Ultrashort Pulses In Optical Fibers Research Articles

Data-driven solutions and parameter discovery of the extended higher-order nonlinear Schrödinger equation in optical fibers

In this paper, we investigate an extended higher-order nonlinear Schrödinger equation that includes third-order and fourth-order dispersion terms. By considering higher-order effects, the equation can more accurately simulate and predict the propagation behavior of ultrashort pulses in optical fibers, e.g., pulse splitting, compression and stability. In the optical fiber sensors, the sensitivity and resolution of the sensor can be improved by utilizing nonlinear effects. The analysis of the extended higher-order nonlinear Schrödinger equation helps to understand how nonlinear effects affect the sensing signal, thereby designing more accurate sensors. Specific coefficients of each term in the equation are studied for different scenarios, such as optical fiber design and signal propagation in optical communications. Under certain conditions, the extended higher-order nonlinear Schrödinger equation can be degenerated into the Hirota equation or the Lakshmanan–Porsezian–Daniel equation. With the development of numerical algorithms, the utilization of deep neural networks for solving equations has become increasingly attractive. With given initial conditions and boundary conditions, the physical information is embedded into the neural network in the form of loss functions. We efficiently derive numerical solutions to the extended equation for one-soliton, two-soliton and rogue-wave cases by training weights and biases in physics-informed neural networks. Compared with traditional numerical methods, physics-informed neural networks yield lower prediction errors with less data volume, thus will reduce the cost and time consumptions for data sampling in practical engineering. Furthermore, we solve the inverse problem associated with the extended equation. This approach is critical for extracting fundamental parameters of optical systems from observable data, thereby deepening our understanding of complex optical behavior and helping to improve the performance of optical fiber communication technologies.

NEW OPTICAL SOLITONS FOR NONLINEAR FRACTIONAL SCHRÖDINGER EQUATION VIA DIFFERENT ANALYTICAL APPROACHES

The primary aim of this work is to investigate the nonlinear fractional Schrödinger equation, which is adopted to describe the ultra-short pulses in optical fibers. A variety of new soliton solutions and periodic solutions are constructed by implementing three efficient mathematical approaches, namely, the improved fractional [Formula: see text]-expansion method, fractional Bernoulli ([Formula: see text]/[Formula: see text]-expansion method and fractional cosine-sine method. Moreover, the dynamic properties of these obtained solutions are discussed by plotting some 3D and 2D figures. The employed three analytical methods can be widely adopted to solve different types of fractional evolution equations.

Unveiling optical solitons: Solving two forms of nonlinear Schrödinger equations with unified solver method

The motivation of this work is to attain optical solitons of the generalized third-order nonlinear Schrödinger equation (NLSE) and the integrable (2+1)-dimensional coupled nonlinear Schrödinger equation (CNLSE). These models have various applications, including ultra-short pulses in optical fibers, making them noteworthy in applied sciences and mathematical physics. To extract the optical solitons of these models, the unified solver method (USM) is applied. The USM is a mathematically modified version of the Riccati equation and its related solutions. A unique advantage of this method is the elimination of the need for a balancing constant, simplifying the analytical process and enhancing the utility of these soliton solutions in practical applications. The obtained solutions include dark, singular, and periodic singular soliton solutions, enriching the understanding of optical solitons. In addition to the analytical solutions, the article also includes graphical representations to visually depict the obtained soliton solutions. These visualizations enhance the understanding and provide a clear picture of how the solitons behave in the given system.

Nonlinear autoregressive with external input neural network for predicting the nonlinear dynamics of supercontinuum generation in optical fibers

Full characterization of the propagation dynamics of ultra-short pulses in optical fibers is of fundamental importance in designing optical devices for several applications in the nonlinear optics field. Such applications range from basic descriptions of the light–matter dynamics to Bose–Einstein condensates, plasma physics, hydrodynamics, high-resolution imaging, and remote sensing, among many others. Nevertheless, ultra-short pulse propagation is a highly nonlinear process, so correctly describing all temporal and spectral features of these pulses is a big challenge, consuming extensive computational resources. Looking for simple solutions to this problem, we present in this paper, for the first time, to the best of our knowledge, a nonlinear autoregressive with external input neural network (NARXNET) capable of predicting the nonlinear dynamics of supercontinuum generation in optical fibers. The NARXNET structure allows low prediction error, fast training as short as 1.45 min, satisfactory generalization ability, and low computational resources for the training and testing stages.

