Amplitude modulation and demodulation of an electromagnetic wave in magnetised acousto-optic diffusive semiconductor plasmas: Hot carrier effects

In communication processes, amplitude modulation is very helpful to save power using a single band transmission. Using the hydrodynamical model of semiconductor plasma analytical investigations are made for the amplitude modulation as well as demodulation of an electromagnetic wave incorporating carrier heating (CH) effects in acousto-optic magnetised semiconductor plasma. The CH effects add new dimensions in the present analysis. Analysis are made under different wave number regions over a wide range of cyclotron frequencies. It is found that incorporation of CH effects modifies the amplitude modulation and demodulation processes effectively. Numerical estimations are made for III–V semiconductor crystal irradiated by pump wave of frequency 1.6×10¹³ s^?1. Complete absorption of the waves takes place in all the possible wavelength regimes when the cyclotron frequency ω_c becomes nearly equal to ω₀, the pump frequency on neglecting the collision term in modulation/ demodulation indices.     

Critical surface wave velocity near phase transitions

The temperature dependent Rayleigh wave velocity is discussed for crystals with a surface layer of depth equal to the correlation length, ξ, with special reference to a critical region near phase transitions. For finite qξ the Rayleigh wave velocity reflects the specific critical properties of the surface layer. Under such conditions the temperature dependence of Rayleigh waves cannot be predicted on the temperature dependence of constants. A phenomenological analysis is made for qξ ≦? 1. Experimental results on SrTiO₃ show bulk-dominated critical Rayleigh wave velocities due to the short correlation length in this material.     

Dispersion relations of waves in a rod embedded in an elastic medium

The dispersion relations of waves propagating in a system consisting of an elastic rod of radius a embedded in a linear elastic medium are investigated, and phase speeds of waves of wavelength λ which propagate under steady state conditions are determined. The dispersive behaviour is found to be dependent on several non-dimensional parameters defined by the geometric ratio $\text{a}\text{λ}$, as well as on non-dimensional ratios of the rod-medium properties. It is shown that the resulting waves which can propagate under steady state conditions are surface waves which decay with the radial distance and which permit no radiation damping of energy. It is further shown that such waves can propagate freely only if the propagation speed of longitudinal waves in the corresponding free rod is less than that of shear waves propagating in the medium. Results are presented by means of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase speeds are established.     

Dynamics of a nonlinear field

A systematic study is made of the plane wave modes of a nonlinear c-number field (λφ⁴ model) and interesting features of the behavior of such fields, which do not seem to have been observed before, are brought out. These relate to the case λ < 0, wherein there are different regimes characterized by different kinds of elliptic-function forms for the waves. We show that when the amplitude of the elliptic function waves approaches critical values corresponding to “phase transition” from one regime to another, the energy density in the field increases without limit (though the amplitude is finite). In two of the regimes which are “tachyonic” in nature, there are frozen wave modes which are spatially periodic but time independent. These turn out however to be unstable against perturbations. Finally we observe that in one of these regimes there exist a lower bound on the energy density in the wave field. The case of fields with higher nonlinearities is briefly considered.     

Nonlinear Evolution of a Gaussian Wave Perturbation in the Presence of a High Power Electromagnetic Plane Wave in the F Region Ionosphere

The interaction of a high power electromagnetic plane wave of uniform intensity with a weak electromagnetic Gaussian wave has been studies analytically. The two waves propagate vertically with almost the same frequency in the F region ionosphre. It is seen that the Gaussian wave acquires an oscillatory structure due to the nonlinear coupling of the strong plane wave and the weak Gaussian wave and the amplitude of these fluctuations grows with height. The growth, however, occurs only above a certain altitude z₀, which is determined by the plasma and wave parameters.     

