Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers

In this letter, under investigation is a nonlinear Schrödinger equation with varying dispersion, nonlinearity and loss for the propagation of ultra-short optical pulses in the normal dispersion regime of optical fibers. By virtue of the modified Hirota's method and symbolic computation, the analytic two-soliton solution is explicitly obtained. Both the bright and dark solitons are observed in the normal dispersion regime of optical fibers with dispersion management. An asymptotic analysis to verify the elastic collision between solitons is performed and the stability of the soliton solutions is investigated. Besides, a new bright solitonic generator for generating high-power and narrow bandwidth pulses is advised. Furthermore, possible applicable soliton control techniques which might be used for the design of optical switch and dispersion-managed systems are proposed.     

Analytic study on bound solitons and soliton collisions for the coupled nonlinear Schrödinger equations

A type of mode-locked fiber laser, which can generate the bound solitons in the anomalous group-velocity dispersion regime, is suggested in this paper via symbolic computation. A transformation is given to convert the coupled nonlinear Schrödinger equations to a simpler form. Analytic two-, three- and N-soliton solutions for the coupled nonlinear Schrödinger equations are obtained. Based on those solutions, formation of the bound solitons is analyzed, and methods for the soliton control are presented. The soliton intensity and collision period can be controlled with the changes in the nonlinearity and group-velocity dispersion of optical fibers. The slight phase shift has a great influence on the bound states of solitons after the soliton collision. To support the results, numerical simulations of three-soliton propagation are performed. Finally, the modulational instability of bound solitons is analyzed.     

Stable spatiotemporal dissipative soliton clusters in the complex Ginzburg–Landau equation

Stable spatiotemporal soliton clusters in the cubic–quintic complex Ginzburg–Landau equation are investigated theoretically. It is revealed that spatiotemporal soliton clusters carrying zero and nonzero topological charges can stably propagate and the clusters don't substantially rotate despite the value of topological charges due to the effect of friction force in such a model. It is found that if the separation of solitons is larger than a critical value, the cluster is maintained, otherwise solitons exhibit too strong an attraction for each other due to being in-phase, which leads to their instability. Prediction of the minimum separation of solitons for bound clusters is demonstrated by use of energy and momentum balance methods.     

Bright,dark and dark-singular soliton solutions of nonlinear Schrödinger's equation with spatio-temporal dispersion

This article presents an analytical study of the propagation of solitons through optical fibres. We consider a nonlinear Schrödinger equation with spatio-temporal dispersion and quadratic–cubic nonlinearity. Jacobi elliptic functions are used as an ansatz to extract optical dark and bright solitons as well as Jacobi elliptic solutions. The extended direct algebraic method gives dark and dark-singular soliton solutions. The constraint conditions which guarantee the existence of soliton solutions are listed.     

Stochastic dark solitons for a higher-order nonlinear Schrödinger equation in the optical fiber

In this paper, a stochastic higher-order nonlinear Schrödinger equation, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is investigated analytically. Via the symbolic computation and white noise functional approach, the stochastic dark one- and two-soliton solutions are obtained, and effects of the Gaussian white noise on the stochastic dark one and two solitons are discussed. For the stochastic dark one soliton, velocity and phase change randomly because of the Gaussian white noise, but the energy, shape and amplitude keep unchanged during the soliton propagation. For the stochastic dark two solitons, effect of the Gaussian white noise leads to the inversion of the velocity directions, while the velocities have the same varying trend so that the interaction appears that the stochastic dark two solitons keep parallel.     

Semi-analytical method for designing finite sets of discriminated solitons and soliton molecules in fibres

An infinite number of solitons, as well as soliton molecules belonging different families, are allowed to propagate stably along a given dispersion-managed optical fibre. In this paper, we propose a semi-analytical method to systematically find a finite number of solitons and two-soliton molecules. Determined solitons and soliton molecules present a greatest power gap between them, to make them sufficiently distinct symbols for encoding several bits of information per symbol in a multilevel modulation format in fibre-optic transmission systems. Furthermore, for illustrative purposes, we discuss the possibility of encoding three bits per symbol.     

Dynamics of optical solitons,multipliers and conservation laws to the nonlinear schrödinger equation in (2+1)-dimensions with non-Kerr law nonlinearity

This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.     

Parallel transmission of solitons without interactions

Soliton interactions affect the pulse quality and capacity of communication systems. In this paper, parallel transmission of solitons without interactions are investigated to improve the pulse quality and capacity. Analytic two-soliton solutions for the variable coefficient nonlinear Schrödinger equation are obtained.The exponential profile of optical fibers is suggested to derive the parallel transmission of solitons, and influences of corresponding parameters are analyzed.     

Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.     

The multiple-scale averaging and dynamics of dispersion-managed optical solitons

Multiple-scale averaging is applied to the nonlinear Schrödinger equation with rapidly varying coefficients, and use the results to analyze pulse propagation in an optical fiber when a periodic dispersion map is employed. The effects of fiber loss and repeated amplification are taken into account by use of a coordinate transformation to relate the pulse dynamics in lossy fibers to that in equivalent lossless fibers. Second-order averaging leads to a general evolution equation that is applicable to both return-to-zero (soliton) and non-return-to-zero encoding schemes. The resulting equation is then applied to the specific case of solitons, and an asymptotic theory for the pulse dynamics is developed. Based upon the theory, a simple and effective design of two-step dispersion maps that are advantageous for wavelength-division-multiplexed soliton transmission is proposed. Theuse of these specifically designed dispersion maps allows simultaneous minimization of dispersive radiation in several different channels.     

