Optical Soliton Transmission Research Articles

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

Abstract When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schrödinger equation, we analytically explore the evolution of optical solitons in the presence of high-order nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.

A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation

In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem.

Optical soliton perturbation of the quintic Gerdjikov-Ivanov model

This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which models optical soliton transmission in the photonic crystal fibers and optical fibers. With the aid of the new Kudryashov scheme, we successful achieved the bright and dark solitons and we simulated their graphical presentation.

Data-driven prediction of spatial optical solitons in fractional diffraction

A quasi-residual physics-informed neural network (QR_PINN) with efficient residual-like blocks, was investigated based on classical physics-informed neural network to solve nonlinear fractional Schrödinger equation and analyze the transmission of spatial optical solitons in saturable nonlinear media with fractional diffraction. A comprehensive verification of stable transmission of various solitons under PT-symmetric potential was carried out using the QR_PINN. In addition, the transmission of spatial optical solitons was studied under simple real potential (stable transmission) and complex Scarf-II potential (unstable transmission). The results show that the QR_PINN can accurately reconstruct the transmission of spatial optical solitons under fractional diffraction. Meanwhile, as the complexity of the potential function increases, the prediction accuracy of the QR_PINN slightly decreases. These results provide a new approach for the application of deep learning in the nonlinear fractional Schrödinger equation.

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers, a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed. In this paper, in order to study the dynamic mechanism of femtosecond solitons in different media, we take the nonlinear Schrödinger equation considering higher-order effects as the theoretical model, discuss the propagation of solitons in single-mode fibers, and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons. The exact solution of the theoretical model is obtained through the bilinear method, and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied. The influence of various conditions on the transmission and interaction of optical solitons is explored. Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested. The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques

The current work uses a (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar (KMN) model to investigate optical soliton transmission across an optical fiber that maintains polarization. Three constructive techniques, namely, the extended power series solution, the new generalized method, and the extended sinh-Gordon expansion method are utilized to find the exact soliton solutions of this model. The invariant analysis has been performed on the (2+1) dimensional time fractional KMN model by using the conformal time fractional derivative. The symmetries obtained using conformal fractional derivative are compared with the symmetries obtained for integer order KMN model because symmetries using Riemann Liouville fractional derivative turned out to be trivial. The given system of fractional PDEs has been reduced by using differential invariants obtained from various linear combinations of vector fields associated with the infinitesimal generator of symmetry transformations. These reduced systems of equations are then investigated for their exact solutions.

Optical solitons in birefringent fibers with the generalized coupled space–time fractional non-linear Schrödinger equations

The nonlinear Schrödinger (NLS) equation is an ideal model for describing optical soliton transmission. This paper first introduces an integer-order generalized coupled NLS equation describing optical solitons in birefringence fibers. Secondly, the semi-inverse and fractional variational method is used to extend the integer‐order model to the space–time fractional order. Moreover, various nonlinear forms of fractional NLS equations are discussed, including the Kerr, power, parabolic, dual-power, and log law. The exact soliton solutions, such as bright, dark, and singular solitons, are given. Finally, the behavior of the solution is shown by three-dimensional figures with different fractional orders, which reveals the propagation characteristics of optical solitons in birefringence fibers described by the generalized coupled space–time fractional NLS equation.

On the investigation of optical soliton solutions of cubic–quartic Fokas–Lenells and Schrödinger–Hirota equations

Purpose:When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic Fokas–Lenells equation is also one of the recently developed equations, which has importance in the field of telecommunications regarding optical soliton transmission in the absence of chromatic dispersion. In this study, in order to examine the optical solitons, the Schrödinger–Hirota equation in the presence of the chromatic dispersion and the cubic–quartic Fokas–Lenells equation discarding the chromatic dispersion were investigated. For this intent, by obtaining certain soliton types using the unified Riccati equation expansion method (UREEM), optical soliton solutions were obtained for both models and graphical representations and comments were made. Methodology:By developing appropriate computer algorithms and applying UREEM in the following ways, symbolic calculation software was made and analytical optical soliton solutions were obtained. Findings:Through computer algebra software, we plotted the obtained results via 3D, 2D views and we also illustrated the investigation of wave behavior caused by parameter change on 2D graphics. Originality:Different soliton behavior under the parameters effect of the Schrödinger–Hirota equation having chromatic dispersion and the cubic–quartic Fokas-Lenells equation is investigated and the obtained results are reported.

