Optical Spatial Solitons and Their Interactions: Universality and Diversity

Coherence-controlled chaotic soliton bunch

Controlling the coherence of chaotic soliton bunch holds the promise to explore novel light-matter interactions and manipulate dynamic events such as rogue waves. However, the coherence control of chaotic soliton bunch remains challenging, as there is a lack of dynamic equilibrium mechanism for stochastic soliton interactions. Here, we develop a strategy to effectively control the coherence of chaotic soliton bunch in a laser. We show that by introducing a lumped fourth-order-dispersion (FOD), the soliton oscillating tails can be formed and generate the potential barriers among the chaotic solitons. The repulsive force between neighboring solitons enabled by the potential barriers gives rise to an alleviation of the soliton fusion/annihilation from stochastic interactions, endowing the capability to control the coherence in chaotic soliton bunch. We envision that this result provides a promising test-bed for a variety of dynamical complexity science and brings new insights into the nonlinear behavior of chaotic laser sources.

Dark solitons and their bound states in a nonlinear fiber with second- and fourth-order dispersion

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit time-domain oscillating structures on a plane wave, and they have two types: the ones with or without the total phase step, while the multi-dark-soliton bound states exhibit different numbers of amplitude humps. By the modified linear stability analysis, we regard the SDSs as the results of the competition between periodicity and localization, and analytically give their existence condition, oscillation frequency, and propagation stability, which show good agreements with numerical results. We also provide a possible interpretation of the formation of the existing striped bright solitons (SBSs), and find that SBS will become the pure-quartic soliton when its periodicity and localization carry equal weight. Our results provide the theoretical support for the experimental observation of striped solitons in nonlinear fibers, and our method can also guide the discovery of striped solitons in other physical systems.

Rotationally symmetric transverse magnetic vector wave propagation for nonlinear optics

In this paper the theory and simulation results are presented for 3D cylindrical rotationally symmetric spatial soliton propagation in a nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential equation method for transverse magnetic polarization. The theory of 3D rotationally symmetric spatial solitons is discussed, and compared with two (1 + 1)D, termed "2D" for this paper, hyperbolic secant spatial solitons, with a phase difference of π (antiphase). The simulated behavior of the 3D rotationally symmetric soliton was compared with the interaction of the two antiphase 2D solitons for different source hyperbolic secant separation distances. Lastly, we offer some possible explanations for the simulated soliton behavior.

Nonisospectral water wave field: Fast and adaptive modal identification and prediction via reduced-order nonlinear solutions

Real-world water wave fields exhibit significant nonlinear and nonisospectral characteristics, making it challenging to predict their evolution by relying solely on numerical simulation or exact solutions using integrable system theory. Hence, this paper introduces a fast and adaptive method of modal identification and prediction in nonisospectral water wave fields using the reduced-order nonlinear solution (RONS) scheme. Specifically, we discuss the coarse graining and mode extraction of wave field snapshots from the data-driven and physics-driven perspectives and utilize the RONS method for principle modal prediction of nonisospectral water wave fields. This is achieved by investigating the standard and nonisospectral Gardner system describing nonlinear water waves as a demonstration. Through detailed comparison and analysis, the fundamental solitary behaviors and dispersive effects in the Gardner system are discussed. Subsequently, a neighbor approximation is developed that combines the essences of symbolic precomputation and numerical computation in the RONS procedure, which exploits the locality of nonlinear interactions in water wave fields.

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.

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.

Topological soliton molecule in quasi 1D charge density wave

Soliton molecules, bound states of two solitons, can be important for the informatics using solitons and the quest for exotic particles in a wide range of physical systems from unconventional superconductors to nuclear matter and Higgs field, but have been observed only in temporal dimension for classical wave optical systems. Here, we identify a topological soliton molecule formed spatially in an electronic system, a quasi 1D charge density wave of indium atomic wires. This system is composed of two coupled Peierls chains, which are endowed with a Z4 topology and three distinct, right-chiral, left-chiral, and non-chiral, solitons. Our scanning tunneling microscopy measurements identify a bound state of right- and left-chiral solitons with distinct in-gap states and net zero phase shift. Our density functional theory calculations reveal the attractive interaction of these solitons and the hybridization of their electronic states. This result initiates the study of the interaction between solitons in electronic systems, which can provide novel manybody electronic states and extra data-handling capacity beyond the given soliton topology.

