Propagation of W-shaped and M-shaped solitons with multi-peak interaction for ultrashort light pulse in fibers

Using the unified solver technique, the rigorous and effective new novel optical progressive and stationary structures are established in the aspects of hyperbolic, trigonometric, rational, periodical and explosive types. These types are concrete in the stochastic nonlinear Schrödinger equations (NLSEs) with operative physical parameters. The obtained stochastic solutions with random parameters that are founded in the form of rational, dissipative, explosive, envelope, periodic, and localized soliton can be utilized in fiber applications. The stochastic modulations of structures' amplitude and frequency caused by dramatic instantaneous influences of both fibers nonlinear, dispersive, losing and noise term effects maybe very important in new fiber communications.

New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics

Acoustic metasurfaces are at the frontier of acoustic functional material research owing to their advanced capabilities of wave manipulation at an acoustically vanishing size. Despite significant progress in the last decade, conventional acoustic metasurfaces are still fundamentally limited by their underlying physics and design principles. First, conventional metasurfaces assume that unit cells are decoupled and therefore treat them individually during the design process. Owing to diffraction, however, the non-locality of the wave field could strongly affect the efficiency and even alter the behavior of acoustic metasurfaces. Additionally, conventional acoustic metasurfaces operate by modulating the phase and are typically treated as lossless systems. Due to the narrow regions in acoustic metasurfaces' subwavelength unit cells, however, losses are naturally present and could compromise the performance of acoustic metasurfaces. While the conventional wisdom is to minimize these effects, a counter-intuitive way of thinking has emerged, which is to harness the non-locality as well as loss for enhanced acoustic metasurface functionality. This has led to a new generation of acoustic metasurface design paradigm that is empowered by non-locality and non-Hermicity, providing new routes for controlling sound using the acoustic version of 2D materials. This review details the progress of non-local and non-Hermitian acoustic metasurfaces, providing an overview of the recent acoustic metasurface designs and discussing the critical role of non-locality and loss in acoustic metasurfaces. We further outline the synergy between non-locality and non-Hermiticity, and delineate the potential of using non-local and non-Hermitian acoustic metasurfaces as a new platform for investigating exceptional points (EPs), the hallmark of non-Hermitian physics. Finally, the current challenges and future outlook for this burgeoning field are discussed.

Non-local and non-Hermitian acoustic metasurfaces.

Abstract The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons. 

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

Spherical traveling wave hypothesis for geometric optical phase with speherical magnetic ferromagnetic system

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers. 

/pdf/w-shaped-profile-and-breather-like-soliton-of-the-fractional-ms7fs43o.pdf

W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

The propagation of the modulated wave (MW) pattern and its instability in the nonlinear medium is an important study from where experimental results are obtained. In this work, we use the nonlinear Schrödinger equation (NLSE) with saturation nonlinearity (SN) which describes the solitonic waves in the molecular chain (MC) model. We set our study on the effectiveness of the acoustic longitudinal velocity (ALV) which is related to the acoustic longitudinal vibration to investigate the behavior of the MW patterns as well as the modulation instability (MI) gain. Its results are that the ALV creates instability zones, increases MI bands, and shortens the transition regime of the MW pattern. For a long time of simulation and a great enough value of the ALV, the MWs feature chaos-like motion. Alongside these results the ALV obvious itself as a tool control of MWs as well as an energy source for the propagation of diverse MW-shaped in the MC.

/pdf/modulation-instability-gain-and-modulated-wave-shape-incited-2i0dlevu.pdf

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

An efficient mass sensor based on exceptional points (EPs), engineered under a synthetic magnetism requirement, is proposed. The benchmark system consists of an electromechanical (optomechanical) system where an electric (optical) field is driving two mechanical resonators that are mechanically coupled through a phase-dependent phonon hopping. This phase induces a series of EPs once it matches the condition of $\ensuremath{\pi}/2(2n+1)$. For any perturbation of the system, the phase-matched condition is no longer satisfied, and this lifts the EP degeneracies, leading to a frequency splitting that scales as the square root of the perturbation strength, resulting in a giant sensitivity-factor enhancement. Owing to the set of EPs, our proposal allows a multiple-sensing scheme and performs better than its anti-$PT$-symmetric sensor counterpart. This work sheds light on platforms that can be used for mass-sensing purposes, opening up new opportunities in nanoparticle or pollutant detection and in water treatment. 

Sensor Sensitivity Based on Exceptional Points Engineered via Synthetic Magnetism

W-shaped Pro le and Breather-like Soliton of the Fractional Nonlinear Schrödinger Equation Describing the Polarization Mode in Optical Fibers

pdf/nonreciprocal-transmission-in-hybrid-atomic-ensemble-0pvtrg6yjsc4.pdf

Nonreciprocal transmission in hybrid atomic ensemble–optomechanical systems

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