Optical spatial solitons: historical overview and recent advances

Dynamics of stable solitons of circular Pearcey Gaussian beams in a photorefractive strontium barium niobate crystal

We explore the behavior of abruptly autofocusing (AAF) beams in a saturable nonlinear medium. Stable solitons with different distribution structures are found under different combinations of external electric field and light field structure. Furthermore, the evolution of circular Pearcey Gaussian (CPG) beams in a photorefractive strontium barium niobate crystal is investigated. In particular, we fixed the external electric field to discuss the nonlinear propagation dynamics versus the initial light power. As the light power increases, the number of foci increases, and the distance between the foci decreases. Our study uncovers a fascinating interplay between AAF beams and the saturable nonlinear medium. We are convinced that the outcomes of our study may find potential applications in the realms of optical communication and photonic-integrated devices.

Evidence of 1+1D Photorefractive Stripe Solitons Deep in the Kerr Limit

The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally occurring real-world 3D settings as solitary walls or stripes, their observation had previously been considered unfeasible because of the strong transverse instability intrinsic to the extended nonlinear perturbation. We report the observation of solitons that are fully compatible with the 1+1D Kerr paradigm limit hosted in a 2+1D system. The waves are stripe spatial solitons in bulk copper doped potassium-lithium-tantalate-niobate (KLTN) supported by unsaturated photorefractive screening nonlinearity. The parameters of the stripe solitons fit well, in the whole existence domain, with the 1+1D existence curve that we derive for the first time in closed form starting from the saturable model of propagation. Transverse instability, that accompanies the solitons embedded in the 3D system, is found to have a gain length much longer than the crystal. Findings establish our system as a versatile platform for investigating exact soliton solutions in bulk settings and in exploring the role of dimensionality at the transition from integrable to nonintegrable regimes of propagation.

Classification of beating solitons, their physical spectra, and second-order nonlinear superpositions

We obtained the full set of multiparameter vector beating soliton solutions for Manakov equations in both focusing and defocusing cases. Based on exact solutions, physical spectra of beating solitons are calculated analytically. It is found that the spectra of moving beating solitons are asymmetric relative to the sign change of the frequency. In contrast, the static beating solitons have symmetric spectra. We also study the second-order vector beating soliton solutions with either equal or unequal velocities. Numerical simulations confirmed the validity of our exact solutions.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

The analytical soliton solutions place a lot of value on birefringent fibres. The major goal of this study is to generate novel forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from optical propagations using birefringent fibres. The (presumably new) extended direct algebraic (EDA) technique is used here to extract a large number of solutions for RKLE. It gives soliton solutions up to thirty-seven, which essentially correspond to all soliton families. This method's ability to determine many sorts of solutions through a single process is one of its key advantages. Additionally, it is simple to infer that the technique employed in this study is really straightforward yet one of the quite effective approaches to solving nonlinear partial differential equations so, this novel extended direct algebraic (EDA) technique may be regarded as a comprehensive procedure. The resulting solutions are found to be hyperbolic, periodic, trigonometric, bright and dark, combined bright-dark, and W-shaped soliton, and these solutions are visually represented by means of 2D, 3D, and density plots. The present study can be extended to investigate several other nonlinear systems to understand the physical insights of the optical propagations through birefringent fibre.

Azimuthons induced by degenerate linear eigenmodes and their conversions under nonlinear modulation

A method for generating azimuthons in a nonlinear Kerr medium is presented. The findings indicate that azimuthons can be represented as a combination of two co-rotational azimuthally modulated degenerate linear eigenmodes, along with an additional shift in the propagation constant. Moreover, the conversions between azimuthons are showcased using longitudinal nonlinear modulation. The results reveal that, under the resonance condition, direct conversion between neighboring azimuthons is possible, leading to the emergence of Rabi oscillation. However, for non-neighboring azimuthons, direct conversion is less effective, requiring cascaded modulation for their conversion.