Wave velocities in shock-compressed cubic and hexagonal single crystals above the elastic limit

When solids are subjected to high-pressure shock-wave loading, multiple stress waves propagate with velocities dependent upon the elastic and inelastic compressibilities of the solid. The present paper shows that the inelastic or plastic waves in cubic and hexagonal single crystals do not necessarily propagate with the bulk sound speed as they do in isotropic elastic-plastic solids. This result is a consequence of anisotropy in the plastic deformation which depends on the slip plane orientation in the crystal and has important consequences with regard to the determination of compressibilities from shock-wave data. In particular, for wave propagation in the <110> directions of cubic crystals the departure from the bulk velocity can be significant (5–25 per cent). For wave propagation normal to the c-axis in hexagonal crystals, the plastic wave velocity also differs from the bulk sound speed (10–25 per cent). Plastic wave velocities are tabulated for a number of cubic crystals on the basis of the various slip systems common to these materials. The calculated velocities are then compared with experimental data on shock-loaded single-crystal aluminum and sodium chloride.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

The effects of wall discontinuities on the propagation of flexural waves in cylindrical shells

The transmission of flexural type waves through various discontinuities in the walls of cylindrical shells is investigated. Theoretical curves of transmission loss are obtained for different circumferential wavenumbers and wave types, as functions of frequency. Material stiffness and extensional phase speed, together with the relationship between radial vibration amplitude and total wave power of propagation, are important factors which are found to strongly influence wave transmission through discontinuities. Some practical results useful for predicting the performance of typical pipe isolators (in vacuo) are obtained.     

Temperature-dependent Brillouin scattering studies of surface acoustic modes in Nd0.5Sr0.5MnO3

Brillouin scattering experiments are carried out to study the surface acoustic waves in Nd_0.5Sr_0.5MnO₃ as a function of temperature in the range of 40-300 K covering the metal-insulator and charge-ordering phase transitions. The surface modes include surface Rayleigh wave, pseudo-surface acoustic wave (PSAW) and high velocity PSAW. The observed softening of the sound velocities for the surface modes below paramagnetic to ferromagnetic transition, T_c is related to the softening of the C₄₄ elastic constant. The subsequent hardening of the sound velocity below the charge ordering transition temperature T_co is attributed to the coupling of the acoustic phonon to the charge ordered state via long range ordering of the strong Jahn-Teller (JT) distortion.     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated using the multiple scales method in (2 + 1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. We convert this equation for the evolution of wave packets in (2 + 1)-dimensions, using the function transformation method, into an exponentional and a Sinh-Gordon equation, and obtain classes of soliton solutions for both the elliptic and hyperbolic cases. The phenomenon of nonlinear focusing or collapse is also studied. We show that the collapse is direction-dependent, and is more pronounced at critical wavenumbers, and dielectric constant ratio as well as the density ratio. The applied electric field was found to enhance the collapsing for critical values of these parameters. The modulational instability for the corresponding one-dimensional nonlinear Schrödinger equation is discussed for both the travelling and standing waves cases. It is shown, for travelling waves, that the governing evolution equation admits solitary wave solutions with variable wave amplitude and speed. For the standing wave, it is found that the evolution equation for the temporal and spatial modulation of the amplitude and phase of wave propagation can be used to show that the monochromatic waves are stable, and to determine the amplitude dependence of the cutoff frequencies.Received: 23 November 2003, Published online: 15 March 2004PACS: 47.20.-k Hydrodynamic stability - 52.35.Sb Solitons; BGK modes - 42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation - 47.65. + a Magnetohydrodynamics and electrohydrodynamicsM.F. El-Sayed: Permanent address: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

