Nonlinear Optical Fiber Research Articles

Distinct exact solutions for the conformable fractional derivative Gerdjikov-Ivanov equation via three credible methods

This paper reveals the conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation, which is applied to nonlinear fibre optics together with photonic crystal fibres. The foremost intent of our operation is adopting the unified method, the modified F-expansion method and the modified Kudryashov method to hunt for definite solutions to the equation. In addition, by selecting fairish values, fluctuation behaviours of the solutions are drafted.

Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the (2+1)-dimensional coupled nonlinear Schrödinger equations with propagation distance dependent diffraction, nonlinearity and gain (loss) using the developing Hirota bilinear method, and analyze the dynamical behaviors of these nondegenerate solitons. The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers, varying diffraction and nonlinearity parameters. In addition, when all the variable coefficients are chosen to be constant, the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons. Finally, it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

Accurate Computation of b-Coefficients in Nonlinear Fourier Transform for the Manakov Equation

In recent years, nonlinear Fourier transform (NFT) has been intensely researched as a scheme for communication over the nonlinear optical fiber and characterizing dynamics in nonlinear optical systems. For the accurate computation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients on discrete eigenvalues, the bidirectional algorithm has been proposed where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients are calculated at a cutting point within the temporal window rather than two boundaries. The performance of the bidirectional algorithm depends severely upon the selection criterion of the cutting-point, which has been investigated in nonlinear Schrodinger equation and Korteweg–De Vries equation but not yet in Manakov equation accounting for the dual-polarization signals over optical fiber. In this paper, we propose a cutting-point criterion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients for the bidirectional algorithm of Manakov equation and compare it with existing criteria. Numerical results show that, the resulting algorithm has much better accuracy compared with existing criteria, especially for signals containing a large number of eigenvalues with large imaginary parts. The bidirectional algorithm with the proposed criterion is useful for decoding the dual-polarization nonlinear frequency division multiplexing (DP-NFDM) signals for communication and characterization of vector soliton dynamics in Manakov equation described systems.

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

In this paper, we succeed at discovering the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering, where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of a concerned model. Finally, this technique is simple, fruitful and reliable to handle nonlinear fractional partial differential equations (NLFPDEs).

On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical fibers. The propagation of solitons in nonlinear optical fibers has garnered substantial interest due to its broad spectrum of applications, particularly in ultrafast signal routing systems and short light pulses for communications. This article focuses on investigating the impact of multiplicative noise on the solutions of this governing model. To achieve this, three distinct methods, namely the enhanced modified extended tanh expansion (METE) method, the generalized Kudryashov (GK) approach and the extended modified auxiliary equation mapping (EMAEM) method are employed to obtain a new variety of stochastic solutions. The perception of how noise intensity impacts the transmission of waves is a fundamental and critical issue in various fields. In the context of this study, an equation describes an exact wave pattern under the condition that s (representing noise intensity) equals zero. In such cases, the observed pattern remains undisturbed and matches the expected theoretical wave pattern. However, as the strength of noise s increases, the observed pattern begins to deviate from the ideal wave pattern and exhibits signs of damage or distortion. Furthermore, the stability analysis for the stochastic NLSE is performed, providing valuable insights into the behavior solutions as the strength of multiplicative noise increases. The validation of computational results through stability analysis enhances the confidence in the findings of the study. All the mathematical calculations, as well as graphical representations, have been meticulously achieved to present a comprehensive and detailed understanding of the impact of multiplicative on soliton propagation in nonlinear optical fibers.

Frequency modes filtering of spectral peaks in optical frequency combs through molecular gas absorption and nonlinear polarization rotation.

Spectral peak generation is a recently reported phenomenon that narrow spectral dips of the optical spectrum turn into sharp peaks as they propagate through nonlinear optical fibers. We demonstrated the nonlinear polarization rotation-based spectral peak mode filtering to increase the signal-to-background ratio (SBR). The spectral peaks with almost constant frequency separation were generated from the femtosecond pulses absorbed by the CH4 gas through the highly nonlinear fiber. The generated spectral peaks were filtered through the polarizing beam splitter by the nonlinear polarization rotation, and the SBR was improved from 9 dB to ∼20 dB. The spectral peak generation phenomenon and the mode filtering were numerically confirmed by solving the coupled nonlinear Schrödinger equations. The demonstrated method can generate strong comb modes with wide frequency spacing which are useful for highly sensitive environmental gas sensing spectroscopy. The wavelengths of the spectral peaks are fixed by the absorption spectra of the used gas cells. Therefore, this method can generate high quality spectral peaks of any wavelengths with wide spectral ranges through proper combinations of gas cells.

