Nonlinear Optical Fiber Research Articles

On the optical wave structures to the fractional nonlinear integrable coupled Kuralay equation

This paper is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. 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. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

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.

Impact of weak nonlocal nonlinearity on modulational instability and chirp-free soliton trains in parabolic law optical fiber

This study considers the generation and evolution of chirp-free soliton trains in a focusing cubic-quintic nonlinear optical fiber media (by utilizing experimental parameters), under the influence of weak nonlocal nonlinearity. Analysis of modulational instability (MI) reveals that the MI gain exist only in the anomalous dispersion regime, with the quintic nonlinear term increasing the maximum gain and sideband frequencies. The nonlocal nonlinearity parameter generally suppresses the impact of MI, because the maximum gain is greatly reduced with increase in nonlocality. By using the subsidiary ordinary differential equation method, stationary periodic soliton trains are obtained; with the intensity of the optical beam greatly reduced and frequency increased as nonlocality is gradually stepped up. However, an increase in nonlocality instead reduces the frequency of the traveling optical signals; derived via an efficient transformation method. Our results strongly suggest that nonlocal nonlinearity has potential applications in the control of laser beams; as nonlinear periodic optical signals can be easily transformed to very weak quasi-plane waves.

Controlled linearly chirped similaritons in inhomogeneous birefringent optical fibers

By similarity transformation, optical similaritons in a nonlinear birefringent optical fiber are investigated within the framework of two coupled nonlinear Schrödinger equations with space-modulated self- and cross-phase modulation nonlinearities, group velocity dispersion, external electro-optic phase modulation, and gain/loss. We find that the birefringent nonlinear medium with spatial parameter variations supports the existence of linearly chirped similariton structures of the W-shaped-dipole and bright-dipole types. These important results indicate that in addition to the usual single-humped localized waves such as bright-bright and dark-dark type waveforms, multihump chirped similaritons can also exist in the inhomogeneous birefringent fiber in the presence of all physical effects. The similariton parameters such as the amplitude, width, phase, and inverse group velocity are found to be dependent on certain controllable fiber parameters, thus enabling us to manage their intensity and consequently their subsequent dynamical evolution. Finally, we investigate the transmission of similaritons for different choices of material parameters.

All-optical Stern-Gerlach effect in the time domain.

The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.

New optical wave solutions of M-fractional nonlinear Schrödinger’s complex hyperbolic model by an efficient method

In this paper, we succeed to obtain the new optical wave solutions to the truncated M-fractional (2+1)-dimensional nonlinear Schrödinger’s complex hyperbolic model by utilizing the Sardar sub-equation method. The obtained solutions are in the form of trigonometric, hyperbolic and mixed form. These solutions have many applications in nonlinear optics, fiber optics, and other areas of physics 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 two-dimensional, three-dimensional and contour plots. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear PDEs.

Unique soliton solutions to the nonlinear Schrödinger equation with weak non-locality and cubic–quintic–septic nonlinearity in nonlinear optical fibers

Unique soliton solutions to the nonlinear Schrödinger equation with weak non-locality and cubic–quintic–septic nonlinearity in nonlinear optical fibers

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I & II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters d 1 and d 3. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

Nonlinear fiber optics with water wave flumes: dynamics of the optical solitons of the derivative nonlinear Schrödinger equation

Nonlinear fiber optics with water wave flumes: dynamics of the optical solitons of the derivative nonlinear Schrödinger equation

Low-loss weak-coupling 6-mode hollow-core negative curvature fiber based on symmetric double-ring nested tube

