Soliton Parameters Research Articles

Structure of soliton bound states in the parametrically driven and damped nonlinear systems

Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven and damped nonlinear Schrödinger equation. We find that the ordinary differential equations, which determine bound soliton solutions, can be transformed into the form resembling the Schrödinger-like equations for eigenfunctions with fixed eigenvalues. We assume that a nonlinear part of the equations is close to the reflectionless potential well occurring in the scattering problem, associated with the integrable equations. We show that symmetric two-hump soliton solution is quite well described analytically by the three-soliton formula with the fixed soliton parameters, depending on the strength of parametric pumping and the dissipation constant.

Nonparaxial solitons and their interaction dynamics in coupled nonlinear Helmholtz systems

It is well-known that the nonparaxiality plays an important role in the fabrication of nanoscale devices. In this paper, we study the existence of nonparaxial solitons in a dimensionless coupled nonlinear Schrödinger system with cross-phase modulation (XPM), which enables the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide. Despite the fact that the system is a nonintegrable one (Tamilselvan et al., 2020), we obtain a bright soliton solution analytically by employing the standard Hirota’s bilinearization method. Subsequently we numerically investigate the scattering dynamics of two and three bright solitary waves using the general solution as the seed one by adopting the split-step Fourier method based on the Feit-Flock algorithm. We explain how the soliton parameters such as separation distance and relative phase influence the interaction between the nonparaxial bright solitons. In particular, we report a bunch of interesting phenomena of soliton interactions, which include oscillating bound solitons when the phase of the two solitary waves are equal and parallel propagation as the phase is changed to out-of phase with a zig-zag pattern. Similarly the in-phase three solitary waves also exhibit a novel interaction which mimics a triple knot structure which has never been observed before in the framework of coupled nonlinear Helmholtz systems. We believe that our results would pave a way for future research generating optical memories based on the nonparaxial solitons.

Self-steepening and intrapulse Raman scattering in the presence of nonlinear gain and its saturation

In this paper we present the results of a detailed numerical investigation of the influence of the self-steepening effect on the parameters of the Raman dissipative solitons in the presence of nonlinear gain and its saturation. It has been established that when the effect of self-steepening prevails under the intrapulse Raman scattering it leads to nonlinear changes in the parameters of the Raman dissipative solitons. Comparing the impact of the intrapulse Raman scattering and self-steepening in the presence of nonlinear gain and its saturation on the dissipative solitons, the following differences have been identified: a much slighter change of the amplitude in the presence of self-steepening; different types of nonlinear dependencies of the frequency and velocity in the presence of intrapulse Raman scattering; and a substantial increase of the velocity under the influence of self-steepening. We have found that under the influence of the saturation of the nonlinear gain the observed nonlinear changes of the parameters of Raman dissipative solitons in the presence of the self-steepening effect are weaker. There has been observed a reduction of the maximum values of the amplitude and velocity as well as the maximum absolute values of the frequency of the Raman dissipative solitons.

Parametric autoresonant generation of dark solitons.

The autoresonant generation of dark solitons of the nonlinear Schrödinger (NLS) equationis discussed. The approach is based on capturing the system into a continuing resonance using a small, chirped frequency parametric driving. Adiabatic control of soliton parameters is achieved if the driving amplitude exceeds a threshold.

Predicting the dynamic process and model parameters of vector optical solitons under coupled higher-order effects via WL-tsPINN

We propose the two-subnet physical information neural network with the weighted loss function (WL-tsPINN) to study the higher-order effects of ultra-short pulses in birefringence fiber transmission and analyze the formation mechanism of vector solitons. We predict the dynamical process of mixed-type single/double soliton and soliton molecules based on the higher-order coupled nonlinear Schrödinger equation (CNLSE) by this WL-tsPINN method. Moreover, we deduce the physical coefficients of the higher-order CNLSE from the mixed single soliton solution. Deep learning based on neural network is a powerful tool for further study of higher-order CNLSE and has potential significance for further study of soliton dynamics.

Modulating chirped Gaussian vector solitons with group-velocity dispersion

We theoretically simulate the modulation of chirped Gaussian vector solitons with group-velocity dispersion at 1-μm. Several different kinds of soliton pulse parameters are considered for variation under the condition of same central wavelength (1064 nm) and slightly different central wavelengths (1063 nm and 1065 nm). The change of these parameters will influence the output properties of pulse shapes and corresponding optical spectra in orthogonal directions. For example, with same central wavelength, “3 + 3″ pseudo-higher-order vector solitons can be generated by changing time delay. And dual-wavelength vector solitons with multiple peaks/dips can be generated in many cases when central wavelengths are slightly different. Our simulations explore the modulation of vector solitons with group-velocity dispersion, which is conductive to the study of vector solitons that exist in long-distance nonlinear optical fiber system.

