Search Results (181)

This study examines the soliton dynamics in the time-fractional cubic–quintic nonlinear non-paraxial propagation model, applicable to optical signal processing, nonlinear optics, fiber-optic communication, and biomedical laser–tissue interactions. The fractional framework exhibits a wide range of nonlinear effects, such as self-phase modulation, wave mixing, and self-focusing, arising from the balance between cubic and quintic nonlinearities. By employing the Multivariate Generalized Exponential Rational Integral Function (MGERIF) method, we derive an extensive catalog of analytic solutions, multi-peakon structures, lump solitons, kinks, and bright and dark solitary waves, while periodic and singular solutions emerge as special cases. These outcomes are systematically constructed within a single framework and visualized through 2D, 3D, and contour plots under both anomalous and normal dispersion regimes. The analysis also addresses modulation instability (MI), interpreted as a sideband amplification of continuous-wave backgrounds that generates pulse trains and breather-type structures. Our results demonstrate that cubic–quintic contributions substantially affect MI gain spectrum, broadening instability bands and permitting MI beyond the anomalous-dispersion regime. These findings directly connect the obtained solution classes to experimentally observed routes for solitary wave shaping, pulse propagation, and instability and instability-driven waveform formation in optical communication devices, photonic platforms, and laser technologies. Full article

The convective Cahn–Hilliard–Oono equation is analyzed under the conditions ${\mu }_1\ge 0$ and ${\mu }_3+{\mu }_4\le 0$. The Lie invariance criteria are examined through symmetry generators, leading to the identification of Lie algebra, where translation symmetries exist in both space and time variables. By employing Lie group methods, the equation is transformed into a system of highly nonlinear ordinary differential equations using appropriate similarity transformations. The extended direct algebraic method are utilized to derive various soliton solutions, including kink, anti-kink, singular soliton, bright, dark, periodic, mixed periodic, mixed trigonometric, trigonometric, peakon soliton, anti-peaked with decay, shock, mixed shock-singular, mixed singular, complex solitary shock, singular, and shock wave solutions. The characteristics of selected solutions are illustrated in 3D, 2D, and contour plots for specific wave number effects. Additionally, the model’s stability is examined. These results contribute to advancing research by deepening the understanding of nonlinear wave structures and broadening the scope of knowledge in the field. Full article

Nanophotonics, the study of light–matter interactions at the nanometer scale, has emerged as a transformative field that bridges photonics and nanotechnology. Using engineered nanomaterials—including plasmonic metals, high-index dielectrics, two-dimensional (2D) materials, and hybrid systems—nanophotonics enables light manipulation beyond the diffraction limit, unlocking novel applications in sensing, imaging, and quantum technologies. This review provides a comprehensive overview of recent advances (post-2020) in nanophotonic materials, fabrication methods, and their cutting-edge applications. We first discuss the fundamental principles governing nanophotonic phenomena, such as localized surface plasmon resonances (LSPRs), Mie resonances, and exciton–polariton coupling, highlighting their roles in enhancing light–matter interactions. Next, we examine state-of-the-art fabrication techniques, including top-down (e.g., electron beam lithography and nanoimprinting) and bottom-up (e.g., chemical vapor deposition and colloidal synthesis) approaches, as well as hybrid strategies that combine scalability with nanoscale precision. We then explore emerging applications across diverse domains: quantum photonics (single-photon sources, entangled light generation), biosensing (ultrasensitive detection of viruses and biomarkers), nonlinear optics (high-harmonic generation and wave mixing), and integrated photonic circuits. Special attention is given to active and tunable nanophotonic systems, such as reconfigurable metasurfaces and hybrid graphene–dielectric devices. Despite rapid progress, challenges remain, including optical losses, thermal management, and scalable integration. We conclude by outlining future directions, such as machine learning-assisted design, programmable photonics, and quantum-enhanced sensing, and offering insights into the next generation of nanophotonic technologies. This review serves as a timely resource for researchers in photonics, materials science, and nanotechnology. Full article

Extreme surface winds and wave heights of tropical cyclones (TCs)—pose serious threats to coastal community, infrastructure and environments. In recent decades, progress in numerical wave modeling has significantly enhanced the ability to reconstruct and predict wave behavior. This review offers an in-depth overview of TC-related wave modeling utilizing different computational schemes, with a special attention to WAVEWATCH III (WW3) and Simulating Waves Nearshore (SWAN). Due to the complex air–sea interactions during TCs, it is challenging to obtain accurate wind input data and optimize the parameterizations. Substantial spatial and temporal variations in water levels and current patterns occurs when coastal circulation is modulated by varying underwater topography. To explore their influence on waves, this study employs a coupled SWAN and Finite-Volume Community Ocean Model (FVCOM) modeling approach. Additionally, the interplay between wave and sea surface temperature (SST) is investigated by incorporating four key wave-induced forcing through breaking and non-breaking waves, radiation stress, and Stokes drift from WW3 into the Stony Brook Parallel Ocean Model (sbPOM). 20 TC events were analyzed to evaluate the performance of the selected parameterizations of external forcings in WW3 and SWAN. Among different nonlinear wave interaction schemes, Generalized Multiple Discrete Interaction Approximation (GMD) Discrete Interaction Approximation (DIA) and the computationally expensive Wave-Ray Tracing (WRT) A refined drag coefficient (C_d) equation, applied within an upgraded ST6 configuration, reduce significant wave height (SWH) prediction errors and the root mean square error (RMSE) for both SWAN and WW3 wave models. Surface currents and sea level variations notably altered the wave energy and wave height distributions, especially in the area with strong TC-induced oceanic current. Finally, coupling four wave-induced forcings into sbPOM enhanced SST simulation by refining heat flux estimates and promoting vertical mixing. Validation against Argo data showed that the updated sbPOM model achieved an RMSE as low as 1.39 m, with correlation coefficients nearing 0.9881. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

