Formation Of Solitons Research Articles

Uni- and Bi-directional Er3+-doped fiber soliton laser mode-locked by GIMF-based SA

In this paper, we have experimentally demonstrated an ultrafast Er-doped fiber laser mode-locked by the GIMF-based saturable absorber without an optical isolator for various soliton behaviors. The adjustment of the polarization controller results in different losses for the counter-propagating lasers. And thus, not only the bidirectional solitons, but also the quasi-unidirectional solitons are realized. For the bidirectional operation, the counterpropagating conventional solitons with the pulse energy of >1.12 nJ demonstrates different central wavelengths, repetition rates, and pulse widths. For the unidirectional operation, the laser operates in either the clockwise or the counter-clockwise directions with an emission strengths difference of larger than 31 dB. Interestingly, the bidirectional operations could show different soliton state of the forward conventional solitons and backward bound solitons. Our research would be beneficial for the further understanding of the formation and transformation of the bidirectional solitons and can find vital applications in gyroscopic and other dual-channel applications.

Origin of nontopological soliton dark matter: solitosynthesis or phase transition

This work demonstrates that nontopological solitons with large global charges and masses, even above the Planck scale, can form in the early universe and dominate the dark matter abundance. In solitosynthesis, solitons prefer to grow as large as possible under equilibrium dynamics when an initial global charge asymmetry is present. Their abundance is set by when soliton formation via particle fusion freezes out, and their charges are set by the time it takes to accumulate free particles. This work improves the estimation of both quantities, and in particular shows that much larger-charged solitons form than previously thought. The results are estimated analytically and validated numerically by solving the coupled Boltzmann equations. Without solitosynthesis, phase transitions can still form solitons from particles left inside false-vacuum pockets and determine their present-day abundance and properties. Even with zero charge asymmetry, solitons formed in this way can have very large charges on account of statistical fluctuations in the numbers of (anti)particles inside each pocket.

Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation in the presence of perturbation term and having Kerr law

Purpose:In this research study, obtaining the analytical and soliton solutions to the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr law nonlinearity is aimed via the generalized projective Riccati equations method (GPREM), a simple version of the new extended auxiliary equation method (SAEM26), and unified Riccati equation expansion method (UREEM). At the same time, the roles of some parameters included in the perturbed RKL equation on soliton dynamics are analyzed. Methodology:The presented methods are successfully employed to the perturbed RKL equation. In the application of the presented methods, to convert the perturbed RKL equation into a nonlinear ordinary differential equation, we choose suitable complex wave transformation for the proposed model. Later, a linear equation system is derived using the GPREM, SAEM26, and UREEM, the system is solved, the appropriate solution sets are obtained, and the soliton solutions are achieved, respectively. Findings:The singular, bright and dark soliton solutions are generated by choosing the suitable set and parameter values. To comprehend the physical dynamics of some solutions, 3D, contour, and 2D graphs are demonstrated. In addition, 2D graphs are drawn to show how some parameters in the main equation have an effect on soliton behaviors. The examination indicates that the model parameters have a substantial effect on the soliton dynamics. Depending on the soliton forms, the effect can be varied. The results presented in this paper will be useful for future works in soliton theory and the presented methods can be effectively implemented to such equations. Originality:The effects of the model parameters included in the perturbed RKL equation on soliton dynamics are analyzed for the first time in this study.

The generation and observation of pulses with switchable single/dual wavelengths and tunable bandwidth from a SWNT mode-locked Er-doped fiber laser