Controllable nonlinear propagation of partially incoherent Airy beams

The self-accelerating beams such as the Airy beam show great potentials in many applications including optical manipulation, imaging and communication. However, their superior features during linear propagation could be easily corrupted by optical nonlinearity or spatial incoherence individually. Here we investigate how the interaction of spatial incoherence and nonlinear propagation affect the beam quality of Airy beam, and find that the two destroying factors can in fact balance each other. Our results show that the influence of coherence and nonlinearity on the propagation of partially incoherent Airy beams (PIABs) can be formulated as two exponential functions that have factors of opposite signs. With appropriate spatial coherence length, the PIABs not only resist the corruption of beam profile caused by self-focusing nonlinearity, but also exhibits less anomalous diffraction caused by the self-defocusing nonlinearity. Our work provides deep insight into how to maintain the beam quality of self-accelerating Airy beams by exploiting the interaction between partially incoherence and optical nonlinearity. Our results may bring about new possibilities for optimizing partially incoherent structured field and developing related applications such as optical communication, incoherent imaging and optical manipulations.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

An Introduction to Nonlinear Integrated Photonics Devices: Nonlinear Effects and Materials

The combination of integrated optics technologies with nonlinear photonics, which has led to the growth of nonlinear integrated photonics, has also opened the way to groundbreaking new devices and applications. Here we introduce the main physical processes involved in nonlinear photonics applications, and we discuss the fundaments of this research area, starting from traditional second-order and third-order phenomena and going to ultrafast phenomena. The applications, on the other hand, have been made possible by the availability of suitable materials, with high nonlinear coefficients, and/or by the design of guided-wave structures, which can enhance the material's nonlinear properties. A summary of the most common nonlinear materials is presented, together with a discussion of the innovative ones. The discussion of fabrication processes and integration platforms is the subject of a companion article, also submitted for publication in this journal. There, several examples of nonlinear photonic integrated devices to be employed in optical communications, all-optical signal processing and computing, or quantum optics are shown, too. We aimed at offering a broad overview, even if, certainly, not exhaustive. We hope that the overall work could provide guidance for those who are newcomers to this field and some hints to the interested researchers for a more detailed investigation of the present and future development of this hot and rapidly growing field.

Suppression of Nonlinear Optical Rogue Wave Formation Using Polarization-Structured Beams

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

Mode-locking in quadratically nonlinear waveguide arrays

A two-dimensional theoretical model is constructed to describe optical mode-locking (ML) in quadratically nonlinear waveguide arrays (QWGAs). Steady-state solutions of the considered model are obtained by a modified pseudo-spectral renormalization algorithm, and the mode-locking dynamics of the model are investigated through direct simulation of the nonlinear evolution and a linear stability analysis of the solutions. It is shown that stable mode-locking of elliptic steady-state solutions in quadratically nonlinear waveguide arrays are possible for a wide range of parameters, suggesting that quadratically nonlinear materials are well suited for producing stable mode-locked states for a wide range of applications.

Periodic evolution of the out-of-phase dipole and the single-charged vortex solitons in periodic photonic moiré lattice with saturable self-focusing nonlinearity media

We survey the propagation properties of the out-of-phase (OOP) dipole solitons and the single-charged vortex (SCV) soliton in a periodic photonic moiré lattice with θ=arctan⁡(3/4) under self-focusing nonlinearity media. Since the rotation angle, periodic photonic moiré lattices have peculiar energy band structures, with highly flat bands and the bandgaps being much more extensive, which is very favorable for the realization and stability of the solitons. When exciting a single point on-site with the OOP dipole beam, its evolution shows a periodic rollover around the lattice axis. Whereas, when exciting a single point on-site with the SCV beam, it transmits counterclockwise rotating periodically. Both the OOP dipole solitons and the SVC soliton maintain the local state, but their phase exhibits different variations. The phase of the OOP dipole solitons is flipped, while that of the SCV is rotated counterclockwise. Our work further complements the exploration of solitons in photonic moiré lattice with nonlinearity.

Intense Wave Formation from Multiple Soliton Fusion and the Role of Extra Dimensions

We experimentally and numerically explore the role of dimensionality in multiple (three or more) soliton fusion supported by nonreciprocal energy exchange. Three-soliton fusion into an intense wave is found when an extra dimension, with no broken inversion symmetry, is involved. The phenomenon is observed for 2+1D spatial waves in photorefractive crystals, where solitons are supported by a spatially local saturated Kerr-like self-focusing and fusion is driven by the leading nonlocal correction, the spatial analog of the nonlinear Raman effect.