Suspended particulate matter (SPM) plays a pivotal role in marine source-to-sink sedimentary systems. Internal solitary waves (ISWs), a prevalent hydrodynamic phenomenon, significantly influence vertical mixing, cross-shelf material transport, and sediment resuspension. Acting as energetic nonlinear waves, ISWs can disrupt the settling trajectories of suspended particles, enhance lateral transport above the pycnocline, and generate nepheloid layers nearshore. Meanwhile, intense turbulent mixing induced by ISWs accumulates large quantities of SPM at both the leading surface and trailing bottom of the waves, thereby altering the structure and dynamics of the intermediate nepheloid layers. This review synthesizes recent advances in the in situ observational techniques for SPM under the influence of ISWs and highlights the key mechanisms governing their interactions. Particular attention is given to representative field cases in the SCS, where topographic complexity and strong stratification amplify ISWs–sediment coupling. Finally, current limitations in observational and modeling approaches are discussed, with suggestions for future interdisciplinary research directions that better integrate hydrodynamic and sediment transport processes. Full article

The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, and further evolution can be achieved by varying the types of dressing fields. However, as the demand for information capacity in quantum communication continues to increase, research on the higher-order seventh-order nonlinear polarizability, based on four-photon states, and the number of coherent channels and resonance positions has gradually come to the forefront. This paper focuses on the simultaneous generation of a seventh-order nonlinear polarizability through a spontaneous eight-wave mixing (SEWM) process in an atomic medium involving four photons. Compared to the fifth-order nonlinear polarizability, the seventh-order polarizability shows an exponential increase in coherent channels and resonance positions due to its strong dressing effect. Additionally, the interaction between the four photons is stronger than that between three photons, making it possible for even the difficult-to-dress eigenvalues to be influenced by the dressing field and dephasing rate, resulting in more complex coherent channels. These are manifested as more complex, damped Rabi oscillations, with periods that can be controlled by the dressing field. These findings may contribute to a promising new method for quantum communication. Full article

Anticyclonic mesoscale eddies are known to trap and modulate near-inertial kinetic energy (NIKE); however, the spatial distribution of NIKE within the eddy core and periphery, as well as the mechanisms driving its energy cascade to smaller scales, remains inadequately understood. This study analyzed the evolution of NIKE in anticyclonic eddies using satellite altimetry and field observations from four mooring arrays. By extracting near-inertial oscillations (NIOs) and subharmonic wave kinetic energy across mooring stations during the same period, we characterized the spatial structure of NIKE within the eddy field. The results revealed that NIKE was concentrated in the eddy core, where strong NIOs (peak velocity ~0.23 m/s) persisted for ~7 days, with energy primarily distributed at depths of 200–400 m and propagating inward from the periphery. Subharmonic waves fD1 generated by interactions between NIOs and diurnal tides highlighted the role of the vertical nonlinear term in energy transfer. A further analysis indicated that under vorticity confinement, NIKE accumulated in the core of the eddy and dissipated through shear instability and nonlinear wave interactions. The migrating anticyclonic eddy thus acted as a localized energy source, driving mixing and energy dissipation in the ocean interior. Full article

We propose a scheme for realizing nonreciprocal optical scattering with non-Hermitian four-wave mixing (FWM) in a double-$\mathsf{\Lambda }$ system of cold atoms driven by coupling and dressing phase-mismatched standing-wave (SW) fields. Four scattering channels—direct transmission, cross transmission, direct reflection, and cross reflection—can be established for a probe and a signal field, some of which are nonreciprocal due to non-Hermitian spatial modulations when the two SW driving fields exhibit a $\pi /4$ phase shift. We find in particular that it is viable to attain single-color unidirectional transport, dual-color unidirectional transport, and single-color directional blockade with respect to a probe and a signal field incident upon this atomic sample from the same side, due to perfect destructive interference between direct and cross scattering channels. This work provides a new paradigm for studying non-Hermitian nonlinear optics and offers a theoretical foundation for designing all-optical atomic devices based on multi-channel nonreciprocal scattering. Full article

