arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 145 records · Page 8Linked to original sources

arXiv2023

Vortex solitons in quasi-phase-matched photonic crystals

We report solutions for stable compound solitons in a three-dimensional quasi-phase-matched photonic crystal with the quadratic ($χ^{(2)}$) nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be realized by means of the available technology. The solitons are built as four-peak vortex modes of two types, rhombuses and squares (intersite- and onsite-centered self-trapped states, respectively). Their stability areas are identified in the system's parametric space (rhombuses occupy an essentially broader stability domain), while all bright vortex solitons are subject to strong azimuthal instability in uniform $χ^{(2)}$ media. Possibilities for experimental realization of the solitons are outlined.

physics.optics↗

arXiv2023

Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential

In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states are obtained under certain parameter constraints, providing a guide to finding the respective generic family. In a parameter region of the unbroken PT symmetry, different families of QDs originating from the linear modes are obtained in the form of multipolar and vortex droplets at low and high values of the norm, respectively, and their stability is investigated. In the spinning regime, QDs become asymmetric above a critical rotation frequency, most of them being stable. The effect of the PT -symmetric potential on the spinning and nonspinning QDs is explored by varying the strength of the gain-loss distribution. Generally, spinning QDs trapped in the PT -symmetric potential exhibit asymmetry due to the energy flow affected by the interplay of the gain-loss distribution and rotation. Finally, interactions between spinning or nonspinning QDs are explored, exhibiting elastic collisions under certain conditions.

quant-ph↗

arXiv2023

All-polarization-maintaining linear cavity fiber lasers mode-locked by nonlinear polarization evolution in stretched pulse regime

Nonlinear polarization evolution (NPE) is among the most advanced techniques for obtaining ultrashort pulses with excellent optical performance. However, it is challenging to design environmentally stable NPE fiber oscillators using only polarization-maintaining (PM) fibers. Here, we use the same PM fiber and non-reciprocal phase shifter to design two different devices, which are capable of acting as effective NPE saturable absorbers (SAs) in two all-PM linear cavity fiber lasers. These two laser setups differ in the position of the non-reciprocal phase shifter, the presence of which is crucial for the proposed fiber lasers to reduce their mode-locking thresholds and achieve high repetition rates above 100 MHz. The mode-locking principle and pulse evolution in the laser cavity are investigated theoretically. The first all-PM fiber oscillator emits sub-200 fs stretched pulses with low peak powers. The second oscillator, with a simpler architecture, directly delivers stretched pulses with high peak powers, the spectral bandwidth greater than 30 nm, and the pulse duration less than 90 fs. To the best of our knowledge, 79 fs achieved in this design is the shortest pulse duration provided by PM fiber lasers using NPE mode-lockers.

physics.optics↗

arXiv2023

Controlled non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation

To study controlled evolution of non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation, we focus on a system of three coupled Gross-Pitaevskii (GP) equations with space-time-dependent external potentials and temporally modulated gain/loss distributions. An integrability condition and a non-isospectral Lax pair for the coupled GP equations are obtained. Using it, we derive an infinite set of dynamical invariants, the first two of which are the mass and momentum. The Darboux transform is used to generate one- and two-soliton solutions. Under the action of different external potentials and gain/loss distributions, various solutions for controlled non-autonomous matter-wave solitons of both ferromagnetic and polar types are obtained, such as self-compressed, snake-like and stepwise solitons, and as well as breathers. In particular, the formation of states resembling rogue waves, under the action of a sign-reversible gain-loss distribution, is demonstrated too. Shape-preserving and changing interactions between two non-autonomous matter-wave solitons and bound states of solitons are addressed too. In this context, spin switching arises in the polar-ferromagnetic interaction. Stability of the non-autonomous matter-wave solitons is verified by means of systematic simulations of their perturbed evolution.

cond-mat.quant-gas↗

arXiv2022

Experimental realisations of the fractional Schrödinger equation in the temporal domain

