Soliton Width Research Articles

Generation of optical UWB signals based on combined bright solitons

We investigate the generation of ultra-wide band (UWB) signal in all optical domain based on combined bright solitons by numerical method. The combined solitons with ultra-wideband characteristics can be obtained by multiple bright solitons. The power spectrum can be modulated by pulse interval, pulse width and phase difference of combined bright solitons to satisfy with the Federal Communications Commission (FCC) spectrum mask. Meanwhile, the transmissions of combined bright solitons in single-mode fibers are discussed. The fiber loss and dispersion effects have the influence on the transmissions of combined bright solitons. In order to eliminate dispersion effects, the stable transmission of signals in dispersion decreasing fibers is proposed.

Localized Dust Acoustic Solitons in Electron-Depleted Dusty Plasmas With κ-Gurevich Distributed Ions

A first theoretical attempt is made to investigate the adiabatically trapped suprathermal ions effect on dust acoustic (DA) solitons in electron-depleted dusty plasmas. Our investigation is motivated by space and laboratory plasma observations of plasmas containing suprathermal particles, resulting from long-tailed distributions, combined with trapped particles in a finite region of phase space. For this goal, the 1-D <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distribution, which describes the adiabatic trapping of suprathermal ions, is constructed, and the associated density expression is derived. The reductive perturbation method (RPM) has been adopted to establish a modified Kortweg-de-Vries (mK-dV)-like equation, and analyze its comportment. The numerical investigation revealed that the main properties (phase velocity, amplitude, and width) of small DA solitons are significantly affected by adiabatically trapped suprathermal ions. In particular, we have found that as the suprathermality of the ions increases, the DA soliton amplitude decreases while its width increases. The significant changes induced by the presence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> -Gurevich distributed ions on the transported energy and electrical field of DA solitons are also analyzed. We have shown that when the ions evolve far from their Maxwellian trapping (i.e., as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula> decreases), the DA soliton energy quantity (bipolar electric field) associated with electronically depleted dusty plasma becomes smaller (stronger). The results of the present study provide new insight into established findings on this issue.

Modulated ion-acoustic wavepackets in a multi-component dense plasma with Thomas-Fermi distribution

Modulated ion acoustic wavepackets have been investigated in a multi-component, dense plasma containing degenerate electrons/positrons, and positive/negative ions. The electrons and positrons assumed to be followed Thomas-Fermi distribution, while the ions considered to be classic. Employing a multi-scale perturbation technique, the nonlinear Schrödinger equation is derived. The criteria for the occurrence of modulational instability of the modulated ion acoustic waves are analyzed. The influences of plasma parameters on the modulational instability and its growth rate have been discussed. The envelope solitons have been discussed as well. The results showed that both modulationally unstable domain and stable domain can be found, depending on the plasma parameters. It is also found that the width of the envelop solitons are significantly modified by related plasma parameters. The present results will be useful in understanding the conditions for modulational instability of ion acoustic waves which are relevant to both space and laboratory dense plasmas.

Long-lived solitons and their signatures in the classical Heisenberg chain.

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with ln(1+S_{i}·S_{j}) interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

Manakov solitons in unbiased photorefractive materials with both the pyroelectric effect and photovoltaic effect

We have shown, for the first time, the existence of Manakov solitons in unbiased photorefractive crystals exhibiting both, the pyroelectric effect and the bulk photovoltaic effect for all three realizations, namely bright-bright, dark-dark, and bright-dark. The two mutually incoherent beams should have the same wavelength and polarization and the total intensity of the two beams should be much smaller than the effective dark irradiance. Analytical solutions for the soliton pair are found out for all three cases. The intensity full width at half maximum and hence the existence curves are found out for all three realizations. The Manakov soliton pair width depends on the magnitude of both, the transient pyroelectric field and the bulk photovoltaic field. The interplay between the photovoltaic effect and the pyroelectric effect in the self trapping process is investigated. Relevant example of a lithium niobate crystal is considered to illustrate our results.

On the dynamics of soliton waves in a generalized nonlinear Schrödinger equation

The main objective of the present paper is to investigate the dynamics of soliton waves in a generalized nonlinear Schrödinger (GNLS) equation. To achieve such a goal, the real and imaginary portions of the GNLS equation are first extracted using a complex wave transformation. Solitons and Jacobi elliptic structures of the governing model, describing the propagation of femtosecond pulses in nonlinear optical fibers, are then constructed through applying the modified Jacobi elliptic expansion method (MJEEM). In the end, by employing a series of 2 and 3D-dimensional numerical representations, it is exposed that the width of bright and dark solitons respectively decreases and increases, while the amplitude of both waves decreases with the increase of nonlinear parameters.

