Pulses In Optical Fibers Research Articles

Transition mechanisms of breather molecules in the Hirota equation

The transition dynamics of the breather molecules are investigated for the Hirota equation, which describes the propagation of ultrashort optical pulses in optical fibers. Based on the two-breather solution, the breather molecules and breather complexes are obtained. The half-transition mechanism of the breather molecules is unveiled and a series of the transformed wave molecules and the corresponding complexes are generated. The superposition mechanisms of breather molecules and transformed wave molecules are explained through the nonlinear superposition principle. It should be noted that the full transition of the breather molecules does not exist in the Hirota equation. The effects of the phase parameters on the transformed wave molecules are discussed. Besides, the collisions for breather molecules and transformed wave molecules are investigated. The distances between atoms in the molecules and the shapes of the transformed waves are changed after the collisions. By means of the phase shift analysis, the nature of shape-changed collisions is shed light on. Finally, the stability of the propagation of molecule waves under small perturbations is performed.

Nonlinear dynamics of short light pulse in birefringent optical fiber

This paper is devoted to the investigation of phase portraits analysis of a vector short pulse equation describing propagation of short light pulses in birefringent optical fiber. Indeed, we introduce transformations that are helpful in decoupling this equation and following the fourth order runge–kutta scheme, we construct phase portraits of the system under interest. The analysis of the phase portrait shows that the system possesses soliton solutions and periodic solutions. We derive Hamiltonian like energy of the system and show that the system is conservative. By double integration, we construct some expressions of the solutions to the system by direct integration which differ from the solutions previously obtained in the literature by the fact that they are difficult to be expressed explicitly as functions of the phase of the wave.

Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in optical fibers

In this paper, the bifurcation, stationary optical solitons and exact solutions in optical fiber propagation are studied. The propagation model is described by a generalized nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index. First, the equation is transformed into a second-order nonlinear ordinary differential equation by an appropriate transformation. Then, the bifurcation of the phase diagram of the obtained ordinary differential equation is established using planar dynamic system theory, and the types of optical solitons and exact solutions are determined. What is more, the stationary optical solitons and exact solutions are obtained by the polynomial complete discriminant system, and are demonstrated in 3D and 2D graphics by using the symbolic computation software Maple. Finally, the obtained stationary optical solitons and exact solutions include the Jacobi elliptic function solution, hyperbolic function solution, rational function solution, trigonometric function solution and exponential function solution. Moreover, the results provide a method to further study stationary optical solitons and exact solutions of propagation pulses in optical fibers.

Optical wave propagation to a nonlinear phenomenon with pulses in optical fiber

Optical wave propagation to a nonlinear phenomenon with pulses in optical fiber

A hybrid analytical and numerical analysis of ultra-short pulse phase shifts

This study uses a simplified third-order generalized nonlinear Schrödinger equation (3-order GNLSE) to investigate the soliton phase shift. Most of the time, this model is used to explain what happens to ultrashort pulses in quantum environments and optical fibers. On the other hand, it could be used as a wave model to show how materials work acoustically. From a quantum-mechanical state function, it might be possible to figure out how atoms and transistors move and act in the real world. The novel the direct algebraic (NDA) method is employed to solve this model through constraining some novel solitary wave solutions. All assessed solutions are put through their paces using two state-of-the-art numeric methods (trigonometric quantic and cubic B–spline). The computational solutions meet all the conditions for creating numerical systems. Two–, three–, and contour diagrams show how analytical and numerical answers match up with the solutions. The comparison between our results and recently studies on this model, shows how our solutions are novel and accurate.

Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers

In this paper, conformable Fokas–Lenells model is under consideration, this model is usually used to simulate the propagation model of femtosecond pulses in single-mode optical fibers. Firstly, the traveling wave transformation is applied to convert the conformable Fokas–Lenells model into two-dimensional planar dynamic system. Secondly, the bifurcation of the dynamics system of the conformable Fokas–Lenells model is discussed by using the theory of the plane dynamics system. What is more, two-dimensional phase portraits, three-dimensional phase portraits and Poincaré sections of the dynamics system with perturbation term are drawn with the help of the Maple mathematical software. Finally, the optical soliton solutions of the conformable Fokas–Lenells model are construct by using the analysis method of planar dynamical system.

Bright and dark solitons for the fifth-order nonlinear Schrödinger equation with variable coefficients

In this work, a fifth-order nonlinear Schrödinger equation with variable coefficients is investigated, which represents the diffusion of ultrashort pulses in incompatible optical fibers. With the aid of two direct functions, some non-traveling wave bright and dark soliton solutions are obtained. Via the G′/G-expansion method, the non-traveling wave hyperbolic-type and trigonometric-type solutions are studied. Finally, we show the dynamic properties and characteristics of these derived results by using some three-dimensional figures and contour figures.

Accurate computational simulations of perturbed Chen–Lee–Liu equation

This research aims to look into alternative unique solitary wave solutions to the perturbed Chen–Lee–Liu (CLL) equation to explain the kinetic and physical aspects of an optical fiber pulse. The perturbed CLL equation is one of the most well-known icon models derived from the well-known Schrödinger equation. Two different analytical methodologies are used to develop novel solitary wave solutions. These responses are then thoroughly evaluated using a well-known numerical approach to establish their underlying veracity. Various graphics are used to show the pulse wave analysis process and outcomes in an optical cable. We show how scientifically unique the study is by explaining the comparison figure that was made from our data and has been used in many recent research studies

Nonlinear Propagation Representation and Control for Ultrashort Pulse in Optical Fibers Based on Deep Learning

Nonlinear Propagation Representation and Control for Ultrashort Pulse in Optical Fibers Based on Deep Learning

Computational Traveling Wave Solutions of the Nonlinear Rangwala–Rao Model Arising in Electric Field

The direct influence of the integrability requirement on mixed derivative nonlinear Schrödinger equations is investigated in this paper. A. Rangwala mathematically formalized these effects in 1990 and dubbed this form the Rangwala–Rao (RR) equation. Our research focuses on innovative soliton wave solutions and their interactions in order to provide a clear picture of the slowly evolving envelope of the electric field and pulse propagation in optical fibers in terms of the dispersion effect. For creating unique solitary wave solutions to the investigated model, three contemporary computational strategies (extended direct (ExD) method, improved F–expansion (ImFE) method, and modified Kudryashov (MKud) method) are employed. These solutions are numerically computed to demonstrate the dynamical behavior of optical fiber pulse propagation. The originality of the paper’s findings is proved by comparing our results to previously published results.

Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

The first- and second-order localized waves for a variable-coefficient coupled Hirota equation describe the vector optical pulses in inhomogeneous optical fiber and are investigated via generalized Darboux transformation in this work. Based on the equation’s Lax pair and seed solutions, the localized wave solutions are calculated, and the dynamics of the obtained localized waves are shown and analyzed through numerical simulation. A series of novel dynamical evolution plots illustrating the interaction between the rogue waves and dark-bright solitons or breathers are provided. It is found that functions have an influence on the propagation of shape, period, and velocity of the localized waves. The presented results contribute to enriching the dynamics of localized waves in inhomogeneous optical fiber.

Explicit solutions from Darboux transformation for the two-component nonlocal Hirota and Maxwell–Bloch system

Based on the two-component Hirota and Maxwell–Bloch (H-MB) system, which describes the propagation of ultra-short pulses in erbium-doped nonlinear optical fibers, we derive two kinds of two-component nonlocal H-MB (NH-MB) systems by choosing suitable symmetries, namely [Formula: see text]-symmetric two-component NH-MB system and reverse space-time two-component NH-MB system. Then the explicit solutions of these two systems are obtained by the Darboux transformation.

Propagation Pulses in Optical Fiber Modeled by the Kudryashov Equation

Kudryashov equation describes the propagation pulses in an optical fiber. By using the trial equation method and complete discrimination system for the polynomial method, the classification of all envelope patterns of the Kudryashov equation is obtained, including solitary wave solutions, double periodic solutions, triangular function solutions, and rational function solutions. In particular, the conditions for the existence of each mode are given, and images of the modes are obtained according to the conditions.

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.

On the dynamics of soliton waves in a generalized nonlinear Schrödinger equation

The main objective of the present paper is to investigate the dynamics of soliton waves in a generalized nonlinear Schrödinger (GNLS) equation. To achieve such a goal, the real and imaginary portions of the GNLS equation are first extracted using a complex wave transformation. Solitons and Jacobi elliptic structures of the governing model, describing the propagation of femtosecond pulses in nonlinear optical fibers, are then constructed through applying the modified Jacobi elliptic expansion method (MJEEM). In the end, by employing a series of 2 and 3D-dimensional numerical representations, it is exposed that the width of bright and dark solitons respectively decreases and increases, while the amplitude of both waves decreases with the increase of nonlinear parameters.

Exact Fractional Solution by Nucci’s Reduction Approach and New Analytical Propagating Optical Soliton Structures in Fiber-Optics

This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wave profiles. The method covers thirty-seven solitonic wave profiles, including approximately all soliton families, in an efficient and generic manner. New solitonic wave patterns are obtained, including a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, trigonometric solution, shock solution, mixed shock singular solution, mixed singular solution, complex solitary shock solution, singular solution and shock wave solutions. The exact fractional solution is obtained using Nucci’s reduction approach. The impact of the fractional order parameter on the solution is considered using both mathematical expressions and graphical visualization. The fractional order parameter is responsible for controlling the singularity of the solution which is graphically displayed. A sensitivity analysis was used to predict the sensitivity of equations with respect to initial conditions. To demonstrate the pulse propagation characteristics, while taking suitable values for the parameters involved, 2-D, 3-D, and contour graphics of the outcomes achieved are presented. The influence of the fractional order ζ is shown graphically. A periodic-singular wave with lower amplitude and dark-singular behaviour is inferred from the graphical behaviour of the trigonometric function solution H1 and the rational function solution H34 from the obtained solutions, respectively.

Stimulated Brillouin Scattering Threshold in Presence of Modulation Instability for Optical Pulse in Long Optical Fiber

A theoretical and experimental study on the stimulated Brillouin scattering (SBS) threshold for optical pulse in the presence of modulation instability (MI) in long optical fiber is presented. The effects of MI on the SBS gain and threshold are analyzed based on the coupled-wave equation. An analytic expression is obtained to calculate the SBS threshold in the presence of MI. Numerical simulation is conducted to study the effects of the repetition rate and amplified spontaneous emission (ASE) noise on the SBS threshold for optical pulses. An experiment is conducted, and the results agree well with the theoretical analysis. The results clearly reveal how MI affects the Brillouin gain and SBS threshold of optical pulses in long optical fiber. The SBS threshold is affected by the ASE noise level and the repetition rate of the optical pulse. The study is helpful for the power evaluation of interferometric fiber sensing systems and optical power transmission systems.

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

Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers

The main purpose of this paper is to discuss the optical soliton solutions and phase portraits of the coupled Sasa–Satsuma model in nonlinear optics. This model is usually used to describe the propagation of femtosecond pulses in optical fibers. By using traveling wave transformation, the coupled Sasa–Satsuma model is simplified into the coupled nonlinear ordinary differential equations. After that, the coupled nonlinear ordinary differential equations are transformed into two-dimensional planar dynamic system with the Hamiltonian system. According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. What is more, some very important optical soliton solutions are also constructed. In order to explain the propagation of optical solitons, three-dimensional diagrams, two-dimensional diagrams and the contour plots of the obtained solutions are drawn by using Maple software.

Chirped localized pulses in a highly nonlinear optical fiber with quintic non-Kerr nonlinearities

We study the existence and propagation properties of chirped localized pulses in a highly nonlinear fiber medium exhibiting self-steepening, self-frequency shift, and quintic non-Kerr nonlinearities. Pulse evolution in such fiber system is governed by a higher-order nonlinear Schrödinger equation incorporating the derivative Kerr and non-Kerr nonlinear terms. We show that bright, dark and kink type solitary waves exist in the presence of all physical processes. A special ansatz is introduced to analyze the existence of solitary waves on a continuous-wave background in the optical fiber medium. It is shown that the obtained localized pulses exhibit a nonlinear chirp which has a quadratic dependence on light intensity. We also find that the magnitude of the associated frequency chirp can be controlled effectively by varying the parameters of self-steepening, self-frequency shift, and derivative non-Kerr nonlinearity effects. The restrictions on the optical fiber parameters are also extracted for the existence of these nonlinearly chirped solitary waves. Results in this study may be useful for experimental realization of shape-preserved pulses in optical fibers and further understanding of their optical transmission properties.