Two dimensional Airy beam soliton

We demonstrate the formation of a two dimensional Airy beam soliton in a photorefractive crystal. By simply varying the nonlinearity strength we identify several scenarios showing the coexistence between an Airy beam and the emerging soliton. The soliton output profile behaves according to the theoretical soliton existence curve and can be tailored by the nonlinearity strength even without modifying the input Airy beam shape. This last feature makes this Airy soliton distinct from the Gaussian beam generated photorefractive soliton.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

Two-Dimensional Solitons in Bose–Einstein Condensates with Spin–Orbit Coupling and Rydberg–Rydberg Interaction

Applying an imaginary time evolution method (AITEM) to the system of Gross–Pitaevskii equations, we find two-dimensional stable solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and the Rydberg–Rydberg interaction (RRI). The stability of 2D solitons by utilizing their norm and energy is discussed in detail. Depending on the SOC and Rydberg–Rydberg interaction, we find stable zero-vorticity and vortical solitons. Furthermore, we show that the solitons can be effectively tuned by the local and nonlocal nonlinearities of this system.

Steady optical beam propagating through turbulent environment

A steady optical beam (SOB) propagating stably in a disorder medium is constructed by using a specially designed aspherical lens. Our theoretical and experimental results show that the generated SOB exhibits much better propagation features with small divergence and long Rayleigh length, as well as weak deformation through turbulent environment as compared with a conventional Gaussian beam. The beam parameter product of the SOB reaches 49.40% of the Gaussian beam by multiple measurements within a certain distance range. The SOB may find applications in optical communications and optical detection in turbulent transmission conditions.

Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

Evidence of Chaotic Dynamics in Three-Soliton Collisions

We observe chaotic optical wave dynamics characterized by erratic energy transfer and soliton annihilation and creation in the aftermath of a three-soliton collision in a photorefractive crystal. Irregular dynamics are found to be mediated by the nonlinear Raman effect, a coherent interaction that leads to nonreciprocal soliton energy exchange. Results extend the analogy between solitons and particles to the emergence of chaos in three-body physics and provide new insight into the origin of the irregular dynamics that accompany extreme and rogue waves.

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrödinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too, in particular, for fast moving solitons and the results produced by the variational approximation. Moreover, dissipative solitons are briefly considered, which are governed by the fractional complex Ginzburg–Landau equation.

Nondegenerate Bright Solitons in Coupled Nonlinear Schrödinger Systems: Recent Developments on Optical Vector Solitons

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the coupled nonlinear Schrödinger (CNLS) family of equations. In the recent past, many types of vector solitons have been identified both in the integrable and non-integrable CNLS framework. In this article, we review some of the recent progress in understanding the dynamics of the so called nondegenerate vector bright solitons in nonlinear optics, where the fundamental soliton can have more than one propagation constant. We address this theme by considering the integrable two coupled nonlinear Schrödinger family of equations, namely the Manakov system, mixed 2-CNLS system (or focusing-defocusing CNLS system), coherently coupled nonlinear Schrödinger (CCNLS) system, generalized coupled nonlinear Schrödinger (GCNLS) system and two-component long-wave short-wave resonance interaction (LSRI) system. In these models, we discuss the existence of nondegenerate vector solitons and their associated novel multi-hump geometrical profile nature by deriving their analytical forms through the Hirota bilinear method. Then we reveal the novel collision properties of the nondegenerate solitons in the Manakov system as an example. The asymptotic analysis shows that the nondegenerate solitons, in general, undergo three types of elastic collisions without any energy redistribution among the modes. Furthermore, we show that the energy sharing collision exhibiting vector solitons arises as a special case of the newly reported nondegenerate vector solitons. Finally, we point out the possible further developments in this subject and potential applications.