Impact of external potential and non-isospectral functions on optical solitons and modulation instability in a cubic quintic nonlinear media

We investigate the non-isospectral generalized higher order NLS equation (GHNLS) with external potential which is unswervingly represents the ultrashort optical soliton transmission in inhomogeneous non-Kerr media with combined effects of external potentials. Lax pair is constructed for GHNLS equation and three soliton solutions obtained with the aid of Darboux transformation. For the first time, we include the effects of inhomogeneous non-isospectral parameters on soliton dynamics. Using two soliton solutions, interaction among double hump solitons and using three soliton solutions, interaction characteristics are studied analytically. Furthermore, in order to understand the stability mechanism, linear stability analysis also has been performed. Effects of non-isospectral parameters and variable coefficients on soliton dynamics are investigated graphically. The predicted results may be observed in the future experiments on nonlinear fiber optics and applications to femtosecond soliton management.

On the amplitude dynamics of solitons in waveguide systems with the generic Kerr nonlinearity coefficient and nonlinear gain-loss

We study the transmission of optical solitons in a nonlinear waveguide with the generic Kerr nonlinearity coefficient, the frequency dependent linear gain-loss, and the Ginzburg-Landau (GL) gain-loss profile. We first derive the expression for the collision-induced amplitude dynamics of two fast single solitons in the presence of weak cubic loss and weak quintic loss. This expression is then used to study the amplitude dynamics of solitons in multichannel optical waveguide systems. We show that the dynamics of soliton amplitudes in two-sequence transmission with the GL gain-loss profile are described by a Lotka-Volterra (LV) model. The stability analysis for the LV model is used to obtain the simple conditions on the physical parameters and to calculate the linear amplifier gain-loss for the transmission stabilization of the soliton sequences. The theoretical calculations are then confirmed by numerical simulations with the corresponding nonlinear Schrödinger (NLS) models. Furthermore, the optimal value of the Kerr nonlinearity coefficient for the robust transmission stabilization of the soliton sequences with the GL gain-loss profile is also proposed.

Coherent control of optical soliton interaction via electromagnetically induced transparency with spatial modulation

We propose a scheme to realize the coherent control of optical soliton propagation and interaction in a three level Λ type electromagnetically induced transparency system with the control field being spatially modulated. We show that the spatial perturbation of the control field has no influence on the linear propagation properties and self-phase modulation of the probe field but can produce an equivalent external potential to affect the nonlinear propagation of the probe field. For single soliton propagation, we realize the transmission and trapping of optical solitons via external potential. For double soliton interaction, we realize the coherent control of attractive and repulsion interactions of two optical solitons and design an XNOR logical operation. Finally, for the triple soliton incident case, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction but also for applications in all optical quantum information processing.

The unified technique for the nonlinear time-fractional model with the beta-derivative

This present study examines the closed-form wave results (CFWRs) of the nonlinear time-fractional model (NLTFM) with Atangana’s conformable fractional derivative (ACFD) through the unified process. ACFD and its properties are included. Then, by proposing the studied approach, the CFWRs of NLTFMs, displayed with the ACFD, are classified. This model defines the transmission of optical solitons in physics and applied mathematics and may be acute to the soliton waves. A lot of new CFWRs have been gained. For a few parameter values involved in the answer functions, physical behaviors on 3D graphics, contour graphics, and 2D graphics for the different values of αwere examined. We apply the unified process on the NLTFM model and provided thirty six CFWRs. Contrary, Y. Gurefe [40] studied the same model model to derive only five CFWRs. As results, our technique in the present paper provides abundant CFWRs. From the observation of the outcomes acquired, it is noticed that the studied process can generate essential effects in taking the closed-form wave results of NLTFMs containing ACFD.