Few-mode optical fibers have played an increasingly important role in breaking through the transmission capacity limitations of single-mode optical fiber and alleviating the bandwidth crisis in optic fiber communication systems in recent years. Nevertheless, traditional solid core few-mode optical fibers usually suffer optical fiber nonlinearity and mode coupling, leading to mode crosstalk between channels. Hollow core negative curvature fibers (HC-NCF) have attracted widespread attention due to their advantages, such as low latency, low nonlinearity, low dispersion, low transmission loss, and large operating bandwidth. In this work, a novel low-loss few-mode HC-NCF with symmetrically double ring nested tube structure is designed, which supports six core modes including LP<sub>01</sub>, LP<sub>11</sub>, LP<sub>21</sub>, LP<sub>02</sub>, LP<sub>31<i>a</i></sub>, and LP<sub>31<i>b</i></sub>. The designed optical fiber is based on silica dioxide substrate and adopts a unique symmetrical double ring nested cladding structure, which can effectively suppress the coupling between the core mode and the cladding mode. The finite element method (FDE) is used to numerically analyze the properties of the proposed few-mode HC-NCF and optimize the structural parameters of the few-mode HC-NCF. Moreover, the confinement loss and bending loss of all core modes are investigated. The simulation results show that the proposed few-mode HC-NCF can support the independent transmission of six weakly coupled core modes (with the effective refractive index difference greater than 1×10<sup>–4</sup> between the adjacent core modes, which greatly avoids the coupling between the adjacent modes in the fiber core). In the 400 nm bandwidth (1.23–1.63 μm, covering the O, E, S, C, and L bands), all six modes in the fiber core maintain low loss transmission. Moreover, in the range of 1.3–1.63 μm, the confinement loss (CL) of LP<sub>01</sub>, LP<sub>11</sub> and LP<sub>21</sub> mode are all less than 1×10<sup>–3</sup> dB/m, and the CL of LP<sub>02</sub> and LP<sub>31<i>b</i></sub> mode are both less than 3×10<sup>–3</sup> dB/m. The CL of each mode reaches the lowest value at 1.4 μm, and the LP<sub>01</sub> mode has the lowest CL of 4.3×10<sup>–7</sup> dB/m. In addition, for a bending radius of 7 cm, each mode maintains the low bending loss characteristic in a certain operating wavelength range. In the range of 1.23–1.61 μm, the BL of LP<sub>01</sub> is less than 4.5×10<sup>–4</sup> dB/m, and the BL of LP<sub>11</sub> is less than 1.3×10<sup>–3</sup> dB/m. The tolerance analysis shows that even with the deviation of structural parameters of ±1%, the few-mode HC-NCF can still maintain the characteristic of low-loss and weak coupling. The designed few-mode HC-NCF has ultra-low CL and bending-insensitive characteristics while supporting independent transmission of six modes, which will find huge potential applications in future high performance mode division multiplexing systems.

Breathers of Gerdjikov-Ivanov equation under background of elliptic function

As one specific type of local solutions of nonlinear evolution equation, the breathers have the characteristic of envelope oscillation structure. This kind of oscillation is periodic. According to the periodicity of the distribution and evolution directions, there are three kinds of breathers, namely, the Kuznetsov-Ma breather (KMB), the Akhmediev breather (AB), and the general breather (GB). In recent years, the propagation of envelope breathers under the periodic background has been observed in many nonlinear physical fields, including nonlinear optical fibers and hydrodynamics. It is believed that the breathers can arise due to the modulational instability of the periodic waves, and they demonstrate many rich physical properties and dynamic behaviors of interactions. Therefore, recently great attention has been paid to the breathers under the periodic background in nonlinear science. As an important integrable model, the Gerdjikov-Ivanov (GI) equation can be used to describe various nonlinear phenomena in many physical fields such as in the quantum field theory, weak nonlinear dispersive water wave, and nonlinear optics. It is very meaningful to solve various types of solutions of this model to describe the propagation of nonlinear waves. As far as we know, the breather solutions for the GI equation have not been given under the elliptic function background. In this study, firstly, elliptic function solutions of the GI equation are solved by the modified squared wave (MSW) function approach and the traveling wave transformation. Then, we obtain the basic solution of the Lax pair corresponding to the Jacobi elliptic function seed solution. Based on the elliptic function transformation formulas and the integral formulas, the potential function solution can be expressed in terms of the Weierstrass elliptic function. Secondly, by the once iterated Darboux transformation, three types of breather solutions under the elliptic function background are constructed including the GB, the KMB and the AB. In addition, we analyze the dynamic behaviors of these three kinds of breathers, and present their three-dimensional space-time structures. By the twice iterated Darboux transformation, under the dn-periodic background we exhibit three types of interactions between two breathers, i.e. a GB and a KMB, an AB and a KMB, and a GB and an AB. Finally, we also present three types of interactions between two breathers under the general periodic background.

