Monomode Optical Fiber Research Articles

Qualitative and quantitative analysis of high-order nonlinear time–space fractional Schrödinger equation in mono-mode optical fibres

Qualitative and quantitative analysis of high-order nonlinear time–space fractional Schrödinger equation in mono-mode optical fibres

Exact soliton and solitary wave solutions to the Fokas system using two variables [formula omitted]-expansion technique and generalized projective Riccati equation method

The simplest (2+1)-dimensional extension of the nonlinear Schrödinger equation is called Fokas system. In the current article, Fokas system has been discussed which describes the nonlinear pulse propagation in monomode optical fibers. Soliton and solitary wave solutions of Fokas system have been retrieved using two algorithmic schemes namely, generalized projective Riccati equation method and the two variables G′G,1G-expansion method. The proposed methods have been employed to extract various types of solutions such as dark solitons, bright solitons and periodic solutions. The acquired solutions are visualized by 3D plots and corresponding 2D contour and density plots. The obtained results demonstrate that both suggested schemes are productive to retrieve wave solutions for many partial differential equations appearing in optics.

Abundant optical soliton structures to the Fokas system arising in monomode optical fibers

Abstract Three effective methods, namely, the simplified extended tanh-function method (SETFM), variational method (VM) and He’s frequency formulation method (HFFM) are employed to investigate the Fokas system that arises in the monomode optical fibers. Fifteen sets of the soliton solutions such as the bright soliton, dark soliton, bright-dark soliton, double-dark soliton, double-bright soliton, triple-bright soliton, kinky periodic soliton and perfect periodic soliton solutions are developed. The dynamic performances of the different soliton solutions are plotted via the 3-D contours and 2-D curves to interpret the physical behaviors by assigning reasonable parameters. From the results obtained from this study, it is found that three proposed methods are promising ways to seek various soliton solutions of the PDEs in optical physics.

Periodic solution of the time-space fractional Sasa-Satsuma equation in the monomode optical fibers by the energy balance theory

Zhang and Wang developed the periodic solution of the time-space fractional Sasa-Satsuma equation by an ancient Chinese algorithm in EPL, 137 (2022) 62001. In this letter, a new method called the energy balance theory (EBT) is used to study the problem. This theory offers a promising approach by constructing the variational principle and the Hamiltonian for the problem. As anticipated, the solution obtained by the EBT is the same as the solution obtained in the above-mentioned EPL paper, which strongly verifies the effectiveness and reliability of the EBT. Finally, graphical simulations of the solution with different fractional orders are presented in the form of 2-D and 3-D surfaces. The discovery of this work is expected to contribute to the study of periodic solutions of the partial differential equations arising in optics.

Optical solitons and single traveling wave solutions for the Triki–Biswas equation describing monomode optical fibers

In this paper, the polynomial complete discriminant system method is introduced to construct optical solitons and single traveling wave solutions for the Triki–Biswas equation, which is one of the most important mathematical and physical equation usually used to simulate phenomena in nonlinear optics, quantum mechanics and plasma physics. The Jacobi elliptic function solutions, dark solitons solutions, bright solitons solutions, singular solitons solutions and other solutions have been presented.

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.

Investigation of the periodic solution of the time-space fractional Sasa-Satsuma equation arising in the monomode optical fibers

In this paper, the time-space fractional Sasa-Satsuma equation is considered. A novel and interesting method called as He's frequency formulation, which is derived from the ancient Chinese algorithm (ACG) Ying Bu Zu Shu, is employed to construct its periodic solution. This ancient algorithm originated from an ancient Chinese mathematics monograph —The Nine Chapters on the Mathematical Art— compiled in the Han Dynasty about the second century AD. As anticipated, the obtained solution is consistent with that of the variational method. It strongly verifies the effectiveness and reliability of the proposed method. Finally, the performances of the solution with different fractional orders are presented through the 2D and 3D surfaces. The discovery of this work is expected to contribute to the study of periodic solutions in physics.

Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative

Abstract This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M- fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa–Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., β=0.1, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders, i.e., β=0.7 and β=0.99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.

Soliton solutions to the Fokas system arising in monomode optical fibers

Under the current study is the Fokas system that is used to model the nonlinear pulse propagation in monomode optical fibers. By using the extended rational sine-cosine and sinh-cosh methods, eight families of the soliton solutions like trigonometric soliton, singular soliton, bright soliton and dark soliton are constructed. The performances of the solutions are described through the 3-D contours. The results reveal that the proposed methods are effective to construct abundant soliton solutions for the partial differential equations arising in optics.

Abundant exact soliton solutions to the Fokas system

In the current work, we consider the Fokas system that describes the nonlinear pulse propagation in monomode optical fibers. By employing the Exp-function method, we succeed in constructing six families(eleven sets) of the exact soliton solutions. And the behaviors of the real, imaginary and absolute parts of the solutions are described through the 3-D contours. It reveals that the Exp-function method is an effective method to construct abundant exact solutions for the partial differential equations arising in optics.

