Wave Envelope Research Articles

Dynamical exploration of optical soliton solutions for M-fractional Paraxial wave equation.

This work explores diverse novel soliton solutions due to fractional derivative, dispersive, and nonlinearity effects for the nonlinear time M-fractional paraxial wave equation. The advanced exp [-φ(ξ)] expansion method integrates the nonlinear M-fractional Paraxial wave equation for achieving creative solitonic and traveling wave envelopes to reconnoiter such dynamics. As a result, trigonometric and hyperbolic solutions have been found via the proposed method. Under the conditions of the constraint, fruitful solutions are gained and verified with the use of the symbolic software Maple 18. For any chosen set of the allowed parameters 3D, 2D and density plots illustrate, this inquisition achieved kink shape, the collision of kink type and rogue wave, periodic rogue wave, some distinct singular periodic soliton waves for time M-fractional Paraxial wave equation. As certain nonlinear effects cancel out dispersion effects, optical solitons typically can travel great distances without dissipating. We have constructed reasonable soliton solutions and managed the actual meaning of the acquired solutions of action by characterizing the particular advantages of the summarized parameters by the portrayal of figures and by interpreting the physical occurrences. New precise voyaging wave configurations are obtained using symbolic computation and the previously described methodologies. However, the movement role of the waves is explored, and the modulation instability analysis is used to describe the stability of waves in a dispersive fashion of the obtained solutions, confirming that all created solutions are precise and stable.

Spatial estimation of unidirectional wave evolution based on ensemble data assimilation

With the limitation of the high sensitivity of nonlinear models to initial conditions, the accurate estimation of wave spatial evolution is difficult to perform at a long distance. At this stage, a helpful approach is to improve the accuracy and robustness of the model through data assimilation technique. A robust data assimilation framework is developed by coupling ensemble Kalman filtering (EnKF) with the nonlinear wave model. The spatial evolution is obtained by numerically integrating the viscous modified Nonlinear Schrödinger (MNLS) equation. The performance of the EnKF-MNLS coupled framework is tested using synthetic data and laboratory measurements. The synthetic data is generated by the MNLS simulation superposing the Gaussian noise. In the synthetic cases, the estimated wave envelopes agree well with the clean solution. The results of laboratory experiments indicate that the EnKF-MNLS framework can improve the accuracy of wave forecasts compared to noised MNLS simulations. This study aims to enhance the noise resistance of the nonlinear wave model in spatial evolution and improve the accuracy of the model forecast.

Triad resonance for internal waves in a uniformly stratified fluid: Rogue waves and breathers.

Three-wave (triad) resonance in a uniformly stratified fluid is investigated as a case study of energy transfer among oscillatory modes. The existence of a degenerate triad is demonstrated explicitly, where two components have identical group velocity. An illuminating example is a resonance involving waves from modes 1, 3, 5 families, but many other combinations are possible. The physical applications and nonlinear dynamics of rogue waves derived analytically in the literature are examined. Exact solutions with four free parameters (two related to the amplitudes of the background plane waves, two related to the frequencies of slowly varying envelopes) describe motions localized in both space and time. The differences between rogue waves of the degenerate versus the nondegenerate cases are highlighted. The phase and profile of the degenerate case rogue waves are correlated. The volume or energy of the rogue wave (defined as the total extent or energy contents of the fluid set in motion for the duration of the rogue wave) may change drastically, if the wave envelope parameters vary. Pulsating modes (breathers) have been studied previously by layered-fluid and modified Korteweg-de Vries models. Here we extend the consideration to stratified fluids but for the simpler case of nondegenerate triads. Instabilities of fission and fusion of breathers are confirmed computationally with Floquet analysis. This knowledge should prove useful for energy transfer processes in the oceans.

Generation and Dynamics of Multiple Pulses in an Ultrafast Fiber Laser with a Single-Mode Fiber–Graded-Index Multimode Fiber–Single-Mode Fiber-Based Saturable Absorber

In this study, we have investigated the evolution process and dynamic characteristics of a multi-pulse regime in an erbium-doped fiber ring laser based on a single-mode fiber–graded-index multimode fiber–single-mode fiber (SMF-GIMF-SMF) structure as an optical modulator. By utilizing the excellent nonlinear optical absorption of the SMF-GIMF-SMF (SMS) device with a modulation depth of ~8.68%, stable single-pulse mode locking at the frequency of 9.84 MHz can be readily observed at low pump power. In addition, the single-pulse operation can evolve into a multiple-pulse regime on account of the peak-power-clamping effect via suitably raising the pump power and carefully regulating the polarization state. Further, the single-shot temporal evolution of multiple pulses is monitored, indicating that this state shows unique and interesting temporal characteristics with variable pulse separations and inconsistent pulse intensities, which, as far as we know, is the first such observation in ultrafast fiber lasers. Additionally, this study, based on the time-stretch dispersive Fourier transformation method, suggests that these multiple pulses consist of chaotic wave envelopes with erratic intensities and changeable pulse energy. We believe that these findings have profound implications for revealing fascinating nonlinear pulse dynamics in ultrafast fiber optics.

