Femtosecond Pulses In Optical Fibers Research Articles

Optical solitary solutions for the stochastic Sasa–Satsuma equation

The stochastic Sasa–Satsuma equation (SSSE) in the Stratonovich sense is considered here. To produce new elliptic, rational, hyperbolic, and trigonometric stochastic solutions, the modified mapping approach is applied. Due to the fact that the Sasa–Satsuma equation is utilized to explain the propagation of femtosecond pulses in optical fibers, the acquired solutions can be used to describe a wide variety of important physical phenomena. To show how multiplicative noise impacts the analytical solutions of the SSSE, we present a variety of 2D and 3D graphs. We show the stabilization of SSSE solutions by multiplicative noise at zero.

Abundant optical solutions for the Sasa-Satsuma equation with M-truncated derivative

Here, we look at the Sasa-Satsuma equation with M-truncated derivative (SSE-MTD). The analytical solutions in the form of trigonometric, hyperbolic, elliptic, and rational functions are constructed using the Jacobi elliptic function and generalizing Riccati equation mapping methods. Because the Sasa–Satsuma equation is applied to explain the propagation of femtosecond pulses in optical fibers, the acquired solutions can be employed to explain a wide range of important physical phenomena. Moreover, we apply the MATLAB tool to generate a series of graphs to address the effect of the M-truncated derivative on the exact solution of the SSE-MTD.

Darboux Transformation and Soliton Solutions of the Generalized Sasa–Satsuma Equation

The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation, is an important integrable equation, which displays the propagation of femtosecond pulses in optical fibers. In this paper, we investigate a generalized Sasa-Satsuma(gSS) equation. The Darboux transformation(DT) for the focusing and defocusing gSS equation is constructed. By using the DT, various of soliton solutions for the generalized Sasa-Satsuma equation are derived, including hump-type, breather-type and periodic soliton. Dynamics properties and asymptotic behavior of these soliton solutions are analyzed. Infinite number conservation laws and conserved quantities for the gSS equation are obtained.

Optical solitary wave solutions in generalized determinant form for Kundu–Eckhaus equation

The Kundu–Eckhaus (KE) equation describes the propagation of ultra-short femtosecond pulses in optical fibers. In this paper, on the basis of Hirota bilinear form of KE equation, a complex matrix is introduced into the differential relation satisfied by determinant elements. By constructing relations among the matrix elements, the solution in generalized double Wronskian determinant form for the KE equation is derived. When the complex matrix introduced in the differential relation of the determinant elements take diagonal matrix and Jordan block matrix respectively, the soliton solutions and Jordan block solutions of the KE equation are obtained and propagation situations are discussed via different parameters.

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.

Optical solitons to the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers

This paper mainly studies the optical soliton solutions of the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity describing the propagation of femtosecond pulses in optical fibers. Firstly, using traveling wave transformation, the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers is simplified into the coupled nonlinear ordinary differential equations. Secondly, according to the trial method of polynomial of rank homogeneous equation, the optical soliton solutions of coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity can be obtained. Finally, in order to explain the propagation of optical solitons, three-dimensional and two-dimensional diagrams of the obtained solutions are drawn.

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.

Soliton solutions of Sasa–Satsuma nonlinear Schrödinger model and construction of modulation instability analysis

This article is about the study of several types of solitions such as periodic soliton and solitary waves have been derived for sasa-satsuma equation by employing Riccati equation mapping technique. The significant model discusses the prolongation of femto-second pulses in optical fibers and also analyzes the prolongation, and connection of the ultra-short pulses in the sub-pico second or femto-second regime. We have also discussed Modulation instability (MI) analysis with the help of linear analysis of standard stability that illustrate all obtained outcomes are stable and exact. The computational work and accomplished outcomes portray the power and efficiency of this method. Furthermore, various other higher order dynamical models can be solved with the help of this simple, effective and powerful technique.

Lax Pair, Improved Γ $\varGamma $ -Riccati Bäcklund Transformation and Soliton-Like Solutions to Variable-Coefficient Higher-Order Nonlinear Schrödinger Equation in Optical Fibers

In this paper, the higher-order nonlinear Schrodinger equation with variable-coefficient for the propagation of femtosecond pulses in optical fibers is analytically investigated. Lax pair is constructed via the Ablowitz-Kaup-Newell-Segur system, an infinite number of conservation laws are derived based on the Lax pair. Introducing an auxiliary function, an improved $\varGamma $ -Riccati Backlund transformation is presented, which can generate successively nonlinear superposition formula. Moreover, one and two soliton-like solutions are obtained.

