Amplitude Of Input Wave Research Articles

Linear and nonlinear optical properties surface plasmon polariton localization in plasmonic crystal metallic nanowires

Functionality and spatial concentration of light in periodic and disordered plasmonic crystal metallic nanowires are investigated under Kerr nonlinearity. The results show that nonlinear transverse localization of surface plasmon polaritons (SPP) in a periodic and disordered array of nanowires embedded in the Kerr medium changes with incident input wave amplitude (A). We study periodic and diagonal disordered nanowire arrays and study the propagation of SSPs under different inputs by solving nonlinear coupling relations. Finally, off-diagonal disordered nanowire arrays are studied. The results show that localization and effective beamwidth of the SPPs increases with an increase in their input amplitudes. Also, the SPPs become more localized with increase of diagonal (δr) and off-diagonal disorder (δd) into the nanowire arrays. Controlling SSPs' localization in the nanowire array using their input amplitude provides a high functional sub-wavelength device that can be utilized in future applications of nanophotonics functions.

Numerical investigation on the propagation and evolution of focused waves over a sloping bed

It is well recognized that wave focusing is one of main mechanisms leading to nonlinear extreme/rouge waves in the real sea. The evolution of this nonlinear focused wave group (i.e., wave generated by wave focusing), characterized by the wave shape and kinematics, is significantly affected by the bottom topography. Since the terrain of the nearshore area is generally in the form of a mild slope, it is of both academic and practical values to investigate its propagation and evolution over a sloping bed. In this paper, a two-dimensional fully nonlinear numerical model is established based on the potential flow theory and the time-domain high-order boundary element method. The hybrid Euler-Lagrangian method is used to track the instantaneous water surface, and the fourth-order Runge-Kutta method is used to update the water surface and the velocity potential at the next time step. The focused wave is generated by prescribing velocities from second-order Stokes wave theory at the immerged sources boundary, and is forced to focus at a pre-defined location and time by the principle of wave focusing. By changing the bed sloping and the input wave amplitude, it was found that the focused wave crest decreases with the increase of the bed sloping, and the actual focal location is somehow shifted behind the theoretical value. When the initial focusing position is pre-defined at the beginning of the slope, the free surface elevations and the wave energy of higher-order harmonics above the slope are both smaller than the corresponding values on the flat bottom. However, when the focusing position is pre-set at the back part of the slope, the conclusions are opposite. The presence of the slope facilitates the energy conversion from low frequencies to high frequencies.

Dynamic Response and Failure Process of a Counter-Bedding Rock Slope under Strong Earthquake Conditions

There are massive landslides and potential landslides along the Three Rivers Basin in the Qinghai–Tibet Plateau, which pose a serious threat to the Sichuan–Tibet Railway. A normal shaking table model test was conducted to study the dynamic characteristics and dynamic response of a symmetrical counter-bedding rock slope based on the Zongrong Village landslide. The influences of the dynamic parameters, seismic wave type, and a weak intercalated layer on the slope’s dynamic response were considered. The results showed symmetry between the growth trend of the acceleration amplification factor and other research results. When the input wave amplitude was constant, the acceleration amplification factor increased at first and then decreased as the frequency increased. When the input frequency was near the slope’s natural frequency, the acceleration amplification factor increased at first and then decreased with an increase in the input amplitude and reached the maximum value at 0.3 g. The acceleration amplification factor increased linearly with height in the vertical direction inside the slope but increased slowly at first and then sharply along the slope surface, reaching the maximum value at the slope’s top and exhibiting an obvious “elevation effect”. When sinusoidal waves, Wolong waves, and Maoxian waves with the same amplitude were input, the slope’s amplification effect on the bedrock wave was more obvious. The weak intercalated layer showed the phenomenon of “thin layer amplification” and “thick layer attenuation” in response to the input seismic wave. The slope’s failure process can be roughly divided into three stages: (1) the formation of tensile cracks at the top and shear cracks at the toe; (2) the extension of cracks and the sliding of the slope-surface block; (3) the formation of the main sliding surface.

