Searcharxiv⌕ Search

arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 361 records · Page 20Linked to original sources
arXiv2014

Localized modes in quasi-2D Bose-Einstein condensates with spin-orbit and Rabi couplings

We consider a two-component pancake-shaped, i.e., effectively two-dimensional (2D), Bose-Einstein condensate (BEC) coupled by the spin-orbit (SO) and Rabi terms. The SO coupling adopted here is of the mixed Rashba-Dresselhaus type. For this configuration, we derive a system of two 2D nonpolynomial Schrödinger equations (NPSEs), for both attractive and repulsive interatomic interactions. In the low- and high-density limits, the system amounts to previously known models, namely, the usual 2D Gross-Pitaevskii equation, or the Schrödinger equation with the nonlinearity of power 7/3. We present simple approximate localized solutions, obtained by treating the SO and Rabi terms as perturbations. Localized solutions of the full NPSE system are obtained in a numerical form. Remarkably, in the case of the attractive nonlinearity acting in free space (i.e., without any 2D trapping potential), we find parameter regions where the SO and Rabi couplings make 2D fundamental solitons dynamically stable.

cond-mat.quant-gas↗
arXiv2014

Emulation of lossless exciton-polariton condensates by dual-core optical waveguides: Stability, collective modes, and dark solitons

We propose a possibility to simulate the exciton-polariton (EP) system in the lossless limit, which is not currently available in semiconductor microcavities, by means of a simple optical dual-core waveguide, with one core carrying the nonlinearity and operating close to the zero-group-velocity-dispersion (GVD) point, and the other core being linear and dispersive. Both 2D and 1D EP systems may be emulated by means of this optical setting. In the framework of this system, we find that, while the uniform state corresponding to the lower branch of the nonlinear dispersion relation is stable against small perturbations, the upper branch is always subject to the modulational instability (MI). The stability and instability are verified by direct simulations too. We analyze collective excitations on top of the stable lower-branch state, which include a Bogoliubov-like gapless mode and a gapped one. Analytical results are obtained for the corresponding sound velocity and energy gap. The effect of a uniform phase gradient (superflow) on the stability is considered too, with a conclusion that the lower-branch state becomes unstable above a critical wavenumber of the flux. Finally, we demonstrate that the stable 1D state may carry robust dark solitons.

physics.optics↗
arXiv2014

Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems

We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta-function, $δ(x)$, and a spatially uniform SDF quintic term. This system gives rise to the most general family of 1D-Townes solitons, the entire family being unstable. However, it is completely stabilized by a finite-width regularization of the $δ$-function. The results are produced by means of numerical and analytical methods. We also consider the system with a symmetric pair of regularized $δ$-functions, which gives rise to a wealth of symmetric, antisymmetric, and asymmetric solitons, linked by a bifurcation loop, that accounts for the breaking and restoration of the symmetry. Soliton families in 2D versions of both the single- and double-delta-functional systems are also studied. The 1D and 2D settings may be realized for spatial solitons in optics, and in Bose-Einstein condensates.

physics.optics↗
arXiv2014

Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity

We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the underlying evolution equation. The increase of the gain-losses strength results, in lieu of the PT-symmetry breaking, in merger of pairs of different soliton branches, such as fundamental and dipole, or tripole and quadrupole ones. The fundamental and dipole solitons remain stable for all values of the gain-loss coefficient.

physics.optics↗
arXiv2014

Mini-review: Spatial solitons supported by localized gain

The creation of stable 1D and 2D localized modes in lossy nonlinear media is a fundamental problem in optics and plasmonics. This article gives a short review of theoretical methods elaborated for this purpose, using localized gain applied at one or several "hot spots" (HSs). The introduction surveys a broad class of models for which this approach was developed. Other sections focus in some detail on basic 1D continuous and discrete systems, where the results can be obtained, partly or fully, in an analytical form (verified by comparison with numerical results), which provides a deeper insight into the nonlinear dynamics of optical beams in dissipative nonlinear media. In particular, considered are the single and double HSs in the usual waveguide with the self-focusing (SF) or self-defocusing (SDF) Kerr nonlinearity, which give rise to rather sophisticated results, in spite of apparent simplicity of the model; solitons attached to a PT-symmetric dipole embedded into the SF or SDF medium; gap solitons pinned to an HS in a Bragg grating; and discrete solitons in a 1D lattice with a "hot site".

physics.optics↗
arXiv2014

$\mathcal{PT}$-symmetric ladders with a scattering core

We consider a $\mathcal{PT}$-symmetric chain (ladder-shaped) system governed by the discrete nonlinear Schrödinger equation where the cubic nonlinearity is carried solely by two central "rungs" of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss non-reciprocity of the transmission associated with them. To relate these results to finite-size wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss.

nlin.PS↗
arXiv2014

Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers

We demonstrate the existence of stable collective excitation in the form of "supersolitons" propagating through chains of solitons with alternating signs (i.e., Newton's cradles built of solitons) in nonlinear optical couplers, including the PT-symmetric version thereof. In the regular coupler, stable supersolitons are created in the cradles composed of both symmetric solitons and asymmetric ones with alternating polarities. Collisions between moving supersolitons are investigated too, by the means of direct simulations in both the regular and PT-symmetric couplers.

physics.optics↗
arXiv2014

Building patterns by traveling vortices and dipoles in periodic dissipative media

We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which are used to stabilize 2D patterns. The pattern-building process is initiated by kicking a localized compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, with the pinned multi-soliton chain playing the role of the Newton's cradle (NC).