Reverse Space-Time Nonlocal Sasa–Satsuma Equation and Its Solutions

The Sasa–Satsuma equation is an integrable high-order nonlinear Schrodinger (NLS) equation, and also is a complex modified KdV-type equation. It can describe the propagation of femtosecond pulses in optical fibers. Very recently, Ablowitz and Mussliman introduced a class of reverse space-time and reverse time nonlinear integrable equations, including the reverse space nonlocal NLS equation, the real and complex reverse space-time nonlocal mKdV, sine-Gordon, Davey–Stewartson equations, etc. So, what is nonlocal version of high-order NLS? In this paper, we introduce a reverse space-time nonlocal Sasa–Satsuma equation, i.e., a reverse space-time nonlocal high-order NLS equation, and derive its solutions with the binary Darboux transformation method. Periodic solutions, and some localized solutions, such as dark soliton, W-shaped soliton, M-shaped soliton and breather soliton of the reverse space-time nonlocal Sasa–Satsuma equation are constructed.

Application of Kudryashov method for high-order nonlinear Schrödinger equation

Higher-order nonlinear Schrodinger equation for describing the propagation of femtosecond pulses in optical fibers is studied. Kudryashov method is used for obtaining exact soliton solutions of this equation.

Dark Bound Solitons and Soliton Chains for the Higher-Order Nonlinear Schrödinger Equation

Dark bound solitons and soliton chains without interactions are investigated for the higher-order nonlinear Schrodinger (HNLS) equation, which can model the propagation of the femtosecond optical pulse under some physical situations in nonlinear fiber optics. Via the modulation of parameters for the analytic solutions, different types of dark bound solitons and soliton chains can be derived for the HNLS equation. In addition, stabilities of those structures are checked through numerical simulations. Our discussions are expected to be helpful in interpreting those new structures, and applied to the long-distance transmission of the femtosecond pulses in optical fibers.

Wavelength-agile laser system based on soliton self-shift and its application for broadband spectroscopy

A novel laser system for rapid-wavelength scanning applications was developed. The wavelength-tuning mechanism is the soliton self-shift of femtosecond pulses in optical fiber. Increased coupling into the fiber causes an increased wavelength red-shift within the fiber. By varying the coupling efficiency, we can generate rapid wavelength scans. Here, we demonstrate tuning between 1.665 and 1.820 μm at 40 kHz repetition rate with 8 mW average output power. We applied this source to measure the overtone of the C–H stretch in gaseous butane.

Effect of nonlinear gradient terms on pulsating, erupting and creeping solitons

The effect of nonlinear gradient terms on the pulsating, erupting and creeping solitons, respectively, of the cubic–quintic complex Ginzburg–Landau equation is investigated. It is found that the nonlinear gradient terms result in dramatic changes in the soliton behavior. They eliminate the periodicity of the pulsating and erupting solitons and transform them into fixed-shape solitons. This is important for potential use, such as to realize experimentally the undistorted transmission of femtosecond pulses in optical fibers. However, the nonlinear gradient terms cause the creeping soliton to breathe periodically at different frequencies on one side and spread rapidly on the other side.

Reverse propagation of femtosecond pulses in optical fibers.

We present a numerical technique for reversing femtosecond pulse propagation in an optical fiber, such that given any output pulse it is possible to obtain the input pulse shape by numerically undoing all dispersion and nonlinear effects. The technique is tested against experimental results, and it is shown that it can be used for fiber output pulse optimization in both the anomalous and normal dispersion regimes.

Direct perturbation theory for solitons of the derivative nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation.

A direct perturbation theory for solitons of the derivative nonlinear Schrödinger (DNLS) equation is developed based on a closure of eigenfunctions of the linearized DNLS equation around a one-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained. Under the known simple gaugelike transformation, these results are transformed into those for the perturbed modified nonlinear Schrödinger (MNLS) equation describing propagation of femtosecond pulses in optical fibers. A calculation of the perturbation-induced radiation fields for the perturbed DNLS and MNLS equations is also made. Our results for the perturbed MNLS equation can be reduced perfectly to those for the perturbed nonlinear Schrödinger equation in the small nonlinear-dispersion limit.

An analysis of the coefficients of a perturbed nonlinear Schrödinger equation for femtosecond behavior in an optical waveguide

An analysis is made for higher-order terms in an extended nonlinear Schrödinger equation. The analysis is in reasonable agreement with recent experiments involving femtosecond pulses in optical fibers.