Deflecting and routing nematicons via orientation programmable liquid crystal array

By designing a liquid crystal cell with comb electrode structure, the alignment modulation of nematic liquid crystal in the cell can be realized after the electric field is applied. In different orientation regions, the incident laser beam can deflect at different angles. At the same time, by changing the incident angle of the laser beam, the reflection modulation of the laser beam on the interface of the liquid crystal molecular orientation change can be realized. Based on the above discussion, we then demonstrate the modulation of liquid crystal molecular orientation arrays on nematicon pairs. In different orientation regions of liquid crystal molecules, nematicon pairs can exhibit various combinations of deflections, and these deflection angles are modulable under external fields. Deflection and modulation of nematicon pairs have potential applications in optical routing and optical communication.

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.

Interactions of Airy beams in nonlinear media with fourth-order diffraction

We investigate to the best of our knowledge the first time the interactions of in-phase and out-of-phase Airy beams in Kerr, saturable and nonlocal nonlinear media with fourth-order diffraction using split-step Fourier transform method. Directly numerical simulations show that normal and anomalous fourth-order diffractions have profound effects on the interactions of the Airy beams in Kerr and saturable nonlinear media. We demonstrate the dynamics of the interactions in detail. In nonlocal media with fourth-order diffraction, nonlocality induces a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy soliton pairs which are always repulsive in local media. Our results have potential applications in all-optical devices for communication and optical interconnects, etc.

Optically Controlled Development of a Waveguide from a Reservoir of Microparticles

Light can be guided without diffraction in prefabricated structures: optical fibers and waveguides or in actively created spatial solitons in optically nonlinear media. Here, an approach in which a self-stabilized optical waveguide develops from a reservoir of building blocks-spherical polymer microparticles (MPs)-and is pushed through an optically passive medium-water-is presented. The optical waveguide, formed by a chain of these microparticles and one microsphere wide, is self-stabilized and propelled by the guided light, while its geometrical and dynamical properties depend on the diameter-to-wavelength ratio. The smallest investigated particles, 500 nm in diameter, form single-mode waveguides up to tens of micrometers long, with the length limited only by optical losses. In contrast, waveguides constructed of larger MPs, 1 and 2.5 µm in diameter, are limited in length to only a few particles due to interference of different modes and beating of light intensity.

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.

Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser

Optical solitons in ultrafast fiber lasers, as a result of dual balances between dispersion and nonlinearity as well as gain and loss, enable various soliton interactions. Soliton collisions are among the most intriguing soliton interactions, which fuel the understanding for particle-like properties of solitons. Here, we experimentally investigate the transient dynamics of collisions between a two-soliton molecule and a soliton singlet in a mode-locked fiber laser. By means of the dispersive Fourier transform technique, the evolving spectral interferograms of different collision scenarios are measured in real time. In particular, the “quasi-elastic” collision is observed, which shows that the soliton-molecule state remains unaltered after the collision and the group-velocity difference between the soliton molecule and the singlet is changed. It is directly demonstrated that a bond exchange occurs between the colliding solitons. By tuning the intra-cavity polarization controller, the dynamic processes of other collision outcomes, including the annihilation of a soliton in the soliton molecule as well as the formation of a stable unequally spaced soliton triplet, are also revealed. Our work facilitates a deeper understanding of soliton collision dynamics in ultrafast fiber lasers.