DYNAMICS OF OPTICAL WAVE PROFILES TO THE FRACTIONAL THREE-COMPONENT COUPLED NONLINEAR SCHRÖDINGER EQUATION

This paper explores the truncated [Formula: see text]-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. 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. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

On some soliton structures for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in mathematical physics

The most important physical structure that is assumed to illustrate the geometry of optical soliton replication in optical fiber theory is the nonlinear Schrödinger equation (NLSE). Optical soliton generation in nonlinear optical fibers is a topic of great contemporary interest because of the numerous applications of ultrafast signal routing systems and short light pulses in communications. This analysis's main goal is to create a large number of soliton solutions for the dynamical model using a variety of contemporary analytical methods. This paper studies different soliton solutions to the perturbed NLSE with Kerr law nonlinearity using two sets of two distinct integration strategies: the mapping approach and the unified auxiliary equation method. The majority of solutions have been found as Jacobi elliptic functions with limiting ellipticity modulus values. Solitons like dark, bright, optical, lonely, and others are also retrieved. We were able to create various single‐type solutions with the help of these strategies. As a result, there is a variety of optical, bell‐shaped, single periodic, and multi‐periodic solutions. In order to validate the computations, the stability of the acquired findings must also be proven. The study provides a highly stunning and suitable strategy for combining numerous exciting wave demonstrations for more advanced models of the present era. Furthermore, we can assert that the outcomes reported here are unique and novel.

Solutions of Resonant Nonlinear Schrödinger’s Equation with Exotic Non-Kerr Law Nonlinearities

The solitary wave solutions of the quadratic-cubic law and Kerr-Law nonlinearity of the resonant nonlinear Schrödinger's Equation are investigated in this study. The solitary wave solutions of the resonant nonlinear Schrödinger's equations are investigated using the well-known extended simple equation method (ESEM). The field of Soliton in nonlinear fiber optics is where these equations are mainly investigated. We have obtained a new dark-bright, bell-shaped, periodic, unique, and periodic Soliton.

Incoherently pumped event horizons in optical fibers

Optical event horizons in fibers, driven by coherent pumps, have been a prominent subject of study within the field of nonlinear optics. Previously, optical event horizons involving a potent pump and a linear-wave were interpreted as phase-matching processes wherein new spectral components are derived from the linear-wave due to the influence of the strong pump. This nonlinear interaction, coupled with the wave mixing mechanism, has been elaborated upon in the spectral domain. It’s portrayed as a cascaded four-wave mixing process, achieving quasi-phase-matching through intermediate spectral components. Until now, research focused on event horizons or soliton linear-wave interactions has predominantly relied on coherent laser pump sources. However, there has been a recent resurgence in the exploration of incoherently pumped nonlinear optics. While the specific dynamics of incoherent light fields and their subsequent nonlinear processes might be elusive due to their inherent random field fluctuations, their incoherent nature unveils a multitude of statistical dynamics for nonlinear phenomena. In this work, we delve into optical event horizons encountered by linear-waves propelled by an incoherent light field within nonlinear optical fibers. Our numerical analysis scrutinizes the dynamics of linear-waves during optical event horizons under incoherent pumping. We further dissect the temporal statistics of the newly birthed idler-waves emerging from these event horizon processes.

Recent advances and future outlook in mode-locked lasers with multimode fibers

Multimode fibers (MMFs) have attracted interest because of their larger mode area and additional spatial degrees of freedom compared with single-mode fibers. Recently, MMFs have been introduced into mode-locked lasers for new cavity structures with better laser performance. Among these lasers, there are two remarkable cases in which MMFs are the key components for mode-locking: One is using a short segment of the MMF as a saturable absorber (SA), which has the advantages of high damage threshold, wide operating bandwidth, and low cost. The other is the construction of multimode cavities with MMFs. Spatiotemporal mode-locking (STML), a general form of mode-locking, can be achieved in such cavities. Herein, we review these two types of mode-locked lasers with MMFs. The principles of MMF-based SA and STML are described based on the common theory of multimode nonlinear fiber optics. Subsequently, we present a detailed overview of the recent progress regarding these lasers, including lasers mode-locked by MMF-based SAs at the 1-, 1.5-, and 2-μm bands, as well as spatiotemporal mode-locked MMF lasers. A perspective for the development of mode-locked lasers with MMFs is also provided.

