Solitons In Optical Metamaterials Research Articles

Bright and dark optical solitons in optical metamaterials using a variety of distinct schemes for a generalized Schrodinger equation

Purpose The purpose of this study is to investigate the nonlinear Schrödinger equation (NLS) incorporating spatiotemporal dispersion and other dispersive effects. The goal is to derive various soliton solutions, including bright, dark, singular, periodic and exponential solitons, to enhance the understanding of soliton propagation dynamics in nonlinear metamaterials (MMs) and contribute new findings to the field of nonlinear optics. Design/methodology/approach The research uses a range of powerful mathematical approaches to solve the NLS. The proposed methodologies are applied systematically to derive a variety of optical soliton solutions, each demonstrating unique optical behaviors and characteristics. The approach ensures that both the theoretical framework and practical implications of the solutions are thoroughly explored. Findings The study successfully derives several types of soliton solutions using the aforementioned mathematical approaches. Key findings include bright optical envelope solitons, dark optical envelope solitons, periodic solutions, singular solutions and exponential solutions. These results offer new insights into the behavior of ultrashort solitons in nonlinear MMs, potentially aiding further research and applications in nonlinear wave studies. Originality/value This study makes an original contribution to nonlinear optics by deriving new soliton solutions for the NLS with spatiotemporal dispersion. The diversity of solutions, including bright, dark, periodic, singular and exponential solitons, adds substantial value to the existing body of knowledge. The use of distinct and reliable methodologies to obtain these solutions underscores the novelty and potential applications of the research in advancing optical technologies. The originality lies in the novel approaches used to obtain these diverse soliton solutions and their potential impact on the study and application of nonlinear waves in MMs.

Chirped solitons in optical metamaterials with anti-cubic law of nonlinearity by trial equation method

Chirped solitons in optical metamaterials with anti-cubic law of nonlinearity by trial equation method

Wave-speed management of dipole, bright and W-shaped solitons in optical metamaterials

Wave-speed management of soliton pulses in a nonlinear metamaterial exhibiting a rich variety of physical effects that are important in a wide range of practical applications, is studied both theoretically and numerically. Ultrashort electromagnetic pulse transmission in such inhomogeneous system is described by a generalized nonlinear Schrödinger equation with space-modulated higher-order dispersive and nonlinear effects of different nature. We present the discovery of three types of periodic wave solutions that are composed by the product of Jacobi elliptic functions in the presence of all physical processes. Envelope solitons of the dipole, bright and W-shaped types are also identified, thus illustrating the potentially rich set of localized pulses in the system. We develop an effective similarity transformation method to investigate the soliton dynamics in the presence of the inhomogeneities of media. The application of developed method to control the wave speed of the presented solitons is discussed. The results show that the wave speed of dipole, bright and W-shaped solitons can be effectively controlled through spatial modulation of the metamaterial parameters. In particular, the soliton pulses can be decelerated and accelerated by suitable variations of the distributed dispersion parameters.

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.

Optical solitons in optical metamaterials with anti-cubic nonlinearity

What the paper will show is how we attempt to study optical solitons of the nonlinear Schrödinger (NLS) equation with anti-cubic (AC) nonlinearity which describes the propagation of pulses in optical metamaterials. By using trial equation method and the complete discrimination system for polynomial, we obtain all the possible forms of optical propagation patterns for the model. Finally, we draw the graphs for several typical patterns and show their temporal-space structures.

Dispersive solitons in optical metamaterials having parabolic form of nonlinearity

This paper studies solitons in highly dispersive optical metamaterials with cubic–quintic nonlinearity in presence of detuning, inter-moda dispersion, self-steepening and nonlinear dispersion. Three forms of integration scheme retrieved solitons and other solutions to the model that included snoidal and snoidal waves. These algorithms retrieved bright, dark, singular as well as dark-singular combo solitons along with their respective existence criteria.

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

BackgroundThis paper studies soliton perturbation in optical metamaterials, with anticubic nonlinearity.MethodsTwo integration approaches, namely, the extended trial equation method (ETEM) and the improved G’/Gexpansion method (IGEM) are presented.ResultsBright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also demonstrated. All solutions have been verified back into its corresponding equation with the aid of maple package program.ConclusionsFinally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in optical metamaterials.

Solitons in optical metamaterials with anti-cubic nonlinearity

This paper studies soliton perturbation in optical metamaterials, with anti-cubic nonlinearity, by implementing three integration schemes. Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also presented.

Solitons in optical metamaterials having parabolic law nonlinearity with detuning effect and Raman scattering

The dynamics of pulse propagation through nonlinear optical metamaterials, maintaining parabolic law nonlinearity, is investigated. The model includes spatio-temporal dispersion, detuning effect, inter-modal dispersion, self-steepening effect, Raman scattering, nonlinear dispersion and third-order dispersion. Bright, dark and singular soliton solutions are derived by the implementation of coupled phase-amplitude formulation. The conditions on the material parameters for the existence of these solitons are also enumerated.

