Solitons In Optical Fibers Research Articles

Highly dispersive optical solitons in birefringent fibers with Lakshmanan–Porsezian–Daniel model having multiplicative white noise

Highly dispersive optical solitons in birefringent fibers with Lakshmanan–Porsezian–Daniel model having multiplicative white noise

Solitons in birefringent optical fibers and polarization mode dispersion

The early work on solitons in optical fibers was all done using single-mode fibers, and these fibers remain important for many applications. The modes in single-mode fibers are for all practical purposes weakly confined plane waves and have two polarizations. The basic equation that describes light evolution in these fibers is the coupled nonlinear Schrödinger equation. The soliton robustness hypothesis and its origins, which were the original motivation for studying these equations, is first described. Limits on robustness due to birefringent walkoff and the impact of random birefringence variations in stabilizing solitons is then described. Questions and controversies that arose shortly after the publication of these equations are addressed. These include their relationship to the Maker and Terhune coefficients, the requirements for the validity of the nonlinear Schrödinger equation and the impact of polarization mode dispersion, and the conditions under which the birefringence can be considered linear. It is a consequence of the fluctuation-dissipation theorem that the birefringence must be linear in any homogeneous, low-loss optical medium with a local dielectric response. Any ellipticity is associated with non-locality, as would occur for example in a twisted optical fiber. This important result, which is not well-known in the optics community, is reviewed.

Effective Control of Three Soliton Interactions for the High-Order Nonlinear Schrödinger Equation

We take the higher-order nonlinear Schrödinger equation as a mathematical model and employ the bilinear method to analytically study the evolution characteristics of femtosecond solitons in optical fibers under higher-order nonlinear effects and higher-order dispersion effects. The results show that the effects have a significant impact on the amplitude and interaction characteristics of optical solitons. The larger the higher-order nonlinear coefficient, the more intense the interaction between optical solitons, and the more unstable the transmission. At the same time, we discuss the influence of other free parameters on third-order soliton interactions. Effectively regulate the interaction of three optical solitons by controlling relevant parameters. These studies will lay a theoretical foundation for experiments and further practicality of optical soliton communications.

A prince for the sleeping beauty - NFT for soliton signal processing

The soliton, the eigen-solution of nonlinear Schrodinger equation (NLSE), has been investigated in many branches of physics. The first prediction of a soliton in optical fiber could be dated back to 1973. Since then, numerous theoretical and experimental works on solitons have been carried out, including soliton communication and soliton generation in fiber lasers. However, due to the constraints of hardware and digital signal processing methods, research on solitons have been stalled for decades. Recently, the nonlinear Fourier transform (NFT) has attracted significant attention in the field of optical fiber communications and soliton-based signal processing, which provides a powerful mathematical framework for analyzing and understanding the behavior of solitons in optical fibers, enabling the development of novel signal processing techniques. The NFT technique has brought the soliton back to life. It has been widely recognized that in nonlinear frequency domain, the nonlinear crosstalk resulting from the Kerr effect is practically negligible, and fiber nonlinearity damage caused by the Kerr effect can be accounted for as a linear transform factor. Moreover, NFT has been demonstrated for the analysis of laser radiation, highlighting its potential in characterizing ultrafast pulses in the nonlinear frequency domain. In this submission, we review the advancements of NFT concerning both in soliton communication and characterization, focusing on practical implementation aspects. With many practical implementation aspects still being open, our mini review is aimed to assist researchers in evaluating the potential, identifying challenges, and envisioning future directions in NFT-based signal processing technologies. And wake up the sleeping beauty – the soliton!

On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical fibers. The propagation of solitons in nonlinear optical fibers has garnered substantial interest due to its broad spectrum of applications, particularly in ultrafast signal routing systems and short light pulses for communications. This article focuses on investigating the impact of multiplicative noise on the solutions of this governing model. To achieve this, three distinct methods, namely the enhanced modified extended tanh expansion (METE) method, the generalized Kudryashov (GK) approach and the extended modified auxiliary equation mapping (EMAEM) method are employed to obtain a new variety of stochastic solutions. The perception of how noise intensity impacts the transmission of waves is a fundamental and critical issue in various fields. In the context of this study, an equation describes an exact wave pattern under the condition that s (representing noise intensity) equals zero. In such cases, the observed pattern remains undisturbed and matches the expected theoretical wave pattern. However, as the strength of noise s increases, the observed pattern begins to deviate from the ideal wave pattern and exhibits signs of damage or distortion. Furthermore, the stability analysis for the stochastic NLSE is performed, providing valuable insights into the behavior solutions as the strength of multiplicative noise increases. The validation of computational results through stability analysis enhances the confidence in the findings of the study. All the mathematical calculations, as well as graphical representations, have been meticulously achieved to present a comprehensive and detailed understanding of the impact of multiplicative on soliton propagation in nonlinear optical fibers.

