Propagation In Optical Fibers Research Articles

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light propagation in nonlinear optical fibers or photonic crystals where the refractive index has a q-deformed structure; and it also can be applied in studying shock waves, turbulence and rogue waves where the deformation introduces corrections to classical wave phenomena. Utilizing the (G′ωG′+G+r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\frac{{\\mathfrak {G}}^{\\prime }}{\\omega {\\mathfrak {G}}^{\\prime }+{\\mathfrak {G}}+r})$$\\end{document}-expansion technique, we derive novel analytical solutions that enhance our understanding of the underlying dynamics. Additionally, we employ a finite element method (extended cubic B-spline method) to validate our analytical findings and explore the behavior of the q-deformed equation under different parameter regimes. Our results demonstrate the versatility of the q-deformed framework in generating rich optical phenomena, paving the way for future research in both theoretical and applied physics.

Soliton solutions of derivative nonlinear Schrödinger equations: Conservative schemes and numerical simulation

In this paper, we numerically study soliton solutions of derivative nonlinear Schrödinger equations based on several conservative finite difference methods. All schemes own second-order accuracy with the convergence order O(τ2+h2) in the discrete L∞-norm, where h denotes the spatial step size and τ denotes the temporal step size. We show that difference schemes preserve some discrete counterparts of continuous conservation laws, and all these schemes are solvable. Extensive numerical examples with soliton solutions are carried out to verify the theoretical results. These results manifest that our schemes have potential application to soliton propagation in optical fibers.

The multi-positon and breather positon solutions for the higher-order nonlinear Schrödinger equation in optical fibers

Under investigation in this paper is the higher-order nonlinear Schrödinger equation, which can imitate the ultrashort pulses propagation in optical fibers. The modulation instability is analyzed based on the plane-wave solution. With the help of the generalized Darboux transformation, the second-, third- and fourth-order positon solutions are constructed. Furthermore, the second-, third- and fourth-order breather positon solutions are obtained, and the influences of parameters for the characteristics of solutions are analyzed.

M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions

The formation of soliton in optical fiber governed by nonlocal nonlinear Schrödinger (NLS) equation with fourth order dispersion is studied. The model of nonlocal NLS equation with fourth order dispersion is solved using the new extended auxiliary method and the solutions are obtained. The solutions are in the form of hyperbolic and trigonometric functions which are based on Jacobi elliptic function m. Shape changing soliton in optical fiber for nonlocal fourth order dispersive NLS equation is discussed by suitably choosing the values of kerr and quintic nonlinearities and by varying fourth order dispersion term. The effect of fourth order dispersion on soliton in fiber for different conditions of kerr and quintic nonlinearity is also discussed. In addition, the phase portraits of the system have been investigated and the stability of wave in optical fiber for nonlocal NLS equation is discussed using fourth order Runge-Kutta algorithm. This paper addresses a significant gap in the current literature by examining the impact of fourth order dispersion on the nonlocal NLS equation in optical fiber.

Unseeded one-third harmonic generation in optical fibers

We propose a new concept to generate efficient one-third harmonic light from an unseeded third harmonic process in optical fibers. Our concept is based on the dynamic constant (Hamiltonian) of the nonlinear third harmonic generation in optical fibers and includes a periodic array of nonlinear fibers and phase compensation elements. We test our concept with a simulation of the nonlinear interaction between the fundamental and third harmonic modes of a realistic optical fiber, demonstrating high-efficiency one-third harmonic generation. Our work opens a new approach to achieving the so far elusive one-third harmonic generation in optical fibers.

Resonant optical soliton solutions for time-fractional nonlinear Schrödinger equation in optical fibers

In this paper, several new optical soliton solutions of the time-fractional generalized resonant nonlinear Schrödinger equation, relevant to pulse propagation in optical fibers, are constructed using the extended simplest equation approach. The new exact solutions are expressed in terms of hyperbolic functions, trigonometric functions, and rational functions. Further, two-dimensional, three-dimensional, and contour graphs of king-type, wave, dark–bright, bright, and bell-shaped optical soliton solutions are plotted to elucidate the significance of the time-fractional generalized resonant nonlinear Schrödinger equation using appropriate values of physical parameters. The dynamic behavior of the present solutions, incorporating the effect of the conformable fractional derivative, is depicted through two-dimensional graphs. The derived optical solutions are considered novel and have presumably not been previously reported in the literature.