Stability analysis of ring-like cavitation bubble cluster structure in standing wave field

Multi-cavitation bubble system can easily produce cavitation clouds with various structure types, including ring-like cavitation structures. Nonetheless, the evolutionary behavior of the structure and the physical mechanism of its formation are less investigated. In this work, high-speed photography and image analysis techniques are used to study the evolution of ring-like cavitation bubble aggregation structure in an ultrasonic cleaning tank with a frequency of 40 kHz. The ring-like structure usually appears near the pressure nodule, and its radius is less than a one-eighth wavelength. The structure involves establishment, stability and disappearance during an envelope wave period, and its morphology is stable. The ring-like cavitation structure exists as a bubble transport phenomenon, and the formed small bubble clusters flow to the outside of the ring and become discrete cavitation bubbles, or the bubble nuclei rejoin the cycle of bubble transport in the main accumulation area of the bubble. The size of the ring structure and the bubble accumulation area oscillate slightly, and there exists the whole structure rotation phenomenon, which depends on the interaction of the main sound field and the secondary radiation field with the bubbles. Furthermore, in this work, a mathematical model of two bubbles is used to investigate the physical mechanism behind the formation of a ring. It is found that the sound field is a key factor in ring formation. The ring chain model is used to analyze the structural stability by taking into account the time delay caused by the secondary acoustic radiation of the bubble. The numerical results show that the equivalent potential energy distribution of a ring bubble chain with a one-eighth wavelength in radius can stabilize each bubble in the potential well, and the radial distribution presents a ring-like barrier structure. The higher the sound pressure, the greater the equivalent potential, and the more the bubbles are clustered. The higher the driving sound field, the more complete the ring chain structure is. However, high sound pressure may cause the agglomeration of bubbles with high number density to disintegrate the stability of the ring aggregation of bubbles and evolve into other types of bubble aggregation structures. The theoretical results are in good consistence with the experimental phenomena.

Tidal Dissipation in Stably Stratified and Semiconvective Regions of Rotating Giant Planets: Incorporating Coriolis Forces

We study how stably stratified or semiconvective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial, and surface gravity waves in rotating giant planets. We explore scenarios in which stable (nonconvective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealized spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semiconvective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors )—sufficient to explain the observed migration rates of Saturn's moons—are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters and hot Neptunes, providing efficient tidal circularization rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.

Simulation of new waves in applied sciences via Schrödinger equations

The perturbed chiral nonlinear Schrö dinger equation (PCNLSE) reflects the quantum actions such as quantum pictures of Bohm potential and internal self-potential properties. Indeed, this equation introduces the basics of the hidden variable theory in quantum mechanics. Two unified solver methods and exp -expansion technique applied to PCNLSE to present many solitonic solutions in an explicit and effective way. The behaviour of these solutions is of qualitatively different structural natures, relying on physical coefficient parameters. The application of three mathematical techniques to our model system provides us with several possible physical property solutions that account for the majority of many phenomena the model under study attempts to depict. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applicable in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and in a lot other applied sciences. The results of this system's solitary structures are consistent with the characteristics of the nonlinear Schrödinger equation systems used to study dispersive modes and higher-order perturbed systems. For more details about the physical dynamical representation of the presented solutions, we have illustrated them with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approach can be applied to several equations arising in all applied sciences.

Interface Engineering and Electron-Hole Wave Function Overlap of InAs/AlSb Superlattice Infrared Detectors

InAs/AlSb is a material system that can be used as a low-noise avalanche detector and operates in the short-wave infrared band. The interface parameters determine the wave function overlap (WFO). Maximizing the WFO of InAs/AlSb superlattices improves the quantum efficiency (QE) of infrared avalanche photodetectors (APDs). However, this remains a huge challenge. Here, the 8-band k·p perturbation method based on Bloch wave envelope function approximation was used to calculate the energy level structure of InAs/AlSb superlattices. The results indicate that the WFO is enhanced with increasing InSb interface thickness or when the InSb (or AlAs) interface is far from the intersection of InAs and AlSb. As the AlAs interface thickness increases, the WFO enhances and then reduces. The maximum increase in WFO is 15.7%, 93%, and 156.8%, respectively, with three different models. Based on the stress equilibrium condition, we consider the interface engineering scheme proposed for enhancing WFO with an increase of 16%, 114%, and 159.5%, respectively. Moreover, the absorption wavelength shift is less than ±0.1 μm. Therefore, the interface layer thickness and position can be designed to enhance the WFO without sacrificing other properties, thereby improving the QE of the device. It provides a new idea for the material epitaxy of APDs.

Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation (NLSE). The first method is to derive a Korteweg–de Vries (KdV)-type equation and then derive the NLSE from the KdV-type equation, while the second one is to directly derive the NLSE from the original equation. It is found that the envelope waves from the two methods have different dispersion relations, different group velocities. The results indicate that two envelope wave solutions from two different methods are completely different. The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one, though both methods are valuable in the range of their corresponding application scopes. It is suggested that, for other systems, both methods to derive NLSE may be correct, but their nonlinear wave solutions are different and their application scopes are also different.

Groupiness effect on irregular wave train propagation and impact on cylinder

A wave flume based on solving the Reynolds-averaged Navier-Stokes equation is modelled to simulate the irregular wave group interacting with a cylinder. The irregular wave groups are generated based on the wave envelope spectrum and the improved JONSWAP spectrum. The wave-making boundary and the momentum source term for wave-making and wave dissipation are developed based on the irregular wave theory. To suppress excessive growth of turbulent viscosity, a modified formula for turbulent viscosity is implemented in the shear stress transport turbulence model. Several sets of irregular waves with different groupiness factors are simulated. The effects of groupiness on the wave parameters, wave run-up height and wave force on the cylinder are investigated. The results show that the wave parameters increase as the groupiness increase. The group height factor has a larger influence on the significant wave height than the group length factor. The group length factor mainly influences the average wave period and average wavelength. When the average wavelength is larger than the diameter of the cylinder, the increase in wave group length results in a decrease in wave run-up height and wave force on the cylinder.

Electric field effect on the intersubband optical absorption of GeSn quantum wells with parabolically graded barriers

In this study, we propose a theoretical simulation of a Ge0.9Sn0.1 rectangular SQW with GeSn parabolically graded barriers (PGBs) in the terahertz (THz) region. The discrete intra-band confined energy levels and their matching wave functions were calculated by solving the stationary Schrödinger equation by the finite difference method taking into account the Compact Density Matrix approach under the framework of both the effective mass and the envelope wave function approximations. In this work, we studied the effect of the quantum square-well width on the intersubband transition and oscillator strength in a GeSn-strained-based Barrier-Well-Barrier GeSn/(Ge,α-Sn) PGBs to obtain the optimum quantum confinement of electrons. The electronic states and their wave functions in the conduction band were computed by solving the Schrödinger equation without and under the effect of an applied external electric field at room temperature. We then investigated the effect of the electric field on the optical absorption coefficient (OAC). Our numerical results show that for external fields (>15 kV/cm), an intersubband transitions (ISBTs) frequency band of 2–14 THz (8–58 meV) was obtained for the specific optimized parameters. These results should be beneficial to the design of devices based on GeSn QWs with PGB structures operating in the THz frequency range.

Routes to chaos and generation of cnoidal wave envelopes in exciton-polariton microcavities

We show the presence of intermittent chaos as a function of the variation of the chemical potential during the condensation of exciton-polaritons using the bifurcation diagram and the Lyapunov Exponent. We then show the possibility of controlling the chaos in the homogeneous solution by the variation of the chemical potential when the pump increases. The influence of the chemical potential is demonstrated in stationary state by studying stability using the Routh-Hurwitz criterion. We also prove the existence of cnoidal waves and through phase portraits, their stabilities in propagation are established using the notion of symmetry. For this, we use a dissipative Gross-Pitaevskii equation for the polariton field, coupled to a reservoir dynamics equation, commonly used to describe polariton condensates under non-resonant pumping.

Nonlinear optical properties of modified Möbius squared potential well: influence of electric and magnetic fields

ABSTRACT This work presents a numerical study on the electronic and optical properties of modified Möbius squared potential well in the presence of static electric and magnetic fields. The potential well is formed within GaAs/AlGaAs hetero structures. Schrödinger’s equation is solved within the framework of effective mass and envelope wave function approximations to get the wave functions and their corresponding energies of states. The optical absorption coefficients and relative refractive index changes are calculated via the expressions derived from the compact density matrix approach. The numerical results present strong blue shifts on the optical responses of modified Möbius squared potential well when the external electromagnetic fields are strengthening.

