Nonlinear Dispersion Research Articles

Dispersive terahertz metasurface fed by a horn antenna for highly oriented 2D beam steering

Highly oriented beam steering will enhance power density and field of view (FOV) in terahertz wireless links. Metasurface can be constructed by deliberate arrangement of subwavelength meta-cells to manipulate the wavefront. This paper explores a dispersive metasurface with a specific phase gradient patterned in a 2-inch aperture, allowing for collimated beamforming and two-dimensional (2D) beam steering by a combination of frequency tuning and metasurface rotation. The metasurface is directly fed by a horn antenna, ensuring a compact integration. Simulation and experiment in the 80-110 GHz band revealed that the gain band crucial for FOV and efficiency is mainly constrained by the nonlinear phase dispersion of the meta-cells. Efforts to optimize the phase linearity resulted in a more efficient metasurface with a gain of 35.7 dBi and an efficiency of 76.6% at 400 GHz. A FOV of 22.5° in the elevation was guaranteed with gain in the 325-500 GHz band (a bandwidth of 42.4%). Imaging of two scattering balls was demonstrated at a distance of 4.1 meters by using the metasurface for 2D beam steering.

Extraction of newly soliton wave structure of generalized stochastic NLSE with standard Brownian motion, quintuple power law of nonlinearity and nonlinear chromatic dispersion

Stochastic optical solitons are a fascinating phenomenon in nonlinear optics where soliton-like behavior emerges in systems affected by stochastic noise. This study investigates the influence of Brownian motion on wave propagation in optical fibers. The propagation is modeled using a stochastic nonlinear Schrödinger equation incorporating quintuple power-law nonlinearity and nonlinear chromatic dispersion. To explore this, the improved modified extended tanh (IMET) scheme, leveraging the extended Riccati equation, is employed. This technique facilitates the extraction of various stochastic solutions, including bright, dark, and singular solitons. Furthermore, solutions in the shapes of exponential, singular periodic, and Weierstrass elliptic forms are investigated. The study looks at how the strength of noise impacts various solutions, and Matlab software is used to create 2D and 3D graphs that show the results. It has been noted that when noise intensity rises, signal level falls and surface flattens.

Dependence of Structure Variation, Pyrolysis, and Nonlinear Optical Dispersion on the Chemical Etching of Poly Allyl Diglycol Carbonate (PADC) Irradiated with $${\alpha}$$-Particles

Dependence of Structure Variation, Pyrolysis, and Nonlinear Optical Dispersion on the Chemical Etching of Poly Allyl Diglycol Carbonate (PADC) Irradiated with $${\alpha}$$-Particles

Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case

In this paper, we study the spectral theory of soliton condensates - a special limit of soliton gases - for the focusing NLS (fNLS). In particular, we analyze the kinetic equation for the fNLS circular condensate, which represents the first example of an explicitly solvable fNLS condensate with nontrivial large scale space-time dynamics. Solution of the kinetic equation was obtained by reducing it to Whitham type equations for the endpoints of spectral arcs. We also study the rarefaction and dispersive shock waves for circular condensates, as well as calculate the corresponding average conserved quantities and the kurtosis. We want to note that one of the main objects of the spectral theory - the nonlinear dispersion relations - is introduced in the paper as some special large genus (thermodynamic) limit the Riemann bilinear identities that involve the quasimomentum and the quasienergy meromorphic differentials.

High‐Order Nonlinear Frequency Conversion in Transparent Conducting Oxide Thin Films

AbstractThe study of conductive oxides has gained momentum within the photonics community due to their unique linear and nonlinear optical properties. Despite recent experiments reporting on high harmonic generation from thin films, the optical/electronic behavior of these compounds at the nanoscale is still not fully understood due to the lack of a suitable theoretical model. In the present work, aluminum zinc oxide is excited near its epsilon‐near‐zero crossing point using incident femtosecond pulses having peak power densities in the 1 TW cm−2 range. A relatively efficient frequency up‐conversion including even and odd harmonics up to the seventh order is observed. A hydrodynamic‐Maxwell theoretical approach is adopted, capable of simultaneously taking into account linear and nonlinear dispersions, nonlocal effects, surface, magnetic, and bulk nonlinearities in a spectral region that spans over two and a half octaves from the UV to the NIR region. The study enables a deeper understanding of the fundamental material parameters regulating optical nonlinearities, providing important insights to engineer this class of materials for applications in sensing, ultra‐fast physics, and spectroscopy.

