Refraction Of Plane Waves Research Articles

Reflection and Refraction of Plane Waves at an Interface of Water and Porous Media with Slip Boundary Effect

Reflection and Refraction of Plane Waves at an Interface of Water and Porous Media with Slip Boundary Effect

Critical Angle Formulation of Nonuniform Plane Waves for Determining Correct Refraction Angles at Planar Interface

The expressions and properties of the critical angles of nonuniform plane waves for determining the correct refraction angle at the infinite planar interface of two linear, isotropic, and homogeneous media are presented. The two media could be lossless or lossy. For the case where the complex wave vector of Adler–Chu–Fano formulation and the normal vector to the interface are coplanar, a critical angle equation, which is simpler than the extant one, under the condition that one or two critical angles exist, is formulated. In addition, for the case where the complex wave vector and normal vector to the interface are noncoplanar, a critical angle equation is formulated, rendering the 3-D nonuniform plane wave refraction feasible for utilization in many areas of optics. The presented critical angle equations were validated for various nonuniform plane waves and media.

Reflection and refraction of plane wave at the junction of two dissimilar pre-stressed functionally graded piezothermoelastic media under different interfacial conditions

The present paper deals with the study of the reflection and refraction of plane waves (quasi P wave, quasi SV wave, electroacoustic wave, and thermal wave) at the common interface of two dissimilar initially stressed functionally graded piezothermoelastic media. The problem has been formulated and solved using suitable boundary conditions, and the results are obtained in a closed matrix form. The effect of mechanical, electrical, and thermal loose bonding of the common interface on the reflection and refraction coefficients are analyzed and theoretical outcomes are presented through graphs under two generalized forms of thermoelasticity (namely, Lord and Shulman (LS) theory, Green and Lindsay (GL) theory). A particular model of CdSe and PZT-5A materials has been considered for the numerical illustration. Moreover, the effect of material gradient; horizontal, transverse, and normal initial stresses; thermal relaxation parameters; and material coefficients on the reflection and refraction coefficients are demonstrated with the help of graphs. The expressions for energy ratios of reflected and refracted waves are derived, and energy conservation is validated with the help of obtained graphs under LS and GL theories. The study finds its application toward the efficient optimization of force sensors, surface acoustic wave (SAW) devices, temperature sensors, and Love wave sensors.

Impact of imperfect corrugated interface in piezoelectric-piezomagnetic composites on reflection and refraction of plane waves.

Defects such as imperfect geometric/mechanical/dielectric/magnetic interfaces affect the performance and life of structural components used in aircraft technology and underwater navigation. The major drawback of an imperfect interface in a system is its disability to transfer stress or potential across the surface effectively. Nondestructive evaluation, particularly P-wave reflection imaging, contributes significantly to detecting defects and in situ conditions of such structural components. The present study encapsulates the reflection/refraction phenomenon of quasi-pressure waves when they strike the mechanically/dieletrically/magnetically imperfect corrugated interfaces of piezoelectric and piezomagnetic half-spaces. The reflected/refracted wave fields not only consist of regular bulk and surface waves but also a spectrum of irregular bulk waves, arising as the result of geometrical irregularities at the interface. The reflection and refraction coefficients (RECs/RACs) of all regular/irregular waves are derived analytically by using Rayleigh's method of slope approximation (first iteration of small perturbation). The existence of the critical angle is interpreted from the slowness curves of the bulk waves. The influences of the corrugation, angular frequency, and interface imperfection on the RECs/RACs are the major findings reported in the study. The reflected/refracted potential waves diminish for the dielectrically/magnetically imperfect interface. The energy coefficients of the reflected/refracted waves are derived, and the energy conservation law is satisfied.

Fundamentals of Lossless, Reciprocal Bianisotropic Metasurface Design

Lossless, reciprocal bianisotropic metasurfaces have the ability to control the amplitude, phase, and polarization of electromagnetic wavefronts. However, producing the responses that are necessary for achieving this control with physically realizable surfaces is a challenging task. Here, several design approaches for bianisotropic metasurfaces are reviewed that produce physically realizable metasurfaces using cascaded impedance sheets. In practice, three or four impedance sheets are often used to realize bianisotropic responses, which can result in narrowband designs that require the unit cells to be optimized in order to improve the performance of the metasurface. The notion of a metasurface quality factor is introduced for three-sheet metasurfaces to address these issues in a systematic manner. It is shown that the quality factor can be used to predict the bandwidth of a homogeneous metasurface, and it can also be used to locate problematic unit cells when designing inhomogeneous metasurfaces. Several design examples are provided to demonstrate the utility of the quality factor, including an impedance matching layer with maximal bandwidth and a gradient metasurface for plane wave refraction. In addition to these examples, several metasurfaces for polarization control are also reported, including an isotropic polarization rotator and an asymmetric circular polarizer.