Development and validation of a computational method to predict unintended auditory brainstem response during transcranial ultrasound neuromodulation in mice

BackgroundTranscranial ultrasound stimulation (TUS) is a promising noninvasive neuromodulation modality. The inadvertent and unpredictable activation of the auditory system in response to TUS obfuscates the interpretation of non-auditory neuromodulatory responses. ObjectiveThe objective was to develop and validate a computational metric to quantify the susceptibility to unintended auditory brainstem response (ABR) in mice premised on time frequency analyses of TUS signals and auditory sensitivity. MethodsUltrasound pulses with varying amplitudes, pulse repetition frequencies (PRFs), envelope smoothing profiles, and sinusoidal modulation frequencies were selected. Each pulse's time-varying frequency spectrum was differentiated across time, weighted by the mouse hearing sensitivity, then summed across frequencies. The resulting time-varying function, computationally predicting the ABR, was validated against experimental ABR in mice during TUS with the corresponding pulse. ResultsThere was a significant correlation between experimental ABRs and the computational predictions for 19 TUS signals (R2 = 0.97). ConclusionsTo reduce ABR in mice during in vivo TUS studies, 1) reduce the amplitude of a rectangular continuous wave envelope, 2) increase the rise/fall times of a smoothed continuous wave envelope, and/or 3) change the PRF and/or duty cycle of a rectangular or sinusoidal pulsed wave to reduce the gap between pulses and increase the rise/fall time of the overall envelope. This metric can aid researchers performing in vivo mouse studies in selecting TUS signal parameters that minimize unintended ABR. The methods for developing this metric can be adapted to other animal models.

Experimental investigation on the interaction between mode-2 internal solitary wave and horizontal transverse cylinder

The experimental study on the interaction between a mode-2 internal solitary wave (ISW) and a horizontal transverse cylinder has been carried out in a large gravity-stratified fluid flume. One kind of making-wave method of “rotating-blade-gate” is proposed to achieve the experimental simulation of the standard mode-2 ISW in the laboratory flume. The conductivity probe array and particle image velocimetry are used to measure the mode-2 ISW and its wave-flow structure of the interaction with the horizontal transverse cylinder, and the micro-amplitude force sensor is used to measure the forces of the mode-2 ISW on the cylinder model. It is shown that the mode-2 ISW geometric structure is characterized by a convex and concave oval wave envelope shape and the counterclockwise and clockwise circulations are formed in its convex and concave domains, respectively. The resulting pair of upper and lower antisymmetric circulations moves forward together, which causes a horizontal strong flow at the symmetric center of the wave envelope consistent with the wave propagation direction. The horizontal transverse cylinder is subjected to the combined action of horizontal flow, vertical flow, and density change induced by the mode-2 ISW, in which the horizontal strong flow, induced flow separation, and vortex structure located at the symmetric center of the wave envelope are the signature features that are different from other positions. The theoretical analysis model of the forces exerted by the mode-2 ISW on a horizontal transverse cylinder is established. The spatial distribution characteristic of the force exerted by the mode-2 ISW on a horizontal cylinder is obtained, and the essential reason for the maximum horizontal and vertical loads on the cylinder is revealed. The horizontal maximum load corresponds to the inhomogeneous change of the horizontal velocity along the depth, and the vertical maximum load depends on the maximum density change along the depth, of which variation trend corresponds to the linear change of wave amplitudes.

Nonlinear computation for focused wave groups on abrupt depth transitions

Focused wave groups in intermediate water depth propagating over varying abrupt depth transitions are studied numerically and experimentally. The experiments well validate the fully nonlinear model by a conformal mapping method. The generation of second-order and third-order harmonics is observed near the top of the submerged step, as well as the decrease of the main (first-order) components propagating along with the step. In addition, an enhancement of kurtosis occurs just after the step with a high-trailed profile, revealing a considerable asymmetry of the surface elevations. In addition, a wave group passing two or three steps is also investigated numerically. More submerged obstacles effectively strengthen the reflection capability in terms of the reflection coefficients computed with the amplitude of wave envelopes. Although the harmonics manifest a higher risk of extreme waves on abrupt depth transitions, the increase of water depth changes might not further enhance the maximum skewness and kurtosis over the varying bottom.

