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1.
Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity
Sahan Dasanayaka 《Physics letters. A》2010,375(2):225-229
We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities. 相似文献
2.
《Physics letters. A》2001,284(6):247-252
We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel “two-tier” solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is retained in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity. 相似文献
3.
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. 相似文献
4.
In this paper we have investigated the propagation characteristics of optical solitons in dispersion managed optical communication systems taking into account of the effect of quintic nonlinearity. Using variational formalism, several ordinary differential equations have been established for pulse parameters. These equations have been solved numerically to investigate the propagation characteristics. It has been noticed that stable periodic pulse propagation is possible over long distance. Numerical simulation has been undertaken to show that parabolic nonlinearity reduces collision distance between neighbouring pulses of the same channel. 相似文献
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6.
W. B. Fraga J. W. M. Menezes C. S. Sobrinho A. C. Ferreira G. F. Guimar?es A. W. Lima Jr. A. F. G. F. Filho H. H. B. Rocha K. D. A. Sabóia F. T. Lima J. M. S. Filho A. S. B. Sombra 《Optical and Quantum Electronics》2009,41(2):121-130
In this paper, we have presented a numerical analysis of the stability of optical bullets (2 + 1), or spatiotemporal solitons (2 + 1), in a planar waveguide with cubic–quintic nonlinearity. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L D) and diffraction (diffraction length, L d) with temporal and spatial auto-focusing behavior, respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic–quintic nonlinearity with the optical fields coupled by cross-phase modulation and considering several values for the non linear parameter α We have shown the existence of stable light bullets in planar waveguide with cubic–quintic nonlinearity through the study of spatiotemporal collisions of the light bullets. 相似文献
7.
In this paper we have investigated the propagation characteristics of optical solitons in dispersion managed optical communication systems taking into account of the effect of quintic nonlinearity. Using variational formalism, several ordinary differential equations have been established for pulse parameters. These equations have been solved numerically to investigate the propagation characteristics. It has been noticed that stable periodic pulse propagation is possible over long distance. Numerical simulation has been undertaken to show that parabolic nonlinearity reduces collision distance between neighbouring pulses of the same channel. 相似文献
8.
The transmission equation of ultrashort optical pulse in the high-order dispersion media with the parabolic law (cubic–quintic) nonlinearity has been studied with the help of the subsidiary ordinary differential equation expansion method. As a result, the optical solitons and triangular periodic solutions are obtained, and the conditions for exact solutions to exist are also given. 相似文献
9.
This letter reports the first results on the coupled modulational instability of copropagating spin waves in a magnetic film. Strong instability was observed for the two waves with either attractive or repulsive nonlinearity. If the two waves have attractive nonlinearity, the instability leads to the formation of bright solitons. If the two waves have repulsive nonlinearity, the process results in the formation of black solitons. The instability was also observed for the two waves in separated attractive-repulsive nonlinearity regimes. 相似文献
10.
The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities. 相似文献
11.
Under investigation in this paper are the generalized coupled nonlinear Schrödinger equations with cubic–quintic nonlinearity which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Via the dependent variable transformation and Hirota method, the bilinear form is derived. Based on the bilinear form obtained, the one-, two- and three-soliton solutions are presented in the form of exponential polynomials with the help of symbolic computation. Propagation and interactions of solitons are investigated analytically and graphically. Evolution of one soliton is discussed with the analysis of such physical quantities as the soliton amplitude, width, velocity, initial phase and energy. Interactions of the solitons appear in the forms of the repulsion or attraction alternately and propagation in parallel. Inelastic and head-on interactions of the solitons are also showed. Finally, via the asymptotic analysis, conditions of the elastic and inelastic interactions are obtained. 相似文献
12.
The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the “radial quantum number” m by one. 相似文献
13.
Analytic soliton solutions of cubic‐quintic Ginzburg‐Landau equation with variable nonlinearity and spectral filtering in fiber lasers 下载免费PDF全文
Long‐Gang Huang Li‐Hui Pang Pring Wong Yan‐Qing Li Shao‐Yi Bai Ming Lei Wen‐Jun Liu 《Annalen der Physik》2016,528(6):493-503
In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.
14.
We analytically study the (1 + 1)-dimensional spatial optical solitons in weakly nonlocal nonlinear media with cubic–quintic nonlinearity (fifth order nonlinear media) and cubic–quintic–septic nonlinearity (seventh order nonlinear media). Explicit solutions are derived, which include optical bright solitons, singular solutions and singular triangular periodic solution. 相似文献
15.
基于包含五次复系数的高阶Ginzburg Landau方程为模型,采用分步傅里叶方法数值研究了啁啾类超短脉冲间的相互作用。结果表明:相邻孤子之间的相互作用对五阶非线性效应非常敏感,即使参数改变很小的值,也会改变其传输特性。适当地选择五阶非线性参数值,能够很好地抑制孤子间的相互作用,提高光纤传输的比特率。当相邻孤子的初始间距为6.8,五阶非线性参数值取-0.001时,可以实现2个孤子长距离的保型传输。最后讨论了五阶非线性作用下多孤子之间的相互作用及抑制。 相似文献
16.
R. Driben B. A. Malomed 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(3):317-323
It is known that optical-lattice (OL) potentials can stabilize solitons and
solitary vortices against the critical collapse, generated by cubic
attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also
stabilize various species of fundamental and vortical solitons against the
supercritical collapse, driven by the double-attractive cubic-quintic
nonlinearity (however, solitons remain unstable in the case of the pure
quintic nonlinearity). Two types of OLs are considered, producing similar
results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential.
Soliton families are obtained by means of a variational approximation, and
as numerical solutions. The stability of all families, which include
fundamental and multi-humped solitons, vortices of oblique and straight
types, vortices built of quadrupoles, and supervortices, strictly
obeys the Vakhitov-Kolokolov criterion. The model applies to optical media
and BEC in “pancake” traps. 相似文献
17.
应用多光子非线性Compton散射模型和非线性薛定谔方程,研究了Compton散射对五阶非线性零色散附近调制不稳定性的影响.将入射光和Compton散射光作为产生调制不稳定性的机制,分析了光纤损耗、四阶色散和五阶非线性对增益谱的影响.结果表明:散射下的正或负五阶非线性分别使零色散附近的增益谱宽和峰值比散射前增大得更大或... 相似文献
18.
In this paper we have presented a theoretical investigation on the propagation properties of incoherent solitons in photorefractive media which is characterized by noninstantaneous saturating nonlinearity. Using mutual coherence function approach, we have obtained the equation of existence curve for such solitons. We have discussed the coherence characteristics of these solitons. We have found that solitons with a particular radius can possess two different critical powers. The dynamical evolution of these solitons has been discussed in detail by both analytical and numerical simulation. 相似文献
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20.
We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional geometry, in the form of a circle with contrast Δg of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation and Vakhitov-Kolokolov stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as ΔN~Δg (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of one-dimensional solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity. 相似文献