Dynamic response characteristics and instability criteria of a slope with a middle locked segment

Stability prediction of rock slopes under seismic loads is important for landslide hazard assessment. For this work we designed and built a model of a slope with a middle locked segment. To investigate its dynamic response characteristics and instability criteria under the influence of an earthquake, comparative experiments on a large-scale shaking table were performed. The results show that the acceleration amplification factor within the model slope is clearly amplified by elevation and surface proximity. There are large differences in the acceleration response for a slope experiencing different types of input wave. The acceleration amplification factor first increases then decreases with the increase of input wave frequency, reaching a maximum value when the frequency is 20 Hz. A similar trend is observed with increasing input wave amplitude; the acceleration amplification factor of the slope generally increases then decreases as the amplitude increases. During the experiments, several cracks form and propagate in the locked segment between the prefabricated crack at the top and the weak interlayer at the bottom. These cracks develop continuously, coalescence into X-shapes, and finally form three sliding surfaces inside the slope. Under continuous vibration, the slope will slide along the three sliding surfaces. Based on cusp catastrophe theory and the experimental data, the relevant instability criteria are established. The critical acceleration amplitude of the dynamic instability of the slope is quantitatively determined to be 0.5 g.

A nonlinear potential flow model for higher-harmonic wave loads and ringing response of a monopile

This paper presents a numerical investigation on the high-frequency wave loads and ringing responses of offshore wind turbine foundations exposed to steep waves. A time-domain nonlinear potential flow model is developed based on the weak-scatterer approximation. On the free surface, an arbitrary Lagrangian-Eulerian (ALE) approach is adopted in the time marching process. The higher-order boundary element method (HOBEM) is employed to solve the corresponding boundary value problem at each time step. The proposed model is verified by a series of nonlinear wave diffraction problems in regular waves. It appears that in terms of the wave run-up and higher-harmonic wave forces, the present results are all in satisfactory agreement with the published experimental results and other theoretical or numerical solutions. The ringing response of a bottom-hinged monopile exposed to moderately steep focused wave groups is subsequently investigated for several different wave conditions. The effects of peak frequency, input wave amplitude and damping ratio on the ringing response are discussed.

Fully nonlinear investigation of focused wave slamming on a freely rotating flap

This paper concerns the focused wave slamming induced by a freely rotating flap using domain-decomposition higher-order boundary element method (HOBEM) with fully nonlinear conditions through which the process of jet detaching from body is successfully captured. The stable results of splash jet are obtained through linearly-varying-potential hypothesis. The time derivative of velocity potential on the body surface is calculated through the auxiliary function method, and the strong mutual dependence between the flap and the fluid flow is further decoupled accordingly. The non-uniform mesh scheme is adopted in the computational domain to guarantee both efficiency and accuracy, i.e., using fine meshes in the slamming region with strong nonlinearity. The abilities of present model to generate the focused wave and simulate wave slamming on a rotating flap, are respectively, verified. Relatively comprehensive parametric studies are performed, and the results based on flap's motion states, free surface profiles and pressure distributions point out the effects of frequency bandwidth, focused position, input wave amplitude, water depth and phase angle on the slamming specifically. It has been found the slamming occurs before wave groups focus completely and focused trough further enlarges the slamming pressure compared with focused crest.

Shaking table test study on dynamic behavior of micropiles in loose sand

Micropiles are small-diameter piles installed in soil. Due to wide application of micropiles in seismically active areas, investigation of their behavior during earthquake is of great significance. In this study, shaking table tests were conducted on a small-scale physical model of micropiles consisting 16 vertical micropiles embedded in loose sand fill and subjected to harmonic sine waves. Influence of amplitude of input excitations, presence of a single degree of freedom superstructure and variation of concentrated mass of this model superstructure on the dynamic response of micropiles system were examined. Response of physical model to the base excitation was investigated in terms of the horizontal acceleration at different locations of physical model and also bending moment generated along two instrumented micropiles during the experiment. Increase in the amplitude of input wave and cyclic nature of shaking resulted in densification of underlying soil and modification of soil-micropile stiffness, which accordingly reduced dynamic amplification and shifted fundamental frequency of vibration of micropile cap. However, presence of superstructure and increase in its concentrated mass resulted in a shift of fundamental frequency the other way. There was a maximum bending moment induced by vibrations in the mid-length of model micropiles which increased with augmentation of amplitude of input wave. Inertial effect of superstructure resulted in significant elevation of bending moment in the vicinity of micropile head, and also caused bending moment in the corner micropile to exceed bending moment in center micropile.