Solitons solutions to the high-order dispersive cubic–quintic Schrödinger equation in optical fibers

In this paper, solitons solutions of higher-order dispersive cubic–quintic Schrödinger equationincluding third-order as well as fourth-order derivatives with respect to time, that describes the dynamics of ultrashort pulses in optical fibers are investigated in detail. In this respect,a solution procedure in the locality of applied mathematics called the hyperbolic function method is appliedusing multi-linear variable separation approach (MLVSA). As an outcome, a bunch of soliton solutions isderived in conjunction with plotting dark and periodic wave solutions. The credibility of the results is examined by setting each solution back into its governing equation. Through portraits, different forms of wave solutions are depicted. Moreover, the restrictions on the parameters are also given for the existence of the obtained solutions.

A variety of solitons and other wave solutions of a nonlinear Schrödinger model relating to ultra-short pulses in optical fibers

A variety of solitons and other wave solutions of a nonlinear Schrödinger model relating to ultra-short pulses in optical fibers

New fascination of solitons and other wave solutions of a nonlinear model depicting ultra-short pulses in optical fibers

New fascination of solitons and other wave solutions of a nonlinear model depicting ultra-short pulses in optical fibers

Novel wave solutions to a generalized third-order nonlinear Schrödinger’s equation

Schrödinger’s equation and its variants play an important role in describing many well-known problems in disciplines such as mathematics and physics. Our main concern in this paper is to investigate some novel analytical solutions to a third-order generalized nonlinear Schrödinger’s equation. This equation is used to model the motion of ultra-short pulses in optical fibers. The model also includes several arbitrary parameters that introduce several well-known nonlinear models as its special case. The main achievements of the paper are determined via two efficient methodologies based upon the modified generalized exponential rational function method and a logarithmic transformation approach. In order to better examine the results, three-dimensional diagrams obtained from analytical answers have been attached to the article. These diagrams are useful tools that facilitate a better description of the capabilities of this model. One of the advantages of the method used in this research over some other techniques is that it is possible to adapt the implemented algorithm to solve other complex new problems.

Feed-forward neural network as nonlinear dynamics integrator for supercontinuum generation.

The nonlinear propagation of ultrashort pulses in optical fibers depends sensitively on the input pulse and fiber parameters. As a result, the optimization of propagation for specific applications generally requires time-consuming simulations based on the sequential integration of the generalized nonlinear Schrödinger equation (GNLSE). Here, we train a feed-forward neural network to learn the differential propagation dynamics of the GNLSE, allowing emulation of direct numerical integration of fiber propagation, and particularly the highly complex case of supercontinuum generation. Comparison with a recurrent neural network shows that the feed-forward approach yields faster training and computation, and reduced memory requirements. The approach is generic and can be extended to other physical systems.

Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation

In this paper, we looked into the generalized third-order nonlinear Schrödinger equation (NLSE). This model has a wide range of applications, including ultra-short pulses in optical fibers. Different analytical approaches such as the Lie symmetry analysis, new extended generalized Kudryashov method and generalized new Kudryashov method are used to secure the optical solutions. Dark, bright, singular and combo bright-singular soliton solutions are among the optical soliton solutions obtained.

Propagation of ultra-short dark soliton pulses in an isotropic medium under the influence of third-order linear dispersion and nonlinearity dispersion

The nonlinear Schrödinger equation (NSE) is well-known and is one of the most commonly used in the field of nonlinear optics. Pulses with picosecond and femtosecond duration are very well described by the NSE, but it does not work for attosecond and phase-modulated femtosecond laser pulses, where the spectral width of the pulse is of the order of the carrying frequency. In such cases, it is more convenient to use the general nonlinear amplitude equation (NAE). During the propagation of ultra-short pulses in optical fibers, the effects of the third-order linear dispersion and dispersion of nonlinearity become significant and have to be taken into account. We expanded the NAE by including these two effects. In this paper, we present an analytical study on the influence of third-order linear dispersion and dispersion of nonlinearity on the evolution of ultra-short optical pulses and on the possibility of dark soliton formation under such conditions in a medium with normal dispersion.

The weakly nonlinear wave propagation of the generalized third-order nonlinear Schrödinger equation and its applications

We investigate the generalized nonlinear Schrödinger equation (NLSE) of third order analytically, that accept the single-parameter family of one hump embedded soliton. This equation has been utilized to model ultra-short pulses in optical fibers. The physical phenomenon of this dynamical equation is revealed through the exact solutions for example solitons, elliptic function solutions, etc. These types of novel explicit solutions are constructed of generalized third-order NLSE via the modified extended direct algebraic method (MEDAM), that have key applications in engineering and applied sciences. Movements of some achieved solutions are described graphically, that assists to know the physical interpretation of this equation. Furthermore, the configuration conditions of dark-bright solitons are also presented. The influence of this scheme is shown in computational work and achieved results.