The fractional Schrödinger equation (FSE) -- a natural extension of the standard Schrödinger equation -- is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional derivative. Here, we report the experimental realisation of an optical FSE for femtosecond laser pulses in the temporal domain. Programmable holograms and the single-shot measurement technique are respectively used to emulate a \textit{Lévy waveguide} and to reconstruct the amplitude and phase of the pulses. Varying the Lévy index of the FSE and the initial pulse, the temporal dynamics is observed in diverse forms, including solitary, splitting and merging pulses, double Airy modes, and ``rain-like'' multi-pulse patterns. Furthermore, the transmission of input pulses carrying a fractional phase exhibits a ``fractional-phase protection'' effect through a regular (non-fractional) material. The experimentally generated fractional time-domain pulses offer the potential for designing optical signal-processing schemes.

physics.optics↗

arXiv2022

Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations

The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values $1\leqα\leq 2$. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance, $ζ$. The management format with the nonlinearity coefficient decaying as $1/ζ$ is considered, too. These management schemes maintain stable propagation of the ring-Airy beams, which maintain their axial symmetry, in contrast to the symmetry-breaking splitting instability of ring-shaped patterns in 2D Kerr media. The instability driven by supercritical collapse at all values $α< 2$ in the presence of the self-focusing cubic term is eliminated, too, by the means of management.

physics.optics↗

arXiv2022

Vortex-ring quantum droplets in a radially-periodic potential

We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term multiplied by a logarithmic factor (as produced by the Lee-Huang-Yang correction to the mean-field theory) and a potential which is a periodic function of the radial coordinate. Narrow vortex rings with high values of the topological charge, trapped in particular circular troughs of the radial potential, are produced. These results suggest an experimentally relevant method for the creation of vortical QDs (thus far, only zero-vorticity ones have been reported). The 2D GP equation for the narrow rings is approximately reduced to the 1D form, which makes it possible to study the modulational stability of the rings against azimuthal perturbations. Full stability areas are delineated for these modes. The trapping capacity of the circular troughs is identified for the vortex rings with different winding numbers (WNs). Stable compound states in the form of mutually nested concentric multiple rings are constructed too, including ones with opposite signs of the WNs. Other robust compound states combine a modulationally stable narrow ring in one circular potential trough and an azimuthal soliton performing orbital motion in an adjacent one. The results may be used to design a device employing coexisting ring-shaped modes with different WNs for data storage.

nlin.PS↗

arXiv2022

Tunable energy-level inversion in spin-orbit-coupled Bose-Einstein condensates

A method to realize controllable inversion of energy levels in a one-dimensional spin-orbit (SO)-coupled two-component Bose-Einstein condensate under the action of a gradient magnetic field and harmonic-oscillator (HO) trapping potential is proposed. The linear version of the system is solved exactly. By adjusting the SO coupling strength and magnetic-field gradient, the energy-level inversion makes it possible to transform any excited state into the ground state. The full nonlinear system is solved numerically, and it is found that the results are consistent with the linear prediction in the case of the repulsive inter-component interaction. On the other hand, the inter-component attraction gives rise to states of superposition and edge types. Similar results are also reported for the system with the HO trap replaced by the box potential. These results suggest a possibility to realize any excited state and observe it in the experiment.

cond-mat.quant-gas↗

arXiv2022

Robust mode-locking in a hybrid ultrafast laser based on nonlinear multimodal interference

We experimentally demonstrate the realization of a half-polarization-maintaining (half-PM) fiber laser, in which mode-locking is provided by a reflective multimode-interference saturable absorber (SA). In the specially designed SA, linearly polarized light is coupled into a 15-cm-long graded-index multimode fiber (GIMF) through the PM fiber, and then reflected back to the PM structure through a mirror pigtailed with a single-mode fiber (SMF). The modulation depth and saturation peak power are measured to be 1.5% and 0.6 W, respectively. The proposed SA device is incorporated into a novel half-PM erbium-doped fiber oscillator, which generates soliton pulses with 409 fs temporal duration at a 33.3 MHz repetition rate. The proposed fiber laser is compared with a conventional non-PM fiber laser mode-locked by nonlinear polarization evolution (NPE) in terms of optical properties such as spectral bandwidth, pulse duration, and stability performance. Short- and long-time stability tests and superior noise performance corroborate robust mode-locking in this setup.

physics.optics↗

arXiv2022

Spontaneous symmetry breaking of dual-layer solitons in spin-orbit-coupled Bose-Einstein condensates