The Physics Research of Optical Information Effect at Low Loss in Nonlinear Optical Fiber Transmission

Both nonlinear effects and dispersion are important factors that affect the transmission of optical pulses in optical fibres. In the anomalous dispersion region, the mutual balance of dispersion and nonlinear effects can achieve optical soliton transmission. Starting from the nonlinear Schrodinger equation of the optical pulse, under the condition of ignoring the dispersion, the nonlinear phase shift and frequency chirp of the Gaussian optical pulse under the nonlinear effect of self-phase modulation (SPM) are derived and simulated; the numerical simulation of the SPM the spectrum of Gaussian optical pulses with different maximum phase shifts without chirp and with positive chirp. The study found that the fusion loss of the fibre obtained by this algorithm is less than 0.11dB than that of the traditional single-mode fibre, and the additional bending loss caused by the wavelength range of 1460nm to 1625nm after winding 100 times on a 60mm cylinder is less than 0.02dB/km.

Controllable soliton transmission structures in birefringence inhomogeneous non-Kerr optical fiber

In this work, inhomogeneous coupled cubic–quintic nonlinear Schrödinger equation which can be imitated the transmission of optical solitons in inhomogeneous non-Kerr birefringence fiber is investigated. Through the Lax pair, by employing Darboux transformation method, soliton propagation in non-Kerr fiber is investigated analytically. Inhomogeneous functions and other related parameters are considered with different functions to analyze the impacts on the soliton transmission in real fiber systems. By studying the soliton propagation properties, we conclude that how to choose the control parameters to control the soliton propagation for various applications. Besides, inhomogeneous functions with control parameters are plays vital role in the evolutional characteristics such as period of oscillation, intensity, width, trajectory and phase shift. For graphical illustration of obtained novel results and to explore the behavior of various physical structures of solutions, Mathematica is employed with symbolic computation. Results obtained in this work is a potential candidate for controlling soliton structures with quintic effect in inhomogeneous optical communication which includes soliton control and soliton shaping in the non-Kerr media.

Periodic transmission and control of optical solitons in optical fibers

The control of the optical soliton is important for the stable transmission, and is studied in optical communication, mathematical physics and other fields. In this paper, analytical soliton solution for the fifth-order variable coefficient nonlinear Schrödinger equation, which can describe the transmission of femtosecond optical solitons in optical fiber, is obtained. Periodic transmission of optical solitons is observed, and the method for control the optical solitons is proposed. Results are useful for the stable transmission of optical solitons in optical fibers.

M-typed dark soliton generation in optical fibers

In this paper, the analytic dark soliton solution for the nonlinear Schrödinger equation with variable coefficients is investigated with the aid of the bilinear method. M-type dark solitons are demonstrated by analyzing relevant parameters in the obtained solution. The influence of parameters on dark soliton transmission is discussed, and the stable transmission of M-type dark solitons in optical fibers is realized. Results of this paper have certain theoretical significance for the stable transmission of optical solitons in actual optical fiber links.

Analytic study on the influences of higher-order effects on optical solitons in fiber laser

Requirements of the transmission rate, transmission distance and transmission capacity of optical communication systems are becoming higher and higher, and studies on the higher-order effects such as third order dispersion are inevitable for the development of systems. In this paper, we study the influences of higher-order effects on the optical soliton transmission. The high-order nonlinear Schrödinger equation, which can be used to describe the optical soliton transmission in the fiber laser, is investigated. Analytic soliton solution for this equation is obtained. The comprehensive analysis of the solution is made. Through choosing different values of the high-order effects, we discuss their influences on optical soliton transmission speed, period and pulse width. Results can be used to guide the generation and transmission of optical solitons in experiments.

