Twin-core Couplers Research Articles

Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity

The main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method. This equation has profound physical significance and application value in the areas of optics and optical communication. Firstly, the traveling wave transformation is applied to convert the beta-derivative Twin-Core couplers with Kerr law non-linearity into the ordinary differential equations. Secondly, phase portraits and Poincaré sections of two-dimensional dynamical system and its perturbation system are plotted by using mathematical software. For different initial values, the planar phase diagram and three-dimensional phase diagram in red and blue are plotted, respectively. Finally, the solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity are obtained by using theory of planar dynamical system. In addition, three-dimensional graphs, two-dimensional graphs, and the contour graphs of the solitary wave solutions are drawn.

Unveiling optical solitons in twin-core couplers with Kerr law of nonlinear refractive index using improved modified extended tanh function method

Unveiling optical solitons in twin-core couplers with Kerr law of nonlinear refractive index using improved modified extended tanh function method

Optical solitons for twin-core couplers in optical metamaterials with Kudryashov’s sextic power law of arbitrary refractive index

Optical solitons for twin-core couplers in optical metamaterials with Kudryashov’s sextic power law of arbitrary refractive index

Exploring solitons in optical twin-core couplers with Kerr law of nonlinear refractive index using the modified extended direct algebraic method

Exploring solitons in optical twin-core couplers with Kerr law of nonlinear refractive index using the modified extended direct algebraic method

Solitons of the Twin-Core Couplers with Fractional Beta Derivative Evolution in Optical Metamaterials via Two Distinct Methods

The rapid advancements in metamaterial research have brought forth a new era of possibilities for controlling and manipulating light at the nanoscale. In particular, the design and engineering of optical metamaterials have created advances in the field of photonics, enabling the development of advanced devices with unprecedented functionalities. Among the myriad of intriguing metamaterial structures, the nonlinear directional couplers with beta derivative evolution have emerged as a significant avenue of exploration, offering remarkable potential for light propagation and manipulation. This study obtains the solitary wave solutions for twin-core couplers having spatial-temporal fractional beta derivative evolution by using two different methods, the Bernoulli method and the complete polynomial discriminant system method. By graphing some of the obtained solutions, the effect of the beta derivative has been shown. The findings would be beneficial to understand physical behaviours in nonlinear optics, particularly twin-core couplers with optical metamaterials.

Sensitive Demonstration of the Twin-Core Couplers including Kerr Law Non-Linearity via Beta Derivative Evolution

To obtain new solitary wave solutions for non-linear directional couplers using optical meta-materials, a new extended direct algebraic technique (EDAT) is used. This model investigates solitary wave propagation inside a fiber. As a result, twin couplers are the subject of this study. Kerr law is the sort of non-linearity addressed there. Because it offers solutions to problems with large tails or infinite fluctuations, the resulting solution set is more generalized than the current solution because it is turned into a fractional-order derivative. Furthermore, the found solutions are fractional solitons with spatial–temporal fractional beta derivative evolution. In intensity-dependent switches, these nonlinear directional couplers also serve as limiters. Non-linearity alters the transmission constants of a system’s modes. The significance of the beta derivative parameter and mathematical approach is demonstrated graphically, with a few of the extracted solutions. A parametric analysis revealed that the fractional beta derivative parameter has a significant impact on the soliton amplitudes. With the aid of the advanced software tools for numerical computations, the categories of semi-dark solitons, singular dark-pitch solitons, single solitons of Type-1 along with 2, intermingled hyperbolically, trigonometric, and rational solitons were established and evaluated. We also discussed sensitivity analysis, which is an inquiry that determines how sensitive our system is. A comparative investigation via different fractional derivatives was also studied in this paper so that one can easily understand the correlation with other fractional derivatives. The findings demonstrate that the approach is simple and efficient and that it yields generalized analytical results. The findings will be extremely beneficial in examining and comprehending physical issues in nonlinear optics, specifically in twin-core couplers with optical metamaterials.

On optical solitons for the nonlinear fractional twin-core couplers with Kerr law nonlinearity

On optical solitons for the nonlinear fractional twin-core couplers with Kerr law nonlinearity

Cubic–quartic solitons in twin-core couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index by using improved modified extended tanh-function method

In this article, the improved modified extended tanh-function method is applied to obtain optical solitons for the cubic–quartic (CQ) twin-core couplers in optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index. Various types of solutions are raised such as bright solitons, dark solitons, singular solitons, periodic solutions, singular periodic solutions, hyperbolic-type solutions, rational-type solution, Jacobi elliptic wave solutions, exponential wave solutions and Weierstrass elliptic doubly periodic-type solutions. Moreover, for the physical illustration of the obtained solutions 2D, 3D and contour graphs are presented.

Construction cubic-quartic solitons in optical metamaterials for the perturbed twin-core couplers with Kudryashov's sextic power law using extended F-expansion method

In this article, we consider the twin-core couplers with Kudryashov's sextic power law of refractive index and perturbation terms. The extended F-expansion method is implemented to construct cubic–quartic solitons in optical metamaterials and other solutions for the proposed model. Bright soliton solutions, singular soliton solutions, periodic solutions and combo periodic solutions are obtained. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

Bright solitons for twin-core couplers and multiple-core couplers having polynomial law of nonlinearity using Jacobi elliptic function expansion method

This paper is an wide account of bright solitons and periodic solutions for twin-core couplers and multiple-core couplers with polynomial law of nonlinearity and nonlinear perturbation terms using the Jacobi elliptic function expansion method. The restrictions on the parameters are considered to guarantee the existence of the obtained solitons. Moreover, graphs of some solutions are presented to show their features.