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

This article concerns new analytical wave solutions of the Kuralay-II equations (K-IIAE and K-IIBE) with exploration of a new definition of the derivative. This model is used in various fields, like nonlinear optics, ferromagnetic materials and optical fibers. For this purpose, the expa function, the extended sinh-Gordon equation expansion scheme, and the generalized Kudryashov schemes were utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by the Mathematica tool. Some of the solutions are explained with 2-D, 3-D and contour plots using the Mathematica tool. The solutions obtained succede the present solutions in the literature. For the first time, the effect of the fractional derivative on the solutions is also shown graphically for this model. The analytical wave solutions are highly desirable as they offer insights into the underlying physics or mathematics of a system and provide a framework for further analysis. The results obtained can also be fruitful for the development of models in the future. The schemes used in this research are effective, easy to apply, and reliably handle other fractional non-linear partial differential equations.

On soliton solutions for higher-order nonlinear Schrödinger equation with cubic-quintic-septic law

The topic of dispersive optical solitons is one of the essential areas of telecommunications engineering. This paper presents the nonlinear Schrödinger equation (NLSE) with the cubic-quintic-septic (CQS) law which includes higher-order dispersion terms. This equation examines the dynamics of dispersive optical solitons propagation in nonlinear optical fibers. The presented model is significant in mathematics and theoretical physics sciences because long-distance optical fibers are used in optical communication utilized for transoceanic and intercontinental data transmission. First, the considered equation is transformed into a nonlinear ordinary differential equation (NLODE) using the traveling wave transformation. Then, two powerful techniques, Sinh-Gordon expansion approach and the auxiliary equation method (AEM), based on the homogeneous balance rule, are operated to produce analytical solutions for the NLSE with CQS law. Thus, bright, dark, singular, and periodic-singular soliton solutions are acquired. We demonstrate the three-dimensional (3D) and two-dimensional (2D) representations to interpret the physical behavior of some derived solutions. Besides, we investigate the effects of some parameters in the model with graphical illustrations. Therefore, it can be noted that the obtained soliton solutions have a significant role in soliton dynamics.

Rhombus-shaped, M-shaped- solitons, 2D-lumps vector and tunneling in perturbed Gerdjikov–Ivanov equation with fourth-order dispersion: Modulation instability and global bifurcation

The Perturbed Gerdjikov–Ivanov Equation (PGIE) describes optical solitons in nonlinear fiber optics and photonic crystal fibers. It was currently studied in the literature. Here, we consider a new complex field equation, the PGIE with fourth-order dispersion. The exact solutions of the aforementioned equation are obtained by implementing the unified method. These solutions are evaluated numerically and they are shown in graphs. Our objectives, here, are to inspect the onset of self- steepening and self-phase modulation and investigate the structures of solitons produced. It is found that these phenomena are launched for high values of the relevant coefficients, and they may be overlapped. Multiple solitons shapes are observed; M-shaped solitons, rhombus shapes, solitons with tunneling, 2D-lumps vector, and solitons- cascade. Further, the analysis of modulation instability (MI) and global bifurcation are carried out. It is established that the MI triggers when the coefficient of Raman scattering exceeds a critical value. It is worth mentioning that two kinds of bifurcations can be studied, namely local and global bifurcations. Here, we are concerned with studying global bifurcation. This is based on constructing the phase portrait via Hamiltonian function.

High-temperature wave thermalization spoils beam self-cleaning in nonlinear multimode GRIN fibers.

In our experiments, we reveal a so-far unnoticed power limitation of beam self-cleaning in graded-index nonlinear multimode optical fibers. As the optical pulse power is progressively increased, we observed that the initial Kerr-induced improvement of the spatial beam quality is eventually lost. Based on a holographic mode decomposition of the output field, we show that beam spoiling is associated with high-temperature wave thermalization, which depletes the fundamental mode in favor of a highly multimode power distribution.