It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spin-orbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a double-layer system, in which two binary condensates, stabilized by the SOC, are linearly coupled by tunneling. By means of the numerical methods, it is found that symmetric two-layer solitons undergo the spontaneous-symmetry-breaking (SSB) bifurcation of the subcritical type. The bifurcation produces families of asymmetric 2D solitons, which exist up to the value of the total norm equal to the norm of the Townes solitons, above which the collapse occurs. This situation terminates at a critical value of the inter-layer coupling, beyond which the SSB bifurcation is absent, as the collapse sets in earlier. Symmetric 2D solitons that are destabilized by the SSB demonstrate dynamical symmetry breaking, in combination with intrinsic oscillations of the solitons, or transition to the collapse, if the soliton's norm is sufficiently large. Asymmetric MMs produced by the SSB instability start spontaneous drift, in addition to the intrinsic vibrations. Consideration of moving 2D solitons is a nontrivial problem because SOC breaks the Galilean invariance. It is found that the system supports moving MMs up to a critical value of the velocity, beyond which they undergo delocalization.

cond-mat.quant-gas↗

arXiv2022

Domain walls in fractional media

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states, in the form of domain walls (DWs) in the two-component system of immiscible fields. Numerical study of the underlying system of fractional nonlinear Schroedinger equations demonstrates the existence and stability of DWs at all values of the respective Levy index (a < 2) which determines the fractional diffraction, and at all values of the XPM/SPM ratio b in the two-component system above the immiscibility threshold. The same conclusion is obtained for DWs in the system which includes the linear coupling, alongside the XPM interaction between the immiscible components. Analytical results are obtained for the scaling of the DW's width. The DW solutions are essentially simplified in the special case of b = 3, as well as close to the immiscibility threshold. In addition to symmetric DWs, asymmetric ones are constructed too, in the system with unequal diffraction coefficients and/or different Levy indices of the two components.

physics.optics↗

arXiv2022

Vortex gap solitons in spin-orbit-coupled Bose-Einstein condensates with competing nonlinearities

The formation and dynamics of full vortex gap solitons (FVGSs) is investigated in two-component Bose-Einstein condensates with spin-orbit coupling (SOC), Zeeman splitting (ZS), and competing cubic and quintic nonlinear terms, while the usual kinetic energy is neglected, assuming that it is much smaller than the SOC and ZS terms. Unlike previous SOC system with the cubic-only attractive nonlinearity, in which solely semi-vortices may be stable, with the vorticity carried by a single component, the present system supports stable FVGS states, with the vorticity present in both components (such states are called here full vortex solitons, to stress the difference from the half-vortices). They populate the bandgap in the system's linear spectrum. In the case of the cubic self-attraction and quintic repulsion, stable FVGSs with a positive effective mass exist near the top of the bandgap. On the contrary, the system with cubic self-repulsion and quintic attraction produces stable FVGSs with a negative mass near the bottom of the bandgap. Mobility and collisions of FVGSs with different topological charges are investigated too.

cond-mat.quant-gas↗

arXiv2022

Self-accelerating solitons

Basic models which give rise to one- and two-dimensional (1D and 2D) solitons, such as the Gross-Pitaevskii (GP) equations for Bose-Einstein condensates (BECs), feature the Galilean invariance, which makes it possible to generate families of moving solitons from quiescent ones. A challenging problem is to find models admitting stable self-accelerating (SA) motion of solitons. SA modes are known in linear systems in the form of Airy waves, but they are poorly localized states. This brief review presents two-component BEC models which make it possible to predict SA solitons. In one system, a pair of interacting 1D solitons with opposite signs of the effective mass is created in a binary BEC trapped in an optical-lattice potential. In that case, opposite interaction forces, acting on the solitons with positive and negative masses, produce equal accelerations, while the total momentum is conserved. The second model is based on a system of GP equations for two atomic components, which are resonantly coupled by a microwave field. The latter model produces an exact transformation to an accelerating references frame, thus predicting 1D and 2D stable SA solitons, including vortex rings.

nlin.PS↗

arXiv2022

Interactions of solitary waves in the Adlam-Allen model

We study the interactions of two or more solitary waves in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model; (b) using the so-called Manton's method. We compare these findings with results of direct simulations, and identify adjustments necessary to achieve a quantitative match between them. Additional connections are made, such as with solitons of the Korteweg--de Vries equation. New challenges are identified in connection to this model and its solitary waves.

