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The exotic behavior of the wave evolution in Levy crystals within a fractional medium.

ABSTRACT: We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By simultaneously adjusting the fractional and nonlinear terms, we create sharp pulses, which is an essential issue in optoelectronic devices. We illustrate that the effects of barrier height and width on the transmission coefficient are strangely different for the standard and fractional Schrödinger equations. We observe fortunately soliton-like localized wave packets in the fractional regime. Thus, we can effectively control the behavior of the wave evolution by adjusting the available parameters, which can excite new ideas in optics.

SUBMITTER: Zakeri Z

PROVIDER: S-EPMC10676430 | biostudies-literature | 2023 Nov

REPOSITORIES: biostudies-literature

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The exotic behavior of the wave evolution in Lévy crystals within a fractional medium.

Zakeri Z Z Solaimani M M Lavaei L L Terohid S A A SAA

Scientific reports 20231125 1

We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By ...[more]

PMID: 38007603

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Project description:This study investigates the paraxial approximation of the M-fractional paraxial wave equation with Kerr law nonlinearity. The paraxial wave equation is most important to describe the propagation of waves under the paraxial approximation. This approximation assumes that the wavefronts are nearly parallel to the axis of propagation, allowing for simplifications that make the equation particularly useful in studying beam-like structures such as laser beams and optical solitons. The paraxial wave equation balances linear dispersion and nonlinear effects, capturing the essential dynamics of wave evolution in various media. It plays a crucial role in understanding phenomena like diffraction, focusing, and self-phase modulation in optical fibers. It substantially contributes to our comprehension of the special characteristics of optical soliton solutions and the dynamics of soliton in a variety of optical systems. We create a range of wave structures using the powerful extended Jacobian elliptic function expansion (EJEFE) method, including periodic waves, lump-periodic waves, periodic breather waves, kink-bell waves, kinky-periodic waves, anti-kinky-periodic waves, double-periodic waves, etc. These solutions have applications in wave dynamics in different optical systems and optical fibre. Furthermore, we investigate chaotic phenomena by analyzing the model qualitatively. We analyze phase portraits in detail for a range of parameter values to provide insights into the behavior of the system. We also investigate the sensitivity analysis for diverse parametric values of the perturbated coefficient. We may use various strategies, including time series and 3D and 2D phase patterns, to identify chaotic and quasi-periodic phenomena by providing an external periodic strength. The above discussion of the suggested method demonstrates adaptability and usefulness in resolving a broad spectrum of mathematics and physical difficulties, indicating its potential for generating such optical solutions.

Dataset Information

The exotic behavior of the wave evolution in Levy crystals within a fractional medium.

Publications

The exotic behavior of the wave evolution in Lévy crystals within a fractional medium.

Similar Datasets

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