Extraction of newly soliton wave structure of generalized stochastic NLSE with standard Brownian motion, quintuple power law of nonlinearity and nonlinear chromatic dispersion

Stochastic optical solitons are a fascinating phenomenon in nonlinear optics where soliton-like behavior emerges in systems affected by stochastic noise. This study investigates the influence of Brownian motion on wave propagation in optical fibers. The propagation is modeled using a stochastic nonlinear Schrödinger equation incorporating quintuple power-law nonlinearity and nonlinear chromatic dispersion. To explore this, the improved modified extended tanh (IMET) scheme, leveraging the extended Riccati equation, is employed. This technique facilitates the extraction of various stochastic solutions, including bright, dark, and singular solitons. Furthermore, solutions in the shapes of exponential, singular periodic, and Weierstrass elliptic forms are investigated. The study looks at how the strength of noise impacts various solutions, and Matlab software is used to create 2D and 3D graphs that show the results. It has been noted that when noise intensity rises, signal level falls and surface flattens.

Exploring the impact of multiplicative white noise on novel soliton solutions with the perturbed Triki–Biswas equation

This study examines the effects of multiplicative white noise on soliton perturbations governed by the Triki–Biswas equation for the first time. Triki–Biswas equation advances research on ultrashort pulse propagation in optical fibers. It modifies the nonlinear Schrödinger equation to describe the behavior of femtosecond pulses more accurately in optical media, becoming a critical tool in the field. The paper employs two innovative methods, the enhanced direct algebraic method and the new projective Riccati equations method to uncover a broad range of soliton solutions, including bright, dark, and singular solitons. The solutions are expressed in terms of Jacobi elliptic functions and exhibit a transition to soliton-type solutions as the elliptic modulus approaches unity. This investigation is the first of its kind to explore the effects of multiplicative white noise within this context, providing new perspectives and methodologies for future research in the field. The study sheds light on previously unexplored aspects of multiplicative white noise and contributes significantly to the body of knowledge in soliton theory and its application to optical fiber technology.

Optical soliton solution of the perturbed Biswas-Milovic equation having cubic-quintic-septic law nonlinearity in the presence of spatio-temporal and chromatic dispersion

In this manuscript, we investigate the analytical and soliton solutions of the cubic-quintic-septic law for the perturbed Biswas-Milovic equation, considering spatio-temporal and chromatic dispersions. The perturbed Biswas-Milovic equation with the spatio-temporal and chromatic dispersion terms provides a comprehensive study for describing nonlinear optical wave propagation in optical fiber. We use the wave transformation to reduce the main equation to a nonlinear ordinary differential equation. The transformation of the original equation into a more simplified form aims to attain a more profound comprehension of the fundamental dynamics of the system. We retrieve the analytical solutions of the presented model by implementing the new Kudryashov technique and a subversion of the new extended auxiliary equation approach. Besides, bright, singular, and V-shape soliton structures are represented. By employing powerful analytical techniques, we systematically derive a wide range of soliton solutions. This approach successfully captures diverse soliton types highlighting the novelty of applying the new Kudryashov technique and a subversion of the new extended auxiliary equation method to this complex model. Moreover, we analyze the soliton behavior influenced by various parameters. The analysis of the parameter influences reveals the complicated relationship governing the dynamics of the perturbed Biswas-Milovic model. Furthermore, this manuscript includes the modulation instability analysis for the presented model. Conducting modulation instability analysis for the presented equation enhances our understanding of the system’s stability and dynamics.

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Internet traffic (IT) is a measure of data transfer across devices. In this paper, an analogy is made between data transfer and soliton propagation in optical fibers. This is achieved by employing the concatenation model (CM) that describes soliton propagation in optical fibers, which is presented recently in the literature. The CM contains nonlinear space-time dispersion effect, that may lead to bottleneck soliton shape (BNSS). Thus, in view of this model, BNSS effect of soliton propagation may occur, which is analogous to a possible BN in IT. So, the prediction of the characteristics of internet traffic can be depicted via the CM, which is studied here with Caputo-q time derivative. Also, a variety of exact solutions of the CM are derived. These solutions are represented graphically and they show multiple shapes of concatenated solitons. Among them, bottleneck, M-shaped, hybrid M shaped, chirped solitons and vector of dromian patterns. On the other side, the speed of IT and chips heating are estimated. It is found that the speed of IT is constant with time and the effects of distributed time delay (recent memory (RM)) is to slow the traffic speed. This is done via varying the fractional order. Also, it is observed, when accounting for RM, that the chip heating is too small. We think that the results for the speed of IT and chip heat are, qualitatively, realistic. The stability of a steady state solution is analyzed and the controlled parameters for stability is determined.

