Fifth-order Nonlinearity Research Articles

Numerical analysis of fractional nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass

This paper focuses on the numerical investigation of the fractional nonlinear oscillator for a restrained cantilever beam with an intermediate lumped mass. A numerical approach based upon the fractional complex transformation and the global residue harmonic balance method (FCT-GRHBM) is suggested for approximately solving this fractional oscillation system of fifth-order nonlinearity. The approximated fractional periodic solutions and frequencies are provided by FCT-GRHBM, which are not touched in the existing literature. Numerical results and sensitive analysis with respect to different parameters are shown to confirm its efficiency.

Third- and fifth-order nonlinearities in quantum dot hybrid systems: Influence of graphene and metal nanoparticles

This work examines the third-order and fifth-order nonlinear susceptibilities in a hybrid system including a semiconductor quantum dot, metallic nanoshell, and graphene nanodisk. The research uses the density matrix method to examine the dipole–dipole interaction that occurs due to the applied field. It assumes that there is an increase in the strength of a continuous-wave electromagnetic field inside the quantum dot. The inclusion of the graphene nanodisk greatly amplifies the nonlinear optical reaction of the quantum dot in this combined system, which is governed by the dipole–dipole interaction. The findings indicate a notable disparity in the nonlinear optical reaction of the semiconductor quantum dot when the parameters are modified. The possible applications of this concept include optical sensors, photonic devices, quantum computing, medical imaging, energy harvesting, and high-density data storage. Additionally, it has the potential to progress terahertz technology and simplify the development of new materials with customized optical properties. The substantial rise in nonlinearities inside the hybrid system presents prospects for advancements in diverse technological and scientific domains.

Z-scan of ITO nanocrystals grown inside glass.

Indium tin oxide (ITO) nanocrystals 1-10 nm in size were grown via thermal treatment of a boroaluminosilicate parent glass. The nonlinear behavior of the obtained glass-ceramic was investigated with the Z-scan technique using 550 ps pulses of a 532 nm source at a 500 Hz repetition rate. The nonlinear response was rich, with the sample exhibiting third- and fifth-order nonlinearities as well as saturable absorption and two-photon absorption (TPA), depending on the locale probed. Photoinduced changes were also observed, with high intensity exposures yielding an increased magnitude of the response when lower power trials were subsequently repeated at the same sample position. The work demonstrates that ITO nanocrystal precipitation in bulk glass yields effective nonlinear response and suggests that with further development may enable more compact devices exploiting ITO and the need for particle deposition routes.

Enhancing the performance of coherent Ising machines in the large-noise regime with a fifth-order nonlinearity

Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.

Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws.

Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang-Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the τ in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the τ in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.

ENTANGLEMENT IN NONLINEAR TWO-QUBIT TAVIS — CUMMINGS
 MODEL

In this work, we have studied the dynamics of entanglement of two identical superconducting qubits resonantly interacting with the one-mode field of a coplanar microwave cavity without loss through single-photon transitions in the presence of third- and fifth-order nonlinearities. Based on the solution of the equation of evolution of the system for the Fock initial states of the cavity field, the criterion of qubits entanglement negativity is calculated. The results of the negativity calculation show that for the initial separable states, the cavity nonlinearity can lead to a significant increase in the maximum degree of qubit entanglement. It is shown that for the initial entangledstates of qubits and intense cavity fields, taking into account nonlinearities leads to stabilization of the degree of entanglement of qubits in the cavity and contributes to the disappearance of the effect of the entanglement sudden death of qubits.

Fifth-order nonlinear optical response of Alq3 thin films

The fifth-order optical nonlinearity of Tris-(8-hydroxyquinoline) aluminium (Alq3) thin films deposited on quartz substrates when exposed to an intense laser excitation of mid-infrared femtosecond pulses is investigated. This property was examined by generating the fifth-harmonic frequency of the driving field whose signal strength as a function of laser intensity is well described by a power-law scaling. The perturbative nature of the underlying mechanism enabled the linking of the process directly to the fifth-order nonlinear optical susceptibility χ(5). We also utilized the open-aperture z-scan for studying the nonlinear absorption aspect of the third-order nonlinear optical properties of the sample. It was found that Alq3 thin-films inherit the same saturable absorption character reported in Alq3 solutions under continuous laser excitation in the visible range, with a comparable value of the nonlinear absorption coefficient βeff (in the order of 10−2 cm/W).

Localization of electromagnetic waves in a zigzag lattice of waveguides with competing cubic and quintic nonlinear responses

The zigzag waveguide array is considered, where even waveguides are composed of optically linear material, and their nearest neighbors are characterized by positive cubic nonlinearity and negative fifth-order nonlinearity. In the continuum (long-wave) approximation the solutions of the system of coupled wave equations are found, which describe waves localized in the lattice and harmonic propagating waves. Keywords: nonlinear waves, discrete photonics, waveguides, solitons.

Third- and fifth-order optical nonlinearities of norbixin

In this work, we investigated the nonlinear response of norbixin (C24H28O4) in acetone. The third- and fifth-order optical nonlinearities were measured using the conventional Z-scan technique, with 357 fs laser pulses at 1040 nm and low-repetition rate (1 kHz). It is shown that, at intensities lower than 99GW/cm2, the nonlinear refraction process was determined by the only third-order process. However, at higher intensities, the third- and fifth-order refractive nonlinearities coexist with opposite signs: n2 = (4.43 ± 0.44) × 10−16 cm2/W and n4 = (−4.65 ± 0.46) × 10−27 cm4/W2. On the other hand, the open-aperture Z-scan measurements show an effective three-photon absorption (3PA) with 9.19±0.92×10-23 cm4/W2. The physical mechanisms of the observed nonlinearity are also discussed.

A new form of general soliton solutions and multiple zeros solutions for a higher-order Kaup–Newell equation

Due to the fact that the higher-order Kaup–Newell (KN) system has more complex and diverse solutions than the classical second-order flow KN system, the research on it has attracted much attention. In this paper, we consider a higher-order KN equation with third-order dispersion and fifth-order nonlinearity. Based on the theory of the inverse scattering, the matrix Riemann–Hilbert problem is established. Through the dressing method, the solution matrix with simple zeros without reflection is constructed. In particular, a new form of solution is given which is more direct and simpler than previous methods. In addition, through the determinant solution matrix, the vivid diagrams and dynamic analysis of single-soliton solution and two-soliton solution are given in detail. Finally, by using the technique of limit, we construct the general solution matrix in the case of multiple zeros, and the examples of solutions for the cases of double zeros, triple zeros, single–double zeros, and double–double zeros are especially shown.

Nonlinear Analysis and Bifurcation Characteristics of Whirl Flutter in Unmanned Aerial Systems

Aerial drones have improved significantly over the recent decades with stronger and smaller motors, more powerful propellers, and overall optimization of systems. These improvements have consequently increased top speeds and improved a variety of performance aspects, along with introducing new structural challenges, such as whirl flutter. Whirl flutter is an aeroelastic instability that can be affected by structural or aerodynamic nonlinearities. This instability may affect the prediction of potentially dangerous behaviors. In this work, a nonlinear reduced-order model for a nacelle-rotor system, considering quasi-steady aerodynamics, is implemented. First, a parametric study for the linear system is performed to determine the main aerodynamic and structural characteristics that affect the onset of instability. Multiple polynomial nonlinearities in the two degrees of freedom nacelle-rotor model are tested to simulate possible structural nonlinear effects including symmetric cubic hardening nonlinearities for the pitch and yaw degrees of freedom; purely yaw nonlinearity; purely pitch nonlinearity; and a combination of quadratic, cubic, and fifth-order nonlinearities for both degrees of freedom. Results show that the presence of hardening structural nonlinearities introduces limit cycle oscillations to the system in the post-flutter regime. Moreover, it is demonstrated that the inclusion of quadratic nonlinearity introduces asymmetric oscillations and subcritical behavior, where large and potentially dangerous deformations can be reached before the predicted linear flutter speed.

Third- and fifth-order optical nonlinearity in PbO-BaO-Na2O-Nb2O5-SiO2 glass and glass-ceramic nanocomposite dielectrics

We investigate the optical nonlinearity in 6PbO–4BaO–20Na2O–40Nb2O5–30SiO2 glass and glass-ceramic containing ferroelectric Ba2NaNb5O15 nanocrystals and Pb2Nb2O7 nanocrystals using Z-scan method. The values of the third-order (n2) and fifth-order (n4) nonlinear refractive indices are quantitatively determined as 1.76 × 10−17 m2/W and −2.29 × 10−31 m4/W2 in glass phase, respectively, and 2.62 × 10−17 m2/W and −2.89 × 10−31 m4/W2 in glass-ceramic, respectively. The values of three-photon absorption coefficient of the glass and glass-ceramic are obtained as 8.60 × 10−27 m3/W2 and 1.22 × 10−26 m3/W2, respectively. The samples satisfy the criterion for all-optical switching and have potential applications for all-optical photonic devices.

Anisotropy of 2PA, 3PA, and Kerr effect in nonpolar ZnO.

Anisotropic optical nonlinearity plays an important role in polarization-dependent optoelectronic devices. Taking the advantage of in-plane crystallographic axis, the polarization dependence of third- and fifth-order nonlinearity in nonpolar ZnO has been investigated by z scan. Here, we established the theory model of anisotropic relation of fifth-order nonlinearity in hexagonal wurtzite crystal. Both two-photon absorption (2PA) and three-photon absorption (3PA) coefficients exhibit anisotropic oscillations with a period of 180°, and the polarization modulation factor and anisotropy coefficient (rp,σ) are measured as (2.10, 1.84) for β2, and (1.66, 1.33) for β3, respectively. This is the first time, to the best of our knowledge, that the anisotropy of the fifth-order optical nonlinear effect has been characterized and confirmed. It is verified that the self-defocusing effect at 500 nm is isotropy, while the self-focusing effect at 800 nm exhibits significant anisotropy. The maximum value of the nonlinear figure of merit is 5.84 along the [0010] crystalline direction, nearly 1.6 times the minimum value, revealing that ZnO exhibits potential for nonlinear applications containing polarization-related all-optical switching components.

Enhanced fifth-order nonlinearity with competing linear and nonlinear susceptibility via Fano interference

Enhanced fifth-order nonlinearity with Fano interference is theoretically studied in asymmetric double quantum wells. The resonant tunneling induces constructive interference for third- and fifth-order nonlinearities. Their competition causes a transparency window at some frequency detuning, where the fifth-order refractive index can be simultaneously enhanced by Fano interference. Simulation results show that fifth-order nonlinearity can be enhanced by about 10 times compared to that without the Fano effect. Also, the influence of different strengths of resonant tunneling coupling and Fano interference on enhanced high-order nonlinearity is discussed.

Emergence of fifth-order optical nonlinearity in 2-(2-Quinolyl)-1,3-indandione with strong third-order nonlinear effect under low power CW laser excitation

The present work reports the presence of fifth-order optical nonlinearity in 2-(2-Quinolyl)-1,3-indandione, an organic dye, at low intensity level. Photophysical, structural and vibrational properties were studied by theoretical and experimental methods. Z-scan study of the dye revealed that the compound has a self-defocusing behaviour at continuous Nd:YAG 532 nm laser excitation and exhibited reverse saturable absorption. The positive fifth-order nonlinear refractive index (n4) is of the order of 10−10 cm4/W2. The nonlinearities present in the compound has both thermal and electronic origin. This study reveals that the material is a potential candidate as an optical limiter at low power.

A Fifth-Order Nonlinear Schrödinger Equation for Waves on the Surface of Finite-Depth Fluid

We derive a high-order nonlinear Schr¨odinger equation with fifth-order nonlinearity for the envelope of waves on the surface of a finite-depth irrotational, inviscid, and incompressible fluid over the flat bottom. This equation includes the fourth-order dispersion, cubic-quintic nonlinearity, and cubic nonlinear dispersion effects. The coefficients of this equation are given as functions of one dimensionless parameter kℎ, where k is the carrier wave number, and ℎ is the undisturbed fluid depth. These coefficients stay bounded in the infinite-depth limit.

Influence of fifth-order nonlinearities on the statistical fluctuations in emission intensities in a photonic open-cavity complex system

High-order nonlinear optical effects have become an important feature of photonic systems, both ordered and disordered. In this work, a very large and robust set of experimental data obtained from the emission spectra of a trivalent neodymium ion-based random laser, whose action mechanism relies upon gain and disorder, was characterized in detail. Using an effective model, it was possible to describe how the optical nonlinearities of the disordered gain medium affect the statistical behavior of the intensity fluctuations of the random laser for excitations close to and well above the laser threshold. A theoretical framework is presented and, in particular, in the regime well above threshold a nice fit to the experimental data is obtained with a distribution that incorporates nonlinearities up to fifth order, the Izrailev distribution.

On the double sphere model of synchronization

The Kuramoto model has many higher-dimensional generalizations with similar synchronization behaviour, such as phase oscillators on the n-sphere which under suitable conditions can synchronize in any dimension n, with applications to swarming and flocking phenomena as well as to consensus and opinion formation. We consider further generalizations in which trajectories lie on the double sphere Sn−1×Sm−1 for any dimension m,n with synchronization properties that depend on the underlying parameters, and reduce to previously studied models for specific m or n. In such systems the synchronization properties on one sphere can be controlled from the other sphere by parameters such as the frequencies of oscillation and the connectivity coefficients. We show in particular that for these models the conformal group SO(n,m) acts as a time-evolution matrix, for example in the special case of the Kuramoto model there is an SO(2,1) matrix at each node which maps the initial value to the final value at any time t. For uniform coupling and identical frequencies, the time evolution of the Kuramoto model is controlled over all nodes by a single SO(2,1) matrix, a property which follows from the Watanabe–Strogatz reduction. This generalizes to the double sphere model with uniform coupling and identical frequency matrices, which we show is partially integrable for any m,n, and the system again evolves by means of a single time-evolution matrix in SO(n,m) which acts over all nodes. We explicitly perform the partial integration by means of a unit map which generalizes linear fractional transformations, equivalently Möbius maps Sn−1→Sn−1 for the case m=1, which have been previously used to reduce the n-sphere equations. As with the Kuramoto model, there exist conserved cross ratios which restrict all solutions to lie in a low-dimensional manifold. We parametrize SO(n,m) and so derive reduced equations, independent of N in number, which exactly solve the double sphere equations for any N. These models, and their further extensions to unit sphere systems with fifth-order nonlinearities, furnish a wide range of exactly reducible synchronization models which can be used to investigate systems for very large N.

Influence of the Fifth-Order Nonlinearity of Gold Nanorods on the Performance of Random Lasers

We present the first experimental evidence for the influence of the fifth-order nonlinearity on the characteristics of Random Lasers with plasmonic nanoparticles as scatterers. The experiments were...

Transmission of M-type combined solitary wave in the birefringent fiber with comprehensive management

In this paper, we reveal the transmission properties of the M-type combined solitary wave in birefringent fiber with third-order dispersion, self-frequency shift, self-steepening, fifth-order nonlinearity and the gain (loss) effects. The numerical simulations show that the M-type solitary wave can be stably transmitted through 300 dispersion lengths via balancing the variety of effects. And it can even be stably transmitted under the condition of limited interference under a small perturbation of noise, amplitude and phase position. The results can provide certain references for the research of optical soliton communication and optical devices.