Establishing the excitation field in tip-enhanced Raman spectroscopy to study nanostructures within two-dimensional systems

The optical field generated by a nanoplasmonic probe is revealed in tip-enhanced Raman spectroscopy (TERS) experiments. The TERS intensity profile of nano-objects smaller than the probe’s apex has a donut-like shape which resembles the magnitude of the field generated by a point-dipole source, being well described by the Dyadic Green’s function. Having prior knowledge on the excitation field generated by the TERS probe, we measured the width of shear solitons caused by lattice reconstruction in low-angle twisted bilayer graphene, a prominent platform for twistronics, and the extend of defect-induced light emission from graphene edges.

Generalized Darboux transformation and solitons for the Ablowitz–Ladik equation in an electrical lattice

In this paper, the Ablowitz–Ladik equation, which describes an electrical lattice employing the inductors and nonlinear capacitors in a transmission line, is investigated. With respect to the complex field amplitude of the electrical lattice, we construct a generalized Darboux transformation in which the multiple spectral parameters are involved. Expressions of the one-soliton solutions are derived. Soliton velocities, amplitudes and widths are presented. Then, solitons, degenerate solitons and interaction among the soliton and degenerate solitons are investigated. We find that when the multi solitons interact with each other/one another, the corrugated regions are generated in the interaction areas. Interactions among the one soliton and degenerate solitons are shown to be elastic.

Nonsymmorphic chiral symmetry and solitons in the Rice-Mele model

The Rice-Mele model has two topological and spatially-inversion symmetric phases, namely the Su-Schrieffer-Heeger (SSH) phase with alternating hopping only, and the charge-density-wave (CDW) phase with alternating energies only. The chiral symmetry of the SSH phase is robust in position space, so that it is preserved in the presence of the ends of a finite system and of textures in the alternating hopping. However, the chiral symmetry of the CDW wave phase is nonsymmorphic, resulting in a breaking of the bulk topology by an end or a texture in the alternating energies. We consider the presence of solitons (textures in position space separating two degenerate ground states) in finite systems with open boundary conditions. We identify the parameter range under which an atomically-sharp soliton in the CDW phase supports a localized state which lies within the band gap, and we calculate the expectation value $p_y$ of the nonsymmorphic chiral operator for this state, and the soliton electric charge. As the spatial extent of the soliton increases beyond the atomic limit, the energy level approaches zero exponentially quickly or inversely proportionally to the width, depending on microscopic details of the soliton texture. In both cases, the difference of $p_y$ from one is inversely proportional to the soliton width, while the charge is independent of the width. We investigate the robustness of the soliton level in the presence of disorder and sample-to-sample parameter variations, comparing with a single soliton level in the SSH phase with an odd number of sites.

Temperature effects on Manakov solitons in biased photorefractive crystals exhibiting the linear and quadratic electro-optic effect simultaneously

We investigate the effect of temperature on Manakov solitons in biased photorefractive crystals having both linear and quadratic electro-optic effects simultaneously. Two different physical quantities, namely, the dielectric constant and the dark irradiance, have a temperature dependence which in turn affects the Manakov solitons. We consider three realizations of the Manakov solitons for our present analysis, namely, the bright–bright, dark–dark and bright–dark Manakov soliton pair. The existence curve and its modification due to temperature has been studied in detail for each of the Manakov soliton pair. A comprehensive investigation of the functional dependence of the soliton width with temperature is undertaken for different parameters like beam intensity and external electric field for each of the Manakov soliton pair. The tuning of photorefractive soliton characteristics by changing of temperature has potential practical applications in optical networks and optical waveguiding.

Bright solitons in fractional coupler with spatially periodical modulated nonlinearity

We study bright solitons in the fractional coupler with a spatially periodical modulated nonlinearity. The results show that the linear coupling constant κ, Lévy index α, chemical potential μ and nonlinear intensity g have a significant influence on the amplitude, width and stability of fundamental solitons, dipole solitons and tripole solitons. We investigate the stability of bright solitons by linear stability analysis and the real-time evolution method. It is found that the bright solitons tend to be stable with the increase of linear coupling constant, Lévy index, chemical potential, and nonlinear intensity in the corresponding parameter interval. The results also show that the distance between adjacent peaks is four times of the nonlinear lattice period for dipole solitons and six times for tripole solitons. We also find that the number of soliton peaks is smaller, and the stable region is wider in the fractional coupler with the spatially periodical modulated nonlinear lattice.