Quasi-monochromatic dynamical system of cubic–quartic optical solitons with Kerr law of nonlinear refractive index

This paper displays the quasi-monochromatic dynamical system of the cubic–quartic soliton parameters that are recovered from the conservation laws of the model. The adiabatic change in soliton velocity in presence of perturbation terms is also presented.

Single and multi-vertices solitons in lattices of active Morse - van der Pol units

The dynamical evolution of one-dimensional lattice of active units (otherwise said particles) endowed with anharmonic Morse interactions and active–dissipative van der Pol negative friction is here studied both analytically and numerically. One of the directions of this evolution is the formation and stable propagation of dissipative soliton-like perturbations (in short solitons) against the background of some stationary displacement of units (pedestal). It is shown that the evolution of units at leading-front of the soliton is determined by mutual repulsive forces, while that of units at trailing-tail of the soliton is determined by the active–dissipative forces. Approximate analytically solvable models of the leading-front and the trailing-tail are obtained, which make it possible to predict soliton parameters and admissible range of pedestal values with high accuracy. There is also a scenario of N-vertices soliton formation emerging from a single soliton and (N-1)-vertices soliton. The possibility of controlling the number of vertices of multi-vertices solitons is offered, a feature which can be used in the problems of energy accumulation and transport in periodic structures.

Parameters controlling of vortex solitons in nonlocal nonlinear medium with gradually characteristic length

This paper discusses the dynamics of vortex beam in nematic liquid crystals with the tunable characteristic length (CL) of response function. It is found that the transition of the soliton states with different widths during propagations can be controlled by changing the CL under the condition that the nonlocal degree is constant. Furthermore, the transitions propagation of different soliton state is stable and can resist noise. In addition, the numerical results prove that the parameters of vortex solitons, such as rotating periods of angles, orbital angular momentum (OAM), gradient force upon micro-particles all can be controlled conveniently at the desired positions. The controllable density of OAM and gradient force have important academic value and application prospect in the field of optical tweezers and spanner.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

Dynamics of nondegenerate vector solitons in a long-wave-short-wave resonance interaction system.

In this paper, we study the dynamics of an interesting class of vector solitons in the long-wave-short-wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of long wave and two short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multisoliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave component, while a single-humped soliton propagates in the two short-wave components. We establish through a detailed analysis that the nondegenerate multisolitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape-preserving, (ii) shape-altering, and (iii) a shape-changing collision, depending on the choice of the soliton parameters. Here, by shape-altering we mean that the structure of the nondegenerate soliton gets modified slightly during the collision process, whereas if the changes occur appreciably then we call such a collision as shape-changing collision. We distinguish each of the collision scenarios, by deriving a zero phase shift criterion with the help of phase constants. Very importantly, the shape-changing behavior of the nondegenerate vector solitons is observed in the long-wave mode also, along with corresponding changes in the short-wave modes, and this nonlinear phenomenon has not been observed in the already known vector solitons. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics when the long-wave-short-wave resonance interaction is taken into account.

Parametric gap solitons in PT-symmetric optical structures

Abstract It is well known that quadratic nonlinearity and feedback through Bragg periodicity are the basis for parametric gap solitons. The major part of the relevant investigations refers to passive systems. At the same time, optical systems supplemented with active elements can demonstrate unusual properties. Asymmetry intrinsic to structures with parity-time (PT) symmetry is a bright confirmation of this statement. The interplay of nonlinearity, Bragg reflection and gain/loss profile can lead to the complicated pattern of wave interactions and novel results. In this study we address the properties of two-color solitons in complex PT symmetric periodic structures with quadratic nonlinearity. We focus on the case of single Bragg resonance. We reveal the region of parameters where stable parametric solitons may exist. We demonstrate that characteristics of forming solitons depend on the order of alteration of amplifying and absorbing layers.

Control of a qubit state by a soliton propagating through a Heisenberg spin chain.

We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a Hamiltonian involving the interaction between the soliton and the qubit. We show that under certain conditions the generic Hamiltonian may be mapped on that of a qubit two-level system with matrix elements depending on the soliton parameters. We considered the action of a bright and a dark soliton depending on the driving nonlinear wave function. We considered a local interaction restricted the closest to the qubit spin in the chain. We computed the expressions of the physical quantities of interest for all cases and analyzed their behavior in some special limits.

Operating Vector Solitons with Chirped Sech Pulse Shapes

In this paper, we report the theoretical results about operating vector solitons with chirped sech pulse shapes. In the operation, the shapes of temporal pulses and corresponding optical spectra in orthogonal directions will change, which are based on soliton parameters. When input orthogonal pulses have the same central wavelength of 1064 nm, the shift from the central wavelength always occurs for orthogonal pulses. When input orthogonal pulses have different central wavelengths of 1063 nm and 1065 nm, output pulse shapes and optical spectra with obvious multiple peak/dip structures can be achieved in orthogonal directions. Our theoretical results are meaningful for the study of vector soliton dynamics and have potential applications in optical communication and optical sensing.