Computational simulations of wave propagation in microcrack-damaged media under prestress

Direct computational simulations of unidirectional wave propagation through uniaxially prestressed, microcrack-damaged media are conducted to study the interaction between the prestress and stress wave parameters. Tensile and compressive waves, tensile and compressive prestresses and various orientational distributions of microcrack damage are analyzed. The relationships among the input wave amplitude, wavelength and prestress magnitude and the output wave speed and wave attenuation are studied. The results show that wave speed and attenuation depend on the prestress and the wavelength in a complex way. In the cases of compressive waves traveling through tensile prestress and tensile waves passing through compressive prestress, the wave response depends on the ratio of the amplitude of the applied stress pulse to the magnitude of the prestress (defined as R). Specifically, the simulations show that the compressive wave speed through tensile prestressed media increases gradually with an increase in R, while the tensile wave speed in media under compressive prestress, decreases with increase in R, but the change is abrupt at a particular R value. In the cases of sufficiently small R, the wave speeds match the results of Su et al. (Eng Fract Mech 74:1436–1455, 2007) where the cracks are always open or always closed. However, above a certain wavelength (a cut-off wavelength), the wave speed is no longer a function of wavelength and, furthermore, this cut-off wavelength varies with R.

Influence of Saturation Degree on Deamplification of P1 Wave through Multilayered Porous Media

The deamplification model developed by Zendagui et al. has been adapted in this study for the case of P1 wave propagation in porous media in order to investigate the effect of saturation degree on motion coherency at depth. The input wave amplitude distribution function is generated compatibly with the suitable free field coherency model and the top wave amplitudes are evaluated using the transfer matrix method following the Biot’s theory. The results show that even if the saturation degree decreases slightly below the complete saturation, it influences the coherencies of horizontal and vertical motion due to P1 wave incidences. Elsewhere, the generation process shows that in this case, the wave front content, necessary to produce a coherency identical to the Luco and Wong model at the free field, is more focus with less intensity than required in the case of a complete saturation.

Statistical Analysis of Langmuir Waves Associated with Type III Radio Bursts: II. Simulation and Interpretation of the Wave Energy Distributions

Abstract We have modeled electrostatic Langmuir waves by an electric field, consisting of superposition of Gaussian wave packets with several probability distributions of amplitudes and with several Poisson distributions of wave packets. The outcome of the model is that the WIND satellite observations, especially in the low frequency domain (the WAVES experiment), do not allow to conclude whether the input wave amplitude distributions are closer to the log-normal than to the Pearson type I or uniform. The average number of wave packets in 1 s is found to be between 0.1 and 50. Therefore, there is a clear need to measure Langmuir wave energy distributions directly at the waveform level, not a posteriori in the spectral domain. This is planned to be implemented on the RPW (Radio and Plasma Wave Analyzer) instrument in the Solar Orbiter mission.

Relation of vectorial structures of diffracted plane waves with the elliptical aperture configuration and the light polarization in the far field

The analytical vectorial structure of a linearly polarized plane wave diffracted by an elliptical aperture is studied in detail based on the vector angular spectrum representation. It is found that the energy flux density spot sizes and the energy fluxes of the TE and TM term depend on the elliptical aperture configuration and the polarization direction of the incident plane wave. And the far fields can have smaller spots and larger energy fluxes for an elliptical aperture compared to a circular aperture with the same input wave amplitude. And its potential application in information encoding and transmission for free space communications is proposed apart from re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.