Reflection and refraction of plane wave in piezo-thermoelastic diffusive half spaces with three phase lag memory dependent derivative and two-temperature

ABSTRACT The current research deals with the analysis of reflection and refraction of plane wave at the imperfect boundary of two dissimilar transversely isotropic piezo-thermoelastic (PT) solid half-spaces with diffusion and two temperature. The formulation is applied in a 2-D model under the purview of three-phase lag (TPL) memory dependent derivative (MDD) heat transfer and TPL MDD diffusion. For the incident QL or QTS wave, there exist four coupled quasi reflected waves: RQL (reflected quasi-longitudinal), RQMD (reflected quasi-mass diffusion), RQT (reflected quasi thermal) and RQTS (reflected quasi-transverse) and four transmitted waves: TQL (transmitted quasi-longitudinal), TQMD (transmitted quasi-mass diffusion), TQT (transmitted quasi thermal) and TQTS (transmitted quasi-transverse) waves propagating with different speeds in two solid half-spaces. The expressions for the amplitude ratios and energy ratios are calculated for the reflected and refracted waves. Calculations for normal force stiffness, transverse force stiffness, thermal contact conductance and welded boundaries are also done as particular cases. Some special cases are also discussed. MATLAB software is used for the numerical and graphical analysis and to show the effect of two-temperature on the amplitude ratios of different reflected and refracted waves for incident QL and QTS waves.

Reflection and refraction of elastic waves at the interface of an elastic solid and partially saturated soils

The present problem deals with the reflection and refraction of plane waves at the interface of an elastic solid and partially saturated soils. A mathematical model of partially saturated soils developed by Ghasemzadeh and Abounouri (Soil Dyn Earthq Eng 51:1–8, 2013) is employed. The incidence of two main waves (P and SV) is considered. As a result of the incident wave, two reflected waves (in an elastic solid) and four refracted waves (in partially saturated soils) are generated. The elastic solid behaves non-dissipative, while partially saturated soils behave dissipative due to the presence of viscous pore fluids, as a result of which the incident and reflected waves are homogeneous and all the refracted waves are inhomogeneous. The coefficients of reflection and refraction for a given incident wave result in a non-singular system of linear equations. Further, these reflection and refraction coefficients are used to obtain the energy shares of various reflected and refracted waves. This study has been numerically tested to determine the effects of various properties of partially saturated soils on the various energy shares. The numerical example confirms that during the reflection or refraction process conservation of incident energy is obtained at each angle of incidence.

Analysis of reflection and refraction of plane wave at the separating interface of two functionally graded incompressible monoclinic media under initial stress and gravity

The present article deals with the reflection and refraction phenomenon of a plane wave at the interface of two distinct functionally (exponentially) graded incompressible monoclinic media in the two separate cases. The first case (Case I) deliberates the influence of initial stress; however, the second case (Case II) analyses the influence of gravity associated with both upper and lower incompressible functionally graded monoclinic media on amplitude ratios of reflected and refracted waves. Two types of waves namely quasi-P and quasi-SV are generated due to the plane wave incident at the common interface of the considered structure. An analytical approach has been employed to compute velocity equations for each of the two cases. The dependency relations of dimensionless amplitude ratio of reflected and refracted waves on various affecting parameters along with angle of incidence have been established in closed form for both the cases. Moreover, the expressions for slowness section have also been derived for the corresponding cases and depicted by the means the graphs. Also as a special case of the problem, the deduced results are validated with the pre-established result. An analysis to unravel the effect of angle of incidence, gravity parameter, material gradient parameter and initial stress associated with lower and upper media on the reflected and refracted waves has also been made meticulously through numerical computations and graphical illustrations. Furthermore, through comparative analysis some important peculiarities in the phenomenon have also been highlighted.

In situ steering of shear horizontal waves in a plate by a tunable electromechanical resonant elastic metasurface

A multifunctional electromechanical coupling metasurface is proposed to steer elastic shear horizontal (SH) waves. The horizontal shear deformation of the metasurface is coupled with a shunting circuit by in-plane polarized piezoelectric patches. A prospective phase distribution along the metasurface can be achieved by adjusting the negative capacitances of the shunting circuit to change the electromechanical resonant response. Multiple functions are demonstrated, including wave focusing and anomalous refraction of plane waves in different frequencies. In addition, an asymmetric wave transmission is produced by designing a dual-layer metasurface. Results show that this metasurface opens up a way toward advanced electromechanical coupling and tunable manipulation of elastic SH waves.

