arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 109 records · Page 6Linked to original sources

arXiv2024

Regular, beating and dilogarithmic breathers in biased photorefractive crystals

The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schrödinger equation (GNLSE). We use the variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystal, finding that the VA equations involve the dilogarithm special function. The VA predicts that solitons and breathers exist, and the Vakhitov-Kolokolov criterion predicts that the solitons are stable solutions. Direct simulations of the underlying GNLSE corroborates the existence of such stable modes. The numerical solutions produce both regular breathers and ones featuring beats (long-period modulations of fast oscillations). In the latter case, the Fourier transform of amplitude oscillations reveals a nearly discrete spectrum characterizing the beats dynamics. Numerical solutions of another type demonstrate spontaneous splitting of the input pulse in two or several secondary ones.

physics.optics↗

arXiv2024

Semi-vortex solitons and their excited states in spin-orbit-coupled binary bosonic condensates

It is known that two-dimensional two-component fundamental solitons of the semi-vortex (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, $N_{\mathrm{thr}}$, in these excited states is higher than the commonly known critical value, $N_{c}\approx 5.85$,associated with the single-component Townes solitons, $N_{\mathrm{thr}}$ 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.

cond-mat.quant-gas↗

arXiv2024

Interactions between fractional solitons in bimodal fiber cavities

We introduce a system of fractional nonlinear Schroedinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber-laser cavities with the effective fractional group-velocity dispersion (FGVD), which were recently made available to the experiment. In the FNLSE system, the FGVD terms are represented by the Riesz derivatives, with the respective Levy index (LI). The FNLSEs, which include the nonlinear self-phase-modulation (SPM) nonlinearity, are coupled by the cross-phase modulation (XPM) terms, and separated by a group-velocity (GV) mismatch (rapidity). By means of systematic simulations, we analyze collisions and bound states of solitons in the XPM-coupled system, varying the LI and GV mismatch. Outcomes of collisions between the solitons include rebound, conversion of the colliding single-component solitons into a pair of two-component ones, merger of the solitons into a breather, their mutual passage leading to excitation of intrinsic vibrations, and the elastic interaction. Families of stable two-component soliton bound states are constructed too, featuring a rapidity which is intermediate between those of the two components.

nlin.PS↗

arXiv2024

Stable patterns in the Lugiato-Lefever equation with a confined vortex pump

We introduce a model of a passive optical cavity based on a novel variety of the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5, stable confined vortex-ring states (vortex pixels) are produced by means of a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump and loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations which break the axial symmetry. The results suggest new possibilities for mode manipulations in passive nonlinear photonic media by means of appropriately designed pump beams.

physics.optics↗

arXiv2024

Spectrum conversion and pattern preservation of Airy beams in fractional systems with a dynamical harmonic-oscillator potential

We investigate the dynamics of optical Airy beams in the one-dimensional fractional Schrödinger equation with a harmonic-oscillator (HO) potential subjected to modulation along the propagation distance. Deriving general solutions for propagating beams and particular solutions for Airy waves with/without chirp, we study analytically the spectrum conversion and pattern preservation for the chirp-free and chirped Airy beams in the fractional system including the HO potential with moiré-lattice, hyperbolic-secant, and delta-functional modulation formats. For the HO-moiré-lattice potential, it is found that the chirp-free Airy beam experiences multiple spectrum conversions between the Airy and Gaussian patterns in the momentum space, preserving the Airy pattern in the coordinate space. The chirp magnitude of the chirped Airy beam determines whether the spectrum conversion occurs in the momentum space, and the splitting and evolution direction of the beam in the coordinate space. For the HO-hyperbolic-secant potential, the chirp-free Airy beam undergoes spectrum conversion and tunneling, with the positions of the spectrum conversion and tunneling significantly depending on parameters of the hyperbolic-secant potential; however, the spectrum conversion and pattern preservation of the chirped Airy beam occurs only under a certain relation of the chirp and parameters of the potential. In the case of the HO-delta-functional potential, the chirp-free Airy beam experiences abrupt spectrum conversion and a two-step spectrum shift; however, for the chirped Airy beam, the spectrum conversion is affected by the relation between the chirp and height of the potential. Effects of the fractional Lévy index on the spectrum conversion and pattern preservation of the Airy beams under the action of the three modulation patterns considered here are also explored in detail.