Light Confinement with Structured Beams in Gold Nanoparticle Suspensions

We carry out an experimental campaign to investigate the nonlinear self-defocusing propagation of singular light beams with various complex structures of phase and intensity in a colloidal suspension of gold nanoparticles with a plasmonic resonance near the laser wavelength (532nm). Studying optical vortices embedded in Gaussian beams, Bessel vortices and Bessel-cosine (necklace) beams, we gather evidence that while intense vortices turn into two-dimensional dark solitons, all structured wavepackets are able to guide a weak Gaussian probe of different wavelength (632.8 nm) along the dark core. The probe confinement also depends on the topological charge of the singular pump.

Controlling cosine-Gaussian beams in linear media with quadratic external potential

We investigate both analytically and numerically the propagation dynamic of on-axis and off-axis cosine-Gaussian (CG) beams in a linear medium with quadratic external potential. CG beam propagation evolves periodically with a period depended on the potential depth (α) and whether the beam shape is symmetrical with respect to optical axis. In each period, the CG beam first splits into two sub-beams with different accelerated direction; they then reverse the accelerated direction owing to the quadratic external potential and finally merge again to reproduce its initial shape, and the whole process repeats periodically. The intensity oscillation period of the off-axis CG beam is double times than that of the on-axis one. At the special position, the beam (or spectral) shape is strongly related to the initial spectral (beam) shape. The corresponding scaled relationship is that the spatial intensity I_x (or spatial frequency axis k) is α times the spectral intensity I_k (or space axis x). The interaction of two spatially separated CG beams still exhibit periodic evolution with complex structure in the regime of focal point. The propagation dynamics of two-dimensional CG beams are also presented. When the propagation distance is exactly an integer multiple of half period, there are four focal points in the diagonal position.

Observation of Universal Quench Dynamics and Townes Soliton Formation from Modulational Instability in Two-Dimensional Bose Gases

We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.

Stable solution of induced modulation instability

In this paper,we discussed the nonlinear evolution of modulation instability and the steady-state process of induced modulation instability in sine-oscillatory response nonlocal nonlinear media. With plane wave plus perturbation as initial conditions, we simulated the long-term evolution of modulation instability in the nonlocal nonlinear Schrodinger equation with sine-oscillatory response numerically. For the input of modulated wave, the approximate analytical solution of the stable solution of the equation is obtained under the assumption that only the fundamental wave and the first harmonic wave are present. For the input of modulated wave with arbitrary harmonic waves, we obtained the exact numerical solution of the stable solution of the induced modulation instability.

Photoprogrammable Mesogenic Soft Helical Architectures: A Promising Avenue toward Future Chiro-Optics

Mesogenic soft materials, having single or multiple mesogen moieties per molecule, commonly exhibit typical self-organization characteristics, which promotes the formation of elegant helical superstructures or supramolecular assemblies in chiral environments. Such helical superstructures play key roles in the propagation of circularly polarized light and display optical properties with prominent handedness, that is, chiro-optical properties. The leveraging of light to program the chiro-optical properties of such mesogenic helical soft materials by homogeneously dispersing photosensitive chiral material into an achiral soft system or covalently connecting photochromic moieties to the molecules has attracted considerable attention in terms of materials, properties, and potential applications and has been a thriving topic in both fundamental science and application engineering. State-of-the-art technologies are described in terms of the material design, synthesis, properties, and modulation of photoprogrammable chiro-optical mesogenic soft helical architectures. Additionally, the scientific issues and technical problems that hinder further development of these materials for use in various fields are outlined and discussed. Such photoprogrammable mesogenic soft helical materials are competitive candidates for use in stimulus-controllable chiro-optical devices with high optical efficiency, stable optical properties, and easy miniaturization, facilitating the future integration and systemization of chiro-optical chips in photonics, photochemistry, biomedical engineering, chemical engineering, and beyond.

Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions

In this paper, we focus on the integrable Hirota equation, which describes the propagation of ultrashort light pulses in optical fibers. First, we numerically study spectral signatures of the spatial Lax pair with distinct potentials [e.g., solitons, Akhmediev-Kuznetsov-Ma (AKM) and Kuznetsov-Ma (KM) breathers, and rogue waves (RWs)] of the Hirota equation. Second, we discuss the RW generation by using the dam-break problem with a decaying initial condition and further analyze spectral signatures of periodized wavetrains. Third, we explore two kinds of noise-derived modulational instabilities: (i) the one case is based on the initial condition (one plus a random noise) such that the KM and AKM breathers, and RWs can be generated, and they agree well with analytical solutions; (ii) another case is to consider another initial condition (one plus a Gaussian wave with a random noise phase) such that some RWs with higher amplitudes can be found. Moreover, we also investigate the spectral signatures of corresponding periodic wavetrains. Finally, we find that the interactions of two waves can also generate the RW phenomena with higher amplitudes. These obtained results will be useful to understand the RW generation in the third-order nonlinear Schrödinger equation and other related models.

Coherent propulsion with negative-mass fields in a photonic lattice

In this Letter, we demonstrate the first, to the best of our knowledge, coherent propulsion with negative-mass fields in an optical analog. We observe a self-accelerating state, driven by a nonlinear coherent interaction of its two components that are experiencing diffractions of opposite signs in a photonic lattice, which is analogous to the interaction of two objects with opposite mass signs. Surprisingly, the coherent propulsion is highly immune to the initial phase of the two components, which is in sharp contrast with the behavior encountered in traditional coherent wave interactions. Compared to its incoherent counter-part, the coherent propulsion exhibits an enhanced acceleration.

Light-controlled skyrmions and torons as reconfigurable particles

Topological solitons, such as skyrmions, arise in field theories of systems ranging from Bose-Einstein condensates to optics, particle physics, and cosmology, but they are rarely accessible experimentally. Chiral nematic liquid crystals provide a platform to study skyrmions because of their natural tendency to form twisted structures arising from the lack of mirror symmetry at the molecular level. However, large-scale dynamic control and technological utility of skyrmions remain limited. Combining experiments and numerical modeling of chiral liquid crystals with optically controlled helical pitch, we demonstrate that low-intensity, unstructured light can control stability, dimensions, interactions, spatial patterning, self-assembly, and dynamics of these topological solitons.

Dynamics of rotating Laguerre-Gaussian soliton arrays

Trajectory control of spatial solitons is an important subject in optical transmission field. Here we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters, which we refer to as initial tangential velocity and displacement, to control the propagation path. The general analytical expression for the evolution of the soliton array is derived and the propagation properties, such as the intensity distribution, the propagation trajectory, the center distance, and the angular velocity are analyzed. It is found that the initial tangential velocity and displacement make the solitons sinusoidally oscillate in the x and y directions, and each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation. A series of numerical examples is exhibited to graphically illustrate these typical propagation properties. Our results may provide a new perspective and stimulate further active investigations of multisoliton interaction and may be applied in optical communication and particle control.

Three-dimensional solitary waves with electrically tunable direction of propagation in nematics

Production of stable multidimensional solitary waves is a grand challenge in modern science. Steering their propagation is an even harder problem. Here we demonstrate three-dimensional solitary waves in a nematic, trajectories of which can be steered by the electric field in a plane perpendicular to the field. The steering does not modify the properties of the background that remains uniform. These localized waves, called director bullets, are topologically unprotected multidimensional solitons of (3 + 2)D type that show fore-aft and right-left asymmetry with respect to the background molecular director; the symmetry is controlled by the field. Besides adding a whole dimension to the propagation direction and enabling controlled steering, the solitons can lead to applications such as targeted delivery of information and micro-cargo.

Plasmonic Metasurface "Bullets" and other "Moving Objects": Spatiotemporal Dispersion Cancellation for Linear Passive Subwavelength Slow Light

A class of plasmonic metasurfaces is introduced with the ability to tailor the dispersion surface of the associated plasmon-polariton into striking novel shapes. Examples include dispersion surfaces with hyperbolic curves, with multiple van Hove singularities of various types or with points of simultaneous spatiotemporal dispersion cancellation leading to unprecedented surface flatness. The latter effect, unseen before in linear passive systems, implies slow propagation of ultrasubwavelength wave packets of any shape devoid of longitudinal or lateral broadening, limited only by absorption.