Mode-locked pulse outputs with switchable single/dual wavelengths and widely tunable spectral bandwidth are demonstrated by fully exploiting multiple soliton formation mechanisms combining single-wall carbon nanotube, intracavity loss tuning and nonlinear polarization rotation. An isolator with single-polarization fiber pigtails is additionally inserted in a ring fiber laser cavity to introduce polarization-dependent loss modulation for gain profile tuning and nonlinear polarization rotation. Mode-locked by a home-made single-wall carbon nanotube saturable absorber, switchable single/dual-wavelength pulses centered in the 1530- or/and 1550-nm gain regions of erbium-doped fiber are experimentally observed by tuning the intracavity loss to tilt the gain profile. Moreover, the spectral bandwidths of single-wavelength pulses centered in the 1530- and 1550 nm regions could be continuously tuned from 2.4 to 4.0 nm, and 2.7 to 9.0 nm, respectively. Such widely tunable spectral bandwidths are attributed to hybrid mode-locked mechanisms combining the nonlinear polarization rotation and single-wall carbon nanotube. Our results give a deep insight into the well-controlled gain profile tuning and provide a relatively simple setup and method to obtain bandwidth-tunable, wavelength-switchable pulse outputs, showing the potential to meet various requirements of ultrafast laser applications.

Compact multicolor two-photon fluorescence microscopy enabled by tailorable continuum generation from self-phase modulation and dispersive wave generation.

By precisely managing fiber-optic nonlinearity with anomalous dispersion, we have demonstrated the control of generating plural few-optical-cycle pulses based on a 24-MHz Chromium:forsterite laser, allowing multicolor two-photon tissue imaging by wavelength mixing. The formation of high-order soliton and its efficient coupling to dispersive wave generation leads to phase-matched spectral broadening, and we have obtained a broadband continuum ranging from 830 nm to 1200 nm, delivering 5-nJ pulses with a pulse width of 10.5 fs using a piece of large-mode-area fiber. We locate the spectral enhancement at around 920 nm for the two-photon excitation of green fluorophores, and we can easily compress the resulting pulse close to its limited duration without the need for active pulse shaping. To optimize the wavelength mixing for sum-frequency excitation, we have realized the management of the power ratio and group delay between the soliton and dispersive wave by varying the initial pulse energy without additional delay control. We have thus demonstrated simultaneous three-color two-photon tissue imaging with contrast management between different signals. Our source optimization leads to efficient two-photon excitation reaching a 500-µm imaging depth under a low 14-mW illumination power. We believe our source development leads to an efficient and compact approach for driving multicolor two-photon fluorescence microscopy and other ultrafast investigations, such as strong-field-driven applications.

The exact solutions of the [formula omitted]–dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized [formula omitted]-expansion method

In this paper 2+1–dimensional Kadomtsev–Petviashvili (KP) equation with variable coefficients is investigated through the extended generalized G′G–expansion technique. One of the most universal model is KP equation, which is used to explain the ion acoustic waves in plasma physics, to model two dimensional shallow water waves, and in ferromagnetic, Bose–Einstein condensation and string theory. The obtained exact solutions of KP equation are in the form of hyperbolic function, trigonometric function, and rational function. With the aid of symbolic computational software Mathematica, the three dimensional surface plots with corresponding contour plots are provided for the obtained closed from solutions, which are of the form of solitary waves, multi solitons and periodic solitary wave like dynamical structures.

Vortex gap solitons in spin–orbit-coupled Bose–Einstein condensates with competing nonlinearities

The formation and dynamics of full vortex gap solitons (FVGSs) are investigated in two-component Bose–Einstein condensates with spin–orbit coupling (SOC), Zeeman splitting (ZS), and competing cubic and quintic nonlinear terms, while the usual kinetic energy is neglected, assuming that it is much smaller than the SOC and ZS terms. Unlike previous SOC system with the cubic-only attractive nonlinearity, in which solely semi-vortices may be stable, with the vorticity carried by a single component, the present system supports stable FVGS states, with the vorticity present in both components (such states are called here “full vortex solitons”, to stress the difference from the half-vortices). They populate the bandgap in the system’s linear spectrum. In the case of the cubic self-attraction and quintic repulsion, stable FVGSs with a positive effective mass exist near the top of the bandgap. On the contrary, the system with cubic self-repulsion and quintic attraction produces stable FVGSs with a negative mass near the bottom of the bandgap. Mobility and collisions of FVGSs with different topological charges are investigated too.