Evolution of Cos–Gaussian Beams in the Periodic Potential Optical Lattice

The evolution of Cos−Gaussian beams in periodic potential optical lattices is theoretically and numerically investigated. By theoretical analysis, a breathing soliton solution of the Gross–Pitaevskii equation with periodic potential is obtained, and the period of the breathing soliton is solved. In addition, the evolution of Cos−Gaussian beams in periodic potential optical lattices is numerically simulated. It is found that breathing solitons generate by appropriately choosing initial medium and beam parameters. Firstly, the effects of the initial parameters of Cos−Gaussian beams (initial phase and width) on its initial waveform and the propagation characteristics of breathing soliton are discussed in detail. Then, the influence of the initial parameters (modulation intensity and modulation frequency) of a photonic lattice on the propagation characteristics of breathing solitons is investigated. Finally, the effects of modulation intensity and modulation frequency on the width and period of the breathing soliton are analyzed. The results show that the number of breathing solitons is manipulated by controlling the initial parameters of Cos−Gaussian beams. The period and width of a breathing soliton are controlled by manipulating the initial parameters of a periodic photonic lattice. The results provide some theoretical basis for the generation and manipulation of breathing solitons.

Quantum tunneling of three-spine solitons through excentric barriers

Macromolecular protein complexes catalyze essential physiological processes that sustain life. Various interactions between protein subunits could increase the effective mass of certain peptide groups, thereby compartmentalizing protein α-helices. Here, we study the differential effects of applied massive barriers upon the soliton-assisted energy transport within proteins. We demonstrate that excentric barriers, localized onto a single spine in the protein α-helix, reflect or trap three-spine solitons as effectively as concentric barriers with comparable total mass. Furthermore, wider protein solitons, whose energy is lower, require heavier massive barriers for soliton reflection or trapping. Regulation of energy transport, delivery and utilization at protein active sites could thus be achieved through control of the soliton width, or of the effective mass of the protein subunits.

Optical and analytical soliton solutions to higher order non-Kerr nonlinear Schrödinger dynamical model

This article studies the propagation of the short pulse optical model governed by higher order nonlinear Schrödinger equation (HNLSE) with non-Kerr nonlinearity. The model is used to describe the propagation of ultrashort photons in highly nonlinear media. Upon establishing the general framework, we discuss the statics and dynamics of HNLSE by employing an extended modified auxiliary equation mapping (EMAEM) architectonic to obtain some new solitary wave solutions like bright dromion (soliton), domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. Obtained optical soliton solutions are analysed graphically to represent features like as width, amplitude, and structure of solitons. We will also discuss our governing model for M-shaped, Homoclinic breathers, multiwave, kink cross rational, and interaction of M-shaped with 1 and 2 kink solutions with the help of various ansatz transformations.

Chiral matter-wave soliton in a Bose-Einstein condensate under density-dependent gauge potential

We theoretically investigate the chiral matter-wave soliton in a Bose-Einstein Condensate (BEC) under a density-dependent gauge potential. By means of the reductive perturbation method, the dark and bright solitons excited upon the background of the system are obtained. The physical mechanism for generating the chirality of the nonlinear excitation is revealed. The coupling of the nonlinear excitation and background of the system leads to a complex competition relationship between the current nonlinearity induced by the gauge potential and the mean-field atomic interaction, which results in rich chiral solitons. Generally, the amplitude and width of the chiral soliton depend on the direction of motion. Interestingly, when the current nonlinearity dominates over the mean-field atomic interaction, unidirectional chiral bright and dark solitons are obtained. The theoretical results are confirmed by the numerical simulations of the full nonlinear GP equation describing the system.

Stability of KdV solitons with respect to transverse perturbations: Absolute and convective instabilities

We study the stability of one-dimensional solitons propagating in an anisotropic medium. We derived the Kadomtsev-Petviashvili equation for nonlinear waves propagating in an anisotropic medium. By a proper variable substitution this equation reduces either to the KPI or to the KPII equation. In the former case solitons are unstable with respect to the normal modes of transverse perturbations, and in the latter they are stable. We only consider the case when the solitons are unstable. We formulated the linear stability problem. Using the Laplace–Fourier transform, we found the solution describing the evolution of an initial perturbation. Then, using Briggs’ method we studied the absolute and convective instabilities. We found that a soliton is convectively unstable unless it propagates at an angle smaller then critical with respect to a critical direction defined by the condition that the group velocity is parallel to the phase velocity. The critical angle is proportional to the ratio of the dispersion length to the soliton width, which is a small parameter. The coefficient of proportionality is expressed in terms of the phase speed and its second derivative with respect to the angle between the propagation direction and the critical direction. As an example we consider the stability of solitons propagating in Hall plasmas.