Multimode soliton collisions in graded-index optical fibers

In this work, we unveil the unique complex dynamics of multimode soliton interactions in graded-index optical fibers through simulations and experiments. By generating two multimode solitons from the fission of an input femtosecond pulse, we examine the evolution of their Raman-induced red-shift when the input pulse energy grows larger. Remarkably, we find that the output red-shift of the trailing multimode soliton may be reduced, so that it accelerates until it collides with the leading multimode soliton. As a result of the inelastic collision, a significant energy transfer occurs between the two multimode solitons: the trailing soliton captures energy from the leading soliton, which ultimately enhances its red-shift, thus increasing temporal separation between the two multimode solitons.

Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps

Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that, for low-power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that a soliton's position is dictated by that of the Wannier state throughout the pump cycle. Furthermore, we describe soliton pumping in two dimensions.

Strongly nonlinear wave dynamics of continuum phononic materials with periodic rough contacts

We investigate strongly nonlinear wave dynamics of continuum phononic material with discrete nonlinearity. The studied phononic material is a layered medium such that the elastic layers are connected through contact interfaces with rough surfaces. These contacts exhibit nonlinearity by virtue of nonlinear mechanical deformation of roughness under compressive loads and strong nonlinearity stemming from their inability to support tensile loads. We study the evolution of propagating Gaussian tone bursts using time-domain finite element simulations. The elastodynamic effects of nonlinearly coupled layers enable strongly nonlinear energy transfer in the frequency domain by activating acoustic resonances of the layers. Further, the interplay of strong nonlinearity and dispersion in our phononic material forms stegotons, which are solitarylike localized traveling waves. These stegotons satisfy properties of solitary waves, yet exhibit local variations in their spatial profiles and amplitudes due to the presence of layers. We also elucidate the role of rough contact nonlinearity on the interrelationship between the stegoton parameters as well as on the generation of secondary stegotons from the collision of counterpropagating stegotons. The phononic material exhibits strong acoustic attenuation at frequencies close to (and fractional multiples of) layer resonances, whereas it causes energy propagation as stegotons for other frequencies. This study sheds light on the wave phenomena achievable in continuum periodic media with local nonlinearity, and opens opportunities for advanced wave control through discrete and local contact nonlinearity.

Incoherent two-color pulse compounds

We study the dynamical evolution of two-frequency pulse compounds, i.e., intriguing bound-states of light, kept together due to their incoherent interaction. A special class of solutions of such compounds is found to be describable in terms of a simplified model. They entail generalized dispersion Kerr solitons and yield their corresponding metasolitons. We use these solutions to study when the interaction of their constituent pulses is independent of their phase. These results are relevant to understand the complex collision dynamics of quasi-group-velocity-matched solitons across a vast frequency gap.

Coupled Helmholtz equations: Chirped solitary waves

We investigate the existence and stability properties of chirped gray and anti-dark solitary waves within the framework of a coupled cubic nonlinear Helmholtz equation in the presence of self-steepening and a self-frequency shift. We show that for a particular combination of self-steepening and a self-frequency shift, there is not only chirping but also chirp reversal. Specifically, the associated nontrivial phase has two intensity dependent terms: one varies as the reciprocal of the intensity, while the other, which depends on non-Kerr nonlinearities, is directly proportional to the intensity. This causes chirp reversal across the solitary wave profile. A different combination of non-Kerr terms leads to chirping but no chirp reversal. The influence of a nonparaxial parameter on physical quantities, such as intensity, speed, and pulse width of the solitary waves, is studied as well. It is found that the speed of the solitary waves can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial solitary waves is achieved by an appropriate choice of parameters.

Symmetrical superfission of optical solitons in a well-type nonlocal system

The dynamical properties of fundamental and dipolar mode solitons, in the process of propagating in the well-type nonlocal system, are provided. During propagating in a deep well-type nonlocal system with a moderate width, a fundamental mode soliton splits into a pair of symmetrical sub-beams, and a dipolar mode soliton can divide into two pairs of symmetrical sub-beams. Furthermore, the propagation directions of these sub-beams can be effectively controlled by adjusting system parameters that include the well depth and well width. These properties could be applied to optical routing, all-optical switching, signal processing, and ultrafast optical communications.