Solitons in optical metamaterials with anti-cubic law of nonlinearity by generalized G′/G-expansion method

This paper studies soliton perturbation in optical metamaterials, with anti-cubic nonlinearity, by implementing an integration approach, namely, the generalized G′/G-expansion method (GGEM). Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also demonstrated. All solutions have been verified back into its corresponding equation with the aid of maple package program. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in optical metamaterials.

Chirped solitons in optical metamaterials with parabolic law nonlinearity by extended trial function method

This paper secures chirped bright and singular soliton solutions in an optical metamaterial that is considered with parabolic law nonlinearity and self-steepening effect. The extended trial function method is the integration scheme adopted in this paper. Several other solutions such as singular periodic waves and elliptic functions naturally emerge as a byproduct of this scheme.

Conservation laws for perturbed solitons in optical metamaterials

Abstract The conservation laws for the dynamics of soliton propagation through optical metamaterials are derived by the aid of Lie symmetry analysis. The proposed model will be studied with two forms of nonlinearity. They are Kerr law and parabolic law.

Exact solitons in optical metamaterials with quadratic-cubic nonlinearity using two integration approaches

The aim of this paper is to present soliton solutions in optical metamaterials. The quadratic-cubic nonlinearity is considered. Two efficient algorithms that are the exp(−Φ(η))-expansion method and extended Jacobi's elliptic function expansion scheme are used to carry out the mathematical analysis. As a result, analytical dark soliton, singular soliton and periodic solutions are obtained.

Novel singular solitons in optical metamaterials for self-steepening effect

We consider the evolution of ultrashort pulses in metamaterials wherein the pulse propagation is governed by the generalized nonlinear Schrödinger equation with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. We present three new types of exact singular soliton-like solutions for the model in the presence of the self-steepening term, whose phase chirping varies as a function of the pulse intensity. The obtained results indicate that the parameters of solutions are directly related the self-steepening parameter. Parametric conditions on physical parameters for the existence of the novel structures are also presented. Particular cases are discussed.

Dipole solitons in optical metamaterials with Kerr law nonlinearity

We investigate a higher-order nonlinear Schrödinger equation including the intermodal dispersion, self-steepening, delayed nonlinear response effect, and different contributions to the nonlinear dispersion. The model describes ultra-short (femtosecond) optical soliton propagation in metamaterials with Kerr law nonlinearity. By adopting a complex amplitude ansatz composed of the product of bright and dark solitary waves, we present exact dipole soliton solution for the model under certain parametric conditions. This type of soliton pulses characteristically exists due to a balance among nonlinear dispersion effects of different nature. Numerical results and discussions are also presented.

Bright and exotic solitons in optical metamaterials by semi-inverse variational principle

This paper addresses solitons in optical metamaterials. The semi-inverse variational principle (SVP) is utilized to secure bright soliton solutions to the governing model. There are five forms of nonlinearity that are studied in this paper. They are Kerr law, power law, parabolic law, dual-power law and finally the log law nonlinearity. In particular for Kerr law nonlinearity, there are two additional forms of soliton solutions obtained. They are cosh-Gaussian pulses and bright-dark combo solitons and these are collectively being referred to as exotic solitons. There are several constraint conditions that naturally emerge for these solitons to exist.

Singular and Topological Solitons in Optical Metamaterials by Kudryashov’s Method and G′/G-Expansion Scheme

Singular and Topological Solitons in Optical Metamaterials by Kudryashov’s Method and <i>G</i>′<i>/G</i>-Expansion Scheme

Solitons in Optical Metamaterials with Trial Solution Approach and Bäcklund Transform of Riccati Equation

Solitons in Optical Metamaterials with Trial Solution Approach and Bäcklund Transform of Riccati Equation

Singular solitons in optical metamaterials by ansatz method and simplest equation approach

This paper derives singular 1-soliton solution for optical metamaterials. There are two integration approaches that obtains the solution. These are the ansatz approach and the simplest equation approach. The second method also leads to an additional set of solutions that emerge as a by-product. These are topological soliton, rational solution and singular periodic solution. The constraint conditions for the existence of these solutions are also exhibited. The numerical simulation of a topological 1-soliton solution is also exhibited.

Bright and dark solitons in optical metamaterials

This paper addresses the dynamics of solitons in optical metamaterials. Both bright and dark soliton solutions are obtained. The ansatz method of integration is employed to extract the 1-soliton solutions to the governing equations. A couple of constraint relations are obtained in order for these solitons to exist. A few numerical simulations are also given to expose the dissipative effects.