Prediction and observation of topological modes in fractal nonlinear optics.

This item from the News and Views (N&V) category aims to provide a summary of theoretical and experimental results recently published in ref. , which demonstrates the creation of corner modes in nonlinear optical waveguides of the higher-order topological insulator (HOTI) type. Actually, these are second-order HOTIs, in which the transverse dimension of the topologically protected edge modes is smaller than the bulk dimension (it is 2, in the case of optical waveguide) by 2, implying zero dimension of the protected modes, which are actually realized as corner or defect ones.

Solitons in composite linear-nonlinear moiré lattices.

We produce families of two-dimensional gap solitons (GSs) maintained by moiré lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the ML may be quasiperiodic or periodic, composed of mutually incommensurate or commensurate sublattices, respectively (in the latter case, the inter-lattice angle corresponds to Pythagorean triples). The GSs include fundamental, quadrupole, and octupole solitons, as well as quadrupoles and octupoles carrying unitary vorticity.

Physics-informed neural network for nonlinear dynamics of self-trapped necklace beams.

A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schrödinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to the rotation of rigid bodies and centrifugal force.

Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers.

We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind).

Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative.

We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equation represents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment.

Strongly Anisotropic Vortices in Dipolar Quantum Droplets.

We construct strongly anisotropic quantum droplets with embedded vorticity in the 3D space, with mutually perpendicular vortex axis and polarization of atomic magnetic moments. Stability of these anisotropic vortex quantum droplets (AVQDs) is verified by means of systematic simulations. Their stability area is identified in the parametric plane of the total atom number and scattering length of the contact interactions.

Optical vortex-antivortex crystallization in free space.

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction.

Semivortex solitons and their excited states in spin-orbit-coupled binary bosonic condensates.

It is known that two-dimensional two-component fundamental solitons of the semivortex (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,..

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

We consider instability and localized patterns arising from the long-wave-short-wave resonance in the nonintegrable 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.

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.

Bimetal Thin Film, Semiconductors, and 2D Nanomaterials in SPR Biosensors: An Approach to Enhanced Urine Glucose Sensing.

This work introduces a systematic approach for the development of Kretschmann configuration-based biosensors designed for non-invasive urine glucose detection. The methodology encompasses the utilization of various semiconductors, including Silicon (Si), Germanium (Ge), Gallium Nitride (GaN), Aluminum Nitride (AlN), and Indium Nitride (InN), in combination with a bimetallic layer (comprising Au and Ag films of equal thickness) to enhance the biosensor sensitivity. Additionally, 2D nanomaterials, such as Black Phosphorus and Graphene, are integrated into the semiconductor layers to enhance performance further.

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.

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) and self-defocusing cubic (χ) nonlinearities is proposed. The photonic crystal is designed with a striped structure, in the form of spatially periodic modulation of the χ 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.

Ring-shaped quantum droplets with hidden vorticity in a radially periodic potential.

We study the stability and characteristics of two-dimensional circular quantum droplets (QDs) with embedded hidden vorticity (HV), i.e., opposite angular momenta in two components, formed by binary Bose-Einstein condensates (BECs) trapped in a radially periodic potential.

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.

Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials.

We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them nonintegrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistant energy spectra (e.g.

One-dimensional Townes solitons in dual-core systems with localized coupling.

The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons.

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.

A solvable model for symmetry-breaking phase transitions.

Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit intrinsic transitions in them. We introduce a solvable model for symmetry-breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for solitons pinned to a combined linear-nonlinear double-well potential, represented by a symmetric pair of delta-functions.

Topological solitonic macromolecules.

Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here we experimentally create and model soliton polymers, which we call "polyskyrmionomers", built of atom-like individual solitons characterized by the topological invariant representing the skyrmion number.

Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers.

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index α. The system represents linearly coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment [Nat. Commun.

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).

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.