nlin.PS↗
arXiv2014

Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{PT}$-symmetric systems

We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the $\mathcal{PT}$ symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac) forcing is applied through periodic modulation of the coefficient accounting for the coupling of the two degrees of freedom. The system may be realized in optics as a dual-core waveguide with the gain and loss applied to different cores, and the thickness of the gap between them subject to a periodic modulation. The onset and development of the parametric instability for a small forcing amplitude ($V_{1}$) is studied in an analytical form. The full dynamical chart of the system is generated by systematic simulations. At sufficiently large values of the forcing frequency, $ω$, tongues of the parametric instability originate, with the increase of $V_{1}$, as predicted by the analysis. However, the tongues following further increase of $V_{1}$ feature a pattern drastically different from that in usual (non-$\mathcal{PT}$)\ parametrically driven systems: instead of bending down to larger values of the dc coupling constant, $V_{0}$, they maintain a direction parallel to the $V_{1}$ axis. The system of the parallel tongues gets dense with the decrease of $ω$, merging into a complex small-scale structure of alternating regions of stability and instability. The cases of $ω\rightarrow 0$ and $ω\rightarrow \infty $ are studied analytically by means of the adiabatic and averaging approximation, respectively. The cubic nonlinearity, if added to the system, alters the picture, destabilizing many originally robust dynamical regimes, and stabilizing some which were unstable.

nlin.PS↗
arXiv2014

Bulk vortices and half-vortex surface modes in parity-time-symmetric media

We demonstrate that in-bulk vortex localized modes, and their surface half-vortex ("horseshoe") counterparts self-trap in two-dimensional (2D) nonlinear optical systems with $\mathcal{PT}$-symmetric photonic lattices (PLs). The respective stability regions are identified in the underlying parameter space. The in-bulk states are related to truncated nonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modes are built, severally, of four and three beams with appropriate phase shifts between them. Their stable complex counterparts, built of up to 12 beams, are reported too.

physics.optics↗
arXiv2014

Three-dimensional hybrid vortex solitons

We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity base. The analysis reveals stability regions for symmetric, antisymmetric, and hybrid states. In addition, bead-shaped modulation profiles give rise to the first example of exact analytical solutions for stable three-dimensional vortex solitons. The predicted states may be realized in media with a controllable cubic nonlinearity, such as Bose-Einstein condensates.

nlin.PS↗
arXiv2014

Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two- and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions.The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.

nlin.PS↗
arXiv2014

Anderson Localization at the Subwavelength Scale and Loss Compensation for Surface-Plasmon Polaritons in Disordered Arrays of Metallic Nanowires

Using a random array of coupled metallic nanowires as a generic example of disordered plasmonic systems, we demonstrate that the structural disorder induces localization of light in these nanostructures at a deep-subwavelength scale. The ab initio analysis is based on solving the complete set of 3D Maxwell equations. We find that random variations of the radius of coupled plasmonic nanowires are sufficient to induce the Anderson localization (AL) of surface-plasmon polaritons (SPPs), the size of these trapped modes being significantly smaller than the wavelength. Remarkably, the optical-gain coefficient, needed to compensate losses in the plasmonic components of the system, is much smaller than the loss coefficient of the metal, which is obviously beneficial for the realization of the AL in plasmonic nanostructures. The dynamics of excitation and propagation of the Anderson-localized SPPs are addressed too.

physics.optics↗
arXiv2014

Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied at selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable or unstable when the nonlinearity includes the cubic loss or gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, while weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are considered too.

nlin.PS↗
arXiv2014

Interactions of spatial solitons with fused couplers

We study dynamical and stationary states of solitons in dual-core waveguides which are locally coupled (fused) at one or several short segments. The model applies to planar optical waveguides, and to BEC in dual traps. Collisions of an incident soliton with single and double locally-fused couplers are investigated by means of systematic simulations and several analytical methods (quasi- linear, fast-soliton, and adiabatic approximations). Excitation dynamics of a soliton trapped by a local coupler is studied by means of the variational approximation, and verified by simulations. Shuttle motion of a soliton trapped in a cavity between two local couplers, and in a finite array of couplers, is studied too.

physics.optics↗
arXiv2014

Spontaneous symmetry breaking in dual-core baby-Skyrmion systems

We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core models previously studied\ in nonlinear optics and BEC, here the symmetry-breaking bifurcation (SBB) in solitons (baby skyrmions) occurs with the increase of the inter-core coupling ($κ$), rather than with its decrease, due to the fact that even in the uncoupled system neither core may be empty. Prior to the onset of the symmetry breaking between the two components of the solitons, they gradually separate in the lateral direction, due to the increase of $κ$, which is explained in an analytical form by means of an effective interaction potential. Such evolution scenario are produced for the originally symmetric states with topological charges in the two cores $\left(B^{(1)},B^{(2)}\right)$, with $% B^{(1)}=B^{(2)}=1,2,3,4$. The evolution of mixed states, of the $\left(1,2\right)$ and $\left(2,4\right)$ types, with the variation of $κ$ is studied too.

hep-th↗
arXiv2014

Localized modes in two-dimensional Schroedinger lattices with a pair of nonlinear sites

We address the existence and stability of localized modes in the two-dimensional (2D) linear Schroedinger lattice with two symmetric nonlinear sites embedded into it, and a generalization for moderately localized nonlinearity featuring two distinct symmetric maxima. The latter setting admits a much greater variety of localized modes. Symmetric, antisymmetric, and asymmetric discrete solitons are found, and a subcritical bifurcation, accounting for the spontaneous symmetry breaking (SSB) of the symmetric modes and transition to asymmetric ones, is identified. Existence and stability of more complex 2D solutions in the form of discrete symmetric and asymmetric vortices are also discussed.

nlin.PS↗