Dynamic behaviors of optical solitons for Fokas-Lenells equation in optical fiber

The Fokas-Lenells (FL) equation describes the propagation of ultra-short pulse in optical fiber. In this paper, optical soliton solutions are obtained through Hirota bilinear method, and the asymptotic behavior analysis and graphical simulation are given to reveal the propagation and dynamical behavior. It's worth noting that novel dynamic characteristics have been found with different choices of the wave numbers in the two-soliton and three-soliton solutions, which present different dynamical behavior from the general case. Moreover, some figures are given to better illustrate the dynamic characteristics.

Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation

In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

Propagation of W-shaped, M-shaped and other exotic optical solitons in the perturbed Fokas–Lenells equation

This work investigates the perturbed Fokas–Lenells equation form which describes the propagation of ultrashort pulses in optical fibers. Based on the complex envelope ansatz method, the study reveals that waves which propagate in this medium are solitary waves type precisely M-shaped and W-shaped solitons. The study of wave propagation and their robustness that are analytically obtained are aligned to numerical study. The profiles have been perturbed with 1% noise level. From this, it appears that these profiles propagate by maintaining their shapes in spite of the disruption; this proves their stability. We have also investigated the impact of 30% noise level on the solutions stability. It reveals that, these solutions have extremely strong capacity of resisting disturbance with respect to higher initial noise level. We have also discussed the impact of the perturbed parameters such as inter-modal dispersion, self-steepening effect and Raman effect. Then, we draw the conclusion that the inter-modal dispersion influences the propagation velocity of the soliton. The self-steepening effect distorts the pulse such a way that it becomes asymmetric. The Raman effect leads to an unstable behavior for relatively small values.

Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

In this work, we consider a nonlinear Schrodinger equation with stimulated Raman scattering and quintic nonlinearity, which works as a model for the propagation of ultrashort pulse in optical fiber and also corresponds to one-dimensional anisotropic Heisenberg ferromagnetic spin chain. Introducing a Galilean transformation, we transform the model into a fifth-order complex modified KdV equation, the integrability of which has been considered in the AKNS technique framework. The N-fold Darboux transformation for the model is derived in terms of the gauge transformation of the associated $$3 \times 3$$ matrix spectral problem. As applications, abundant intriguing types of nonlinear waves are obtained in zero and nonzero boundary conditions. The dynamical evolution of these nonlinear waves can be well controlled under stimulated Raman scattering and quintic nonlinearity management. Beside that, we also find some novel and interesting conversion phenomena, where a high-order term plays a pivotal role.

Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation

The present paper explores the generalized third-order nonlinear Schrödinger (GTONLS) equation which is used to model ultra-short pulses in optical fibers. The analysis is carried out systematically by adopting a complex transformation for reducing the GTONLS equation to a couple of nonlinear ordinary differential equations (NLODEs) with specific conditions such that the resulting NLODEs can be solved through the use of well-designed techniques such as the expa -function and unified methods. As an outcome, different wave structures including dark and bright solitons as well as Jacobi elliptic solutions to the model are formally constructed.

Invariant solutions of the Eckhaus-Kundu model with nonlinear dispersion and non-Kerr nonlinearities

This paper will study Eckhaus-Kundu equation from the perspective of Lie symmetry analysis. We will systematically construct similarity reductions in order to perform the explicit invariant solutions of this version of the nonlinear Schrödinger equation with nonlinear dispersion and cubic-quintic nonlinearities, describing the propagation of ultrashort pulses in optical fibers. Some new wave solutions with real and imaginary parts of trigonometric type or of a compound of trigonometric and hyperbolic types will be pointed out.

Dynamics of the breathers and rogue waves in the higher-order nonlinear Schrödinger equation

In this paper, the higher-order nonlinear Schrödinger equation, which can be widely used to describe the dynamics of the ultrashort pulses in optical fibers, is under investigation. By means of the modified Darboux transformation, the hierarchies of breather wave and rogue wave solutions are generated from the trivial solution. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that the extreme behavior of the breather wave yields the rogue wave for the higher-order nonlinear Schrödinger equation.

Numerical methods for accurate description of ultrashort pulses in optical fibers

We consider a one-dimensional first-order nonlinear wave equation, the so-called forward Maxwell equation (FME), which applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity and spatial homogeneity in the propagation direction. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.