Dipole Solitons Research Articles

Periodic evolution of the out-of-phase dipole and the single-charged vortex solitons in periodic photonic moiré lattice with saturable self-focusing nonlinearity media.

We survey the propagation properties of the out-of-phase (OOP) dipole solitons and the single-charged vortex (SCV) soliton in a periodic photonic moiré lattice with θ=arctan⁡(3/4) under self-focusing nonlinearity media. Since the rotation angle, periodic photonic moiré lattices have peculiar energy band structures, with highly flat bands and the bandgaps being much more extensive, which is very favorable for the realization and stability of the solitons. When exciting a single point on-site with the OOP dipole beam, its evolution shows a periodic rollover around the lattice axis. Whereas, when exciting a single point on-site with the SCV beam, it transmits counterclockwise rotating periodically. Both the OOP dipole solitons and the SVC soliton maintain the local state, but their phase exhibits different variations. The phase of the OOP dipole solitons is flipped, while that of the SCV is rotated counterclockwise. Our work further complements the exploration of solitons in photonic moiré lattice with nonlinearity.

Manipulation of dipole soliton for higher order nonlinear Schrödinger equation in the nonuniform management systems

The extended nonlinear Schrödinger equation which can be used to describe the propagation of the femtosecond soliton pulse has been investigated. A type of quartic and dipole soliton solutions is constructed based on the extended nonlinear Schrödinger equation with varying third-order and fourth-order dispersions, self-steepening and Raman effects. Parameter modulation of self-similar dipole soliton in some non-uniform management systems is also discussed in detail. The results show that with different forms of four-order dispersion and nonlinear coefficients, it exhibits different propagation dynamics. Modulation of the certain parameters, the amplitude and the trajectory of self-similar dipole soliton can be manipulated.

Stable high-dimensional solitons in nonlocal competing cubic-quintic nonlinear media

We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic, and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45° counterclockwise around the origin of coordinate are found. For the dipole solitons and those after rotation, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.

Superexponential amplification, power blowup, and solitons sustained by non-Hermitian gauge potentials

We introduce a continuous one-dimensional non-Hermitian matrix gauge potential and study its effect on dynamics of a two-component field. The model is emulated by a system of evanescently coupled nonlinear waveguides with distributed gain and losses. The considered gauge fields lead to a variety of unusual physical phenomena in both linear and nonlinear regimes. In the linear regime, the field may undergo superexponential convective amplification. A total power of an input Gaussian beam may exhibit a finite-distance blowup, which manifests itself in absolute delocalization of the beam at a finite propagation distance, where the amplitude of the field remains finite. The defocusing Kerr nonlinearity initially enhances superexponential amplification, while at larger distances it suppresses the growth of the total power. The focusing nonlinearity at small distances slows down the power growth and eventually leads to the development of the modulational instability. Complex periodic gauge fields lead to the formation of families of stable fundamental and dipole solitons.

Elliptic vortex beam in a fractional complex Ginzburg–Landau model

We have investigated the elliptical vortex structures in dissipative media governed by the fractional complex cubic-quintic Ginzburg–Landau model. Stable regions of generating dissipative fundamental, dipole, tripole and fourpole solitons are found for relatively small elliptical coefficient (e ) at values of (LI) , which can produce critical or supercritical collapse in free space. By adjusting the system parameters, the elliptical vortex can evolve into the circular ones and remain stable circular vortex structure with given topological charge of the vorticity S (from 1 to 4). Effects of the value of the respective LI on stability regions of generation stable circular vortex solitons have been investigated in detail. These results have potential applications in optical signal processing.

Fundamental and multipole solitons in amplitude-modulated Fibonacci lattices.

We investigated the existence and stability of fundamental and multipole solitons supported by amplitude-modulated Fibonacci lattices with self-focusing nonlinearity. Owing to the quasi-periodicity of Fibonacci lattices, families of solitons localized in different waveguides have different properties. We found that the existence domain of fundamental solitons localized in the central lattice is larger than that of solitons localized in the adjacent central waveguide. The former counterparts are completely stable in their existence region, while the latter have a narrow unstable region near the lower cut-off. Two families of dipole solitons were also comprehensively studied. We found the outer lattice distribution can significantly change the existence region of solitons. In addition, we specifically analyzed the properties of four complicated multipole solitons with pole numbers 3, 5, 7, and 9. In the Fibonacci lattice, their field moduli of multipole solitons are all asymmetrically distributed. The linear-stability analysis and direct simulations reveal that as the number of poles of the multipole soliton increases, its stable domain is compressed. Our results provide helpful insight for understanding the dynamics of nonlinear localized multipole modes in Fibonacci lattices with an optical nonlinearity.