An improved analytical approach to establish the soliton solutions to the time‐fractional nonlinear evolution models

The time‐fractional Schrödinger (higher dimensional) and the Zakharov–Kuznetsov (ZK) models are the noteworthy modeling equations to interpret the propagation of signal in nonlinear optical fibers, small‐amplitude gravity waves on the surface water, high frequency acoustic waves, the interactions of small amplitude waves, the ion acoustic waves, nonlinear optics, Bose‐Einstein condensates, dynamics of plasma particles, etc. In this article, in order to develop advanced and broad‐spectrum closed‐form soliton solutions of the previously described nonlinear models, the advanced auxiliary equation approach has been put in used with reference to the beta‐derivative concept. The established soliton solutions are further comprehensive and typical and found in the form fractional, exponential, hyperbolic, and trigonometric functions and their variation. We depict 3D shape of the obtained solitons and explain the physical significance of the solitons. The accomplished solutions affirm that the method is effective and powerful and yields compatible solutions to fractional nonlinear evolution equations.

A variety of M-truncated optical solitons to a nonlinear extended classical dynamical model

This article secures optical pulses modeled by higher order generalized extended classical nonlinear Schrödinger equation (GECNLSE). The studied equation is discussed by the assistance of truncated M-fractional derivative and composed of self-steepening, and stimulated Raman scattering effects in nonlinear optical fibers. Because of their versatility in explaining a wide range of complicated physical events and their richer dynamical structures of localized wave solutions, the NLSE equations have received increased attention. The solutions are extracted with the assistance of modified Sardar sub-equation method (MSSEM), one of the newest integration methods. A variety of optical solitons are extracted like, bright, dark, combo, and singular soliton solutions. Furthermore, periodic, exponential, and hyperbolic type solutions are obtained. Assuming the right values for the parameters, various graph shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems.

Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation approach and the improved F-expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Also, the stability of the outcomes is effectively examined. Several graphs have been sketched under appropriate parametric values to reinforce some reported findings. Computational work along with a graphical demonstration confirms the exactness of the proposed methods. The issue has not previously been investigated by taking into account the impact of the third order dispersion parameter. The main objective of this study is to obtain the different kinds of traveling wave solutions of fractional extended NLSE which are absent in the literature which justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of nonlinear sciences and optical engineering because these solutions will enables a through understanding of the development and dynamic nature of such models. The obtained results indicate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable traveling wave solutions to nonlinear equations emerging in various branches of scientific, technological, and engineering domains.

Modal phase-locking in multimode nonlinear optical fibers.

Spatial beam self-cleaning, a manifestation of the Kerr effect in graded-index multimode fibers, involves a nonlinear transfer of power among modes, which leads to robust bell-shaped output beams. The resulting mode power distribution can be described by statistical mechanics arguments. Although the spatial coherence of the output beam was experimentally demonstrated, there is no direct study of modal phase evolutions. Based on a holographic mode decomposition method, we reveal that nonlinear spatial phase-locking occurs between the fundamental and its neighboring low-order modes, in agreement with theoretical predictions. As such, our results dispel the current belief that the spatial beam self-cleaning effect is the mere result of a wave thermalization process.

Exact chirped solutions for the NLSE having Kudryashov’s law with dual form of generalized non-local nonlinearity

This paper devotes to investigating the chirped solutions for the nonlinear Schrödinger equation with Kudryashov’s law with dual form of generalized non-local nonlinearity in optical fibers. By implementing the trial equation method and the complete discriminant system for polynomial method, we obtain nineteen exact chirped solutions, whose types include elliptic function doubly-periodic solutions, solitary wave solutions and singular solutions. After selecting specific parameters, 2D and 3D graphs of several typical solutions are drawn to demonstrate their accurate physical behaviors. These solutions recovered abundant patterns of the chirped wave propagations of the model.

