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, and 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.

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 Laskin's 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 Lévy 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.

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 the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (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 (χ(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 condensate, and others. The article presents a review of the 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.

Semidiscrete optical vortex droplets in quasi-phase-matched photonic crystals.

What we believe is a new scheme for producing semidiscrete self-trapped vortices ("swirling photon droplets") in photonic crystals with competing quadratic (χ(2)) and self-defocusing cubic (χ(3)) nonlinearities is proposed. The photonic crystal is designed with a striped structure, in the form of spatially periodic modulation of the χ(2) susceptibility, which is imposed by the quasi-phase-matching technique. Unlike previous realizations of semidiscrete optical modes in composite media, built as combinations of continuous and arrayed discrete waveguides, the semidiscrete vortex "droplets" are produced here in the fully continuous medium. This work reveals that the system supports two types of semidiscrete vortex droplets, viz., onsite- and intersite-centered ones, which feature, respectively, odd and even numbers of stripes, N. Stability areas for the states with different values of N are identified in the system's parameter space. Some stability areas overlap with each other, giving rise to the multistability of states with different N. The coexisting states are mutually degenerate, featuring equal values of the Hamiltonian and propagation constant. An experimental scheme to realize the droplets is outlined, suggesting new possibilities for the long-distance transmission of nontrivial vortex beams in nonlinear media.

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.

Formation of Rogue Waves and Modulational Instability with Zero-Wavenumber Gain in Multicomponent Systems with Coherent Coupling.

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multicomponent systems-in particular, in the massive Thirring model.

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.

Dichromatic "Breather Molecules" in a Mode-Locked Fiber Laser.

Bound states of solitons ("molecules") occur in various settings, playing an important role in the operation of fiber lasers, optical emulation, encoding, and communications. Soliton interactions are generally related to breathing dynamics in nonlinear dissipative systems, and maintain potential applications in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are created in a synchronized mode-locked fiber laser. Real-time delay-shifting interference spectra are measured to display the temporal evolution of the DBMs, that cannot be observed by means of the usual real-time spectroscopy. As a result, robust out-of-phase vibrations are found as a typical intrinsic mode of DBMs. The same bound states are produced numerically in the framework of a model combining equations for the population inversion in the mode-locked laser and cross-phase-modulation-coupled complex Ginzburg-Landau equations for amplitudes of the optical fields in the fiber segments of the laser cavity. The results demonstrate that the Q-switching instability induces the onset of breathing oscillations. The findings offer new possibilities for the design of various regimes of the operation of ultrafast lasers.

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.

Temporal cavity solitons in a laser-based microcomb: a path to a self-starting pulsed laser without saturable absorption.

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not require saturation of the gain, the results offer an alternative to standard techniques that provide laser mode-locking.

Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrödinger equation with a PT-symmetric potential.

We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrödinger equation with cubic or cubic-quintic (CQ) nonlinearity and a parity-time-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a "blueprint" for the evolution of genuine localized modes in the system.

Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities.

We demonstrate that the fractional cubic-quintic nonlinear Schrödinger equation, characterized by its Lévy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital angular momentum. They can be built, in the respective optical setting, as circular chains of fundamental solitons linked by a vortical phase field. We predict semi-analytically that the metastable necklace-shaped clusters persist, corresponding to a local minimum of an effective potential of interaction between adjacent solitons in the cluster. Systematic simulations corroborate that the clusters stay robust over extremely large propagation distances, even in the presence of strong random perturbations.

Tunable nonlinear spectra of anti-directional couplers.

We produce transmission and reflection spectra of the anti-directional coupler (ADC) composed of linearly coupled positive- and negative-refractive-index arms, with intrinsic Kerr nonlinearity. Both reflection and transmission feature two highly amplified peaks at two distinct wavelengths in a certain range of values of the gain, making it possible to design a wavelength-selective mode-amplification system. We also predict that a blend of gain and loss in suitable proportions can robustly enhance reflection spectra that are detrimentally affected by the attenuation, in addition to causing red and blue shifts owing to the Kerr effect. In particular, ADC with equal gain and loss coefficients is considered in necessary detail.

Reversible ultrafast soliton switching in dual-core highly nonlinear optical fibers.

We experimentally investigate a nonlinear switching mechanism in a dual-core highly nonlinear optical fiber. We focus the input stream of femtosecond pulses on one core only, to identify transitions between inter-core oscillations, self-trapping in the cross core, and self-trapping of the pulse in the straight core. A model based on the system of coupled nonlinear Schrödinger equations provides surprisingly good agreement with the experimental findings.

Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers.

We study quantum fluctuations of macroscopic parameters of a nonlinear Schrödinger breather-a nonlinear superposition of two solitons, which can be created by the application of a fourfold quench of the scattering length to the fundamental soliton in a self-attractive quasi-one-dimensional Bose gas. The fluctuations are analyzed in the framework of the Bogoliubov approach in the limit of a large number of atoms N, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio setting by construction, leads to a reasonable agreement, within 20% accuracy, with fluctuations of the relative velocity of constituent solitons obtained from the exact Bethe-ansatz results [Phys. Rev. Lett. 119, 220401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.220401] in the opposite low-N limit (for N≤23). We thus confirm, for macroscopic N, the breather dissociation time to be within the limits of current cold-atom experiments. Fluctuations of soliton masses, phases, and positions are also evaluated and may have experimental implications.

Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation.

Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap are investigated by combining techniques of variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Control schemes considered in the paper include imaginary trap frequencies at short time scales, i.e., the HO potential replaced by the quadratic repulsive one. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help us to address fundamental problems of the quantum speed limit and thermodynamics.

Self-interaction of ultrashort pulses in an epsilon-near-zero nonlinear material at the telecom wavelength.

Dynamics of femtosecond pulses with the telecom carrier wavelength is investigated numerically in a subwavelength layer of an indium tin oxide (ITO) epsilon-near-zero (ENZ) material with high dispersion and high nonlinearity. Due to the subwavelength thickness of the ITO ENZ material, and the fact that the pulse's propagation time is shorter than its temporal width, multiple reflections give rise to self-interaction in both spectral and temporal domains, especially at wavelengths longer than at the ENZ point, at which the reflections are significantly stronger. A larger absolute value of the pulse's chirp strongly affects the self-interaction by redistributing energy between wavelengths, while the sign of the chirp affects the interaction in the temporal domain. It is also found that, when two identical pulses are launched simultaneously from both ends, a subwavelength counterpart of a standing-wave state can be established. It shows robust energy localization in the middle of the sample, in terms of both the spectral and temporal intensity distributions.

Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser.

We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n = 1, while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.

Asymptotic dynamics of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes.

We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell's equations, taking into account the field inhomogeneity along the nanotube axis beyond the approximation of slowly varying amplitudes and phases. A model is proposed for the analysis of the dynamics of an electromagnetic pulse in the form of an effective equation for the vector potential of the field. Our numerical analysis demonstrates the possibility of a satisfactory description of the evolution of the pulse field at large times by means of a three-dimensional generalization of the sine-Gordon and double sine-Gordon equations.

Nonlinear anti-directional couplers with gain and loss.

Following the concept of PT-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multistability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratios between the input and output intensities leading to an efficient way of controlling light with light.