Solitons in spin-orbit-coupled systems with fractional spatial derivatives

We demonstrate the existence of various types of solitons in the spin-orbit-coupled systems with the fractional dimension based on Lévy random flights, including the systems with or without Zeeman splitting. Specifically, the systems without Zeeman splitting can support families of symmetric solitons, whereas the systems with Zeeman splitting can support families of stable asymmetric solitons. These coupled solitons may come in the form of fundamental single solitons or dipole solitons. The Lévy index, the strength of self- and cross-phase modulation, and the propagation constant strongly affect the waveforms and stability domains of coupled solitons. The stability and instability domains of such single and dipole solitons are calculated by the method of linear stability analysis and are confirmed by the numerical simulation of perturbed propagation. The general conclusion is that for the Lévy index close to 2, corresponding to the normal nonlinear optics, the solitons tend to be stable, while in the opposite case of Lévy index close to 1, corresponding to Cauchy random flights, the solitons tend to become unstable.

Topological dipole Floquet solitons

We theoretically introduce a new type of topological dipole solitons propagating in a Floquet topological insulator based on a kagome array of helical waveguides. Such solitons bifurcate from two edge states belonging to different topological gaps and have bright envelopes of different symmetries: fundamental for one component, and dipole for the other. The formation of dipole solitons is enabled by unique spectral features of the kagome array which allow the simultaneous coexistence of two topological edge states from different gaps at the same boundary. Notably, these states have equal and nearly vanishing group velocities as well as the same sign of the effective dispersion coefficients. We derive envelope equations describing components of dipole solitons and demonstrate in full continuous simulations that such states indeed can survive over hundreds of helix periods without any noticeable radiation into the bulk.

Merging and splitting dynamics between two bright solitons in dipolar Bose–Einstein condensates* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11875220 and 12047502).

We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose–Einstein condensates. Under different dipolar strengths, the two bright solitons can merge into a breathing wave, and then split or propagate constantly after several oscillating periods. We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting,and analyze their formation mechanism by the system’s energy evolution. Also, the change of initial phase difference brings distinct effects on the soliton interaction. Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons.

Solitons in Kerr media with two-dimensional non-parity-time-symmetric complex potentials

Our results indicate that continuous soliton families can exist and be stable in Kerr media with two-dimensional (2D) non-parity-time (PT)-symmetric complex potentials. There are several discrete eigenvalues in the linear spectra of these complex potentials. Fundamental solitons bifurcate from the largest discrete eigenvalue while the dipole solitons bifurcate from the second- or third- largest discrete eigenvalue. We further find that eigenvalues of the soliton linear-stability spectra emerge as complex conjugate pairs. The effect of different parameters of the complex potentials on soliton stability is discussed in detail. Moreover, we study the transverse energy flow vector of the solitons in these complex potentials.

Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

We construct families of fundamental, dipole, and tripole solitons in the fractional Schr\"{o}dinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the L\'{e}vy index (LI)\ that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.

Propagation of dark soliton in nonlocal nonlinear coupler

The characteristics of fundamental and mutipole dark solitons in the nonlocal nonlinear couplers are studied through numerical simulation in this work. Firstly, the fundamental dark solitons with different parameters are obtained by the Newton iteration. It is found that the amplitude and beam width of the ground state dark soliton increase with the enhancement of the nonlocality degree. As the nonlinear parameters increase or the propagation constant decreases, the amplitude of the fundamental dark soliton increases and the beam width decreases. The power of the fundamental dark soliton increases with the nonlocality degree and nonlinear parameters increasing, and decreases with the propagation constant increasing. The refractive index induced by the light field decreases with the nonlocality degree increasing and the propagation constant decreasing. The amplitudes of the two components of the fundamental dark soliton can be identical by adjusting the coupling coefficient. These numerical results are also verified in the case of multipole dark solitons. Secondly, the transmission stability of fundamental and mutipole dark solitons are studied. The stability of dark soliton is verified by the linear stability analysis and fractional Fourier evolution. It is found that the fundamental dark solitons are stable in their existing regions, while the stable region of the multipolar dark solitons depends on the nonlocality degree and the propagation constant. Finally, these different types of dark dipole solitons and dark tripole solitons are obtained by changing different parameters, and their structures affect the stability of dark soliton. It is found that the multipole dark soliton with potential well is more stable than that with potential barrier. The refractive-index distribution dependent spacing between the adjacent multipole dark solitons favors their stability.

Asymmetric dissipative solitons in a waveguide lattice with non-uniform gain-loss distributions.

We address the existence and stability of two types of asymmetric dissipative solitons, including fundamental and dipole solitons, supported by a waveguide lattice with non-uniform gain-loss distributions. Fundamental solitons exist only when the linear gain width is greater than or equal to the linear loss width, while dipole solitons exist only when the linear gain width is less than or equal to the linear loss width. With an increase in the relative gain depth, the effective width of the soliton gradually decreases. In addition, we find that both asymmetric fundamental and dipole solitons are stable in a considerable part of their lower edge of existence regions, and solitons beyond this range are unstable.