nlin.PS↗

arXiv2022

Observation of SQUID-like behavior in fiber laser with intra-cavity epsilon-near-zero effect

Establishing relations between fundamental effects in far-flung areas of physics is a subject of great interest in the current research. We here report realization of a novel photonic system akin to the radio-frequency superconducting quantum interference device (RF-SQUID), in a fiber laser cavity with epsilon-near-zero (ENZ) nanolayers as intra-cavity components. Emulating the RF-SQUID scheme, the photonic counterpart of the supercurrent, represented by the optical wave, circulates in the cavity, passing through effective optical potential barriers. Different ENZ wavelengths translate into distinct spectral outputs through the variation of cavity resonances, emulating the situation with a frequency-varying tank circuit in the RF-SQUID. Due to the presence of the ENZ element, the optical potential barrier is far lower for selected frequency components, granting them advantage in the gain-resource competition. The findings reported in this work provide a deeper insight into the ultrafast ENZ photonics, revealing a new path towards the design of nanophotonic on-chip devices with various operational functions, and offer a new approach to study superconducting and quantum-mechanical systems.

physics.optics↗

arXiv2022

Multidimensional dissipative solitons and solitary vortices

This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or dispersion, and between loss and gain. Due to these conditions, dissipative solitons (DSs) exist not in families, but as isolated solutions. The main issue is stability of 2D and 3D DSs, especially vortical ones. First, stable 2D DSs are presented in the framework of the complex Ginzburg-Landau equation with the cubic-quintic (CQ) nonlinearity, which combines linear and quintic loss with cubic gain. In addition to fundamental (zero-vorticity) DSs, stable spiral DSs are presented too, with vorticities 1 and 2. Stable 2D solitons were also found in a system of two linearly-coupled fields, with linear gain acting in one and linear loss in the other. In this case, the cubic loss (without quintic terms) is sufficient for the stability of fundamental and vortex DSs. In addition to truly localized states, weakly localized ones are presented too, in a model with nonlinear loss without explicit gain, the losses being compensated by influx of power from infinity. Other classes of 2D models which are considered here use spatially modulated loss or gain to predict many species of robust DSs, including ones featuring complex periodically recurring metamorphoses. Stable fundamental and vortex solitons are also produced by models with a trapping or spatially periodic potential. In the latter case, 2D gap DSs are considered. Further, 2D dissipative models with spin-orbit coupling give rise to stable semi-vortices, with vorticity carried by one component. Along with the 2D solitons, the review includes 3D fundamental and vortex DSs, stabilized by the CQ nonlinearity and/or external potentials, and collisions between them.

nlin.PS↗

arXiv2022

Two-dimensional solitons in nonlocal media: a brief review

This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history. Some findings, such as optical solitons supported by thermal nonlinearity, and by the orientational nonlinearity in liquid crystals, have been reviewed in the literature, therefore they are outlined in the present review in a brief form. Some other studies, such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have started recently, therefore it will be relevant to review them in detail when more results are accumulated; the present article provides a short outline of the latter topic. The main part of the article is a summary of results obtained for two-dimensional (2D) solitons in specific models originating in studies of Bose-Einstein condensates (BECs), which are sufficiently mature but have not yet been reviewed. These are, in particular, anisotropic quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms, and giant vortex solitons, which are stable for high values of the winding number, as well as 2D vortex solitons of the latter type moving with self-acceleration. The vortex solitons are states of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a microwave field which couples the two atomic states. Some other topics are included in the review in a brief form.

physics.optics↗

arXiv2022

General higher-order breathers and rogue waves in the two-component long-wave--short-wave resonance-interaction model

General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbits. There are three families of RW solutions, which correspond to a simple root, two simple roots, and a double root of an algebraic equation related to the dimension reduction procedure. The first family of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs, the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWs coexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of different bounded state ($N,N_1,N_2$ being positive integers), while the third one have ${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$ fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negative integers). The second family can be regarded as the superpositions of the first family, while the third family can be the degenerate case of the first family under particular parameter choices. These diverse RW patterns are illustrated graphically.

nlin.SI↗