Cubic-quartic optical solitons in couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index

This article applies the addendum to Kudryashov’s method to secure the optical soliton solutions for the cubic–quartic (CQ) twin-core couplers and multiple-core couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index. The coupling with nearest neighbors and the coupling with all neighbors are introduced. The used method investigate the combo-bright–singular, bright and singular solitons solutions for the three models.

Inelastic soliton interactions for nonlinear directional couplers in optical metamaterials with Kerr nonlinearity modulation stability

A directional coupler is made up of two parallel monolayer wave guides filled with high nonlinear optical metamaterial. The model equations of the directional twin-core couplers, which are coupled nonlinear Schrödinger equations (CNLSEs), were proposed in the literature. These equations have received the attention of a variety of works. The results found, therein, show mainly dark, bright or singular soliton solutions. The objective of this work is to search for different soliton geometric structures, which show novel patterns. To this issue a novel transformation, with complex amplitude, is introduced. It allows to inspect the waves produced via soliton periodic wave collision. The collision is elastic whenever the waves generated are, everywhere, smooth. Otherwise it is inelastic. Here, the unified method is used to find the traveling wave solutions of the CNLSEs. The solutions obtained are evaluated numerically and they are used to display the amplitude and the real part of the optical field in figures. These figures exhibit super-lattices, zig-zag soliton with rhombus modulation and graded solitons with blow up. These behaviors occur due to inelastic collisions. The contour plots show lattice waves with gap (region of blow up) or without gap. Also, ripples that occur currently in optical cables are observed. Furthermore, it is found that modulation instability (MI) is triggered for positive nonlinear phase shift coefficients or in the case when the coupling coefficients exceed a critical value. As far as MI holds, this leads to traveling waves blow up and gaps.

Cubic-quartic optical solitons in couplers with optical metamaterials having parabolic non-local law nonlinearity

The main goal of this article is to investigate the optical soliton solutions for the cubic–quartic (CQ) twin-core couplers and multiple-core couplers having optical metamaterials with parabolic non-local law nonlinearity and nonlinear perturbation terms. The couplings with nearest neighbors and with all neighbors are discussed. The unified Riccati equation expansion approach and the addendum to Kudryashov’s approach are applied. Straddled, combo-bright-singular, dark, bright, singular solitons solutions as long as periodic and rational solutions are found.

Cubic–quartic optical solitons in couplers with optical metamaterials having Kudryashov’s law of arbitrary refractive index

This article applies the unified Riccati equation expansion method and the addendum to Kudryashov’s method. The two used methods secure the optical soliton solutions for the cubic–quartic (CQ) twin-core couplers and multiple-core couplers with optical metamaterials having Kudryashov’s law of arbitrary refractive index. Two forms of multiple-core couplers are introduced, namely the coupling with nearest neighbors and the coupling with all neighbors. Straddled, combo bright–singular, dark, bright, singular solitons solutions as long as periodic and rational solutions are investigated.

Cubic-quartic optical solitons and other solutions for twin-core couplers with polynomial law of nonlinearity using the extended F-expansion method

In this article, the extended F-expansion method is applied to secure cubic–quartic optical solitons for twin-core couplers with polynomial law of nonlinearity. Bright, singular, and bright–singular combo cubic–quartic solitons are derived. Also, periodic solutions, combo periodic solutions, exponential solutions and rational solutions are obtained. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

Optical solitons in twin-core couplers with the nearest neighbor coupling

In this work, we concern with the soliton solutions to an optical twin-core coupler that occur with four sorts of nonlinearities viz. Kerr law, power law, parabolic law, and dual power-law nonlinearity. The twin-core couplers with the nearest neighbor linear coupling are considered and bright, dark, and singular optical solitons are extracted with the aid of the integration algorithm of the new mapping method. The appropriate constraint conditions are naturally emerged to secure the existence of these solitons. For physical classification of the newly acquired solutions, we have expressed them graphically to describe the physical interpretation of distinct shaped solutions more evidently.

Cubic–quartic solitons in couplers with optical metamaterials having quadratic–cubic law of nonlinearity

This paper acquires cubic–quartic solitons in couplers with optical metamaterials that maintain quadratic–cubic nonlinear form. Two integration schemes, namely unified Riccati equation expansion scheme and an addendum to Kudryashov’s approach have made this retrieval possible. Both multiple-core couplers as well as twin-core couplers are considered. A full spectrum of soliton solutions have emerged from these couple of algorithms.

Cubic–quartic solitons for twin-core couplers in optical metamaterials

This paper obtains a spectrum of soliton solutions in optical couplers that are with Kerr form of nonlinear refractive index. These are cubic–quartic solitons where the usual chromatic dispersion is replaced by a collective effect of third and fourth order dispersions. Two integration schemes are implemented to recover these soliton solutions.

Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods

This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials.

Cubic–quartic solitons in couplers with optical metamaterials having power law of refractive index

This paper studies couplers in optical metamaterials that come with power law of nonlinear refractive index. The Kudryashov’s approach reveals bright, singular as well as bright-singular straddled optical soliton solutions. Both twin-core couplers and multiple-core couplers are studied.