Equilibrium distribution of the wave energy in a carbyne chain

The steady-state energy distribution of thermal vibrations at a given ambient temperature has been investigated based on a simple mathematical model that takes into account central and noncentral interactions between carbon atoms in a one-dimensional carbyne chain. The investigation has been performed using standard asymptotic methods of nonlinear dynamics in terms of the classical mechanics. In the first-order nonlinear approximation, there have been revealed resonant wave triads that are formed at a typical nonlinearity of the system under phase matching conditions. Each resonant triad consists of one longitudinal and two transverse vibration modes. In the general case, the chain is characterized by a superposition of similar resonant triplets of different spectral scales. It has been found that the energy equipartition of nonlinear stationary waves in the carbyne chain at a given temperature completely obeys the standard Rayleigh–Jeans law due to the proportional amplitude dispersion. The possibility of spontaneous formation of three-frequency envelope solitons in carbyne has been demonstrated. Heat in the form of such solitons can propagate in a chain of carbon atoms without diffusion, like localized waves.     

Nonlinear acoustic response through minute surface cracks: FEM simulation and experimentation

The second harmonic of a Rayleigh wave passing through a minute surface crack has been numerically analyzed by semi-explicit FEM including special elements which account for a nonlinear stress-strain relation at crack surfaces. Minute cracks perpendicular to a free, flat surface close under compressive stress when width of the crack opening is less than the longitudinal amplitude of the Rayleigh wave. Thereafter, compressive and shear stresses are partially transmitted through the closed cracks, whereas tensile and shear stresses are not transmitted through cracks that remain open. This leads to marked nonlinear ultrasonic response. Calculation was performed for an aluminum block having a surface crack. The transverse component of the Rayleigh wave propagating through the cracks shows distorted waveforms, making the second harmonic amplitude clearly noticeable. In an experiment, the second harmonic component of the leaky Rayleigh wave was detected for a simple crack model consisting of two aluminum blocks, by use of a PVDF line-focused transducer. The results of the experiment show that the second harmonic amplitude is a second-order function of the fundamental wave amplitude, and is more pronounced for low compressive stress applied to close the crack surfaces.     

A stability analysis of fifth-order water wave models

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.     

Complex singularity of a stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H _max/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is the wave height and λ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance ν _c from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for ν _c → 0 we suggest a new power law scaling ν _c ∝ (H _max ? H)^3/2 as well as new estimate H _max/λ ? 0.1410633.     

Interaction of a Defect Density Wave With a Modulated Structure in Incommensurate-Phase Crystals

Experimental and theoretical studies of the optical birefringence increment in the transition and metastable states of the incommensurate phase of Rb₂ZnBr₄, [N(CH₃)4]₂MeCl₄ (Me = Zn, Cu, Fe) crystals have been made. It has been established that in the modulated structure field a defect density wave is formed. It has been shown that when the period of the defect density wave coincides with the period of the modulation wave, the region of existence of the metastable state expands; when the periods of these waves do not coincide, their superposition occurs, with the formation of a wave with a difference value of the modulation vector. The presence of defect density waves in the incommensurate phase leads to a temperature hysteresis and kinetics of the physical quantities in the vicinity of T_c. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 5, pp. 632–639, September–October, 2005.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Effects of harmonic phase on nonlinear surface acoustic waves in the (111) plane of cubic crystals

Spectral evolution equations are used to perform numerical studies of nonlinear surface acoustic waves in the (111) plane of several nonpiezoelectric cubic crystals. Nonlinearity matrix elements which describe the coupling of harmonic interactions are used to characterize velocity waveform distortion. In contrast to isotropic solids and the (001) plane of cubic crystals, the nonlinearity matrix elements usually cannot be written in a real-valued form. As a result, the harmonic components are not necessarily in phase, and dramatic variations in waveforms and propagation curves can be observed. Simulations are performed for initially monofrequency surface waves. In some directions the waveforms distort in a manner similar to nonlinear Rayleigh waves, while in other directions the velocity waveforms distort asymmetrically and the formation of shocks and cusped peaks is less distinct. In some cases, oscillations occur near the shocks and peaks because of phase differences between harmonics. A mathematical transformation based on the phase of the matrix elements is shown to provide a reasonable approximation of asymmetric waveform distortion in cases where the matrix elements have similar phase.