Pulses In Optical Fibers Research Articles

Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers

In this study, the Fokas system which represents the spread of irregular pulse in monomode optical fibers is investigated via the Jacobi elliptic function expansion (JEFE) method. This method is the most powerful technique to explore solutions for a wide range of various models. As a result, different solutions such as dark–bright, singular, bright, Jacobi elliptic function, and exponential solutions are obtained. In addition, 3D and 2D graphics for the obtained solutions are investigated with the assist of a computer program by assigning particular values to the parameters involved.

Integrability and multisoliton solutions of the reverse space and/or time nonlocal Fokas–Lenells equation

This paper studies reverse space and/or time nonlocal Fokas–Lenells (FL) equation, which describes the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered, by Hirota bilinear method. Firstly, we construct variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations. Secondly, the multisoliton and quasi-periodic solutions of the reverse space nonlocal FL equation are derived through Hirota bilinear method, and the soliton solutions of reverse time and reverse space-time nonlocal FL equations are given through variable transformations. Also, dynamical behaviors of the multisoliton solutions are discussed in detail by analyzing their wave structures. Thirdly, asymptotic analysis of two- and three-soliton solutions of reverse space nonlocal FL equation is used to investigate the elastic interaction and inelastic interaction. Finally, the infinite conservation laws of three types of nonlocal FL equations are found by using their lax pairs. The results obtained in this paper possess new properties that different from the ones for FL equation, which are useful in exploring novel physical phenomena of nonlocal systems in nonlinear media.

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.

The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods

The nonlinear Schrödinger hierarchy has a wide range of applications in modeling the propagation of light pulses in optical fibers. In this paper, we focus on the integrable nonlinear Schrödinger (NLS) equation with quintic terms, which play a prominent role when the pulse duration is very short. First, we investigate the spectral signatures of the spatial Lax pair with distinct analytical solutions and their periodized wavetrains by Fourier oscillatory method. Then, we numerically simulate the wave evolution of the quintic NLS equation from different initial conditions through the symmetrical split-step Fourier method. We find many localized high-peak structures whose profiles are very similar to the analytical solutions, and we analyze the formation of rouge waves (RWs) in different cases. These results can be helpful to understand the excitation of nonlinear waves in some nonlinear fields, such as the Heisenberg ferromagnetic spin system in condensed matter physics, ultrashort pulses in nonlinear optical fibers, and so on.

Modulation Method for High-Capacity Fibre Channel Switch and High-Speed Pulse Network Data

Fibre channel (FC) switches are widely used in storage area networks and avionics systems. In this work, the FC protocol, the switching structure and the scheduling algorithm of the FC switch are deeply studied, and a 48-port FC switch is completed on a single-chip field-programmable gate array (FPGA). In addition, an improved scheduling algorithm for Inter-System Link Protocol (iSLP) is proposed for the input and scheduling of optical fiber pulse network data. On this basis, the overall architecture of the FC switch is proposed, the x690tffg1158 FPGA chip is selected, and the FC port control module is designed, which is composed of the receiving controller, the interface state machine, the sending controller, and the flow control. The routing table lookup module of FC switch is designed, the unicast routing table format and multicast routing table format are proposed, and the corresponding unicast and multicast routing table lookup table module architectures are designed. Aiming at the characteristics of high reliability and low distortion in the transmission of high-speed pulse network signals by FC switches, the modulation and demodulation of Bias-T (BIAS-T) are redesigned. The experiment is implemented using Verilog hardware description language (HDL), and Modelsim 10.5 software is adopted to simulate each module of the switch. The switch adopts an 8×N switching structure, which can accurately perform word synchronization. After the link is initialized, the transceivers can send and receive data frames normally. The redesigned BIAS-T is applied to solve the instability of the end of the analog modulation method, and then realize the low distortion and data integrity of the high-speed pulse signal of the FC switch.

Darboux Transformation for the Hirota Equation

The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions. The multisoliton and breather solutions of the Hirota equation are given explicitly.