physics.optics↗

arXiv2024

Motion dynamics of two-dimensional fundamental and vortex solitons in the fractional medium with the cubic-quintic nonlinearity

We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a nontrivial problem, as the fractional diffraction breaks the Galilean invariance of the underlying equation. The addition of the defocusing quintic term to the focusing cubic one is necessary to stabilize the solitons against the collapse. The setting presented here can be implemented in nonlinear optical waveguides emulating the fractional diffraction. Systematic consideration identifies parameters of moving fundamental and vortex solitons (with vorticities 0 and 1 or 2, respectively) and maximum velocities up to which stable solitons persist, for characteristic values of the Levy index which determines the fractionality of the underlying model. Outcomes of collisions between 2D solitons moving in opposite directions are identified too. These are merger of the solitons, quasi-elastic or destructive collisions, and breakup of the two colliding solitons into a quartet of secondary ones.

nlin.PS↗

arXiv2024

Discrete and semi-discrete multidimensional solitons and vortices: Established results and novel findings

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schroeodinger (DNLS) equations and their generalizations, such as a system of discrete Gross- Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (chi^(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensates, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

nlin.PS↗

arXiv2024

Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime

We consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and instability with a bubble-like spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.

nlin.PS↗

arXiv2024

Solitons supported by a self-defocusing trap in a fractional-diffraction waveguide

We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schrödinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity growing steeply enough from the center to periphery. The model can be implemented in a planar optical waveguide. Stability regions are identified for the fundamental and dipole (single-node) states in the plane of the Lévy index and the total power (norm), while states of higher orders are unstable. Evolution of unstable states is investigated too, leading to spontaneous conversion towards stable modes with fewer node.

nlin.PS↗

arXiv2024

Stable semivortex gap solitons in a spin-orbit-coupled Fermi gas

We demonstrate the existence of semivortex (SV) solitons, with vorticities $0$ and $1$ in the two components, in a two-dimensional (2D) fermionic spinor system under the action of the Rashba-type spin-orbit coupling in the combination with the Zeeman splitting (ZS). In the ``heavy-atom" approximation, which was previously elaborated for the bosonic system, the usual kinetic energy is neglected, which gives rise to a linear spectrum with a bandgap. The model includes the effective Pauli self-repulsion with power $7/3$, as produced by the density-functional theory of Fermi superfluids. In the general case, the inter-component contact repulsion is included too. We construct a family of gap solitons of the SV type populating the spectral bandgap. A stability region is identified for the SV solitons, by means of systematic simulations, in the parameter plane of the cross-repulsion strength and chemical potential. The stability region agrees with the prediction of the anti-Vakhitov-Kolokolov criterion, which is a relevant necessary stability condition for systems with self-repulsive nonlinearities. We also test the stability of the SV solitons against a sudden change of the ZS strength, which initiates robust oscillations in the spin state of the soliton due to transfer of particles between the system's components.

nlin.PS↗

arXiv2024

Energy-level inversion for vortex states in spin-orbit coupled Bose-Einstein condensates

We investigate vortex states in Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC), gradient magnetic field, and harmonic-oscillator trapping potential. The linear version of the system is solved exactly. Through the linear-spectrum analysis, we find that, varying the SOC strength and magnetic-field gradient, one can perform energy-level inversion. With suitable parameters, initial higher-order vortex states can be made the ground state (GS). The nonlinear system is solved numerically, revealing that the results are consistent with the linear predictions in the case of repulsive inter-component interactions. On the other hand, inter-component attraction creates the GS in the form of mixed-mode states in a vicinity of the GS phase-transition points. The spin texture of both vortex- and mixed-mode GSs reveals that they feature the structure of 2D (baby) skyrmions.

