D and 3D models that give rise to the solitons. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is search for physical settings in which 2D and 3D solitons may be stabilized. The brief review addresses one well-established topic, viz., the stabilization of the 3D and 2D states, with S = 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic which was developed very recently: the stabilization of 2D and 3D free-space solitons, which juxtapose components with S = 0 and (+/-)1 (semi-vortices and mixed modes), in a binary system with the spin-orbit coupling (SOC) between its components. The former model is based on the single cubic nonlinear Schroedinger/Gross-Pitaevskii equation (NLSE/GPE), while the latter one is represented by a system of two coupled GPEs. In both cases, generic situations are drastically different in the 2D and 3D geometries. In the 2D settings, the stabilization mechanism creates a stable ground state (GS, which was absent without the stabilization), whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow to create a GS, but metastable solitons can be constructed.

cond-mat.quant-gas↗

arXiv2016

Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

nlin.SI↗