Semi-rational vector rogon–soliton solutions and asymptotic analysis for any [formula omitted]-component nonlinear Schrödinger equation with mixed boundary conditions

In this paper, we investigate the wave structures of any n-component nonlinear Schrödinger (alias n-NLS) equation with mixed nonzero and zero boundary conditions, which can be used to describe the interactions of many bodies in differential fields. As a consequence, we find its semi-rational vector rogon–soliton solutions (non-zero backgrounds) and soliton-like solutions (zero backgrounds) with the aid of the modified Darboux transform and the multiple root of an (n+1)th degree characteristic polynomial equation. Moreover, the semi-rational vector rogon–soliton solutions can be shown to be PT-symmetric for chosen parameters, and decomposed into rational rogons and grey-like solitons for the bigger parameters. Finally, the maximum amplitudes and average amplitudes are analysed for the semi-rational vector rogon–soliton solutions for some choice of parameters. These results will be useful to better understand the relative physical phenomena in the n-NLS equation or other related multi-component nonlinear physical models.

Transient soliton dynamics in a mode-locked fiber laser: from stationary to pulsation.

We report the experimental observation of the transformation process from a stationary soliton to a pulsating soliton in a mode-locked fiber laser. The detailed soliton dynamics, including soliton parameter changings and sideband variation in the transition, are analyzed by the dispersive Fourier transformation technique. This Letter unveils the great enhancement of intracavity periodic perturbations resulting from the slight increase of soliton intensity induced soliton modulation instability, leading to the occurrence of parametric sidebands and multi-periodic pulsing instability. Our experimental results can shed some light on the intrinsic mechanism of soliton pulsation, as well as contribute to the study of soliton stability and laser dynamics.

Impact of nonlocality and quintic local nonlinearity on the pulses interaction and the dynamical characteristics parameters of soliton in weakly nonlinear nonlocal media

We study the impact of nonlocality and local quintic nonlinearity on the dynamic characteristic parameters of spatial optical bright soliton and on their interaction and collision in weakly nonlocal nonlinear media. For this purpose, we establish the propagation equation governing this dynamic which is a nonlinear cubic-quintic Schrödinger equation. We approach the solution of this equation by a secant hyperbolic ansatz. By the means of the variational method, we bring out the action mode of the nonlocality and quintic nonlinearity on the pulse parameters. Subsequently, a numerical analysis is made and allows us to conclude on their role on the dynamic of pulse in these media. It follows that quintic nonlinearity contributes to the pulse compression and the increase of phase-front curvature, while nonlocality participates in enlargement and the decrease of the phase-front curvature. Taking into account the two effects helps stabilize the soliton during its propagation by generating a new dynamic state depending on whether the quintic nonlinearity and the nonlocality add up, compensate each other, or that one of the two effects is more important than the other. Concerning their interaction, we showed that quintic nonlinearity provides a repulsive force when nonlocality provides an attractive force. In the case of collision, quintic nonlinearity can induce elastic or inelastic collision.

Solitonic model of the condensate

We consider a spatially extended box-shaped wave field that consists of a plane wave (the condensate) in the middle and equals zero at the edges, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. Within the inverse scattering transform theory, the scattering data for this wave field is presented by the continuous spectrum of the nonlinear radiation and the soliton eigenvalues together with their norming constants; the number of solitons N is proportional to the box width. We remove the continuous spectrum from the scattering data and find analytically the specific corrections to the soliton norming constants that arise due to the removal procedure. The corrected soliton parameters correspond to symmetric in space N-soliton solution, as we demonstrate analytically in the paper. Generating this solution numerically for N up to 1024, we observe that, at large N, it converges asymptotically to the condensate, representing its solitonic model. Our methods can be generalized for other strongly nonlinear wave fields, as we demonstrate for the hyperbolic secant potential, building its solitonic model as well.

Multifrequency Solitons in Commensurate-Incommensurate Photonic Moiré Lattices.

We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the condition for phase matching between the waves to the value that matches the edges of the eigenmode bands, thereby shifting the properties of all soliton families. Moreover, the phase-mismatch bandwidth for soliton generation is dramatically broadened in the moiré patterns relative to latticeless structures.

Optical solitons via the collective variable method for the classical and perturbed Chen–Lee–Liu equations

Abstract In this article, the collective variable method to study two types of the Chen–Lee–Liu (CLL) equations, is employed. The CLL equation, which is also the second member of the derivative nonlinear Schrödinger equations, is known to have vast applications in optical fibers, in particular. More specifically, a consideration to the classical Chen–Lee–Liu (CCLL) and the perturbed Chen–Lee–Liu (PCLL) equations, is made. Certain graphical illustrations of the simulated numerical results that depict the pulse interactions in terms of the soliton parameters are provided. Also, the influential parameters in each model that characterize the evolution of pulse propagation in the media, are identified.