Collapse on the line - how synthetic dimensions influence nonlinear effects

Power induced wave collapse is one of the most fascinating phenomena in optics as it provides extremely high intensities, thus stimulating a range of nonlinear processes. For low power levels, propagation of beams in bulk media is dominated by diffraction, while above a certain threshold self-focusing is steadily enhanced by the action of a positive nonlinearity. An autocatalytic blow-up occurs, which is only stopped by saturation of the nonlinearity, material damage or the inherent medium discreteness. In the latter case, this leads to energy localization on a single site. It is commonly believed that for cubic nonlinearities, this intriguing effect requires at least two transverse dimensions to occur and is thus out of reach in fiber optics. Following the concept of synthetic dimensions, we demonstrate that mixing short and long-range interaction resembles a two-dimensional mesh lattice and features wave collapse at mW-power levels in a genuine 1D system formed by coupled fiber loops.

Super chirped rogue waves in optical fibers

The super rogue wave dynamics in optical fibers are investigated within the framework of a generalized nonlinear Schrödinger equation containing group-velocity dispersion, Kerr and quintic nonlinearity, and self-steepening effect. In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n+1 times the background level, which results from the superposition of n(n+1)/2 Peregrine solitons. Particularly, we demonstrate that these super rogue waves involve a frequency chirp that is also localized in both time and space. The robustness of the super chirped rogue waves against white-noise perturbations as well as the possibility of generating them in a turbulent field is numerically confirmed, which anticipates their accessibility to experimental observation.

Valley Vortex States and Degeneracy Lifting via Photonic Higher-Band Excitation

We demonstrate valley-dependent vortex generation in photonic graphene. Without breaking inversion symmetry, the excitation of two valleys leads to the formation of an optical vortex upon Bragg reflection to the third equivalent valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without a synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase-mediated topological phenomena in other systems.

Optical force-induced nonlinearity and self-guiding of light in human red blood cell suspensions

Osmotic conditions play an important role in the cell properties of human red blood cells (RBCs), which are crucial for the pathological analysis of some blood diseases such as malaria. Over the past decades, numerous efforts have mainly focused on the study of the RBC biomechanical properties that arise from the unique deformability of erythrocytes. Here, we demonstrate nonlinear optical effects from human RBCs suspended in different osmotic solutions. Specifically, we observe self-trapping and scattering-resistant nonlinear propagation of a laser beam through RBC suspensions under all three osmotic conditions, where the strength of the optical nonlinearity increases with osmotic pressure on the cells. This tunable nonlinearity is attributed to optical forces, particularly the forward-scattering and gradient forces. Interestingly, in aged blood samples (with lysed cells), a notably different nonlinear behavior is observed due to the presence of free hemoglobin. We use a theoretical model with an optical force-mediated nonlocal nonlinearity to explain the experimental observations. Our work on light self-guiding through scattering bio-soft-matter may introduce new photonic tools for noninvasive biomedical imaging and medical diagnosis.

Tunable self-focusing and self-defocusing effects in a triple quantum dot via the tunnel-enhanced cross-Kerr nonlinearity

Kerr-nonlinearity induced self-focusing or self-defocusing effect provides the opportunity for exploring fundamental phenomena related to the light-matter interactions. Here we show that the linear and nonlinear dispersion responses are significantly sensitive to both the detunings and the tunneling strengths of the indirect-excitonic (IX) states in an asymmetric triple quantum dot system. In particular, the nonlinear dispersion properties are dominated by the tunnel-enhanced cross-Kerr nonlinearity from one of the IX states. Meanwhile, by varying the detunings of other IX states, we reveal that the tunnel-enhanced cross-Kerr nonlinearity gives rise to the realization of the self-focusing and self-defocusing effects. Moreover, by taking into account the effect of the longitudinal-acoustic-phonon induced dephasing of the IX states, it is possible to modulate the height and position of the peak of the self-focusing or self-defocusing effect. Our results may have potential applications in nonlinear-optics and quantum-optics devices based on the tunnel-enhanced nonlinearities in this solid-state system.