Analyzing the dynamics of multi-solitons and other solitons in the perturbed nonlinear Schrödinger equation

The perturbed nonlinear Schrödinger equation is employed to characterize the dynamics of optical wave propagation when confronted with dissipation (or gain) and nonlinear dispersion that vary with both time and space. This equation serves as a fundamental model for investigating pulse dynamics within optical fibers and has application to nanofiber applications. This study successfully discovers optical solitons within this framework using the unified solver, Jacobi elliptic function, and simplest equation methods. We extract solutions using hyperbolic, trigonometric, and rational functions, including multi-solitons, dark, singular, bright, and periodic singular solitons. This study thoroughly compares our results with existing literature to provide novelty and significance of our findings. We have incorporated a detailed comparison between the methods employed in our study, which highlights their importance and strength. We have derived soliton solutions for the examined equations and generated 3D contour and 2D visual representations of the resulting solution functions. Alongside obtaining the soliton solutions, we offer a graphical exploration of how the parameters in the considered equations influence the system.

Linear and nonlinear exciton polariton dispersion in MoS2 nanosheets and its nickel doping dependence

In this paper, we study the influence of Ni-doping on A- and B-exciton polariton dispersion in MoS2 nanosheets. In particular, we have calculated the effect of the Ni-concentration on the energy dispersion and therefore we have deduced the effective masses by adjusting the hopping parameter. The E A , E B -exciton transition energies and the hopping parameter are discerned from the PL of Ni-MoS2 nanosheets. It is shown that the Ni changes considerably the bandgap and as a result the electronic band structure, the effective masses, the optical transition, and the hopping term. We found that the increasing concentration of Ni-dopant can modulate and favors the mixture of A- and B-exciton peaks of MoS2 nanosheets. The diverging Ni-concentration of A- and B-exciton polariton dispersion are also discerned and discussed. Finaly, we can predict that these changes caused by the influence of Ni-doping can be used in most applications involving exciton polariton dispersion for photonics and optoelectronics devices.

Chirped gray and singular optical solitons with generalized quadratic-cubic law of self-phase modulation and nonlinear chromatic dispersion

Chirped gray and singular optical solitons with generalized quadratic-cubic law of self-phase modulation and nonlinear chromatic dispersion

Visualization of non-linear continuous wave dispersion effects on fiber grating with spreadsheets in online learning

Spreadsheet software is a practical and straightforward computing and graphics tool. The use of Spreadsheets can reduce the risk of practicum in class and can be used remotely. This research presents a simple way to build a physics simulation based on mathematical equations in spreadsheet software. The simulation aims to visualize the effect of non-linear continuous wave dispersion on fiber gratings. Simulations can visualize different modes. The mathematical equations in fiber optics for non-linear effects are quite complex. Visualization can assist students in interpreting mathematical equations and making connections between theoretical and experimental modeling.

Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media

Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media

Novel Spectrometer Designs for Laser-Driven Ion Acceleration

We propose novel spectrometer designs that aim to enhance the measured spectral range of ions on a finite-sized detector. In contrast to the traditional devices that use a uniform magnetic field, in which the deflection of particles increases inversely proportional to their momentum, in a gradient magnetic field, the deflection of particles will decrease due to the reduction of the magnetic field along their propagation. In this way, low-energy ions can reach the detector because they are deflected less, compared to the uniform field case. By utilizing a gradient magnetic field, the non-linear dispersion of ions in a homogeneous magnetic field approaches nearly linear dispersion behavior. Nonetheless, the dispersion of low-energy ions, using a dipole field, remains unnecessarily high. In this article, we discuss the employed methodology and present simulation results of the spectrometer with an extended ion spectral range, focusing on the minimum detectable energy (energy dynamic range) and energy resolution.

M-truncated fractional form of the perturbed Chen–Lee–Liu equation: optical solitons, bifurcation, sensitivity analysis, and chaotic behaviors

This investigation discusses the modified M-truncated form of the perturbed Chen–Lee–Liu (pCLL) dynamical equation. The pCLL equation is a generalization of the original CLL equation, which describes the propagation of optical solitons in optical fibers. The pCLL equation includes additional terms that account for various influences such as chromatic dispersion, nonlinear dispersion, inter-modal dispersion, and self-steepening. A new version of the generalized exponential rational function method is utilized to obtain multifarious types of soliton solutions. Moreover, the planar dynamical system of the concerned equation is created using a Hamiltonian transformation, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are added to the analytical results to better understand the dynamic behavior of these solutions. The study’s findings could be extremely useful in solving additional nonlinear partial differential equations.

