Spatiotemporal Solitons Research Articles

Dissipative spatiotemporal soliton in a driven waveguide laser

A distributed Kerr-lens mode locking regime can be realized in a waveguide laser by spatial profiling of the pump beam, thus creating a spatio-temporal soliton. Additional slow temporal modulation of the pump source stabilizes the spatio-temporal solution in a broad range of parameters defined by the dynamic gain saturation. We choose a Cr:ZnS waveguide laser as a practical example, but such a regime is feasible in various waveguide and fiber oscillators. A far-reaching analogy with Bose–Einstein condensates allows this approach to stabilize the weakly dissipative BECs.

Dynamic of stationary soliton to soliton pulsation transition in spatiotemporal mode-locked fiber lasers

This paper presents the experimental observation of the transition from stationary spatiotemporal soliton (STS) to spatiotemporal soliton pulsation (STSP) in spatiotemporal mode-locked fiber lasers for the first time. Three STSs maintain an asynchronous pulsating state with the same period, while another STS remains in a stationary mode-locked state. Through numerical analysis, the dynamic transition process of STS to STSP is studied. Numerical analysis reveals that STSP occurs under specific cavity parameters when the energy is comparatively high. As pulse energy increases, a stationary STS gradually transitions to a pulsation state. The modes have undergone distinct evolutionary trajectories, and the pivotal role of the saturable absorption effect as well as the interaction among modes has been demonstrated to be crucial for STSP. Our study contributes to understanding the formation mechanism of STSP.

Rydberg-Induced Topological Solitons in Three-Dimensional Rotation Spin–Orbit-Coupled Bose–Einstein Condensates

Abstract We introduce a novel approach for generating stable three-dimensional (3D) spatiotemporal solitons (SSs) within a rotating Bose-Einstein Condensates, incorporating Spin-Orbit-Coupling (SOC), a weakly anharmonic potential and cold Rydberg atoms. This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges |m| ≤ 3 in two spinor components, potentially exhibiting diverse spatial configurations. Our findings reveal that the Rydberg long-range interaction, spin-orbit coupling, and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons. Notably, the Rydberg interaction contributes to a reduction in the norm of topological solitons, while the SOC plays a key role in stabilizing the SSs with finite topological charges. This research of SSs exhibit potential applications in precision measurement, quantum information processing, and other advanced technologies.

Spatiotemporal soliton solutions in three dimensional combined linear-harmonic potentials with varying sources

Spatiotemporal soliton solutions in three dimensional combined linear-harmonic potentials with varying sources

Generation of high-temporal-quality sub-two-cycle pulses by self-cleaning of spatiotemporal solitons in air-plasma channels

Generation of high-temporal-quality sub-two-cycle pulses by self-cleaning of spatiotemporal solitons in air-plasma channels

Collisions of Light Bullets with Different Circular Polarizations

Collisions of left- and right-polarized spatiotemporal optical solitons have been numerically simulated for a locally isotropic focusing Kerr medium with anomalous chromatic dispersion. The stable propagation of such “light bullets” in a moderate nonlinear regime is ensured by a transverse parabolic profile of the refraction index in a multimode waveguide. The transverse motion of centers of mass of wave packets in such systems occurs on classical trajectories of a harmonic oscillator, whereas the motion in the longitudinal direction is uniform. Therefore, collisions of two solitons can be not only head-on but also tangential. An inelastic collision of two solitons with opposite circular polarizations can result either in two binary light bullets combining the left and right polarization or in more complex bound systems.

Pure quartic three-dimensional spatiotemporal Kerr solitons in graded-index media

Pure quartic three-dimensional spatiotemporal Kerr solitons in graded-index media

Spatiotemporal dual-periodic soliton pulsation in a multimode fiber laser

Spatiotemporal mode-locked (STML) fiber lasers have become a new platform for investigating nonlinear phenomena. In this work, spatiotemporal dual-periodic soliton pulsation (SDSP) is firstly observed in an STML fiber laser. It is found that in the SDSP, the long-period pulsations (LPPs) of different transverse modes are synchronous, while the short-period pulsations (SPPs) exhibit asynchronous modulations. The numerical simulation confirms the experimental results and further reveals that the proportion of transverse mode components can manipulate the periods of the LPP and SPP but does not affect the synchronous and asynchronous pulsations of different transverse modes. The obtained results bring the study of spatiotemporal dissipative soliton pulsation into the multi-period modulation stage, which helps to understand the complex spatiotemporal dynamics in STML fiber lasers and discover new dynamics in high-dimensional nonlinear systems.

Few-cycle two-frequency spatiotemporal solitons in the absence of group velocity dispersion at one of the components

The second harmonic generation by few-cycle pulses is studied when the group velocity dispersion coefficient is equal to zero at the fundamental or doubled frequency. Using numerical simulation, it is shown that in both cases, in the presence of a negative third-order dispersion, the formation of stable two-frequency spatiotemporal solitons is possible.