Soliton waves with optical solutions to the three-component coupled nonlinear Schrödinger equation

This study uses the modified Sardar sub-equation method to find novel soliton solutions to the nonlinear three-component coupled nonlinear Schrödinger equation (NLSE), which is used for pulse propagation in nonlinear optical fibers. Multi-component NLSE equations are widely used because they can represent a wide range of complex observable systems and more dynamic patterns of localized wave solutions. The optical solutions proposed in this study are novel and can be described using hyperbolic, trigonometric, and exponential functions. These solutions are categorized as bright, dark, singular, combo bright-singular, and periodic solutions. Some solutions’ dynamic behaviors are demonstrated by selecting appropriate physical parameter values. The results and computational analysis indicate that the techniques provided are simple, effective, and adaptable. They can be applied to a variety of nonlinear evolution equations, whether stable or unstable, and can be used in fields such as mathematics, mathematical physics, and applied sciences.

Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system

In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark–bright, singular, periodic, bright–dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose–Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.

Bright–dark envelope-optical solitons in space-time reverse generalized Fokas–Lenells equation: Modulated wave gain

Here, we investigate the impact of space-time reverse (STR) problems, a result of parity-time symmetry in optics and quantum mechanics, on soliton propagation in optical fibers. The STR problems are characterized by the existence of a field and its reverse. The research introduces a new classification of two scenarios: non-interactive and interactive fields and reverse fields. The solutions for the generalized Fokas–Lenells equation (gFLE) with STR and third-order dispersion are derived. To tackle this, adaptive transformations for the field and its reverse are introduced, employing a unified method. In the non-interactive scenario, both exact and approximate solutions are found. However, in the interactive case, only exact solutions are discovered. This work reveals that the presence of the field and its reverse unveils new soliton structures, including bright–dark envelope solitons and right and left envelope-solitons. In the non-interactive case, the field displays a right envelope-soliton, while the reverse field exhibits a left envelope-soliton (or vice versa). The study hypothesizes that the presence of a reverse field might impede soliton propagation in optical fibers. The research also includes an analysis of modulation instability (MI), determining that MI is initiated when the coefficient of Raman scattering exceeds a critical value. Furthermore, the study examines the modulated wave gain and explores global bifurcation through phase portrait by constructing the Hamiltonian function.

Femtosecond laser writing of robust waveguides in optical fibers with enhanced photosensitivity

We report the femtosecond laser writing of meter-long optical waveguides inscribed through the coating of specifically designed optical fibers. In order to improve the material photosensitivity and to ensure non-guiding optical fibers for subsequent laser processing of the waveguiding core, a depressed refractive index core design is implemented by co-doping a large portion of the optical fiber with germanium oxide and fluorine. The enhanced photosensitivity provided by further deuterium loading these fibers allows laser-writing of large refractive index contrast waveguides over wide cross sections. To mitigate the formation of photoinduced color centers causing high propagation losses in the photo-written waveguides, thermal annealing up to 400°C is performed on polyimide-coated laser-written fibers. Although the refractive index contrast decreases, the propagation losses are drastically reduced down to 0.08 dB/cm at 900nm allowing a robust single-mode guiding from visible to near infrared. Our results pave the way towards the development of a new generation of optical fibers and photonic components with arbitrarily complex designs.

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

Modulation instability and comparative observation of the effect of fractional parameters on new optical soliton solutions of the paraxial wave model

This work focuses on the study of the paraxial wave model with a space–time fractional form. This model has more importance for describing light propagation in nonlinear optical fibers and telecommunication lines. The main aim of this work is to observe the effect of the fractional parameters and compare the truncated M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M$$\\end{document}-fraction with the beta-fraction, conformable fraction form, and classical form of the PW model. For this observation, we applied the Simplest equation technique to acquire analytical solutions to the space–time (spatiotemporal) M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M$$\\end{document}-fractional paraxial wave model. We are able to acquire several new optical soliton solutions, including periodic waves, kink-type waves, rogue-type waves, and several novel periodic waves, by providing the appropriate fractional parametric values. These solutions have significance for shedding light on a number of physical phenomena in the realms of optical fiber and communication sciences. The diverse values of fractional parameters and the three-dimensional and contour plot graphs of certain chosen solutions are depicted, which are the most accurate physical characterizations of the outcomes. We also sketch the comparative graph of diverse fractional forms and the classical form of the paraxial wave equation in two-dimensional plots. Consequently, our findings represent an important breakthrough in this complex area and help further develop our comprehension of the behavior of solitons.