Realization of a Townes Soliton in a Two-Component Planar Bose Gas

Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: Starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.

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.

Crossover from two-frequency pulse compounds to escaping solitons

The nonlinear interaction of copropagating optical solitons enables a large variety of intriguing bound-states of light. We here investigate the interaction dynamics of two initially superimposed fundamental solitons at distinctly different frequencies. Both pulses are located in distinct domains of anomalous dispersion, separated by an interjacent domain of normal dispersion, so that group velocity matching can be achieved despite a vast frequency gap. We demonstrate the existence of two regions with different dynamical behavior. For small velocity mismatch we observe a domain in which a single heteronuclear pulse compound is formed, which is distinct from the usual concept of soliton molecules. The binding mechanism is realized by the mutual cross phase modulation of the interacting pulses. For large velocity mismatch both pulses escape their mutual binding and move away from each other. The crossover phase between these two cases exhibits two localized states with different velocity, consisting of a strong trapping pulse and weak trapped pulse. We detail a simplified theoretical approach which accurately estimates the parameter range in which compound states are formed. This trapping-to-escape transition allows to study the limits of pulse-bonding as a fundamental phenomenon in nonlinear optics, opening up new perspectives for the all-optical manipulation of light by light.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Scalar and vector supermode solitons owing to competing nonlocal nonlinearities

We investigate scalar and vector multi-hump spatial solitons resulting from competing Kerr-like nonlinear responses excited in a nonlocal medium by either one or two (mutually incoherent) light beams. Two-color vector supermode solitons are more amenable to control but exhibit an intriguing form of spontaneous symmetry breaking in propagation.

Soliton evolution and associated sonic horizon formation dynamics in two-dimensional Bose-Einstein condensate with quintic-order nonlinearity

This study explored the two-dimensional Bose-Einstein condensate with an inter-particle nonlinear interaction up to quintic order. Based on the two-dimensional Gross-Pitaevskii equation model with quintic-order nonlinearity, we first derived the bright soliton solution for the system based on the self-similar approach and the modified variational method. We identified that the kinematic quantities derived from the two methods agreed very well. The two-dimensional sonic horizon formation dynamics was then calculated based on the bright soliton solution that was obtained. The periodic formation and evolution patterns of the two-dimensional sonic horizon were quantitatively analyzed and pictorially illustrated. The results can be used to guide sonic black hole related phenomenon observations in a two-dimensional Bose-Einstein condensate with quintic-order nonlinearity.

Real-time multispeckle spectral-temporal measurement unveils the complexity of spatiotemporal solitons

The dynamics of three-dimensional (3D) dissipative solitons originated from spatiotemporal interactions share many common characteristics with other multi-dimensional phenomena. Unveiling the dynamics of 3D solitons thus permits new routes for tackling multidisciplinary nonlinear problems and exploiting their instabilities. However, this remains an open challenge, as they are multi-dimensional, stochastic and non-repeatable. Here, we report the real-time speckle-resolved spectral-temporal dynamics of a 3D soliton laser using a single-shot multispeckle spectral-temporal technology that leverages optical time division multiplexing and photonic time stretch. This technology enables the simultaneous observation on multiple speckle grains to provide long-lasting evolutionary dynamics on the planes of cavity time (t) - roundtrip and spectrum (λ) - roundtrip. Various non-repeatable speckly-diverse spectral-temporal dynamics are discovered in both the early and established stages of the 3D soliton formation.

Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media

The nonlinear perturbed Schrödinger equations (NPSEs) with nonlinear terms as Kerr law, power law, quadratic-cubic law, and dual-power law nonlinearity media play an important role in optical fibers. In this article we implement the rational solitary wave method to study the NPSEs when nonlinear terms take some different forms. Additionally, we use the q-deformed hyperbolic function and q-deformed trigonometric function methods to study the exact solutions to NPSEs. Different kind of soliton solutions are obtained such as bright, dark, and singular periodic solutions to the NPSEs.