Quantum key distribution via frequency translation in a nonlinear optical fiber

Quantum key distribution via frequency translation in a nonlinear optical fiber

Design of dispersion-flattened photonic crystal fiber with 800 nm wide low-dispersion band

We propose a new design for a dispersion-flattened photonic crystal fiber with 800 nm wide low-dispersion band by employing the imaginary-distance beam propagation method and the transparent boundary condition using BeamPROP simulation software. The chromatic dispersion of the fiber is −1.4 to 4.8 ps/nm·km in an 800 nm wavelength range of 1.1–1.9 μm. The effective mode area at a wavelength of 1.55 μm is 12.2 μm2 and the fiber can be easily joined to conventional nonlinear optical fiber with a small core. The calculated effective index is extremely linear via the wavelength, and the decision coefficient with an approximately straight function is 0.999996, this means the waveguide dispersion of the proposed PCF completely compensates for the material dispersion curves.

Exact soliton solutions and stability analysis to (3 + 1)-dimensional nonlinear Schrödinger model

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics.

An extension to the enhanced Gaussian noise model in optical bus considering various links spectrum

Physical layer impairment modeling has considerably influenced optical networking in optimizing resource allocation for fulfilling a required quality of transmission. Among these impairments, the modeling of optical fiber non-linearity has enjoyed widespread applications by vendors and network operators, giving rise to the two well established Gaussian noise (GN) and enhanced Gaussian noise (EGN) models. In this work, we introduce an extension to the EGN model for a point-to-point bus transmission, where a demand is not typically routed over a single link. More specifically, we assume that a lightpath is routed over a bus and multiple interferers occasionally add and drop along the links, resulting in a mixture of coherent and incoherent non-linear propagation. We propose a mathematical formulation in the optical bus scenario, taking into account the spectrum variation of the links along the bus. To more accurately address their mutual statistical correlation in non-linear interference estimation, we make use of extra lightpath information. Along with presenting the new formulation, we modify the non-linear link function to include the spectrum variation of a lightpath links. The exploited optical bus topology is capable of approximating a real network lightpaths to enable design optimization of optical networks. Our numerical results show approximately 0.4 dB and 0.6 dB improvements versus the GN and EGN models in long bus scenarios with moderate number of channels and lightpaths, and around 0.3 dB minimum improvement.

Some specific optical wave solutions and combined other solitons to the advanced (3+1)-dimensional Schrödinger equation in nonlinear optical fibers

Some specific optical wave solutions and combined other solitons to the advanced (3+1)-dimensional Schrödinger equation in nonlinear optical fibers

Modulation instability in inhomogenous nonlinear optical fiber

Modulation instability in inhomogenous nonlinear optical fiber

Bifurcation analysis and optical solitons for the concatenation model

This work carries out the bifurcation analysis of the concatenation model that arises from nonlinear fiber optics. The fixed points of the dynamical system are recovered and classified. The Hamiltonian of the system is presented. The phase portraits of the system are also addressed. Subsequently, integrating along the periodic orbit, the soliton solutions for the model are retrieved.

Symmetry and conservation laws of the (2+1)-dimensional nonlinear Schrödinger-type equation

In this work, we study the (2+1)-dimensional nonlinear Schrödinger-type equation that is related to many physical phenomena in nonlinear optical fibers and water waves. Some properties of the (2+1)-dimensional nonlinear Schrödinger-type equation are considered. We determine the infinitesimal generators, an optimal system and a commutator table of the Lie algebra by using Lie symmetry analysis. Also the conservation laws of the equation are obtained using the new conservation theorem proposed by Ibragimov.

Soliton structures for a generalized unstable space–time fractional nonlinear Schrödinger model in mathematical physics

One of the most important physical models for describing the dynamics of optical soliton propagation in the theory of optical fibers is the nonlinear Schrödinger equation (NLSE). Since there are so many uses for ultrafast signal routing systems and brief light pulses in telecommunication, optical soliton propagation in nonlinear optical fibers is a subject of intense current interest. The conventional Khater approach and the extended direct algebraic method are used in this research to study a generalized unstable space–time fractional NLS model in mathematical physics. This leads to the discovery of solutions for the bright, dark, periodic, rational and elliptic functions. To illustrate the physical nature of the nonlinear model, the contour plots in 3D, 2D and 2D are produced by assigning the appropriate values to the arbitrary constants. Additionally, consideration is given to the stability analysis of the solutions to the governing equation. In the current era of communications network technology and nonlinear optics, the applied strategy appears to be a more potent and effective way for producing precise optical solutions to a number of various modern models of recent generations.