Growth rate of modulation instability driven by superregular breathers

We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolute difference of group velocities of SR breathers coincides exactly with the linear MI growth rate. This link holds for a series of nonlinear Schrödinger equations with infinite-order terms. For the particular case of SR breathers with opposite group velocities, the growth rate of SR breathers is consistent with that of each quasi-Akhmediev breather along the propagation direction. Numerical simulations reveal the robustness of different SR breathers generated from various non-ideal single and multiple initial excitations. Our results provide insight into the MI nature described by SR breathers and could be helpful for controllable SR breather excitations in related nonlinear systems.

Nonlocal and Nonlinear Surface Plasmon Polaritons and Optical Spatial Solitons Induced by the Thermocapillary Effect

We study the propagation of surface plasmon polaritons (SPPs) on a metal surface which hosts a thin film of a liquid dielectric. The Ohmic losses that are inherently present due to the coupling of SPPs to conductors' electron plasma, induce temperature gradients and fluid deformation driven by the thermocapillary effect, which lead to a nonlinear and nonlocal change of the effective dielectric constant. The latter extends beyond the regions of highest optical intensity and constitutes a novel thermally self-induced mechanism that affects the propagation of the SPPs. We derive the nonlinear and nonlocal Schrödinger equation that describes propagation of low intensity SPP beams, and show analytically and numerically that it supports a novel optical spatial soliton excitation.

Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications

Traditional objective lenses in modern microscopy, based on the refraction of light, are restricted by the Rayleigh diffraction limit. The existing methods to overcome this limit can be categorized into near-field (e.g., scanning near-field optical microscopy, superlens, microsphere lens) and far-field (e.g., stimulated emission depletion microscopy, photoactivated localization microscopy, stochastic optical reconstruction microscopy) approaches. However, they either operate in the challenging near-field mode or there is the need to label samples in biology. Recently, through manipulation of the diffraction of light with binary masks or gradient metasurfaces, some miniaturized and planar lenses have been reported with intriguing functionalities such as ultrahigh numerical aperture, large depth of focus, and subdiffraction-limit focusing in far-field, which provides a viable solution for the label-free superresolution imaging. Here, the recent advances in planar diffractive lenses (PDLs) are reviewed from a united theoretical account on diffraction-based focusing optics, and the underlying physics of nanofocusing via constructive or destructive interference is revealed. Various approaches of realizing PDLs are introduced in terms of their unique performances and interpreted by using optical aberration theory. Furthermore, a detailed tutorial about applying these planar lenses in nanoimaging is provided, followed by an outlook regarding future development toward practical applications.

Numerical realization of the variational method for generating self-trapped beams

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Manipulating discrete solitons and routing the light-transmitting paths in the silicon waveguide array by a d.c. electric-field

Discrete solitons (DS), which could propagate without diffraction in the waveguide array (WA), have attracted great attention. However, its applications are limited to incident light with high power. Here, based on the d.c. Kerr effect in the silicon, we propose and demonstrate theoretically an electrically reconfigurable ridge waveguide array. By applying sech-function bias voltages on the WA, a Kerr-type DS could be mimicked by a low-power incident light. The transmitting paths of DS and low-power light in the WA can be rerouted with great flexibility by changing the local bias voltages applied on the waveguide. Our proposed silicon WA provides new opportunities for electric-controlled optical devices, which may open a gateway towards rerouting light on-chip and designing integrated optics devices.

Observation of gain spiking of optical frequency comb in a microcavity

Optical frequency combs are crucial for both fundamental science and applications that demand a wide frequency range and ultra-high resolution. Recent advances in optical frequency combs based on the nonlinear Kerr effect in microcavities have opened up new opportunities with such compact platforms. Although optical frequency combs have previously been well studied in the steady state, some fundamental perspectives such as nonlinear phase modulation during comb generations are yet explored. Here we demonstrate transient nonlinear dynamics during the formation of optical frequency combs inside a Kerr microcavity. We show that gain spiking forms due to nonlinear phase modulation causing comb lines' self-detuning from nearby cavity resonances, which provides one key mechanism to stabilize optical frequency combs. Moreover, we have observed nonlinear beating by injecting an external probe to examine nonlinear cross-phase modulation between comb lines. These nonlinear dynamics reveal the hidden features of self-stabilization and cross modulation during transient comb generations, which may enable new applications in mode-locking comb and tunable comb generation in microcavities.

