Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.

Broad-Band All-Optical Wavelength Conversion of Differential Phase-Shift Keyed Signal Using an SOA-Based Nonlinear Polarization Switch

Broad-band all-optical wavelength conversion of differential phase-shift keyed （DPSK） signal is experimentally demonstrated. This scheme is composed of a one-bit delay interferometer demodulation stage followed by a semiconductor optical amplifier （SOA） based nonlinear polarization switch. A wavelength converter for the 10 G b/s DPSK signal is presented, which has a wide wavelength range of more than 30 nm. The converted signals experience small power penalties less than 1.4 dB compared with the original signal, at a bit error rate of 10-9. Additionally, the optical spectra, the measured waveforms and the open eye diagrams of the converted signals show a high quality wavelength conversion performance.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

Performance of Post-Nonlinearity Compensation for Differential-Phase-Shifted-Keying Links with Transmitter Imperfections

We study the post nonlinearity compensation of differential-phase-shift-keying links employing pure soliton transmissions over a large number of spans.In addition to the distributed amplified spontaneous noises added by the inline amplifiers,lumped intensity noises initially resulting from transmitter imperfections are also considered.Based on the soliton perturbation theory,we derive simple and accurate formulae for the optimum operating phase,the variance of the residue phase noise,and the phase Q-factor improvement of the post nonlinearity compensation.We validate these derived formulae by comparing their results with numerical simulations built upon the split-step Fourier method.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Underwater four-quadrant dual-beam circumferential scanning laser fuze using nonlinear adaptive backscatter filter based on pauseable SAF-LMS algorithm

The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.

Resonantly enhanced second-and third-harmonic generation in dielectric nonlinear metasurfaces

Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Quaternion Approach to Solve Coupled Nonlinear Schrdinger Equation and Crosstalk of Quarter-Phase-Shift-Key Signals in Polarization Multiplexing Systems

The quaternion approach to solve the coupled nonlinear Schrodinger equations （CNSEs） in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled quater- nion. The crosstalk of quarter-phase-shift-key signals caused by fiber nonlinearity in polarization multiplexing systems with 100 Cbps bit-rate is investigated and simulated. The results demonstrate that the crosstalk is like a rotated ghosting of input constellation. For the 50 km conventional fiber link, when the total power is less than 4roW, the crosstalk effect can be neglected; when the power is larger than 20roW, the crosstalk is very obvious. In addition, the crosstalk can not be detected according to the output eye diagram and state of polarization in Poincare sphere in the trunk fiber, making it difficult for the monitoring of optical trunk link.

Geometric Programming for Nonlinear Satellite Buffer Networks With Time Delays under L_(1)-Gain Performance

Dear Editor,This letter concerns the parameter tuning problem for nonlinear satellite buffer networks with communication delays, aiming to optimize their stability properties under L_(1)-gain. We first model the satellite buffer networks by a nonlinear time-delay positive system and propose a novel characterization under which the nonlinear system is asymptotically stable with a prescribed L_(1)-induced performance.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Microscopic Theory of Nonlinear Hall Effect in Three-Dimensional Magnetic Systems

Nonlinear Hall effect(NLHE)has been detected in various of condensed matter systems.Unlike linear Hall effect,NLHE may exist in physical systems with broken inversion symmetry in crystals.On the other hand,real space spin texture may also break inversion symmetry and result in NLHE.We employ the Feynman diagrammatic technique to calculate non-linear Hall conductivity(NLHC)in three-dimensional magnetic systems.The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture.The leading order contribution of NLHC,χ_(abb),is proportional to the emergent toroidal moment T_(α)^(e),which reflects how the spin textures wind in three dimensions.

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Nonlinear-Optical Analogies in Nuclear-Like Soliton Reactions:Selection Rules,Nonlinear Tunneling and Sub-Barrier Fusion–Fission

The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics,which still remain hidden from us.We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons.On the base of this model,we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton selfinduced sub-barrier transparency effect.We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions.The main finding of this study concerns the conservation of total number of nucleons(or the baryon number)in nuclear-like soliton reactions.We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a“cloud”of“dressing”spectral side-bands appears in the frequency spectra of the solitons.This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter.Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors.We show that the nuclear-like reactions between well-dressed solitons are realized by“exchange”between“particle-like”side bands in their spectra.

Nonlinear Robust Stabilization of Ship Roll by Convex Optimization

Dear Editor,This letter presents a nonlinear robust controller design method for ship roll stabilization by combining the dual of Lyapunov's stability theorem with the sum of squares(SOS) technique. Varying initial metacentric height and ship speed are regarded as uncertainties, sea waves are considered as external disturbances, and then the robust nonlinear controller is designed. Taking a container ship as an example, simulations are performed to verify the effectiveness of the proposed design scheme.

Stability Analysis of a Class of Nonlinear Fractional Differential Systems With Riemann-Liouville Derivative

Dear Editor,This letter investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative.By using the Mittag-Leffler function,Laplace transform and the Gronwall-Bellman lemma,one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in(0,2).According to this theory,if the nonlinear term satisfies some conditions,then the stability condition for nonlinear fractional differential systems is the same as the ones for corresponding linear systems.Two examples are provided to illustrate the applications of our result.

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Ultrahigh-brightness 50 MeV electron beam generation from laser wakefield acceleration in a weakly nonlinear regime

We propose an efficient scheme to produce ultrahigh-brightness tens of MeV electron beams by designing a density-tailored plasma to induce a wakefield in the weakly nonlinear regime with a moderate laser energy of 120 mJ.In this scheme,the second bucket of the wakefield can have a much lower phase velocity at the steep plasma density down-ramp than the first bucket and can be exploited to implement longitudinal electron injection at a lower laser intensity,leading to the generation of bright electron beams with ultralow emittance together with low energy spread.Three-dimensional particle-in-cell simulations are carried out and demonstrate that high-quality electron beams with a peak energy of 50 MeV,ultralow emittance of28 nm rad,energy spread of 1%,charge of 4.4 pC,and short duration less than 5 fs can be obtained within a 1-mm-long tailored plasma density,resulting in an ultrahigh six-dimensional brightness B6D,n of2×1017 A/m2/0.1%.By changing the density parameters,tunable bright electron beams with peak energies ranging from 5 to 70 MeV,a small emittance of B0.1 mm mrad,and a low energy spread at a few-percent level can be obtained.These bright MeV-class electron beams have a variety of potential applications,for example,as ultrafast electron probes for diffraction and imaging,in laboratory astrophysics,in coherent radiation source generation,and as injectors for GeV particle accelerators.