The polarization-aided tunable high-power femtosecond Raman solitons generation from 1.96 to 3.1 μm in fibers cascaded system

We present the demonstration of a polarization-aided high-power ultra-broadband tunable mid-infrared (MIR) Raman soliton-based femtosecond laser in fibers cascaded nonlinear system. We found and verified that the incident pulse polarization has effects on the characteristics of the Raman solitons generation in different types of fluoride fibers. For the first time to the best of our knowledge, we achieved the MIR Raman solitons with central wavelength continuously tunable from 1.96 to 3.1 µm by optimizing the input pulse parameters. The solitons with a maximum average power of above 350 mW, accounting for nearly 83% of the total output power, and the pulse width of these tunable Raman solitons remains below 200 fs. Thanks to the nearly all-fiber configuration, which results in the pump laser with root mean square (RMS) value of power fluctuation around 0.24% in 2 h, and the 3.1-µm soliton with far-field beam M2 value around 1.1. Additionally, the corresponding numerical simulations on these solitons radiation were also conducted, the results are in good agreement with the experimental one.

Dissipative solitons of the nonlinear fractional Schrödinger equation with PT-symmetric potential

We study the fractional dissipative solitons with nonlinear loss and linear gain supported by a special class of PT-symmetric potential in focused nonlinear Kerr medium. The effective width, existence and stability of fractional solitons are discussed. In such a potential, the stability of solitons changes at lower energy. Once the stability of symmetric solitons is destroyed, asymmetric solitons and symmetric solitons coexist. With the increase of linear gain coefficient, the effective width decreases first and then increases. With the increase of Lévy index, the amplitude of solitons decreases. In addition, the change of nonlinear loss coefficient has almost no effect on the soliton contour.

Negative mass effects of a spin soliton in Bose-Einstein condensates

We investigate the energy-velocity dispersion relation of spin solitons with arbitrary initial velocities. Based on the dispersion relation, we further characterize the inertial mass of a spin soliton and find two critical velocities to distinguish between the positive mass and negative mass. One critical velocity separates the initial negative and positive masses, and the other denotes the velocity for negative-positive mass transition during an acceleration process. With the aid of the two critical velocities, we further propose two possible ways to observe the pure negative mass effect of a spin soliton. Moreover, the relations between the soliton's width and its velocity are discussed according to the variational results. We report that the soliton width can become narrower with larger moving speed (when a spin soliton possesses positive mass), in sharp contrast to the dark solitons reported before. These results would motivate experiments to observe negative mass effects of solitons in Bose-Einstein condensates.

New Optical Solitons with Variational Principle and Collective Variable Strategy for Cold Bosons in Zig‐Zag Optical Lattices

The theme of this piece of research is to investigate the collective variable (CV) as well as semi‐inverse techniques to explore a significant model of cold bosonic atoms in a zig‐zag optical lattice. The system is reduced to an important equation by utilizing the continuum approximation and explains the soliton’s dynamics in sense of pulse variables. These parameters are amplitude, temporal position, chirp, width, frequency, and phase which are termed as collective variables (CVs). The proposed methods are more straightforward, succinct, accurate, and simple to calculate. Furthermore, to employ the computational counterfeit on the system of six ordinary differential equations that denote all the CVs incorporated in the supposed ansatz, a well‐established computational method which is the Runge–Kutta scheme of order four is applied. The CV method is exerted to resolve the evolution of pulse parameters with the propagation distance and graphical illustrations which are also given. Moreover, figures reveal the fascinating periodic oscillations of frequency, width, amplitude, and chirp of soliton. Solitons and their numerical behavior to interpret fluctuations in CVs are presented for several values of super‐Gaussian pulse parameters. Also, the results for the semi‐inverse method which are bright solitons are provided in the form of 2D, 3D, and density plots for the distinct values of the fractal parameter to understand their physical significance. This scheme is effective in finding variational principles of various nonlinear evolution equations. Some compelling characteristics pertaining to the current scrutiny are also deduced.