Utilizing the phase-matching conditions of inter-modal four-wave mixing in an elliptical-core few-mode fiber supporting three non-degenerate modes, we experimentally demonstrate schemes for generating orbital-angular-momentum (OAM)-entangled photon pairs with high mode purity and for achieving highly mode-selective frequency conversion of beams in OAM-compatible (LP_11a, LP_11b) mode basis. These techniques expand the toolbox for using OAM modes in both classical and quantum communications and information processing. Full article

While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using and controlling electronic and optical mesoscopic systems with bilayer graphene (BLG), representing an easily accessible anisotropic material for electrons when trigonal warping is present, we investigate billiards of various anisotropies and geometries using a trajectory-tracing approach founded on the concept of ray–wave correspondence. We find that the presence of anisotropy can change the billiards’ dynamics dramatically from its isotropic counterpart. It may induce chaotic and mixed dynamics in otherwise integrable systems and may stabilize originally unstable trajectories. We characterize the dynamics of anisotropic billiards in real and phase space using Lyapunov exponents and the Poincaré surface of section as phase space representation. Full article

In this article, we propose a cell-free network architecture for an unmanned aerial vehicle (UAV) base station (BS), i.e., UBS, incorporating high-altitude platform stations (HAPSs) as central processing units (CPUs). The goal is to guarantee the quality of service (QoS) of user equipment (UE), reduce energy consumption, extend communication time, and facilitate rescue operations. The millimeter-wave (mmWave) frequency band is deployed in access and backhaul links to satisfy UE QoS requirements and high backhaul demands. The proposed framework jointly optimizes user association, backhaul bandwidth allocation, and power allocation to maximize energy efficiency while meeting QoS requirements. The optimization problem, modeled as non-convex mixed-integer nonlinear fractional programming, is solved through a three-stage iterative algorithm. This includes (1) optimizing power allocation based on Dinkelbach transformation and a successive convex approximation (SCA) method, (2) clustering UBSs using the Lagrangian method, and (3) deriving a closed-form bandwidth allocation factor. The proposed algorithm significantly outperforms many traditional algorithms in performance while maintaining low computational complexity. Full article

The year 2024 marks the 30-year anniversary of the quantum cascade laser (QCL), which is becoming the leading laser source in the mid-infrared (mid-IR) range. Since the first demonstration, QCL has undergone tremendous development in terms of the output power, wall plug efficiency, spectral coverage, wavelength tunability, and beam quality. Owing to its unique intersubband transition and fast gain features, QCL possesses strong nonlinearities that makes it an ideal platform for nonlinear photonics like terahertz (THz) difference frequency generation and direct frequency comb generation via four-wave mixing when group velocity dispersion is engineered. The feature of broadband, high-power, and low-phase noise of QCL combs is revolutionizing mid-IR spectroscopy and sensing by offering a new tool measuring multi-channel molecules simultaneously in the μs time scale. While THz QCL difference frequency generation is becoming the only semiconductor light source covering 1–5 THz at room temperature. In this paper, we will introduce the latest research from the Center for Quantum Devices at Northwestern University and briefly discuss the history of QCL, recent progress, and future perspective of QCL research, especially for QCL frequency combs, room temperature THz QCL difference frequency generation, and major challenges facing QCL in the future. Full article

A nonlinear $(3+1)$-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention. Various wave solutions are produced with the aid of the Hirota bilinear and Cole–Hopf transformation techniques. By selecting the appropriate polynomial function and implementing the distinct transformations in bilinear form, bright lump waves, dark lump waves, and rogue waves (RWs) are generated. A positive quadratic transformation and cosine function are combined in Hirota bilinear form to evaluate the RW solutions. Typically, RWs have crests that are noticeably higher than those of surrounding waves. These waves are also known as killer, freak, or monster waves. The lump periodic solutions (LPSs) are obtained using a combination of the cosine and positive quadratic functions. The lump-one stripe solutions are computed by using a mix of positive quadratic and exponential transformations to the governing equation. The lump two-stripe solutions are obtained by using a mix of positive quadratic and exponential transformations to the governing equation. The interactional solutions of lump, kink, and periodic wave solutions are obtained. Additionally, mixed solutions with butterfly waves, X-waves and lump waves are computed. The Ma breather (MB), Kuznetsov–Ma breather (KMB), and generalized breathers GBs are generated. Furthermore, solitary wave solution is obtained and a relation for energy of the wave via ansatz function technique. Full article

In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann–Liouville and Caputo fractional derivatives with orders $0<\alpha <1$ and $1<\beta <2$. We identify the infinitesimal generator of the cosine family and analyze the stability of the mild solution using both Hyers–Ulam–Rassias and Hyers–Ulam stability methodologies, ensuring robust and reliable results for fractional dynamic systems with delay. In order to guarantee that the features of invariance under transformations, such as rotations or reflections, result in the presence of fixed points that remain unchanging and represent the consistency and balance of the underlying system, fixed-point theorems employ the symmetry idea. Lastly, the results obtained are applied to a fractional order nonlinear wave equation with finite delay with respect to time. Full article