Internet traffic prediction analog to solitons propagation in optical fibers via the concatenation model and stability analysis

Internet traffic (IT) is a measure of data transfer across devices. In this paper, an analogy is made between data transfer and soliton propagation in optical fibers. This is achieved by employing the concatenation model (CM) that describes soliton propagation in optical fibers, which is presented recently in the literature. The CM contains nonlinear space-time dispersion effect, that may lead to bottleneck soliton shape (BNSS). Thus, in view of this model, BNSS effect of soliton propagation may occur, which is analogous to a possible BN in IT. So, the prediction of the characteristics of internet traffic can be depicted via the CM, which is studied here with Caputo-q time derivative. Also, a variety of exact solutions of the CM are derived. These solutions are represented graphically and they show multiple shapes of concatenated solitons. Among them, bottleneck, M-shaped, hybrid M shaped, chirped solitons and vector of dromian patterns. On the other side, the speed of IT and chips heating are estimated. It is found that the speed of IT is constant with time and the effects of distributed time delay (recent memory (RM)) is to slow the traffic speed. This is done via varying the fractional order. Also, it is observed, when accounting for RM, that the chip heating is too small. We think that the results for the speed of IT and chip heat are, qualitatively, realistic. The stability of a steady state solution is analyzed and the controlled parameters for stability is determined.

A novel semi-implicit WLS scheme for time-memory nonlinear behavior in 2D variable-order TF-NLSEs

In this paper, a novel hybrid semi-implicit meshless weighted least-squares (WLS) scheme H-SIFPM is developed for the first time by coupling the semi-implicit finite point-set method and finite difference method (FDM), and then applied to predict the time-memory nonlinear behavior dominated by a 2D variable-order time-fractional nonlinear Schrödinger equation (TF-NLSE). The proposed H-SIFPM for TF-NLSE is mainly derived from that: firstly, the variable-order time-fractional with Caputo derivative is approximated by a FDM scheme and then imposed to the approximation of WLS as a boundary condition; secondly, the hybrid process is implicitly discretized in temporal level, and an implicit meshless FPM scheme is developed; thirdly, an iterative technique is adopted to treat the implicit format. Subsequently, the estimated error and stability of the proposed scheme is tentatively proved. Moreover, the accuracy and capacity of the proposed H-SIFPM are also tested by solving several examples with constant/variable-order cases, in which a second-order numerical convergent rate is illustrated. We also demonstrate the advantages of the meshless method by solving the problem on complex irregular domain with local refinement. Finally, the nonlinear dispersion behavior dominated by 2D TF-NLSE/TF-GPE with different boundary conditions are predicted, and the FDM results are also presented for comparison. All numerical results show that the proposed H-SIFPM scheme for TF-NLSEs is stable, accurate and flexible.

Correction: Implicit quiescent optical solitons for Lakshmanan–Porsezian–Daniel model having nonlinear chromatic dispersion and power-law of self-phase modulation by Lie symmetry

Correction: Implicit quiescent optical solitons for Lakshmanan–Porsezian–Daniel model having nonlinear chromatic dispersion and power-law of self-phase modulation by Lie symmetry

Nonlinear metasurface engineering with disordered gold nanorods on ITO: a cost-effective approach to broadband response, polarization-independence, and weak nonlinear index dispersion.

The strong coupling of epsilon-near-zero materials with nanoantennas has demonstrated enhanced nonlinear optical responses, yet practical challenges persist. Here, we propose an alternative: an ultrathin metasurface featuring broadband response with a weakly dispersive nonlinear index, achieved through a simple implementation. Our metasurface, comprising a disordered gold nanorod array on indium tin oxide, exhibits polarization-independent behavior and a large average nonlinear refractive index of 5 cm2/GW across a broad wavelength range (1000-1300 nm). Enhanced performance is attributed to the weak coupling between gold nanorods and indium tin oxide, offering a cost-effective method for nonlinear optical metasurfaces and a flexible design in nanophotonic applications.

Quiescent optical solitons for Fokas–Lenells equation with nonlinear chromatic dispersion and a couple of self-phase modulation structures

The focus of the current paper is on the retrieval of quiescent optical solitons from Fokas–Lenells equation with nonlinear chromatic dispersion and having quadratic–cubic as well as quadratic–cubic–quartic forms of self-phase modulation structures. Two integration algorithms are implemented to carry out to seek such soliton solutions. They are the enhanced Kudryashov’s approach and the projective Riccati equation approach. In this context, both linear temporal evolution and generalized temporal evolution effects are addressed. A full spectrum of quiescent optical solitons is thus recovered.

Extended Lie Method for Mixed Fractional Derivatives, Unconventional Invariants and Reduction, Conservation Laws and Acoustic Waves Propagated via Nonlinear Dispersive Equation

Extended Lie Method for Mixed Fractional Derivatives, Unconventional Invariants and Reduction, Conservation Laws and Acoustic Waves Propagated via Nonlinear Dispersive Equation

Analytical insights into the behavior of finite amplitude waves in plasma fluid dynamics

This study introduces innovative analytical solutions for the [Formula: see text]-dimensional nonlinear Jaulent–Miodek ([Formula: see text]) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of [Formula: see text] waves. Within the realm of nonlinear fluid dynamics, the [Formula: see text] equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the [Formula: see text] equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the [Formula: see text] equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the [Formula: see text]-dimensional [Formula: see text] equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field.

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution