Pulse Propagation In Optical Fibers Research Articles

Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect

In this study, the integrability conditions on mixed derivative nonlinear Schrödinger equations are the focus of this work. A. Rangwala mathematically defined these effects and dubbed this form the Rangwala–Rao equation ([Formula: see text]) in 1990. Using innovative soliton wave solutions and their interactions, we hope to better understand how dispersion affects the electric field and pulse propagation in optical fibers. Generalized Khater (GKhat.) provides unique solitary wave solutions to the [Formula: see text] problem. The pulses’ dynamical behavior through optical fibers is seen in these numerical simulations. The originality of the paper’s conclusions may be seen by contrasting our findings with those of other researchers.

Self-phase modulation via similariton solutions of the perturbed NLSE Modulation instability and induced self-steepening

The perturbed nonlinear Schrodinger equation (PNLSE) describes the pulse propagation in optical fibers, which results from the interaction of the higher-order dispersion effect, self-steepening (SS) and self-phase modulation (SPM). The challenge between these aforementioned phenomena may lead to a dominant one among them. It is worth noticing that the study of modulation instability (MI) leads to the inspection of dominant phenomena (DPh). Indeed, the MI triggers when the coefficient of DPh exceeds a critical value and it may occur that the interaction leads to wave compression. The PNLSE is currently studied in the literature, mainly on finding traveling wave solutions. Here, we are concerned with analyzing the similarity solutions of the PNLSE. The exact solutions are obtained via introducing similarity transformations and by using the extended unified method. The solutions are evaluated numerically and they are shown graphically. It is observed that the intensity of the pulses exhibits self steepening which progresses to shock soliton in ultra-short time (or near t = 0). Also, it is found that the real part of the solution exhibits self-phase modulation in time. The study of (MI) determines the critical value for the coefficients of SS, SPM, or high dispersivity to occur.

Physics-based deep learning for modeling nonlinear pulse propagation in optical fibers.

A physics-based deep learning (DL) method termed Phynet is proposed for modeling the nonlinear pulse propagation in optical fibers totally independent of the ground truth. The presented Phynet is a combination of a handcrafted neural network and the nonlinear Schrödinger physics model. In particular, Phynet is optimized through physics loss generated by the interaction between the network and the physical model rather than the supervised loss. The inverse pulse propagation problem is leveraged to exemplify the performance of Phynet when in comparison to the typical DL method under the same structure and datasets. The results demonstrate that Phynet is able to precisely restore the initial pulse profiles with varied initial widths and powers, while revealing a similar prediction accuracy compared with the typical DL method. The proposed Phynet method can be expected to break the severe bottleneck of the traditional DL method in terms of relying on abundant labeled data during the training phase, which thus brings new insight for modeling and predicting the nonlinear dynamics of the fibers.

Conservation laws of the complex short pulse equation and coupled complex short pulse equations

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated.

Extraction of some optical solutions to the (2+1)-dimensional Kundu–Mukherjee–Naskar equation by two efficient approaches

The Kundu–Mukherjee–Naskar (KMN) model is considered for describing the pulse propagation in optical fibres and communication systems. Two efficient approaches via the exp (−φ(ξ))-expansion and the improved F-expansion schemes are applied to the KMN model and in order to convert the KMN equation to an ODE, we test the complex wave conversions and present some optical soliton solutions, which are expressed in terms of hyperbolic, rational and trigonometric functions. We create three dimensional and two-dimensional images to explain the underlying optical wave properties of the KMN equation and compare our solutions with the ones in the literature. Our example shows that the two adopted methods provide an efficient mathematical tool for constructing new optical wave solutions to nonlinear partial differential equations arising in fibre optic communication systems.