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.

Experimental demonstration of emission of solitons from a resonant localized wave

We demonstrate the emission of solitons from a resonantly excited localized standing wave in a nonlinear chain of spring-coupled masses. The localized wave in this system is induced by a properly designed "impurity" and vibrates around the "impurity" with an intrinsic frequency. We observe that, when subjected to an external forcing, it is amplified to a large amplitude under the nonlinear resonance, and, then, its wave envelope splits apart leading to the release of most of its energy in the form of a large-amplitude traveling soliton. The experiment also shows that the rate of the emission can be controlled by finely tuning the driving parameters, thereby providing a feasible and controllable way for creation of solitons.

Subharmonic Entrainment Breather Solitons in Ultrafast Lasers

We study theoretically and experimentally the subharmonic entrainment (SHE) breather soliton in mode-locked lasers for the first time, in which the ratio of the breather period to the round-trip time is an integer. We build a non-Hermitian degeneracy map of breather soliton, and illustrate that SHE arises between the two exceptional points (EPs). We obtain SHE at the ratio of 20, observe the evolution of breather soliton when tuning the gain and/or cavity loss, and prove that this phenomenon can improve the stability of breather soliton. Our research brings insight into the EP physics of ultrafast lasers and makes the mode-locked laser a powerful test bed for non-Hermitian degeneracy, which may open a new course in ultrafast laser research.

Velocity and acceleration freely tunable straight-line propagation light bullet

Three-dimensional (3-D) light solitons in space–time, referred to as light bullets, have many novel properties and wide applications. Here we theoretically show how the combination of diffraction-free beam and ultrashort pulse spatiotemporal-coupling enables the creation of a straight-line propagation light bullet with freely tunable velocity and acceleration. This light bullet could propagate with a constant superluminal or subluminal velocity, and it could also counter-propagate with a very fast superluminal velocity (e.g., − 35.6c). Apart from uniform motion, an acceleration or deceleration straight-line propagation light bullet with a tunable instantaneous acceleration could also be produced. The high controllability of the velocity and the acceleration of a straight-line propagation light bullet would enable very specific applications, such as velocity and/or acceleration matched micromanipulation, microscopy, particle acceleration, radiation generation, and so on.

Observation of Floquet solitons in a topological bandgap

Topological protection is a universal phenomenon that applies to electronic, photonic, ultracold atomic, mechanical, and other systems. The vast majority of research in these systems has explored the linear domain, where interparticle interactions are negligible. We experimentally observed solitons-waves that propagate without changing shape as a result of nonlinearity-in a photonic Floquet topological insulator. These solitons exhibited distinct behavior in that they executed cyclotron-like orbits associated with the underlying topology. Specifically, we used a waveguide array with periodic variations along the waveguide axis, giving rise to nonzero winding number, and the nonlinearity arose from the optical Kerr effect. This result applies to a range of bosonic systems because it is described by the focusing nonlinear Schrödinger equation (equivalently, the attractive Gross-Pitaevskii equation).

Heteronuclear soliton molecules in optical microresonators

Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibres to mode-locked lasers, they provide insights into the fundamental interactions between solitons and the underlying dynamics of the nonlinear systems. Here, we enter the multistability regime of a Kerr microresonator to generate superpositions of distinct soliton states that are pumped at the same optical resonance, and report the discovery of heteronuclear dissipative Kerr soliton molecules. Ultrafast electrooptical sampling reveals the tightly short-range bound nature of such soliton molecules, despite comprising cavity solitons of dissimilar amplitudes, durations and carrier frequencies. Besides the significance they hold in resolving soliton dynamics in complex nonlinear systems, such heteronuclear soliton molecules yield coherent frequency combs whose unusual mode structure may find applications in metrology and spectroscopy.

Spatio-temporal-spectral imaging of non-repeatable dissipative soliton dynamics

Dissipative solitons (DSs) are multi-dimensionally localized waves that arise from complex dynamical balances in far-from-equilibrium nonlinear systems and widely exist in physics, chemistry and biology. Real-time observations of DS dynamics across many dimensions thus have a broad impact on unveiling various nonlinear complexities in different fields. However, these observations are challenging as DS transitions are stochastic, non-repeatable and often strongly coupled across spatio-temporal-spectral (STS) domains. Here we report multi-dimensional (space xy + discrete time t + wavelength λ) DS dynamics imaged by STS compressed ultrafast photography, enabling imaging at up to trillions of frames per second. Various transient and random phenomena of multimode DSs are revealed, highlighting the importance of real-time multi-dimensional observation without the need for event repetition in decomposing the complexities of DSs.

Due to three-dimensional, stochastic and non-repeatable transitions of dissipative solitons, it is challenging to monitor their full dynamics. Here, the authors resolve the dynamics by wavelength and along two spatial dimensions with up to trillions of frames per second using compressed ultrafast photography.

Opto-chemo-mechanical transduction in photoresponsive gels elicits switchable self-trapped beams with remote interactions

Next-generation photonics envisions circuitry-free, rapidly reconfigurable systems powered by solitonic beams of self-trapped light and their particlelike interactions. Progress, however, has been limited by the need for reversibly responsive materials that host such nonlinear optical waves. We find that repeatedly switchable self-trapped visible laser beams, which exhibit strong pairwise interactions, can be generated in a photoresponsive hydrogel. Through comprehensive experiments and simulations, we show that the unique nonlinear conditions arise when photoisomerization of spiropyran substituents in pH-responsive poly(acrylamide-co-acrylic acid) hydrogel transduces optical energy into mechanical deformation of the 3D cross-linked hydrogel matrix. A Gaussian beam self-traps when localized isomerization-induced contraction of the hydrogel and expulsion of water generates a transient waveguide, which entraps the optical field and suppresses divergence. The waveguide is erased and reformed within seconds when the optical field is sequentially removed and reintroduced, allowing the self-trapped beam to be rapidly and repeatedly switched on and off at remarkably low powers in the milliwatt regime. Furthermore, this opto-chemo-mechanical transduction of energy mediated by the 3D cross-linked hydrogel network facilitates pairwise interactions between self-trapped beams both in the short range where there is significant overlap of their optical fields, and even in the long range--over separation distances of up to 10 times the beam width--where such overlap is negligible.

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.

Soliton Molecules with Two Frequencies

We demonstrate a peculiar mechanism for the formation of bound states of light pulses of substantially different optical frequencies, in which pulses are strongly bound across a vast frequency gap. This is enabled by a propagation constant with two separate regions of anomalous dispersion. The resulting soliton compound exhibits moleculelike binding energy, vibration, and radiation and can be understood as a mutual trapping providing a striking analogy to quantum mechanics. The phenomenon constitutes an intriguing case of two light waves mutually affecting and controlling each other.

Super-regular breathers in nonlinear systems with self-steepening effect

A family of super-regular (SR) breather solutions in systems with self-steepening effect and in the case of either normal or anomalous dispersion is derived analytically. Derivation is based on the Darboux transformation with a quadratic spectral parameter. In contrast to the SR breather solutions in t-symmetric systems such as the nonlinear Schrödinger equation, the new breathers found in the present work evolve asymmetrically even if started from symmetric initial conditions. The initial stage of this process is modulation instability. Numerical simulations confirm the excitation of the SR breathers when started from the approximate initial conditions leading at first to modulation instability. Our results offer the possibility of experimental observations of SR breather dynamics in systems with self-steepening effects, such as optical frequency-doubling crystals or magnetized plasmas.