Analytical simulations of the Fokas system; extension (2 + 1)-dimensional nonlinear Schrödinger equation

This paper studies novel analytical solutions of the extended [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which is also known with [Formula: see text]-dimensional complex Fokas ([Formula: see text]D–CF) system. Fokas derived this system in 1994 by using the inverse spectral method. This model is considered as an icon model for nonlinear pulse propagation in monomode optical fibers. Many novel computational solutions are constructed through two recent analytical schemes (Ansatz and Projective Riccati expansion (PRE) methods). These solutions are represented through sketches in 2D, 3D, and contour plots to demonstrate the dynamical behavior of pulse propagation in breather, rogue, periodic, lump, and solitary characteristics. The stability property of the obtained solutions is examined based on the Hamiltonian system’s properties. The obtained solutions are checked by putting them back into the original equation through Mathematica 12 software.

Optical 1-soliton solutions of Triki-Biswas equation by the First Integral Method and the sine-cosine Method

In this paper, the First Integral Method and the Sine-Cosine Method are being used in constructing optical 1-soliton solutions of Triki-Biswas Equation that plays a vital role in the study of soliton dynamics of sub-pico-second optical pulses in mono-mode optical fibers with non-Kerr law nonlinearity and subsequently some soliton and non-soliton solutions are formally obtained. Â

Optical Fiber Spool Acoustic Wave Resonances Employing a Mach-Zehnder Interferometer in Vacuum Chamber

Abstract The longitudinal, flexural, and torsional modes of acoustical resonances are presented for a long and small thickness cylindrical fiber spool. The fiber spool is built using a monomode optical fiber tightly wound in a helix form around a cylindrical Styropor. The acoustical resonance values are obtained using a Mach Zehnder interferometer with the fiber spool in the long (2 km) arm and a small linewidth laser. To reduce spurious signals, the interferometer was placed inside a vacuum chamber. The measured and theoretical results reasonably agree up to the first fifteen resonant longitudinal modes and for the first five flexural and torsional resonant modes, with a span from 10 Hz up to 200 Hz.

Classification of conserved vectors of the Triki–Biswas equation describing monomode optical fibres

We completely classify the conserved vectors of the Triki–Biswas equation describing monomode optical fibres using the invariance and multiplier approach. For the general case, three obtained multipliers were used to compute conserved vectors with two of them leading to blowup of the density and the flux when the parameter (k) equals negative one. We show that both quantities in the blowup case equal ln|ψ| and further exhibit second order multipliers at zero value of the parameter (k).

Polarization control in single mode optical fibers

Satisfactory operation of a dual beam laser Doppler anemometer system requires that the maximum fringe contrast is achieved. This implies, in turn, that the two intersecting beams should have the same intensity and the same state of polarization. This requirement is achieved in many systems by careful adjustment of the polarization state, often at the time when the laser Doppler anemometer system is first aligned. The present paper describes a compact and relatively cheap device that enables the polarization of the light transmitted through a step index mono-mode optical fiber to be controlled. Design methods for this device are discussed and a prototype opto-mechanical system is described. Finally, some experimental data are presented from which the performance of the device in adjusting the polarization of a laser beam can be assessed.

Optical solutions of the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using two different methods

This paper studies the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation. The first integral of this equation, the phase portraits and the effective potentials are provided. Two different methods are applied to find exact analytical solutions. These methods are the arbitrary nonlinear parameters and the new Jacobi elliptic function expansion method. To give a behavior of the equation studied, some representations are done. In the context of mono-mode optical fibers and in many other domains like nonlinear transmission lines, Bose-Einstein capacitors and so on, the results obtained may be used. We have also established that the solutions obtained here are different from those encounter in the literature concerning the same model.

Soliton solutions of the Sasa–Satsuma equation in the monomode optical fibers including the beta-derivatives

The main goal of the present paper is to steer an investigation on the dynamics of soliton solutions of a nonlinear model in the monomode optical fibers. In this respect, first, soliton solutions of the model termed as the Sasa–Satsuma (SS) equation describing the propagation of short light pulses are derived in the presence of the beta-derivatives; then, the dynamics of soliton solutions in the monomode optical fibers is analyzed for different values of the parameter β. The soliton solutions presented in this study are categorized in the most common classes of solitons namely bright and dark soliton solutions.

Soliton Solutions of a Nonlinear Fractional Sasa-Satsuma Equation in Monomode Optical Fibers

Soliton Solutions of a Nonlinear Fractional Sasa-Satsuma Equation in Monomode Optical Fibers

Propagation of dipole solitons in inhomogeneous highly dispersive optical-fiber media.

We consider ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a type of exact self-similar soliton solution that takes the structure of a dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical-fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed. By performing numerical simulations, the self-similar soliton solutions are found to be stable under slight disturbance of the constraint conditions and the initial perturbation of white noise.