Continuous limit and location-manageable discrete loop rogue wave solutions for the semi-discrete complex short pulse equation

This paper focuses on the semi-discrete complex short pulse equation which may describe the ultra-short pulse propagation in optical fiber. First, we study the continuous limit of the semi-discrete complex short pulse equation and establish a certain connection with a continuous complex short pulse equation. Then the discrete generalized (p,N−p)-fold Darboux transformation is constructed to generate three kinds of location-manageable discrete localized wave solutions including loop rogue wave, loop periodic wave, and their mixed collision loop structures. With the help of the hodograph transformation, we find a class of implicit solutions of semi-discrete complex short pulse equation, and some specific parameters are added to the analytical expressions so that we can theoretically manage these loop structures where we want them to appear. These unique structures may help researchers better grasp the characteristics of location-manageable loop localized wave solutions and explain many physical phenomena in nonlinear optics.

The closed-form soliton solutions of the time-fraction Phi-four and (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff model using the recent approach

The Phi-four (PF) model is a variation of the familiar Klein–Fock–Gordon​ (KFG) model. Quantum effects, ultra-short pulse propagation in optical fibers, character of de-Broglie waves, wave-particle duality, composite particles of spineless relativistic, etc. are investigated through the PF model. The interface of Riemann waves in two spatial dimensions is explained by the Calogero–Bogoyavlenskii–Schiff (CBS) model. Many physical phenomena such as, the magneto-sound waves in plasmas, tsunami and tidal in rivers, and the internal waves in oceans can be describe through the Riemann wave. This article investigates the unique and wide-ranging analytic soliton solutions to the above-stated models in the sense of the fractional conformable derivative by using the auxiliary equation technique in terms of exponential, trigonometric, hyperbolic, and rational functions. To analyze the underlying wave structures and to examine the active behavior of the obtained solutions, three-dimensional (3D) and contour graphs are plotted using the Wolfram Mathematica program. The attained solutions demonstrate that the method is compatible, effective, and scientifically efficient.

Optimal system of Lie subalgebra for symmetry reductions, group invariant solutions and exact solutions to the coupled Hirota–Maccari system driving pulse propagation in optical fiber

In this paper, Lie symmetry analysis has been proposed by utilizing the Lie group of continuous point transformation for obtaining the new exact soliton solutions of the (2+1)-dimensional Hirota–Maccari system. Lie infinitesimals and possible geometric vector fields are obtained by applying the third-order prolongation on this system. Also, their commutative product and adjoint relations have been presented in Tables 1 and 2. By considering the resulting symmetries, one-dimensional optimal system of Lie subalgebra is obtained. Meanwhile, the Hirota–Maccari system is reduced to a system of ordinary differential equations with the help of optimal subalgebras. Furthermore, the simplest equation method has been used to obtain the abundant exact soliton solutions of the reduced system. At last, conservation laws of Hirota–Maccari system have been extracted by utilizing the generalized “new conservation theorem” invoked by Ibragimov.

Optical solitons with Kudryashov’s sextic power-law nonlinearity

Objective –The main objective of this paper is to investigate analytic soliton solutions of a nonlinear Schrödinger equation (NLSE), including Kudryashov’s sextic power-law nonlinearity by introducing different approaches of two efficient analytical methods. The considered equation has been recently introduced by N. A. Kudryashov to describe pulse propagation in optical fibers. The refractive index in the equation comprises six terms, each of the terms containing a power-law component. Methods –Applying a wave transformation to the considered NLSE and splitting up the real and imaginary parts, the NLSE is converted to the nonlinear ordinary differential equations (NLODEs). Then, the solutions of NLODEs are considered as suggested in the proposed method and suggested solutions that include some unknown parameters are substituted into the NLODE. An algebraic equations system is acquired by collecting the same power of the unknown function and equating all coefficients to zero. The unknown parameters in the system, and so the solutions of the NLSE, are found by solving the system. In the proposed first method, the modified extended tanh method is enhanced by proposing more solutions. The proposed second method, a different version of auxiliary methods, can remarkably reduce calculations to easily get solutions for the NLSEs with higher-order or power-law nonlinearity. Results –The two proposed methods are successfully applied to the considered NLSE and the abundant solutions of the NLSE are attained. Besides, 2D, 3D and contour graphs are demonstrated in figures for the physical illustrations of the gained solutions. Conclusion –Obtaining the solutions of NLSEs with higher-order or power-law nonlinearity has crucial importance but still challenging work. So, we propose different approaches of two efficient analytical methods, namely, enhanced modified extended tanh expansion method and an auxiliary function method. The derived results imply that the used methods are very efficient, reliable and powerful such that they can be easily implemented to many nonlinear NLSEs with higher-orders or higher power-law nonlinearities that describe real-life phenomena.