Dissipative soliton generation and real-time dynamics in microresonator-filtered fiber lasers

Optical frequency combs in microresonators (microcombs) have a wide range of applications in science and technology, due to its compact size and access to considerably larger comb spacing. Despite recent successes, the problems of self-starting, high mode efficiency as well as high output power have not been fully addressed for conventional soliton microcombs. Recent demonstration of laser cavity soliton microcombs by nesting a microresonator into a fiber cavity, shows great potential to solve the problems. Here we study the dissipative soliton generation and interaction dynamics in a microresonator-filtered fiber laser in both theory and experiment. We bring theoretical insight into the mode-locking principle, discuss the parameters effect on soliton properties, and provide experimental guidelines for broadband soliton generation. We predict chirped bright dissipative soliton with flat-top spectral envelope in microresonators with normal dispersion, which is fundamentally forbidden for the externally driven case. Furthermore, we experimentally achieve soliton microcombs with large bandwidth of ~10 nm and high mode efficiency of 90.7%. Finally, by taking advantage of an ultrahigh-speed time magnifier, we study the real-time soliton formation and interaction dynamics and experimentally observe soliton Newton’s cradle. Our study will benefit the design of the novel, high-efficiency and self-starting microcombs for real-world applications.

The noise sense effects on the characteristic nonlinearly Schrödinger equation solitary propagations

The nonlinearly stochastic Schrödinger equation (NLSSE) predicts the nonlinear process that produces the waves decay in many physics applications. The unified method has been used in obtaining different new stochastic forms for NLSSE damped by noises in Itô sense. The derived structures appear in the form of rational, solitons, soliton-like shocks, and explosive propagations. The new stochastic solutions investigated the change of frequencies by noise term in NLSSE in nonlinear process that may be produced in many nonlinear wave applications. Finally, wave picture properties may controlled by noise term in Itô sense effect, which gives new information’s for NLSSE in physics applications which is believed to be affected by the influence of Brownian motion that change the shape and structures of the generated decaying and damping waves.

Generation and routing of nanoscale droplet solitons without compensation of magnetic damping

A magnetic droplet soliton is a localized dynamic spin state which can serve as a nanoscale information carrier and nonlinear oscillator. The present opinion is that the formation of droplet solitons requires the compensation of magnetic damping by a torque created by a spin-polarized electric current or pure spin current. Here, we demonstrate theoretically that nanoscale droplet solitons can be generated and routed in ferromagnetic nanostructures with voltage-controlled magnetic anisotropy in the presence of uncompensated magnetic damping. Performing micromagnetic simulations for the MgO/Fe/MgO trilayer with almost perpendicular-to-plane magnetization, we reveal the formation of the droplet soliton under a nanoscale gate electrode subjected to a subnanosecond voltage pulse. The soliton lives up to 50 ns at room temperature and can propagate over micrometer distances in a ferromagnetic waveguide due to nonzero gradient of the demagnetizing field. Furthermore, we show that electrical routing of the soliton to different outputs of a spintronic device can be realized with the aid of an additional semiconducting nanostripe electrode creating controllable gradient of the perpendicular magnetic anisotropy.

Drag-induced dynamical formation of dark solitons in Bose mixture on a ring

Andreev-Bashkin drag plays a very important role in multiple areas like superfluid mixtures, superconductors and dense nuclear matter. Here, we point out that the drag phenomenon can be also important in physics of solitons, ubiquitous objects arising in a wide array of fields ranging from tsunami waves and fiber-optic communication to biological systems. So far, fruitful studies were conducted in ultracold atomic systems where nontrivial soliton dynamics occurred due to inter-component density-density interaction. In this work we show that current-current coupling between components (Andreev-Bashkin drag) can lead to a substantially different kind of effects, unsupported by density-density interactions, such as a drag-induced dark soliton generation. This also points out that soliton dynamics can be used as a tool to experimentally study the dissipationless drag effect.