(Invited) Spatiotemporal soliton stability in multimode fibers: A Hamiltonian approach

We introduce a Hamiltonian approach to study the stability of three-dimensional spatiotemporal solitons in graded-index multimode optical fibers. Nonlinear light bullet propagation in these fibers can be described by means of a Gross–Pitaevskii equation with a two-dimensional parabolic potential. We apply a variational approach, based on the Ritz optimization method, and compare its predictions with extensive numerical simulations. We analytically find that, in fibers with a pure Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low energies, in perfect agreement with numerical simulations. However, above a certain energy threshold, simulations reveal that the spatiotemporal solitons undergo wave collapse, which is not captured by the variational approach.

Dynamics and optical solitons in polarization-preserving fibers for the cubic–quartic complex Ginzburg–Landau equation with quadratic–cubic law nonlinearity

In this paper, the cubic–quartic complex Ginzburg–Landau (CGL) equation is investigated by using the trial function method. The traveling wave hypothesis is applied to convert the CGL equation to an ordinary differential equation (ODE), which is equivalent to a dynamic system. The qualitative behavior, bifurcation of the phase portraits for this system is studied. Furthermore, the chaotic motions in system involving external periodic perturbation are considered. Some new optical solitons, such as Jacobian elliptic function solutions, for CGL equation with quadratic–cubic law nonlinearity are constructed using the complete discrimination system for polynomial method. Moreover, two-dimensional graphs, three-dimensional, corresponding contour and density plots for some acquired solutions are depicted to carry out the physical properties of optical pulse propagation.

W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using the Jacobi elliptic function and the auxiliary equation methods. We obtain Jacobi elliptic function solutions as well as kink, bright, dark, and W-shaped solitons as a result. For specific values of the Jacobi elliptic modulus, we depict bright, dark, and W-shaped soliton solutions as suitable parameters of the structure. Using the auxiliary equation method gives the combined bright–bright and dark–dark optical solitons in optical fibers. One result emerges from this analysis: the potential parameters and free parameters of the method can be employed to degenerate W-shaped bright and dark solitons. The acquired results are general and can be used for many applications in nonlinear dynamic systems.

(Invited) Golden jubilee of solitons in optical fibers: For young scientists who love creative works

A memoir related to the discovery of optical soliton is presented with an intention of stimulating motivation of young scientists for creative works. Soliton is clearly a more desirable pulse for stable transmission of information in optical fiber medium. However, I would like to emphasize additional capability of a soliton pulse as information carrier without increasing thermodynamical entropy and invite the reader’s attention to possible relation to information processing in biological systems.

Bifurcations and traveling wave solitons in optical fibers with the nonlinear Kaup–Newell system

The main objective of this work is to study the dynamical behavior and traveling wave solution for the nonlinear Kaup–Newell system in optical fibers. Here, we have constructed periodic wave solutions, kink-shaped solitary solutions and anti-kink solitary solutions through the theory of planar dynamical system. In addition, some other traveling wave solutions of the nonlinear Kaup–Newell system are derived by means of the polynomial complete discriminant system method and symbolic computation, respectively. The trigonometric function solutions, solitary wave solutions, rational function solutions, the hyperbolic function solutions and the Jacobian function solutions are obtained. Finally, 3D-diagram and 2D-diagram of the nonlinear Kaup–Newell system are also plotted.

Dispersive optical solitons in birefringent fibers for stochastic Schrödinger–Hirota equation with parabolic law nonlinearity and spatiotemporal dispersion having multiplicative white noise

Object:The objective of this article is to study the stochastic Schrödinger–Hirota equation with parabolic law nonlinearity and spatiotemporal dispersion (STD) in birefringent fibers having multiplicative white noise in the Itô sense. Method:The Jacobi-elliptic expansion approach and the extended auxiliary equation algorithm are utilized. Result:The Jacobi-elliptic solutions, bright solitons, dark solitons, singular solitons and periodic solutions of the given system are introduced.

