Weak Nonlinearity Research Articles

Features of dispersion properties of a waveguide with a modified Kerr weak nonlocal nonlinearity coated with a metal thin film

Features of dispersion properties of a waveguide with a modified Kerr weak nonlocal nonlinearity coated with a metal thin film

Engineering dynamical photon blockade with Liouville exceptional points.

We investigate the dynamical blockade in a nonlinear cavity and demonstrate the connection between the correlation function g(2)(t) and system parameters in the entire nonlinear region. Utilizing the Liouville exceptional points (LEPs) and quantum dynamics, a near-perfect single-photon blockade (1PB) can be achieved. By fine-tuning system parameters to approach the second-order LEP (LEP2), we improved single-photon statistics in both weak and strong nonlinearity regimes, including a significant reduction of g(2)(t) and a pronounced increase in the single-photon occupation number. In the strong nonlinearity region, the maximum photon population may correspond to stronger antibunching effect. Simultaneously, the time window and period of blockade can be controlled by selecting detuning based on the LEP2. Furthermore, the 1PB exhibits robustness against parameter fluctuations, and this feature can be generalized to systems for implementing single-photon sources with nonharmonic energy levels.

Defect-induced discrete breather in dissipative optical lattices with weak nonlinearity

It is widely believed that the discrete breather (DB) can only be created when the nonlinearity is strong in nonlinear systems. However, we here establish that this belief is incorrect. In this work, we systemically investigate the generation of DBs induced by coupling of the defects and nonlinearity for Bose-Einstein condensates in dissipative optical lattices. The results show that, only in a clean lattice is strong nonlinearity a necessary condition for generating of DB; whereas, if the lattice has a defect, the DBs can also be discovered even in weak nonlinearity, and its generation turns out to be controllable. In addition, we further reveal a critical interval of the defect in weak nonlinearity, within which DBs can be found, while outside DBs do not exist. Furthermore, we also explore the impact of multiple defects on the generation of DBs, and analyze the underlying physical mechanisms of these interesting phenomena. The results not only have the potential to be used for more precise engineering in the DB experiments, but also suggest that the DB may be ubiquitous since the defects and dissipation are unavoidable in real physics.

Divergent Richtmyer–Meshkov instability under different shock strengths

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.

Effect of weak nonlocal nonlinearity on generalized sixth-order dispersion modulational instability in optical media

Effect of weak nonlocal nonlinearity on generalized sixth-order dispersion modulational instability in optical media

Mechanical characteristics analysis of high dimensional vibration isolation systems based on high-static-low-dynamic stiffness technology

Large floating raft vibration isolation systems (FRVISs) based on high-static-low-dynamic stiffness (HSLDS) technology offer excellent low frequency vibration isolation performance with broad application prospects. However, the design process for these complex high-dimensional coupled nonlinear systems remains poorly developed, particularly when applied for ocean-going vessels that experience rolling and pitching motions. The present work addresses this issue by establishing a six-degree-of-freedom HSLDS vibration isolation model for FRVISs composed of eight isolators, and the model is applied to fully analyze the swing stability and multidimensional vibration isolation performance of these systems. The influence of nonlinearity on the mechanical properties of the vibration isolators is analyzed more clearly by assuming that each vibration isolator realizes nonlinear HSLDS characteristics in the z direction and linear characteristics in the x and y directions. The results demonstrate that the swing displacement responses of the system are greatly reduced under weak nonlinearity, which reflects the high static stiffness and high static stability characteristics of an HSLDS system. The multidimensional vibration isolation performance of the system is evaluated according to the impacts of nonlinearity, the installation height Hz of the isolators, and the relative position Dr of the two middle isolators. The results of analysis demonstrate that applying a value of Hz = 0 produces the best vibration isolation performance overall under strong nonlinearity by avoiding unnecessary secondary peaks in the force transmission rate under harmonic mechanical excitation and ensuring a maximum high-frequency vibration isolation effect. However, applying a weak nonlinearity is better than a strong nonlinearity if Hz is not zero. In contrast, Dr has little effect on the vibration isolation effect of the raft in the x, y, and z directions. Therefore, an equidistant installation with Dr = 0.5 would be considered ideal from the standpoint of installation stability.

Improved uniform error bounds on an exponential wave integrator method for the nonlinear Schrödinger equation with wave operator and weak nonlinearity

In this paper, we establish the improved uniform error bounds for the Lawson-type exponential wave integrator Fourier pseudo-spectral (LEWIFP) method for the nonlinear Schrödinger equation with wave operator (NLSW) and weak nonlinearity characterized by a small constant ε∈(0,1]. We first convert the NLSW to a coupled system and then consider the LEWIFP method for the coupled system. The LEWIFP method is proved to be time symmetric and mass-conservative which is very important from the point of view of numerical geometric integration. Through careful and rigorous convergence analysis, we establish improved uniform error bounds for the full-discretization at O(hm+ε2pτ2) in the long-time domain up to O(1/ε2p) where m is determined by the regularity conditions. These error bounds are much better than the classical error bounds O(hm+τ2) provided by the traditional error analysis. In error analysis, in addition to the classical tools such as mathematical induction and energy method, we adopt the regularity compensation oscillation (RCO) technique to analyze the accumulation of errors carefully. The numerical experiments support our error estimates and demonstrate the discrete mass-conservation. In addition, the numerical results show that the discrete energy is stable in the time domain up to O(1/ε2p).

Generation of five-photon hyperentangled cluster state with three-photon GHZ state and Bell state via weak cross-Kerr nonlinearity

Generation of five-photon hyperentangled cluster state with three-photon GHZ state and Bell state via weak cross-Kerr nonlinearity

Impact of weak nonlocal nonlinearity on modulational instability and chirp-free soliton trains in parabolic law optical fiber

This study considers the generation and evolution of chirp-free soliton trains in a focusing cubic-quintic nonlinear optical fiber media (by utilizing experimental parameters), under the influence of weak nonlocal nonlinearity. Analysis of modulational instability (MI) reveals that the MI gain exist only in the anomalous dispersion regime, with the quintic nonlinear term increasing the maximum gain and sideband frequencies. The nonlocal nonlinearity parameter generally suppresses the impact of MI, because the maximum gain is greatly reduced with increase in nonlocality. By using the subsidiary ordinary differential equation method, stationary periodic soliton trains are obtained; with the intensity of the optical beam greatly reduced and frequency increased as nonlocality is gradually stepped up. However, an increase in nonlocality instead reduces the frequency of the traveling optical signals; derived via an efficient transformation method. Our results strongly suggest that nonlocal nonlinearity has potential applications in the control of laser beams; as nonlinear periodic optical signals can be easily transformed to very weak quasi-plane waves.

Propagation of fundamental gap solitons in the fractional Schrödinger equation with combined linear and nonlinear optical lattices

The propagation of two-dimensional fundamental gap solitons is investigated in the framework of fractional Schrödinger equation with combined linear and nonlinear optical lattices. It is revealed that solitons exist in the first gap and can be stable in a large region. With a phase tilt, the fundamental gap solitons undergo oscillation during the propagation. And the oscillation is enhanced with the increase of the tilt. In addition, propagation of fundamental gap solitons are also studied by longitudinal modulation of Lévy index, nonlinear strength, and period of nonlinear lattices, respectively. With the sudden variation of Lévy index, the fundamental gap solitons undergo oscillation and become unstable, whereas the gradual variation generates the stable soliton. However, both sudden and gradual decreases of nonlinear strength can lead to the distortion of the soliton due to the weak nonlinearity. Interestingly, the small longitudinal modulation of the period of the nonlinear lattice has little effect on the propagation of fundamental gap soliton, while the effect of the large variation of the period of the nonlinear lattice is apparent.

Large‐Range Beam Steering through Dynamic Manipulation of Topological Charges

AbstractDynamic tuning of light properties by external stimuli is at the core of various applications such as electro‐optical modulators, beam steering, and spatial light modulators. The conventional mechanism involves fine‐tuning the eigenmode of an optical system through adjusting the effective refractive index. However, the weak nonlinearity results in low modulation efficiency, leading to devices with poor performance and large size. Polarization topological charge is a significant concept that has facilitated the development of innovative optical devices like low‐threshold lasers and vortex generators. But the devices reported so far are static in nature. Here, a method for dynamically controlling light by actively manipulating the evolution of topological charges in momentum space is first presented. By switching between integer and half‐integer states of topological charges, the device's radiation properties undergo a significant transformation. The beam direction can be tuned up to 160°, which, to the best of the authors' knowledge, is the largest tuning angle among similar beam steering devices. Furthermore, the device demonstrates high radiation efficiency while maintaining a compact device size. This light controlling method can be applied in various fields, including optical communication, tunable lasers, and light detection and ranging.

Structured interpolation for multivariate transfer functions of quadratic-bilinear systems

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting large-scale nonlinear systems. The high dimensionality of the dynamics causes computational bottlenecks, especially when these large-scale systems need to be simulated for a variety of situations such as different forcing terms. This motivates model reduction where the goal is to replace the full-order dynamics with accurate reduced-order surrogates. Interpolation-based model reduction has been proven to be an effective tool for the construction of cheap-to-evaluate surrogate models that preserve the internal structure in the case of weak nonlinearities. In this paper, we consider the construction of multivariate interpolants in frequency domain for structured quadratic-bilinear systems. We propose definitions for structured variants of the symmetric subsystem and generalized transfer functions of quadratic-bilinear systems and provide conditions for structure-preserving interpolation by projection. The theoretical results are illustrated using two numerical examples including the simulation of molecular dynamics in crystal structures.

Jacobian elliptic wave trains in fourth-order dispersive nonlinear Schrödinger equation and the modulational instability

We analytically and numerically explore the existence of explicit exact Jacobian elliptic solutions of a nonlinear Schrödinger model with fourth-order dispersion and weak nonlocality. We delineate the parameter domain in which these highly dispersive doubly periodic waves balanced by the weak nonlocality and Kerr nonlinearity exist. Additionally, we have studied the modulational instability (MI) of these waves with the aid of linear stability analysis. We observe that in the presence of fourth-order dispersion, the MI gain increases with increasing the nonlocality parameter.

Final value problem governed by a class of time‐space fractional pseudo‐parabolic equations with weak nonlinearities

We study the final value problem involving a class of semilinear fractional pseudo‐parabolic equations, where the nonlinearity probably takes values in fractional Sobolev spaces. By establishing some estimates for resolvent operators and employing the embedding related to Hilbert scales and fractional Sobolev spaces, we are able to obtain the existence and uniqueness result to the mentioned problem. In addition, the behavior of solutions at initial time is analyzed with respect to the final data. It will be shown that various cases of the nonlinearity functions meet our setting, including functions with gradient term.

Some new lump molecules and hybrid molecular states of a (3 + 1)-dimensional generalized variable coefficient Kadomtsev–Petviashvili equation

In this paper, a (3 + 1)-dimensional generalized variable coefficient Kadomtsev–Petviashvili equation is investigated systematically, which can characterize evolution of the long water waves and small amplitude surface waves with the weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. We investigate one lump and lump molecules obtained from one breather and breather molecules by a new degenerating breather method, respectively. In addition, the bound state of lump molecules and other localized waves is derived theoretically by velocity resonance. Considering the condition of variable coefficient, the several sets of interesting solutions having a complex structure are obtained, which include the type of parabolic, S-shaped, and periodic. The analysis method can also help us to study lump molecules existing in other integrable systems from a new perspective.

Infinite time blow-up of solutions for a plate equation with weak damping and logarithmic nonlinearity

This paper considers a plate equation with weak damping and logarithmic nonlinearity, which can be used to model the deformations and internal forces of an elastic plate under external factors such as lateral loads. We prove the solution blows up at infinity with subcritical and critical initial energies. Moreover, we establish the infinite time blow-up result at arbitrarily high initial energy. These results complement earlier results in the literature.

Numerical and experimental investigations on quasistatic pulse generation of ultrasonic guided waves in fiber reinforced composite pipes

The quasistatic pulse (QSP) generation of ultrasonic guided waves in composite pipes can exhibit many features that are useful for early-stage material characterization and structural health monitoring. The intrinsic relationship between the QSP generation and the weak elastic nonlinearity of solids is complex. It has yet promised for developing the nonlinear ultrasonic guided wave technique that combines its advantages of high sensitivity to microdamage and low ultrasonic attenuation in composite materials. This study presents a systematic investigation of the QSP generation in fiber reinforced composite pipes. Using a three-dimensional finite element simulation with a nonlinear material model, the temporal waveform, mode conversion effect, cumulative effect, generation efficiency, and duration effect of QSP generation are revealed. The nonlinear QSP signals in laminated composite pipes are confirmed as the fastest wave mode that only has axial displacement. The shape of QSP depends on the group velocity difference between the QSP and the primary wave. The magnitude of QSP is related to the excitation level, frequency, and tone-burst duration of the primary wave. Experiments are conducted using carbon fiber reinforced composite pipes and the signals are measured using a laser vibrometer scanning system for verifying the QSP generation. The experimental results are consistent with the numerical findings. A relative nonlinear acoustic parameter based on the QSP generation is proposed and used to evaluate the early-stage thermal fatigue damage in the pipes. The measured nonlinear acoustic parameter demonstrates high sensitivity to the damage, indicating considerable potential for industrial applications.

Large second-order susceptibility from a quantized indium tin oxide monolayer.

Due to their high optical transparency and electrical conductivity, indium tin oxide thin films are a promising material for photonic circuit design and applications. However, their weak optical nonlinearity has been a substantial barrier to nonlinear signal processing applications. In this study, we show that an atomically thin (~1.5 nm) indium tin oxide film in the form of an air/indium tin oxide/SiO2 quantum well exhibits a second-order susceptibility χ2 of ~1,800 pm V-1. First-principles calculations and quantum electrostatic modelling point to an electronic interband transition resonance in the asymmetric potential energy of the quantum well as the reason for this large χ2 value. As the χ2 value is more than 20 times higher than that of the traditional nonlinear LiNbO3 crystal, our indium tin oxide quantum well design can be an important step towards nonlinear photonic circuit applications.

Source identification problems for a class of subdiffusion equations with weak nonlinearities

Source identification problems for a class of subdiffusion equations with weak nonlinearities

Uniform Error Bounds of an Energy-Preserving Exponential Wave Integrator Fourier Pseudo-Spectral Method for the Nonlinear Schrödinger Equation with Wave Operator and Weak Nonlinearity

Uniform Error Bounds of an Energy-Preserving Exponential Wave Integrator Fourier Pseudo-Spectral Method for the Nonlinear Schrödinger Equation with Wave Operator and Weak Nonlinearity