Few-Cycle Two-Frequency Spatiotemporal Solitons in the Absence of Group Velocity Dispersion at One of the Components

Few-Cycle Two-Frequency Spatiotemporal Solitons in the Absence of Group Velocity Dispersion at One of the Components

All-fiber spatiotemporal mode-locked based on Mamyshev mechanism with high energy noise-like pulse generation at 1550 nm

Intermodal dispersion is the main problem restricting the establishment and stability of spatiotemporal mode-locking (STML) in the anomalous dispersion region. In the experiment, we employ the multimode Er-Yb double-clad fiber to carry out the multimode operation as a gain medium. The nonlinear multimode interference is used to enhance the mode coupling and spatial filtering in the cavity, achieve the purpose of suppressing the intermodal dispersion, and successfully realize the 1550 nm spatiotemporal noise-like solitons of Mamyshev oscillator based on the multimode gain fiber. The noise-like spatiotemporal soliton pulse energy reaches ∼171.29 nJ, and the corresponding peak power is ∼30.32 kW. The intermodal dispersion suppression based on nonlinear multimode interference performance makes this laser an attractive tool for practical applications.

Dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients

In this paper, we study the dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients in analytical and numerical forms. The characteristics and physical applications of the soliton solutions are investigated under different modulations of the coefficients depicting diffraction, potential, nonlinearity, source, and gain. We find that structures of these soliton solutions can be effectively manipulated by appropriately selecting the source term. Besides, the impact of gate effect on soliton propagation is investigated by employing the hyper-Gaussian and rectangle functions as diffraction coefficients. The results show that (i) the hyper-Gaussian modulation can be replaced by the rectangle modulation for large exponent and (ii) the solitons undergo a broadening in width and a sudden decrease in amplitude when passing through the gate functions. Our findings may have potential applications for the investigation of soliton control in the fields of nonlinear optics and Bose–Einstein condensations.

Spatiotemporal dissipative soliton resonances in multimode fiber lasers

Spatiotemporal mode-locking in multimode fiber lasers is intriguing for the complex nonlinear dynamics and the increase of theoretical energy limit. In this paper, we enrich spatiotemporal mode-locking with dissipative soliton resonances, a kind of solitons which is characterized by large pulse energy in single mode fiber lasers, and demonstrate their emergence in multimode fiber lasers by employing the reverse saturable absorption effect from real saturable absorbers. The spatiotemporal dissipative soliton resonances are expected to raise the energy limit further by the locking of dissipative soliton resonances in different transverse modes, whose energy is about twice the maximum single-mode energy in our results. Moreover, properties of spatiotemporal dissipative soliton resonances are investigated by tailoring parameters of the multimode fiber laser, where evolution and transformation of the proposed pulses including shaping and broadening are disclosed. The spatiotemporal dissipative soliton resonances in multimode fiber lasers may open up new avenue for high-power and spatiotemporally engineered coherent light fields in laser dynamics and nonlinear optics.

Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross–Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations compare variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, with progressively increasing energies, solitons eventually undergo wave collapse: this occurs below the theoretical limit, which is predicted within the variational approach. In a self-defocusing scenario, a similar trend is found, where the good agreement persists for low energies. For large soliton energies, however, complex spatiotemporal dynamics emerge.

Light gap bullets in defocusing media with optical lattices

Searching for three-dimensional spatiotemporal solitons (also known as light/optical bullets) has recently attracted keen theoretical and experimental interests in nonlinear physics. Currently, optical lattices of diverse kinds have been introduced to the stabilization of light bullets, while the investigation for the light bullets of gap type – nonlinear localized modes within the finite gap of the underlying linear Bloch spectrum – is lacking. Herein, we address the formation and stabilization properties of such light gap bullets in periodic media with defocusing nonlinearity, theoretically and in numerical ways. The periodic media are based on two-dimensional periodic standing waves created in a coherent three-level atomic system which is driven to the regime of electromagnetically induced transparency, which in principle can also be replaced by photonic crystals in optics or optical lattices in ground-state ultracold atoms system. The temporal dispersion term is tuned to normal (positive) group velocity dispersion so that to launch the light gap bullets under self-repulsive nonlinearity; two types of such light gap bullets constructed as three-dimensional gap solitons and vortices with topological charge m=1 within the first finite gap are reported and found to be robustly stable in the existence domains. On account of the light bullets were previously limited to the semi-infinite gap of periodic media and continuous nonlinear physical systems, the light gap bullets reported here thus supplement the missing type of three-dimensional spatiotemporal localized modes in periodic media which exhibit finite band gaps.