cond-mat.quant-gas↗

arXiv2024

Stable higher-order vortex quantum droplets in an annular potential

We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring-shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and trapping potential supports two VQD branches, controlled by the radius, width and depth of the potential profile. While the lower-branch VQDs, bifurcating from the system's linear modes, are completely unstable, the upper branch is fully stable for all values of the topological charge $m$ and potential's parameters. Up to $m=12$ (at least), stable VQDs obey the {\it anti-Vakhitov-Kolokolov} criterion. In the limit of an extremely tight radial trap, the modulational instability of the quasi-1D azimuthal VQDs is studied analytically. We thus put forward an effective way to produce stable VQDs with higher vorticity but a relatively small number of atoms, which is favorable for experimental realization.

cond-mat.quant-gas↗

arXiv2024

Basic fractional nonlinear-wave models and solitons

This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from fractional quantum mechanics and more experimentally relevant setups emulating fractional diffraction in optics, are based on the Riesz definition of fractional derivatives, which are characterized by the respective Levy indices. Basic species of one-dimensional solitons, produced by the fractional models which include cubic or quadratic nonlinear terms, are outlined too. In particular, it is demonstrated that the variational approximation is relevant in many cases. A summary of the recently demonstrated experimental realization of the fractional group-velocity dispersion in fiber lasers is also presented.

nlin.PS↗

arXiv2023

Multidimensional Soliton Systems

This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison with commonly known one-dimensional solitons, which are, normally, stable modes, a challenging problem is the propensity of 2D and 3D solitons to instability, caused by the occurrence of the critical or supercritical wave collapse (catastrophic self-compression) in the same spatial dimension. A remarkable feature of multidimensional solitons is their ability to carry vorticity; however, 2D vortex rings and 3D vortex tori are subject to strong splitting instability. Therefore, it is natural to categorize the basic results according to physically relevant settings which make it possible to maintain stability of fundamental (non-topological) and vortex solitons against the collapse and splitting, respectively. The present review is focused on schemes that were recently elaborated in terms of Bose-Einstein condensates and similar photonic setups. These are two-component systems with spin-orbit coupling, and ones stabilized by the beyond-mean-field Lee-Huang-Yang effect. The latter setting has been implemented experimentally, giving rise to stable self-trapped quasi-2D and 3D "quantum droplets".

nlin.PS↗

arXiv2023

Analysis of High-Contrast All-Optical Dual Wavelength Switching in Asymmetric Dual-Core Fibers

We systematically present experimental and theoretical results for the dual-wavelength switching of 1560 nm, 75 fs signal pulses (SPs) driven by 1030 nm, 270 fs control pulses (CPs) in a dual-core fiber (DCF). We demonstrate a switching contrast of 31.9 dB, corresponding to a propagation distance of 14 mm, achieved by launching temporally synchronized SP-CP pairs into the fast core of the DCF with moderate inter-core asymmetry. Our analysis employs a system of three coupled propagation equations to identify the compensation of the asymmetry by nonlinearity as the physical mechanism behind the efficient switching performance.

physics.optics↗

arXiv2023

Angular-momentum modes in a bosonic condensate trapped in the inverse-square potential

In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/r^2 is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l+1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.

cond-mat.quant-gas↗

arXiv2023

Multipole solitons in competing nonlinear media with an annular potential

We address the existence, stability, and propagation dynamics of multipole-mode solitons in cubic-quintic nonlinear media with an imprinted annular (ring-shaped) potential. The interplay of the competing nonlinearity with the potential enables the formation of a variety of solitons with complex structures, from dipole, quadrupole, and octupole solitons to necklace complexes. The system maintains two branches of soliton families with opposite slopes of the power-vs.-propagation-constant curves. While the solitons' stability domain slowly shrinks with the increase of even number $n$ of lobes in the multipole patterns, it remains conspicuous even for $n>16$. The application of a phase torque gives rise to stable rotation of the soliton complexes, as demonstrated by means of analytical and numerical methods.

physics.optics↗

arXiv2023

Three-dimensional solitons in Rydberg-Dressed cold atomic gases with spin-orbit coupling

We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose-Einstein condensates of Rydberg atoms under the action of the spin-orbit coupling (SOC). By means of systematic numerical computations, we demonstrate that the interplay of SOC and long-range spherically symmetric Rydberg interactions stabilize the 3D solitons, improving their resistance to collapse. We find how the stability range depends on the strengths of the SOC and Rydberg interactions and the soft-core atomic radius.

cond-mat.quant-gas↗