Breathers, rogue waves, and interaction solutions for the variable coefficient Kundu-nonlinear Schrödinger equation

With the inhomogeneity of optical fiber media taken into account, under investigation in this paper is the variable coefficient Kundu-nonlinear Schrödinger equation, which describes the pulses propagation in optical fibers. Based on Lax pair, the Nth-order Darboux transformation is constructed. Depending on plane wave solution, the first- and second-order breather solutions are derived and the interactions between breathers are graphically analyzed. The Kuznetsov–Ma breather, Akhmediev breather, and spatial-temporal breather have been obtained. Moreover, the first-, second-, and third-order rogue wave solutions have been constructed. The usual rogue waves and first- and second-order line rogue waves are observed. The weak and strong interactions between the first-, second-order rogue waves, and spatial-temporal period breather are studied. Furthermore, variable coefficient δ(t) causes rogue waves to produce some interesting evolutionary phenomena, which have been systematically analyzed. In addition, the influences of parameters for the properties of solutions are discussed.

A Kundu-nonlinear Schrödinger equation: Rogue waves, breathers, and mixed interaction solutions.

A Kundu-nonlinear Schrödinger equation that can be utilized to simulate the pulse propagation in optical fibers is researched in this paper. First, the Lax integrability of the above equation is proved and its modulational instability (i.e., the main mechanism for producing the rogue wave solutions and the breather solutions) is calculated. Subsequently, using the generalized perturbation (n,N-n)-fold Darboux transformation, the rogue waves, breathers, and mixed interaction solutions are acquired, as well as the impact of various parameters on the solutions is examined. In particular, when we assume that the coefficient of the equation is θ=mx+dt, some new wave structures are found based on parameter variations, such as the rotational separation of first-order rogue waves, scale-like structures generated by second-order breathers, etc., which offer novel ideas for producing different signals via optical fibers. Ultimately, the classification numbers of mixed solutions of rogue waves and breathers are provided, which can better observe how the two types of the local waves are combined, in accordance with the distributions of the increasing numbers of algebraic equations.

Dynamical analysis of optical soliton solutions for CGL equation with Kerr law nonlinearity in classical, truncated [formula omitted]-fractional derivative, beta fractional derivative, and conformable fractional derivative types

The study of optical soliton solutions plays a vital role in nonlinear optics. The foremost area of optical solitons research encompasses around optical fiber, telecommunication, meta-surfaces and others related technologies. The aim of this work is to integrate optical soliton solutions of the complex Ginzburg-Landau (CGL) model with Kerr law nonlinearity, also showing the effect of diverse fraction derivative and comparing it with the classical form. Here, the local derivative is used as the conformable wisdom known as the truncated M-fractional derivative, beta fractional derivative, and conformable fraction derivative. We also deliberated on some assets satisfied by the derivative. The CGL model is useful to describe the light propagation in optical communications, optical transmission, and nonlinear optical fiber. Under the right circumstances, the affectionate unified scheme is implemented for the complex Ginzburg-Landau model to generate the optical wave pattern. For α1=2α2, the unified scheme generates the solution of CGL model in terms of hyperbolic, trigonometric, and rational function solutions. This scheme provides some novel optical solitons such as periodic waves, periodic with rogue waves, breather waves, different types of periodic rogue waves, a singular soliton solution, and rogue with the periodic wave for the special value of the free parameters. For α2=-ρ+6α18, the unified scheme generates the solutions of CGL model in terms of hyperbolic, trigonometric, and rational function solutions. This scheme offers some fresh optical solitons such as periodic rogue waves, multi-rogue waves, double periodic waves, and periodic waves. In numerical argument, the wave patterns are offered with 3-D and density plots. To test the stability of the obtained solutions, we show diverse fractional forms such as beta time fractional, and conformable time fractional derivative and compare these fractional derivatives with their classical form in 2D plots. The investigation reveals innovative and explicit solutions, providing insight into the dynamics of the related physical processes. This paper provides a comprehensive examination of the obtained solutions, emphasizing their distinct features and depictions using unified technique. These findings are especially advantageous for specialists in the fields of nonlinear science and mathematical physics, providing significant insights into the behavior and development of nonlinear waves in various physical situations.