Strong and weak interactions of rational vector rogue waves and solitons to anyn-component nonlinear Schrödinger system with higher-order effects

The higher-order effects play an important role in the wave propagations of ultrashort (e.g. subpicosecond or femtosecond) light pulses in optical fibres. In this paper, we investigate anyn-component fourth-order nonlinear Schrödinger (n-FONLS) system with non-zero backgrounds containing then-Hirota equation and then-Lakshmanan–Porsezian–Daniel equation. Based on the loop group theory, we find the multi-parameter family of novel rational vector rogue waves (RVRWs) of then-FONLS equation starting from the plane-wave solutions. Moreover, we exhibit the weak and strong interactions of some representative RVRW structures. In particular, we also find that the W-shaped rational vector dark and bright solitons of then-FONLS equation as the second- and fourth-order dispersion coefficients satisfy some relation. Furthermore, we find the higher-order RVRWs of then-FONLS equation. These obtained rational solutions will be useful in the study of RVRW phenomena of multi-component nonlinear wave models in nonlinear optics, deep ocean and Bose–Einstein condensates.

Dynamics of optical pulses in fiber optics

In this paper, we pay attention to the nonlinear dynamical behavior of ultra-short pulses in optical fiber. The new Hamiltonian amplitude equation is used as a governing model to analyze the pulses. We secure the ultra-short pulses in the forms of bright, dark, singular, combo and complex soliton solutions by the utilization of three of sound computational integration techniques that are protracted (or extended) Fan-sub equation method (PFSEM), the generalized exponential rational function method (GERFM), extended Sinh-Gordon equation expansion method (ShGEEM). Moreover, Jacobi’s elliptic, trigonometric, and hyperbolic functions solutions are also discussed as well as the constraint conditions of the achieved solutions are also presented. In addition, we discuss the different wave structures by the assistance of logarithmic transformation. The findings demonstrate that the examined equation theoretically contains a large number of soliton solution structures. By selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in 3D and 2D profiles. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex phenomena. The resulting solutions are novel, intriguing, and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics. Our new results have been compared to these in the literature.

Helical plasma filaments from the self-channeling of intense femtosecond laser pulses in optical fibers.

We experimentally and numerically study the ignition of helical-shaped plasma filaments in standard optical fibers. Femtosecond pulses with megawatt peak power with proper off-axis and tilted coupling in the fiber core produce plasma skew rays. These last for distances as long as 1000 wavelengths thanks to a combination of linear waveguiding and the self-channeling effect. Peculiar is the case of graded-index multimode fibers; here the spatial self-imaging places constraints on the helix pitch. These results may find applications for fabricating fibers with helical-shaped core micro-structuration as well as for designing laser components and three-dimensional optical memories.

Soliton solutions for the nonlocal reverse space Kundu–Eckhaus equation via symbolic calculation

The Kundu–Eckhaus (KE) equation describes the propagation of ultrashort femtosecond pulses in optical fibers. In this paper, the Hirota bilinear method is used to deal with nonlocal KE equation which is also called nonlocal integrable nonlinear Schrödinger equation with cubic and quintic nonlinearities. The N-soliton solution for the nonlocal KE equation is derived by virtue of symbolic calculation. Based on that, the exact solution expressions of two-soliton and three-soliton can be obtained. Several propagation situations are demonstrated and discussed for the combinatorial solutions of nonlocal KE equation under different parameters, including one periodic solitary wave evolution, two parallel, perpendicular and periodic solitary waves collision.

One- and two-hump solutions of a singularly perturbed cubic nonlinear Schrödinger equation

The paper considers the existence of one- or two-hump solutions of a singularly perturbed nonlinear Schrödinger (NLS) equation, which is the standard NLS equation with a third order perturbation. In particular, this equation appears in the field of nonlinear optics, where it is used to describe pulses in optical fibers near a zero dispersion wavelength. It has been shown formally and numerically that the perturbed NLS equation has one- or multi-hump solutions with small oscillations at infinity, called generalized one- or multi-hump solutions. The main purpose of the paper is to provide the first rigorous proof of the existence of generalized one- or two-hump solutions of the singularly perturbed NLS equation. The several invariant properties of the equation, i.e., the translational invariance, the gauge invariance and the reversibility property, are essential to obtain enough free constants to prove the existence. The ideas and methods presented here may be applicable to show existence of generalized 2k-hump solutions of the equation.

On the construction of the general solution of the Fokas–Lenells equation

In this communication we consider the Fokas–Lenells equation which describes the propagation of the nonlinear optical pulses in mono mode fibers when higher-order nonlinear effects are taken into consideration. Based on the traveling wave ansatz, we construct the general solution for the envelope of the wave packet in terms of the Jacobi elliptic sine function. The special case of solitary wave solutions is shown to emerge when the arbitrary constant in the general solution is set to zero. Analytical forms of the solutions are studied for different values of parameters and qualitative features of the solutions are also described.

Localized pulses in optical fibers governed by perturbed Fokas–Lenells equation

We study the existence and properties of propagating solitary waves in an optical fiber medium described by the perturbed Fokas-Lenells equation. Additional effects to the usual Fokas-Lenells equation include third- and fourth-order dispersions, inter-modal dispersion, nonlinear dispersion and self-steepening effect. The model applies to the description of light pulse propagation applicable to a femtosecond or subpicosecond regime. We introduce an efficient ansatz for the field amplitude that enables us to obtain solitary waves with the governing model. More pertinently, we find that solitary wave solutions of bright and dipole shape do exist in the presence of all orders of dispersion and various nonlinear effects. We also find that the energy associated to the obtained structures depends on all material parameters. The requirements concerning the optical fiber parameters for the existence and uniqueness of such solitary waves are presented.

Propagation of diverse ultrashort pulses in optical fiber to Triki–Biswas equation and its modulation instability analysis

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations.

Local well-posedness of a generalized nonlinear Schrödinger equation with cubic–quintic nonlinearity

In this article, we study the Cauchy Problem associated to the generalized cubic–quintic Schrödinger equation which has been used for the description of propagation pulses in optical fibers. Using gauge transforms and a derivation process, we prove under some regularity assumptions, the local well-posedness. Additionally, a global H1 bound is established for the solution.

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.

New optical solitons of perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion

The perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated in this study using an improved Sardar sub-equation method. The Kerr and power laws of nonlinearity are taken into account. As a result of this improved technique, many constraint conditions required for the existence of soliton solutions emerge. We retrieved several solutions such as the bright solitons, dark solitons, singular solitons, mixed bright–dark solitons, singular-bright combo solitons, periodic, and other solutions. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.

On new abundant solutions of the complex nonlinear Fokas–Lenells equation in optical fiber

Variational method is important since it can reduce the order of the differential equation to make the equation simpler and obtain the optimal solution by the stationary condition. In this paper, we mainly study the complex nonlinear Fokas–Lenells equation (CNFLE), which is used to describe the propagation of short pulses in optical fibers. The traveling wave transformation is used to convert the CNFLE into the ODE, and the variational principle of the solution is obtained by the semi‐inverse method. Based on the variational principle, the extended He′s variational method, which is based on the Ritz‐like method, is employed to investigate the bright soliton, bright‐like soliton, bright–dark soliton, and periodic wave solution. The absolute, real, and imaginary parts of the novel computational solutions are plotted through one example in the form of 3‐D and 2‐D contours. In addition, the physical explanation of the solutions is elaborated in detail. The results reveal that the variational method is straightforward, simple, and effective, which is expected to bring a light to the study of the traveling wave theory.

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.

Periodic solution of the time-space fractional complex nonlinear Fokas-Lenells equation by an ancient Chinese algorithm

As is known to all, the complex nonlinear Fokas-Lenells equation is widely used to describe the propagation of short pulses in optical fibers. In this work, we aim to study its time-space fractional modified form. An ancient Chinese algorithm called the Ying Bu Zu Shu (盈不足术), which is from an ancient Chinese mathematics monograph-The Nine Chapters on the Mathematical Art (九章算术) in about second century AD, is used to find its periodic solution. The solution obtained by our proposed method is the same as the one obtained via the variational method, which strongly proves the effectiveness and reliability of the proposed method. Finally, we plot the solution with different fractional orders in the form of 2-dimensional and 3-dimensional surfaces. The finding in this work is expected to be helpful for the study of the periodic solution in physics.