Bright, dark and kink exact soliton solutions for perturbed Gerdjikov–Ivanov equation with full nonlinearity

In this paper, the perturbed Gerdjikov-Ivanov equation (PGI) which describes the dynamics of the soliton in optical fiber is investigated. Using traveling wave transformation, the nonlinear PGI equation is transformed into two nonlinear ordinary differential equations. Consequently, these equations are reduced to a first -order ordinary differential equation that has a well-known exact solution. The exact solutions for the PGI equation will be introduced including Weierstrass, Jacobi elliptic, and hyperbolic functions. Various types of optical soliton solutions were raised such as bright, dark, and kink soliton solution. The obtained optical soliton solutions are presented graphically to clarify some of its physical parameters.

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.

Dispersive Optical Solitons with Differential Group Delay Having Multiplicative White Noise by Itô Calculus

The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The G′/G-expansion approach and the enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions with the white noise component reflected in the phase of the soliton.

Solitons in dual-core optical fibers with chromatic dispersion

Solitons in dual-core optical fibers with chromatic dispersion

Temperature Sensing Characteristics of Two Fundamental Solitons in a Glycerin-Filled Microstructured Optical Fiber

In this paper, the temperature sensing characteristics of two fundamental solitons in a glycerin-filled six-hole microstructured optical fiber (MOF) were systematically exploited through experiment and simulation. The six-hole MOF has a large duty cycle, which can increase the space to fill the temperature-sensitive material glycerin for improving the temperature sensing sensitivity. By detecting the center wavelength shift of 3dB bandwidth of two fundamental solitons at 1050 nm, 390 mW, a maximum sensitivity of -0.601 nm/ °C was obtained based on the first fundamental soliton and -0.598 nm/ °C was obtained based on the second. Simulation results combined with the experimental results showed that the higher the average pump power, the higher the temperature sensitivity, and the temperature sensitivity of the first was slightly higher than that of the second. The difference in sensing characteristics between the two fundamental solitons discovered in this study could provide a novel solution to solve the cross-sensitivity of dual-parameter sensing. To the best of our knowledge, this is the first research about utilizing two fundamental solitons for temperature sensing, which broadens the boundary of the nonlinear-based sensors, and has promising prospects in the fields of national defense security, disease monitoring, agriculture production, etc.

Pioneering experiments on optical solitons in fibres

Fifty years ago, the concept of solitons in optical fibres was proposed numerically by F. Tappert and A. Hasegawa from Bell Labs. Seven years later in 1980, experiments confirmed that dispersion and the Kerr nonlinearity could combine to yield a coherent ultrashort pulse able to propagate without distortion. The implications of this discovery go well beyond the sector of telecommunications as initially suggested, and solitons now play a major role in modern ultrafast nonlinear photonics.

Characterization of Multimode Soliton Self-Frequency Shift

Optical solitons in multimode fibers exhibit complex dynamics, and peculiar characteristics in terms of pulse duration and energy, which distinguish them from their single-mode counterparts. We propose a theory for Raman-induced soliton self-frequency shift in multimode fibers, that is compared against experimental data of 1-km multimode soliton propagation. Specific values of pulsewidth and energy are found, at which solitons show long-distance stability and better correspondence with the theory of self-frequency shift; those values depend on the input wavelength, but are not related to the duration of the input pulse. Raman delay is affected by a jitter, characterized by a Gaussian statistical distribution, whose standard deviation tends to stabilize to a constant value for increasing pulse energies.

Exact analytical soliton solutions of N-component coupled nonlinear Schrödinger equationswith arbitrary nonlinear parameters.

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not hold in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in N-component coupled nonlinear Schrödinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameter regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

Effect of near -symmetric potentials on nonlinear modes for higher-order generalized Ginzburg–Landau model

In this paper, we study the higher-order generalized Ginzburg–Landau model which contributes to describing the propagation of optical solitons in fibers. By means of the Hirota bilinear method, the analytical solutions are obtained and the effect of relevant parameters is analyzed. Modulated by the near parity-time-symmetric potentials, the nonlinear modes with 5% initial random noise are numerically simulated to possess stable evolution. Furthermore, the evolution of nonlinear modes is displayed through the adiabatical change of some parameters. The investigation of the present work is intended as a contribution to the work for the higher-order generalized Ginzburg–Landau model.