Optical spatiotemporal solitary wave solutions of the generalized (3+1)-dimensional Gross–Pitaevskii equation with distributed coefficients

In this work, the extended Jacobi elliptic function expansion approach is used to analyze a generalized [Formula: see text]-dimensional Gross–Pitaevskii equation with distributed time-dependent coefficients because of its use in the Bose–Einstein condensation. The Gross–Pitaevskii equation plays a significant role in Bose–Einstein condensation, where it characterizes the dynamics of the condensate wave function. By using this approach with a homogeneous balance principle, the spatiotemporal soliton solutions and exact extended traveling-wave solutions of governing equation have been successfully obtained. A few double periodic, trigonometric and hyperbolic function solutions from the Jacobi elliptic function solutions have been found under specific constraints on a parameter. It is obvious that the proposed approach is the most straightforward, efficient and useful way to handle numerous nonlinear models that arise in applied physics and mathematics in order to generate various exact solutions. A case with variable gain, constant diffraction and parabolic potential strength has been considered in this study to derive exact solutions. Numerous novel varieties of traveling-wave solutions have been revealed in this work, including the double periodic singular, the periodic singular, the dark singular, the dark kink singular, the periodic solitary singular and the singular soliton solutions and these newly obtained results differ from those previously investigated for this governing equation. In addition to addressing a scientific explanation of the analytical work, the results have been graphically presented by 3D plots and contour plots for some suitable parameter values to understand the physical meaning of the derived solutions. Due to their applicability to a variety of quantum systems, the acquired solutions are of considerable importance.

(Invited) Spatiotemporal soliton stability in multimode fibers: A Hamiltonian approach

We introduce a Hamiltonian approach to study the stability of three-dimensional spatiotemporal solitons in graded-index multimode optical fibers. Nonlinear light bullet propagation in these fibers can be described by means of a Gross–Pitaevskii equation with a two-dimensional parabolic potential. We apply a variational approach, based on the Ritz optimization method, and compare its predictions with extensive numerical simulations. We analytically find that, in fibers with a pure Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low energies, in perfect agreement with numerical simulations. However, above a certain energy threshold, simulations reveal that the spatiotemporal solitons undergo wave collapse, which is not captured by the variational approach.

At the threshold of distributed Kerr-lens mode-locking in a Cr:ZnS waveguide laser

We demonstrate feasibility of spatiotemporal mode-locking in a mid-IR Cr:ZnS waveguide laser based on the nonlinear spatial mode coupling. The experiment shows efficient power scaling with the excitation of intramode beatings, causing a pronounced Q-switching, which could result in nonlinear mode-coupling. The contribution of such multimode beatings and resulting Q-switching is confirmed numerically. We suggest that a particularly high nonlinearity in Cr:ZnS combined with multimode waveguide leads to a soft aperture induced by a pump beam. The numerical simulations demonstrate that such an aperture could provide an effective spatial mode control in a nonlinear multimode waveguide, which, thereby, opens the way to the birth of a spatiotemporal dissipative soliton, or light bullet, formation, thus forming the basis for the future distributed Kerr-lens mode locking in the energy-scalable solid-state waveguide (or yet unrealized fiber) laser.

Multidimensional optical solitons and their manipulation in a cold atomic gas with a parity-time-symmetric optical Bessel potential

We propose a scheme to realize an optical Bessel potential with parity-time ($\mathcal{P}T$) symmetry and investigate the existence, propagation, and manipulation of multidimensional optical solitons through the interplay among diffraction, Kerr nonlinearity, and potential confinement in a cold atomic gas under the condition of electromagnetically induced transparency (EIT). We show that the system supports not only two-dimensional stationary optical solitons but also rotary ones; the stability of such solitons can be actively controlled by the gain-loss component (imaginary part), while the rotary motions can be tuned by the refractive-index component (real part) of the $\mathcal{P}T$-symmetric potential. Moreover, we demonstrate that the system allows the existence of stable three-dimensional spatiotemporal optical solitons, i.e., optical bullets, which have ultraslow propagation velocity and display helicoidal motions with controllable propagation trajectories. Due to the Kerr nonlinearity enhanced by the EIT effect, extremely low power is needed to create these multidimensional optical solitons. The results reported here are useful not only for the generation and manipulation of high-dimensional solitons via $\mathcal{P}T$-symmetric potentials, but also for promising applications in optical information processing and transmission.

Unveiling the complexity of spatiotemporal soliton molecules in real time

Observing the dynamics of 3D soliton molecules can hold great opportunities for unveiling the mechanism of molecular complexity and other nonlinear problems. In spite of this fantastic potential, real-time visualization of their dynamics occurring on femtosecond-to-picosecond time scales is still challenging, particularly when high-spatiotemporal-resolution and long-term observation are required. In this work, we observe the real-time speckle-resolved spectral-temporal dynamics of 3D soliton molecules for a long time interval using multispeckle spectral-temporal measurement technology. Diverse real-time dynamics of 3D soliton molecules are captured for the first time, including the speckle-resolved birth, spatiotemporal interaction, and internal vibration of 3D soliton molecules. Further studies show that nonlinear spatiotemporal coupling associated with a large average-chirp gradient over the speckled mode profile plays a significant role in these dynamics. These efforts may shed new light on decomposing the complexity of 3D soliton molecules, and create an analogy between 3D soliton molecules and chemical molecules.