Cnoidal waves and dark solitons with linear third-order dispersion and self-steepening effect

The present paper investigates the conditions needed for the generation and propagation of cnoidal waves in the form of dark solitons under the influence of self-steepening effect and linear third-order dispersion. This kind of optical pulses could be obtained in single-mode waveguides due to the precise balance between higher orders of nonlinear and dispersive phenomena. As a basic equation, it is used the nonlinear amplitude equation (NAE). It is found a new analytical solution of this equation in the form of a cnoidal wave (Jacobi elliptic sine function). In the article it is presented that the solution can be reduced to dark soliton at specific values of the modulus of ellipticity κ.

Formation of microwave soliton combs under cyclotron resonance interaction of electron beam with counter-propagating waveguide mode

We theoretically study the formation of periodical trains of microwave self-induced-transparency solitons (M\W-SIT soliton combs), which arise under cyclotron resonant interaction of an initially rectilinear electron beam with a steady-state electromagnetic wave counter-propagating in a cylindrical waveguide. Depending on the contained energy, solitons can either propagate toward the electron beam (i.e., in the direction of the unperturbed group velocity) or be entrained by the beam in the direction of its translational motion. As a result, a kind of feedback arises, leading to the appearance of soliton combs emitted from both the left and right boundaries of the system. This process can be described by the non-stationary self-consistent model, which is based on the parabolic equation for the field evolution taking into account the waveguide dispersion. Within the framework of the developed model, it is shown that waveguide dispersion does not prevent the formation of ultrashort solitons with duration of about several dozens wave periods. Moreover, the peak power of the entrained solitons can anomalously increase as the frequency of the incident wave approaches the cutoff frequency of the operating mode.

Solution of stochastic Allen–Cahn equation in the framework of soliton theoretical approach

In this paper, the Allen–Cahn equation with time noise is under consideration. The extended fan-sub technique is used to find the exact solutions. The solutions are successfully extracted in the form of hyperbolic, trigonometric and mixed forms of solitons. Importantly, the physical unique value problems of the solutions are discussed using the different values of parameters. The 2D, 3D, and their corresponding contour behaviors of these solutions are depicted by choosing the different values of parameters. The stability is controlled through the Borel coefficient in the noise term.

Energy optimization of diffraction managed accessible solitons

We present the generation, stability analysis, and energy optimization of diffraction managed accessible breather solitons in highly nonlocal nonlinear media comprising an array of alternately positive and negative diffracting media. The system has been modeled using a nonlocal nonlinear Schrödinger equation and solved both analytically and numerically. The initial beam energy for the diffraction managed solitons has been determined and tabulated for a large range of both local and average diffraction. At comparatively higher diffraction values, the diffraction managed system requires significantly less energy for soliton formation than in a constant diffraction system, while it requires a little more for lower diffraction values. Naturally, an intermediate diffraction value offers the energy matching point for diffraction managed and constant diffraction systems, which in turn eases the use of both systems in a single network if necessary. The diffraction managed system requires less tuning of initial beam energy for soliton formation, and it is more prominent for negative average diffraction. The diffraction managed accessible solitons show a variety of bifurcations. They are robust against randomness in diffraction and/or nonlinearity.

Effects of frequency-dependent Kerr nonlinearity on higher-order soliton evolution in a photonic crystal fiber with one zero-dispersion wavelength

We show that the higher-order soliton evolution can be considerably affected by the relative positions of the zero-nonlinearity wavelength (ZNW) and zero-dispersion wavelength (ZDW) with respect to the input wavelength in photonic crystal fibers (PCFs) with frequency-dependent Kerr nonlinearity. By regulating the magnitude of nonlinear dispersion, the position of the ZNW and the strength of the doping Kerr nonlinearity can vary to a large extent, which significantly changes the general process of higher-order soliton evolution in the PCFs. Particularly, some interesting phenomena observed numerically in the PCFs with one ZDW and one ZNW are as follows: the formation of a blueshifted fundamental soliton that satisfies the phase-matching and group-velocity-matching conditions with a redshifted fundamental soliton, the tunneling effect of a fundamental soliton that transfers from one solitonic region to another one through a spectrally limited nonsolitonic region, and the generation of the high-intensity blueshifted dispersive wave and redshifted dispersive wave.