Optical solitons of the model with generalized anti-cubic nonlinearity

The mathematical model for description of pulse propagation in optical fiber for the generalized anti-cubic nonlinearity with arbitrary refractive index is considered. The Cauchy problem for this partial differential equation cannot be solved by the inverse scattering transform and the analytical solutions of this mathematical model are found taking into account the traveling wave reduction. First integral of nonlinear ordinary differential equation is presented. Analytical solutions in the form of periodic and solitary waves are found using some transformations. Partial cases of the mathematical model for the generalized anti-cubic nonlinearity are studied.

The soliton analysis for optical fibers models

Optical fibers have a major role in the industry and daily life. To simulate the pulse propagation in optical fibers, numerous models are seen in the literature. In this work, the Kundu-Mukherjee-Naskar (KMN) model and the anti-cubic Schrödinger equation are considered. To solve these models, ansatz-based methods are considered and also, the problem about the determination of transformation is replied so that it is not clear in the literature. The results of the proposed models will play a key role in applications in nonlinear optics, fluid dynamics, quantum mechanics and various other branches of science.

Abundant optical solitons of the (2 + 1)-dimensional Biswas-Milovice equation arising in optical fiber

In this study, we aim to investigate the (2 + 1)-dimensional Biswas-Milovice equation that describes the pulse propagation in optical fiber. With the help of the Exp-function based method and He’s frequency formulation, eleven sets of the optical solitons such as bright soliton, dark soliton, bright-dark soliton, kinky bright-dark soliton and periodic soliton solutions are obtained. The behaviors of the results are presented through the 3-D plot and 2-D curve. The findings of this paper are expected to opened up new horizons for the study of the soliton theory in optics.

Soliton interaction of a generalized nonlinear Schrödinger equation in an optical fiber

Under investigation in this work is a generalized nonlinear Schrödinger (NLS) equation with high-order dispersion and quintic nonlinear terms, which can describe a subpicosecond pulse propagation in optical fibers. By developing Hirota method, the bilinear form and analytical one- and two-soliton solutions are derived. Based on the analytical solutions, we give the corresponding soliton patterns to analyse dynamics of the pulse solitons. It shows that high order dispersion term may change the periodicity of propagation. The interaction of two pulse solitons is an elastic collision. By choosing suitable parameter values, we can obtain the two parallel solitons. It can be applied to improve transmission quality and capacity of information in optical fiber.

Dynamical properties of the generalized model for description of propagation pulses in optical fiber with arbitrary refractive index

A partial differential equation for description of pulse propagation in optical fiber with arbitrary refractive index is considered. Using Melnikov method, an analytical condition for the existence of horseshoe chaos is obtained for the traveling wave reduction of the investigated equation. A way to control chaos in the dynamical system is proposed. An analytical prediction is tested numerically by plotting basins of attraction.

Optical solitons of the [formula omitted]-dimensional Biswas–Milovic equation using modified extended [formula omitted]-function method

In this paper, we study the novel exact solutions of the (2+1)-dimensional Biswas–Milovic equation for the description of pulse propagation in optical fiber. We successfully constructed some important solutions, such as dark, singular, combined dark-singular soliton, singular periodic wave and rational function solutions, have been analytically obtained using the extended tanh method. These solutions might play an important role in the engineering and physics fields. It is shown that the considered method provide a straightforward and powerful mathematical tool for solving problems in nonlinear optic and other physical phenomena.