Transmission characteristics of vortex beams in a sixfold photonic quasi-crystal fiber

In an optical fiber communication system, vortex beams have aroused great interest in the last several decades. Vortex beams possess many intriguing properties. For example, they have the ability to carry orbital angular momentum (OAM) which is mutually orthogonal. The OAM is a fundamental physical quantity of light which can be used as information carriers for transmission channel of optical fiber. Combined with the existing multiplexing techniques such as wavelength division multiplexing technique, advanced multilevel amplitude modulation formats, etc., the vortex beams provide an alternative to the increase of the transmission capacity and spectral efficiency of the optical fiber transmission system. Recently, long-length transmission of vortex-beam in optical fiber has been realized and there have also occurred some new designs of optical fiber on vortex beams, such as air-core ring shaped fiber, graded index vortex fiber, multi-ring fiber, and supermode fiber. Photonic crystal fiber (PCF) is flexible in design. Therefore, it is easy to regulate the transmission performance of PCF by adjusting the radius and the pitch of the air holes and so on. In this paper, we propose a newly designed sixfold photonic quasi-crystal fiber (SPQCF) to transmit vortex beams stably. Transmission characteristics of this newly designed fiber are simulated and calculated by using COMSOL multiphysics software. When the wavelength of the incident light is 1550 nm, the effective index difference between the vortex modes in a group is more than 10<sup>–4</sup> which is large enough to preclude the LP modes from being formed, and to transmit 7 vector modes (10 OAM modes). Changing the radius and pitch of the air holes, we can regulate the dispersion characteristic and confinement loss of the SPQCF flexibly. At 1550 nm, the confinement loss of the SPQCF maintains 10<sup>–8</sup>−10<sup>–7</sup> which is low enough to confine the vortex beams in the fiber core. When the incident light wavelength of HE<sub>21</sub> ranges from 1500 nm to 1800 nm (<i>r</i><sub>0</sub> = 1.9 μm), the dispersion coefficient of the SPQCF is between 63.51−65.42 ps·nm<sup>–1</sup>·km<sup>–1</sup> which tends to be flat. By changing <i>r</i><sub>0</sub>, the flat trend is adjusted to different wavelength range. This dispersion characteristic possesses great potential for the transmission of optical solitons. The effective mode area (HE<sub>21</sub>) is about 40 μm<sup>2</sup> and the nonlinear coefficient (HE<sub>21</sub>) is maintained on the order of 10<sup>–3</sup> between 1500−1600 nm. These features suppress the generation of nonlinear effect in the fiber and benefit the transmission of vortex beams. The stable transmission distance is longer than 1 km. In summary, we design a new type of PCF featuring quasi-crystal structure which has a ring shaped fiber core and supports the transmission of vortex beams stably.

Dispersion Management in Optical Soliton Transmission Systems: A Review

Dispersion Management in Optical Soliton Transmission Systems: A Review

Higher-order interaction-induced effects between strong dispersion-managed solitons with dissimilar powers

We address one of the major penalties associated with the transmission of optical solitons in fiber-optic networks: the intrachannel interactions between pulses in a single channel strong dispersion-managed transmission link. We calculate the interaction length between sets of two and three pulses as a function of the ratio of dissimilar peak powers of interacting solitons by means of a variational approach to the generalized nonlinear Schrodinger equation describing the evolution of optical soliton pulses. We find a maximum of this colliding length for specific values of pulse energies. The effect of higher-order perturbation terms, such as third-order dispersion, Raman scattering, and self-steepening, shows an enhancement of the interaction distance in a broad range of dispersion difference values. We conclude that the transmission characteristics of soliton trains may be improved by means of using specific values of unequal energies and taking into account higher-order correction terms.