Collision of two action potentials in a single excitable cell

BACKGROUND

It is a common incident in nature, that two waves or pulses run into each other head-on. The outcome of such an event is of special interest, because it allows conclusions about the underlying physical nature of the pulses. The present experimental study dealt with the head-on meeting of two action potentials (AP) in a single excitable plant cell (Chara braunii internode).

METHODS

The membrane potential was monitored with multiple sensors along a single excitable cell. In control experiments, an AP was excited electrically at either end of the cell cylinder. Subsequently, stimuli were applied simultaneously at both ends of the cell in order to generate two APs that met each other head-on.

RESULTS

When two action potentials propagated into each other, the pulses did not penetrate but annihilated (N=26 experiments in n=10 cells).

CONCLUSIONS

APs in excitable plant cells did not penetrate upon meeting head-on. In the classical electrical model, this behavior is specifically attributed to relaxation of ion channel proteins. From an acoustic point of view, annihilation can be viewed as a result of nonlinear material properties (e.g. a phase change).

GENERAL SIGNIFICANCE

The present results suggest that APs in excitable animal and plant cells belong to a similar class of nonlinear phenomena. Intriguingly, other excitation waves in biology (intracellular waves, cortical spreading depression, etc.) also annihilate upon collision and are thus expected to follow the same underlying principles as the observed action potentials.

Kinetics of Light-Induced Concentration Patterns in Transparent Polymer Solutions

When exposed to weak visible laser light, solutions of common polymers like poly(isoprene) and poly(butadiene) respond by local concentration variations, which in turn lead to refractive index changes. Various micropatterns have been recently reported, depending mostly on the solvent environment and the irradiation conditions. Here, we focused on the simpler case of single polymer-rich filaments and we employed phase contrast microscopy to systematically investigate the influence of laser illumination and material parameters on the kinetics of the optically induced local concentration increase in the polydiene solutions. The refractive index contrast of the formed filaments increased exponentially with the laser illumination time. The growth rate exhibited linear dependence on the laser power and increased with polymer chain length in semidilute solutions in good solvents. On the contrary, the kinetics of the formed filaments appeared to be rather insensitive to the polymer concentration. Albeit the origin of the peculiar light field-polymer concentration coupling remains yet elusive, the new phenomenology is considered necessary for the elucidation of its mechanism.

Steering and switching of soliton-like beams via interaction in a nanocolloid with positive polarizability

We unveil different regimes for the interaction between two orthogonally polarized soliton-like beams in a colloidal suspension of nanoparticles with positive polarizability. The interaction is always attractive. However, it noticeably changes as a function of the angle and the power distribution between the input beams. For small angles, both interacting solitons fuse into a single entity, whose propagation direction can be continuously steered. As the interaction angle increases, the resulting self-collimated beam can be practically switched between two positions when the power imbalance between the beams is changed. For interaction angles larger than ∼10°, the result is no longer a single emerging soliton when the input power is balanced between the two beams.

Elastic Vector Solitons in Soft Architected Materials

We demonstrate experimentally, numerically, and analytically that soft architected materials can support the propagation of elastic vector solitons. More specifically, we focus on structures comprising a network of squares connected by thin and highly deformable ligaments and investigate the propagation of planar nonlinear elastic waves. We find that for sufficiently large amplitudes two components-one translational and one rotational-are coupled together and copropagate without dispersion. Our results not only show that soft architected materials offer a new and rich platform to study the propagation of nonlinear waves, but also open avenues for the design of a new generation of smart systems that take advantage of nonlinearities to control and manipulate the propagation of large amplitude vibrations.

Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave. Further, an order-n b-positon gives an order-n rogue wave under a limit λ_{1}→λ_{0}. Here, λ_{0} is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the b-positon at a certain position z_{0}. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order b-positon generated by above ideal initial pulses when λ_{1} is very close to the λ_{0}. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal-to-noise ratio and analytical solutions of order-2 b-positon supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multibreathers through the double degeneration.