Two dimensional spacial soliton in atomic gases with PT-symmetry potential.

We propose a realistic physical scheme to realize linear Gaussian optical potential with parity-time (PT) symmetry and two dimensional (2D) spacial solitons in a coherent atomic gas. It is shown that the PT-symmetric potential can be created through the spatial modulation of the control and relevant atomic parameters. We find that the Gaussian PT potential parameters, the imaginary part and the width and the position, play crucial roles in the occurrence of the PT phase transition. We demonstrate that the system supports stable 2D dipole solitons and vortex solitons, which can be managed via tuning PT potential. Furthermore, the dynamic characteristics of the symmetric scatter and collision of solitons are shown.

Quartic and dipole solitons in a highly dispersive optical waveguide with self-steepening nonlinearity and varying parameters

We show theoretically that highly dispersive optical media characterized by a Kerr nonlinear response may support the existence of quartic and dipole solitons in the presence of the self-steepening effect. The existence and stability properties of these localized pulses are examined in the presence of all the material parameters. Regimes for the modulation instability of a continuous-wave signal propagating inside the nonlinear medium are investigated and an analytic expression for the gain spectrum is obtained and shown to be dependent on the self-steepening parameter in addition to second- and fourth-order group velocity dispersion parameters. Self-similar soliton solutions are constructed for a generalized nonlinear Schr\odinger equation with distributed second-, third-, and fourth-order dispersions, self-steepening nonlinearity, and gain or loss describing ultrashort pulse propagation in the inhomogeneous nonlinear media via the similarity transformation method. The evolutional dynamics of the self-similar structures are investigated in a periodic distributed waveguide system and an exponential dispersion decreasing waveguide.

Propagation of dipole solitons in inhomogeneous highly dispersive optical-fiber media.

We consider ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a type of exact self-similar soliton solution that takes the structure of a dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical-fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed. By performing numerical simulations, the self-similar soliton solutions are found to be stable under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Two dimension PT symmetry spacial soliton in atomic gases with linear and nonlinear potentials

We present a physical scheme to realize combined linear and nonlinear optical potentials with parity-time (PT) symmetry and two dimensional (2D) spacial solitons in a coherent atomic gas. It is shown that the combined PT-symmetric potentials can be created through the spatial modulation of the control and relevant atomic parameters. We find that the imaginary part of the nonlinear PT potential plays a crucial role for the occurrence of the PT phase transition. We demonstrate that the system supports stable 2D dipole solitons and vortex solitons, which can be managed via tuning PT potentials.

Optical bright, dark and dipole solitons with derivative nonlinearity in the presence of parity-time-symmetric lattices

This paper deals with the study of optical solitons in the presence of new linear and nonlinear parity-time [Formula: see text]-symmetric modulation lattices. The nonlinear medium is a derivative term with arbitrary power. Inverse engineering scheme is utilized to retrieve bright, dark, dipole and singular soliton solutions. These solutions are presented for four new [Formula: see text]-symmetric potentials. The results reveal that optical bright, dark and dipole solitons can exist for those new physical settings.

Nonlocal solitons supported by non-parity-time-symmetric complex potentials

We report on the existence and stability of fundamental and out-of-phase dipole solitons in nonlocal focusing Kerr media supported by one-dimensional non-parity-time (PT)-symmetric complex potentials. These fundamental and dipole solitons bifurcate from different discrete eigenvalues in the linear spectra. Below the phase transition of the non-PT-symmetric complex potentials, these solitons are stable in the low power region. While above the phase transition, they are stable in the moderate power region. The eigenvalues in linear-stability spectra of solitons appear as conjugation pairs (δ, δ*). The transverse power flow and the nonlinear contribution to refractive index are asymmetric functions. Moreover, the degree of nonlocality can also influence the stability of these solitons.

Gap solitons supported by two-dimensional parity-time-symmetric optical lattices in saturable media with fourth-order diffraction

The existence and the stability of in-phase dipole gap solitons in two-dimensional (2D) parity-time (PT)-symmetric optical lattices with defocusing saturable nonlinearity and a fourth-order diffraction property are investigated. When different values are used for the coupling constant of the fourth-order diffraction, the critical threshold of the 2D PT-symmetric optical lattices remains unchanged. The in-phase dipole solitons exist in the first finite gap and are shown to be stable in the moderate power region. The existence and stability of dipole solitons with different fourth-order diffraction coupling constants and different saturation parameters are therefore studied. We also investigate the transverse power-flow vector of these gap solitons.