Analytical solutions for the coupled Hirota equations in the firebringent fiber

Under investigation in this paper are the coupled Hirota (CH) equations, which describe the collision of two waves in the deep ocean and the propagation of the ultrashort optical pulses in a birefringent fiber. Based on the bilinear method, multi-soliton solutions for the CH equations are given. From the perspective of analysis, the interaction dynamics of solitons are obtained. The head-on and overtaking interactions of two/three solitons are analyzed. The elastic and inelastic interactions of two/three solitons are presented. The soliton velocity can be controlled by adjusting the physical parameters ϕj,(j=1,2,…N) and ϵ. The energy exchange occurs between the variables u and v before and after the collision. The local interference of two/three solitons is observed. The closer to the center of the interaction, the more significant the interference. The real and imaginary parts of the parameters ϕj,(j=1,2,…N) have the effects on the numbers of peaks and holes in the collisions. The structure of four eyes and one peak is observed during the two-soliton interaction. The three-soliton interactions are given with two peaks and local interference. It is hoped that the results of this study can provide some reference for the wave interaction in deep ocean, pulse propagation in optical fiber, financial option pricing, valuation of intangible assets in sports and so on.

Interactions of Soliton in Weakly Nonlocal Nonlinear Media

Solitary waves or solitons is a nonlinear phenomenon which has been studied intensively due to its application in solid-state matter such as Bose-Einstein condensates state, plasma physics, optical fibers and nematic liquid crystal. In particular, the study of nonlinear phenomena occurs in the structure of waves gained interest of scholars since their discovery by John Russell in 1844. The Nonlinear Schrödinger Equation (NLSE) is the theoretical framework for the investigation of nonlinear pulse propagation in optical fibers. Nonlocality can be found in an underlying transport mechanisms or long-range forces like electrostatic interactions in liquid crystals and many-body interactions with matter waves in Bose-Einstein condensate or plasma waves. The length of optical beam width and length of response function are used to classify nonlocality in optical materials. The nonlocality can be categorized as weak nonlocal if the width of the optical beam broader than the length of response function and if the width of the optical beam is narrower than the length of response function, it is considered as highly nonlocal. This work investigates the interactions of solitons in a weakly nonlocal Cubic NLSE with Gaussian external potential. The variational approximation (VA) method was employed to solve non integrable NLSE to ordinary differential equation (ODE). The soliton parameters and the computational program are used to simulate the propagation of the soliton width and its center-of-mass position. In the presence of Gaussian external potential, the soliton may be transmitted, reflected or trapped based on the critical velocity and potential strength. Direct numerical simulation of Cubic NLSE is programmed to verify the results of approximation method. Good agreement is achieved between the direct numerical solution and VA method results.

First integrals and general solutions of the Biswas-Milovic equation

The Biswas-Milovic equation for description of pulse propagation in optical fiber is considered. Solutions of the equation are looked for using the traveling wave reduction. The first integrals for a system of equations are found. These first integrals allow us to reduce the system of equations to nonlinear first-order differential equation. The general solution of first-order differential equation with three arbitrary constants is presented in the form of a quadrature. The parameter values of the equation are given for which the general solution is written in an analytical form via elementary functions and the Weierstrass and Jacobi elliptic functions.

Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation

The generalized nonlinear eighth-order Schrödinger equation with third, fifth, seventh and ninth power of nonlinearity is studied. This equation can be used for description of the pulse propagation in optical fiber. It is demonstrated that this equation has highly dispersive optical solitons which are presented in the analytical form.

Tuning of group delay with stimulated Raman scattering-induced dispersion in gas-filled optical fiber

We report the first demonstration of group delay tuning with stimulated Raman scattering-induced dispersion in a hydrogen-filled hollow-core optical fiber. A pump laser induces a sharp refractive index change near the S0(0) Raman transition of hydrogen molecules, enabling the control of the group velocity of signal pulses around the Stokes wavelength. Experiments with an 80-m-long hollow-core fiber filled with 2.5 bar hydrogen achieved continuous tuning of the pulse delay up to 1.42 ns by varying the Raman amplification from 0 to 10 dB. The tunable pulse delay is realized by changing the pump power as well as the hydrogen pressure. This work provides a new technique for controlling the pulse propagation in optical fibers with high flexibility.