Theory of soliton propagation in nonlinear photonic crystal waveguides

Propagation of the temporal soliton in Kerr-type photonic crystal waveguide is investigated theoretically and numerically. An expression describing the evolution of the envelope of the soliton based on the full-wave modal analysis, taking into account all space-harmonics, is rigorously obtained. The nonlinear coefficient is derived, for the first time, based on a modification of the refractive indices for each space-harmonic due to the Kerr-type nonlinearity. For illustrating the general formulation and results, we performed extensive computational electromagnetics simulations for the propagation of gap solitons in an experimentally feasible photonic crystal waveguides, endorsing the correctness and usefulness of the proposed formalism.

Plasmon-mediated discrete diffraction behaviour of an array of responsive waveguides

We investigate the discrete diffraction phenomenon in a Polymer-Liquid Crystal-Polymer Slices (POLICRYPS) overlaying a random distribution of gold nanoparticles (AuNPs, plasmonic elements). We study the propagation of a CW green laser beam through the waveguide structure as a function of beam polarization, laser intensity and sample temperature. It turns out that the plasmonic field created at the interface between AuNPs and POLICRYPS waveguides enables and stabilizes the optical field propagation within the responsive nematic liquid crystal channels. The active role of the liquid crystal is pointed out by a polarization, temperature and beam divergence experimental analysis and evidenced by a peculiar trumpet-shaped discrete diffraction pattern. Theoretical simulations confirm that the observed optical behavior is governed by the interaction of the nematic liquid crystal with optical and plasmonic fields.

3-D Spiraling Self-Trapped Light Beams in Photochemical Systems

A pair of visible laser beams self-trap and spiral about each other as they propagate through polymer gels undergoing two different photochemical reactions. When launched into gels that undergo photopolymerization of methacrylate substituents or photo-oxidation of iodide anion, two non-coplanar (skewed) Gaussian beams collide and spiral about each other as they advance through the evolving medium. In the absence of chemical reactions, the linearly polarized beams broaden naturally and propagate along their original, straight-pathed trajectories. By contrast, refractive index gradients generated by the photochemical reactions elicit self-trapping and introduce an attractive interaction between the self-trapped beams. The self-trapped beams spiral about each other when this mutual attraction perfectly counterbalances their original tendency to diverge away from each other. These findings show that the photochemically mediated interactions of incident optical fields within the gel medium impart a helical trajectory and angular velocity to the self-trapped beam pair.

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.

Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser

Recent progress in time-stretch spectroscopy accelerates the exploration of ultrafast dynamics in mode-locked lasers through mapping the spectral information into time domain. Here, we report on real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser mode-locked by a 45° tilted fiber grating. By virtue of the dispersive Fourier transform process, spectral information of the pulse trains under multi-pulse states can be resolved. It is identified that soliton singlets and soliton molecules coexist in one cavity roundtrip with different assembling forms. In addition, consecutive recordings of the shot-to-shot spectra further enable insight into the transient dynamics of soliton molecules. Particularly, varieties of internal motions, including the diverging/oscillating phase evolution and the temporal separation vibration, are validated loosely bound intra-soliton molecules. All of these findings unveil the scenarios of multi-soliton phenomena in fiber lasers, as well as highlight the significance of pulse interaction towards both scientific research and practical applications.

Observation of incoherently coupled dark-bright vector solitons in single-mode fibers

We report experimental observation of incoherently coupled dark-bright vector solitons in single-mode fibers. Properties of the vector solitons accord well with those predicted by the respective systems of incoherently coupled nonlinear Schrödinger equations. To our knowledge, this is the first experimental observation of temporal incoherently coupled dark-bright solitons in single-mode fibers.

Logic gates on stationary dissipative solitons

Stable dissipative solitons are perfect carries of optical information due to remarkable stability of their waveforms that allows the signal transmission with extremely dense soliton packing without losing the encoded information. Apart from unaffected passing of solitons through a communication network, controllable transformations of soliton waveforms are needed to perform all-optical information processing. In this paper we employ the basic model of dissipative optical solitons in the form of the complex Ginzburg-Landau equation with a potential term to study the interactions between two stationary dissipative solitons under the control influences and use those interactions to implement various logic gates. In particular, we demonstrate not, and, nand, or, nor, xor, and xnor gates, where the plain (fundamental soliton) and composite pulses are used to represent the low and high logic levels.