Ultrafast pulse propagation in graphene-comprising nanophotonic waveguides considering nonperturbative electrodynamic nonlinearity

We outline a comprehensive model for ultrafast optical pulse propagation along nonlinear graphene-comprising integrated photonic waveguides. An electrodynamic graphene hot-electron model (GHEM) is used to capture the temporal dynamics and intertwined absorptive and refractive nonlinearity to explore a strongly nonperturbative photoconductivity regime that transcends third-order phenomena. We propose a formalism to abstract the 2D material-related modal properties of the waveguides in the static/continuous-wave regime that can also be plugged into a generalized nonlinear Schrödinger equation (NLSE) framework. Our model of optical pulse propagation consists of a coupled NLSE along with the nonlinear equation system of the GHEM. We demonstrate pulsed applications pertinent to integrated photonic components, namely, improvement of the extinction ratio (ER) of a nonreturn-to-zero (NRZ)-modulated bitstream, pulse shaping, spectral broadening, and optical-shock formation leading to pulse breaking and soliton formation. Our NLSE-GHEM extracts graphene nonlinearity from fundamental physics without resorting to phenomenological correction terms or fitted parameters, shows good agreement with recent experiments, and can potentially be used in the study of high-power on-chip applications such as pulsed lasers and frequency combs.

Nonlinear optics in diamond-fin photonic nanowires: soliton formation and frequency comb generation.

We present a detailed study of the nonlinear optical properties of newly developed subwavelength diamond-fin waveguides, along with an analysis of soliton generation and pulse spectral broadening in these structures. Our rigorous mathematical model includes all the key linear and nonlinear optical effects that govern the pulse dynamics in these diamond waveguides. As a relevant application of our investigations, we demonstrate how these waveguides can be employed to efficiently generate frequency combs in the visible spectral domain.

Electromagnetic solitons and their stability in relativistic degenerate dense plasmas with two electron species

The evolution of electromagnetic (EM) solitons due to nonlinear coupling of circularly polarized intense laser pulses with low-frequency electron-acoustic perturbations is studied in relativistic degenerate dense astrophysical plasmas with two groups of electrons: a sparse population of classical relativistic electrons and a dense population of relativistic degenerate electron gas. Different forms of localized stationary solutions are obtained and their properties are analyzed. Using the Vakhitov-Kolokolov stability criterion, the conditions for the existence and stability of a moving EM soliton are also studied. It is noted that the stable and unstable regions shift around the plane of soliton eigenfrequency and the soliton velocity due to the effects of relativistic degeneracy, the fraction of classical to degenerate electrons and the EM wave frequency. Furthermore, while the standing solitons exhibit stable profiles for a longer time, the moving solitons, however, can be stable or unstable depending on the degree of electron degeneracy, the soliton eigenfrequency and the soliton velocity. The latter with an enhanced value can eventually lead to a soliton collapse. The results should be useful for understanding the formation of solitons in the coupling of highly intense laser pulses with slow response of degenerate dense plasmas in the next generation laser-plasma interaction experiments as well as the novel features of x-ray and γ-ray pulses that originate from compact astrophysical objects.

Analytical solutions of conformable Drinfel’d–Sokolov–Wilson and Boiti Leon Pempinelli equations via sine–cosine method

In this paper, we studied the Drinfel’d–Sokolov–Wilson equation (DSWE) and Boiti Leon Pempinelli equation (BLPE) in the conformable sense. The sine–cosine method is utilized to achieve various traveling wave solutions to the suggested nonlinear systems. It is an easy approach to use and does not require sophisticated mathematical software or a knowledgeable coder. It can also be used for various linear and nonlinear fractional issues, making it pervasive. The obtained solutions in the form of solitons emerge with the necessary constraints to ensure their existence. The obtained results hold significant role in elucidating some important nonlinear problems in applied sciences and engineering.