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger–Maxwell–Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.     

Hidden possibilities in soliton switching through tunneling in erbium doped birefringence fiber with higher order effects

In this paper, coupled higher order nonlinear Schrödinger–Maxwell–Bloch equations are studied for the ultrashort pulse propagation in erbium-doped birefringent fiber system. Lax pair is constructed for the CHNLS–MB system. Through the Darboux method and symbolic computation, analytic two-soliton solution is obtained. To analyze the specific problem, we design an optimal system by properly choosing the special form of variable coefficients. Here, using obtained two-soliton solution, tunneling of femtosecond soliton through barrier and well is investigated. While solitons are passing through barrier and well, some unexpected behavior is observed and hidden possibilities in switching action through tunneling is investigated.     

Analytic study on soliton-effect pulse compression in dispersion-shifted fibers with symbolic computation

The soliton-effect pulse compression of ultrashort solitons in a dispersion-shifted fiber (DSF) is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion (TOD), self-steepening (SS) and stimulated Raman scattering (SRS). By using Hirota's bilinear method with a set of parametric conditions, the analytic one-, two- and three-soliton solutions of this model are obtained. According to those solutions, the higher-order soliton is shown to be compressed in the DSF for the pulse with width in the range of a few picoseconds or less. An appealing feature of the soliton-effect pulse compression is that, in contrast to the second-order soliton compression due to the combined effects of negative TOD and SRS, the third-order soliton can significantly enhance the soliton compression in the DSF with small values of the group-velocity dispersion (GVD) at the operating wavelength.     

Soliton interactions in dispersion-decreasing fibers with the exponential dispersion profile

In this paper, soliton interactions in dispersion-decreasing fibers with the exponential dispersion profile will be investigated. Analytic two-soliton solutions will be obtained with Hirota’s method. With the different dispersion profile of dispersion-decreasing fibers, the propagation characteristics of solitons will be exhibited, and some soliton properties will be adjusted. Results presented in this paper could be used in soliton control in the dispersion-decreasing fibers.     

光纤中光孤子传输演化及相互作用研究

基于非线性薛定谔方程,采用分步傅立叶方法模拟了基阶、二阶和三阶皮秒光孤子以及光孤子对在光纤中的传输演化.结果表明,在长距离传输过程中基阶孤子的幅度和脉宽基本不变,是进行光孤子通信的理想载体.高阶孤子的幅度和脉宽变化较大,并呈现一种周期性的变化;孤子对的传输与两个脉冲的初始相位和输入强度相关.考虑三阶色散的飞秒量级孤子在光纤中的传输将不再出现对称性和周期性,脉冲的中心位置将发生偏移,同时脉冲的波形也会发生扭曲.     

Dark solitons for a discrete variable-coefficient Ablowitz–Ladik equation for an electrical/optical system

Under investigation in this paper is a discrete variable-coefficient Ablowitz–Ladik equation, which has certain applications in the electrical and optical systems. Employing the Hirota method and symbolic computation, we obtain the dark one- and two-soliton solutions under a variable-coefficient constraint. Linear-, parabolic-, periodic- and s-shaped dark one solitons are observed: We find that the space-time-modulated inhomogeneous frequency shift only affects the velocity of the dark soliton, the coefficient of tunnel coupling between the sites only affects the amplitude of the dark soliton, the time-modulated effective gain/loss term has no effect on either the dark soliton’s velocity or amplitude, and the velocity of the dark soliton decreases as the lattice spacing increases with the amplitude unchanged. Via the asymptotic analysis, we prove that the interactions between the dark two solitons are elastic on the soliton solutions. Overtaking interactions between the linear- and parabolic-shaped dark two solitons, as well as parallel linear- and s-shaped dark two solitons are plotted.     

Soliton collisions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system for an erbium-doped optical fiber

In this paper, we construct soliton solutions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system, which can describe the ultrashort optical pulse propagation in a nonlinear, dispersive fiber doped with two-level resonant atoms. Under certain transformations and constraints, one- and two-soliton solutions are obtained via the Hirota method and symbolic computation, and soliton collisions are graphically presented and analyzed. One soliton is shown to maintain its amplitude and shape during the propagation. Soliton collision is elastic, while bright two-peak solitons and dark two-peak solitons are also observed. We discuss the influence of the coefficients for the group velocity, group-velocity dispersion (GVD), self-phase modulation, distribution of the dopant, and Stark shift on the soliton propagation and collision features, with those coefficients are set as some constants and functions, respectively. We find the group velocity and self-phase modulation can change the solitons’ amplitudes and widths, and the solitons become curved when the GVD and distribution of the dopant are chosen as some functions. When the Stark shift is chosen as a certain constant, the two peaks of bright two-peak solitons and dark two-peak solitons are not parallel. In addition, we observe the periodic collision of the two solitons.     

Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.     

Incoherently coupled gray–gray soliton pairs in biased photorefractive–photovoltaic crystals

We show that incoherently coupled gray–gray soliton pairs and multicomponent gray solitons are possible in biased photorefractive–photovoltaic crystals under steady-state conditions. These soliton pairs and multicomponent solitons can be obtained provided that the carrier beams share the same polarization, wavelength, and are incoherent with one another. When the bulk photovoltaic effect is neglectable, these soliton pairs and multicomponent solitons predict incoherently coupled gray–gray soliton pairs and multicomponent gray solitons for screening solitons. When the external field is absent, these soliton pairs and multicomponent solitons predict incoherently coupled gray–gray soliton pairs and multicomponent gray solitons for photovoltaic solitons.