Wave Groups and Small Scale Variability of Wave Heights Observed by Altimeters

AbstractRecent satellite altimeter retracking and filtering methods have considerably reduced the noise level in estimates of the significant wave height (Hs), allowing to study processes with smaller spatial scales. In particular, previous studies have shown that wave‐current interactions may explain most of the variability of Hs at scales 20–100 km. As the spatial scale of the measurement is reduced, random fluctuations emerge that should be associated to wave groups. Here we quantify the magnitude of this effect, and the contribution of wave groups to the uncertainty in Hs measurements by altimeters, with a particular focus on extreme extra‐tropical storms. We take advantage of the low orbit altitude of the China‐France Ocean Satellite (CFOSAT), and the low noise level of the nadir beam of the SWIM instrument. Our estimate of wave group effects uses directional wave spectra measured by off‐nadir beams on SWIM, and signal processing theory that gives statistical properties of the wave envelope, and thus the local wave heights, from the shape of the wave spectrum. We find that the standard deviation of Hs associated to wave groups is a function of satellite altitude, wave height and spectral peakedness. For CFOSAT these fluctuations generally account for about 25% of the variance measured over a 80 km distance. This fraction is largest in storms and in the presence of long swells. When the estimated effect of wave groups is subtracted from the variance of Hs measurements, the remaining variability is higher in regions of strong currents.

Abundant dynamical structure of solutions to truncated M-fractional modified Korteweg–de Vries model: Effects of dispersion, nonlinearity and fractionality

This work explores various wave pattern dynamics due to fractional derivative, dispersive and nonlinearity effects for the nonlinear time M-fractional modified Korteweg–de Vries (tM-fMKDV) model. To reconnoiter such dynamics, the unified and new form of modified Kudryashov’s techniques execute to integrate the nonlinear tM-fMKDV model for achieving diverse solitonic and travelling wave envelopes. As a result, trigonometric, hyperbolic and rational solutions have been found via a unified technique, and constants base wave solutions have been derived via the novel Kudryashov’s technique. The dynamical behaviors of the obtained solutions in the pattern of periodic waves, different types of periodic rogue waves, kink waves, and different types of double periodic waves have been illustrated with 3D and density plots for arbitrary choice of the permitted parameters. Analyzing the effect, anyone can observe that an increase in dispersion coefficient causes strictly shock to slopy shocked, an increase of nonlinearity reduces the wavelength and reduces fractionality causing smoothly banding wave shape to strictly banding. As a result, our findings demonstrate that the proposed schemes are highly effective, efficient, and accurate in capturing the characteristics of waves. Compared to other approaches, the solutions obtained from our tM-fMKDV models are more abundant.

Electrostatic wave propagation and self-streaming effect in an electron-hole plasma

Electrostatic nonlinear waves which transfer energy through the semiconductor are investigated. A quantum hydrodynamic plasma system composed of self-streaming electrons and holes is examined. The basic equations are reduced to one evolution equation called a modified nonlinear Schrödinger (mNLS) equation. The stability and instability regions are studied with respect to the wavenumber and different plasma effects such as degenerate pressure, Bohm potential, and collisions. The mNLS equation is solved analytically to obtain three kinds of nonlinear envelope wave packet modes. It is found that there are different regions of stability and instability depending on various quantum effects. The electrons’ and holes’ self-streaming velocity is studied and manipulated for the three types of nonlinear envelope waves ‘dark soliton, bright soliton, and rogue wave’. The dark envelope wave packet is generated in a stable region. When the electrons and holes streaming velocities become faster, the wave amplitude becomes taller and the pulses have higher frequency. The bright envelope wave packet exists in the unstable region. For low streaming velocities, the rogue wave amplitude becomes shorter, however, when the streaming velocities reach a critical value the amplitude increases suddenly six times. The self-heating could be produced as the tunneling electrons and holes exchange their energy with the lattice, which may decrease the lifetime of the semiconductors. The present results are helpful in realizing the physical solution to the intrinsic heating problem in semiconductors.

Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics’ fractional Hall effect edge states. The sine-Gordon expansion technique (SGET) was implemented to extract stochastic solutions for the CNLSE through multiplicative noise effects. This method accurately described a variety of solitary behaviors, including bright solitons, dark periodic envelopes, solitonic forms, and dissipative and dissipative–soliton-like waves, showing how the solutions changed as the values of the studied system’s physical parameters were changed. The stochastic parameter was shown to affect the damping, growth, and conversion effects on the bright (dark) envelope and shock-forced oscillatory wave energy, amplitudes, and frequencies. In addition, the intensity of noise resulted in enormous periodic envelope stochastic structures and shock-forced oscillatory behaviors. The proposed technique is applicable to various energy equations in the nonlinear applied sciences.