Breather Wave Molecules

We present both a theoretical description and experimental observation of the nonlinear mutual interactions between a pair of copropagative breathers in the framework of the focusing one-dimensional nonlinear Schrödinger equation. As a general case, we show that the resulting bound state of breathers exhibits moleculelike behavior with quasiperiodic oscillatory dynamics (i.e., internal coherent interactions and pulsations), while for commensurate conditions the molecule oscillations become exactly periodic. Our theoretical model is confirmed by an experimental observation of shaped moleculelike breather light waves propagating in a nearly conservative optical fiber system. Our work sheds new light on the existence of localized wave structures and recurrence dynamics beyond the multisoliton complexes.

Solitonic State in Microscopic Dynamic Failures

Onset of permanent deformation in crystalline materials under a sharp indenter tip is accompanied by nucleation and propagation of defects. By measuring the spatio-temporal strain field near the indenter tip during indentation tests, we demonstrate that the dynamic strain history at the moment of a displacement burst carries characteristics of the formation and interaction of local excitations, or solitons. We show that dynamic propagation of multiple solitons is followed by a short time interval where the propagating fronts can accelerate suddenly. As a result of such abrupt local accelerations, duration of the fast-slip phase of a failure event is shortened. Our results show that formation and annihilation of solitons mediate the microscopic fast weakening phase, during which extreme acceleration and collision of solitons lead to non-Newtonian behavior and Lorentz contraction, i.e., shortening of solitons’ characteristic length. The results open new horizons for understanding dynamic material response during failure and, more generally, complexity of earthquake sources.

Anomalous Collisions of Elastic Vector Solitons in Mechanical Metamaterials

We investigate via a combination of experiments and numerical analyses the collision of elastic vector solitons in a chain of rigid units connected by flexible hinges. Because of the vectorial nature of these solitons, very unusual behaviors are observed: while, as expected, the solitons emerge unaltered from the collision if they excite rotations of the same direction, they do not penetrate each other and instead repel one another if they induce rotations of the opposite direction. Our analysis reveals that such anomalous collisions are a consequence of the large-amplitude characteristics of the solitons, which locally modify the properties of the underlying media. Specifically, their large rotations create a significant barrier for pulses that excite rotations of the opposite direction and this may block their propagation. Our findings provide new insights into the collision dynamics of elastic solitary waves. Furthermore, the observed anomalous collisions pave new ways towards the advanced control of large amplitude mechanical pulses, as they provide opportunities to remotely detect, change, or destruct high-amplitude signals and impacts.

Free-space creation of ultralong anti-diffracting beam with multiple energy oscillations adjusted using optical pen

A light beam propagating over an infinite anti-diffracting distance requires infinite power to preserve its shape. However, the fundamental barrier of finite power in free space has made the problem of diffraction insurmountable in recent decades. To overcome this limitation, we report an approach that employs the multiple energy oscillation mechanism, thereby permitting the creation of a light beam with an ultralong anti-diffracting distance in free space. A versatile optical pen is therefore developed to manipulate the number, amplitude, position and phase of energy oscillations for a focusing lens so that multiple energy oscillations can be realized. A light beam with a tunable number of energy oscillations is eventually generated in free space and propagates along a wavy trajectory. This work will enable the extension of non-diffractive light beams to an expanded realm and facilitate extensive developments in optics and other research fields, such as electronics and acoustics.

Incoherently coupled two-color vector dark solitons in self-defocusing media

We investigate the stability of incoherently coupled two-color vector dark and grey solitons in a nonlinear self-defocusing media. We employ the variational technique to derive approximate solutions of the two-color vector dark solitons. The relations between the soliton parameters and the representation of the transverse velocities of the vector solitons are analytically obtained. We also demonstrate numerically the propagation dynamics of the two-color vector solitons, which shows that the two-color vector dark and grey solitons with different wavelengths are always unstable.