A simplified model for extreme-wave kinematics in deep sea

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

Effect of adhesion force between crack planes on subharmonic and DC responses in nonlinear ultrasound

Subharmonic and DC responses in nonlinear ultrasound have been expected as a possible means of detecting closed cracks. Recently, it has been reported that subharmonics in a closed crack markedly increases above a certain input wave amplitude. Such a phenomenon is called “threshold behavior”. However, the mechanism of threshold behavior has yet to be elucidated. To clarify this, we introduced adhesion force as a short-range force into the previous analytical model, which expresses the nonlinear contact vibrations of crack planes with intense ultrasound and provides a DC displacement as an approximation of the subharmonic response. Consequently, upward convex curves of displacement against input wave amplitude above the threshold were reproduced for the first time. The validity of the derived analytical solution is discussed by comparison with experimentally observed subharmonics.

Matrix-Based Analytical Model of Critical Coupling Length of Titanium In-Diffused Integrated-Optic Directional Coupler on Lithium Niobate Substrate

The critical coupling length Lc is the most important design parameter of an integrated-optic directional coupler, which is the basic building block of a variety of optical integrated circuits. The existing methods of estimating Lc of a Ti in-diffused waveguide directional coupler on LiNbO3 substrate are based on the beam propaga tion method (BPM), which requires huge computing time. A considerably simpler and computationally faster analytical method involving only multiplication of 2 x 2 matrices with no iterations is described in this article. A staircase type step-index profile is generated from the one-dimensional effective index profile in the lateral direction by partitioning the latter into a large number of thin sections of different refractive indices. The overall transfer matrix of the step-index layered structure so obtained may be computed by the progressive multiplication of individual transfer matrices (2 x 2) relating the field components in adjacent layers. Hence the wave amplitude in any layer may be computed as a function of the input wave amplitude for different angles of incidence. This method has been successfully employed to compute the propagation constants for symmetric and asymmetric guided modes in the coupled region of the directional coupler and hence compute the coupling length. The values of Lc computed for a variety of devices agree closely with the published experimental results reported by several research groups. The computer program implementing the model runs reasonably fast in an ordinary PC and is versatile enough to consider arbitrary waveguide dimensions. Ti film thickness, and diffusion parameters for any wavelength of input light and for both transverse electric and transverse magnetic polarizations.

Linear and nonlinear amplification in the magnetosphere during a 6.6‐kHz transmission

Reception at Dunedin of the magnetospheric signal at 6.6 kHz transmitted from Anchorage, Alaska, showed both linear and nonlinear amplification during an event lasting some 20 min near local midnight. Linear amplification of the transmitter signal was ∼20 dB. Natural whistlers were also amplified but often at frequencies sharply limited to those from the transmitter frequency upward. Nonlinear amplification (NLA) produced a signal positively offset from the transmitter frequency by 20–150 Hz at amplitudes over 40 dB above the unamplified transmitter signal. This signal appeared as a largely self‐sustaining embryo emission (EE) under the control of the transmitter signal. The phase of this EE signal in each NLA event was tracked with respect to a recorded phase reference. These phase studies showed that the accumulating phase of the offset EE signal is frequently interrupted by negative phase steps (‘N events’) which tend to reduce the offset frequency. Five of the NLA events during key‐down transmission were quenched by whistlers which themselves triggered free emissions at ½ƒBO. The theory of nonlinear wave‐wave interaction between the transmitter or input wave (IW) and the embryo emission is developed to explain these features. It is shown that coupling depends on the offset frequency δƒ and the ‘control frequency’ Fc: for δƒ > Fc the emission is effectively free; for δƒ < Fc, EE is controlled by IW. Curiously, Fc is determined by the EE amplitude (Bw) as Fc ∞ BW1/2, and is almost independent of IW amplitude. This control applies whether the emission was originally generated by IW or captured by it. Fc is determined from Bw measurement to be 60–120 Hz, which fits the observed behavior quite well. For δƒ < Fc a fraction of the phase‐bunched electrons are trapped by IW as they are detrapped by EE in the growth region. This superimposes a strong component oscillating in phase which can produce N events, effectively phase locking the low‐amplitude end of EE to IW. Amplitude fluctuations, δƒ, and Fc are interrelated in a complicated way which gives rise to short‐term instabilities and somewhat longer‐term stabilizing influences.