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and double-porosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves (i.e., incident and reflected) in an elastic medium are considered as homogeneous (i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous (i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

Reflection and refraction of plane waves at the loosely bonded common interface of piezoelectric fibre-reinforced and fibre-reinforced composite media

The rapid development of the modern age has increased the urge of using composite structures having applications in the realm of various engineering fields. Specifically, fibre-reinforced piezoelectric composites are in the forefront of the present era because of its light weight, great strength and hence improved performance over the piezoelectric materials alone. Therefore, the present paper delves with the problem of reflection and refraction of plane waves when it is incident at the interface of a Piezoelectric Fibre-reinforced Composite (PFRC) medium and Fibre-reinforced Composite (FRC) medium. It is assumed that the media are loosely bonded to each other and are under horizontal initial stresses. It is established that the boundary conditions are satisfied by the set of three coupled waves associated with the PFRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV), electrostatic wave (EA)) and two coupled waves associated with the FRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV)). The amplitude ratio of reflected and refracted waves are obtained with the aid of suitable boundary conditions at the common interface of the two media. The effect of anisotropy, initial stresses and loose bonding on the amplitude ratio are studied numerically and demonstrated by means of graphs. The effect of anisotropy is also studied on the slowness curves, plotted in slowness surface. Moreover, the relation for energy partition is also derived and it is established that the total normal energy flux balance at the interface is unity.

Bianisotropic Huygens’ Metasurface Pairs for Nonlocal Power-Conserving Wave Transformations

Bianisotropic Huygens’ metasurfaces are subwavelength thin surfaces that have been used to achieve wide-angle reflectionless refraction of plane waves, among other applications. These metasurfaces can realize any wave transformation, with a lossless and passive structure, provided that local power is conserved over the metasurface at every point. However, there are numerous practical wave transformations that satisfy total power conservation, but break this local power conservation requirement, such as antenna beamforming. In this letter, a method for realizing these wave transformations using a pair of cascaded bianisotropic Huygens’ metasurfaces is proposed. A summation of plane waves is assumed between the two metasurfaces, and their coefficients are obtained based on the stipulated input and output waves. Finally, a case study of converting a cylindrical wave to a truncated plane wave is presented with full-wave simulations.

Whistler modes in highly nonuniform magnetic fields. I. Propagation in two-dimensions

The propagation of whistler wave packets is studied in a large laboratory plasma with nonuniform ambient magnetic fields. The wave packets are excited by magnetic loop antennas and, for uniform fields, have the topology of helicon modes in unbounded plasmas. The waves propagate across the separatrix of X-type nulls and across circular field lines of magnetic islands. Classical wave refraction is not observed when the magnetic gradient scale length becomes shorter than the wavelength. Since the ambient magnetic field is generated by a line current, it is two dimensional and the wave magnetic field is measured and displayed in transverse planes. Using wave bursts, the space-time evolution of wave packets is observed. The group velocity has been measured. Waves can cross a separatrix and refract into nearly parallel whistler modes. The phase rotation of helicons is lost on a strongly curved field. In highly nonuniform magnetic fields, the phase velocity is determined from multipoint magnetic hodograms, the group velocity from the Poynting vector fields. The energy flow is highly field aligned while the phase flow can be highly oblique to the ambient magnetic field without encountering cyclotron resonance absorption. In the limiting case of circular field lines, counter propagating waves create azimuthal standing waves while still propagating radially. Standard concepts of plane wave refraction do not apply to whistler modes in highly nonuniform magnetic fields. Implications of these observations on research in space plasmas and helicon devices will be pointed out.

Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium

In the present paper, we have considered a layered medium of two semi-infinite nonlocal elastic solids with intermediate transversely isotropic magnetothermoelastic solid. The intermediate slab is of uniform thickness with the effects of two temperature, rotation and Hall current and with and without energy dissipation. A plane longitudinal or transverse wave propagating through one of the nonlocal elastic solid half spaces, is made incident upon transversely isotropic slab and it results into various reflected and refracted waves. The amplitude ratios of various reflected and refracted waves are obtained by using appropriate boundary conditions. The effect of nonlocal parameter on the variation of various amplitude ratios with angle of incidence are depicted graphically. Some cases of interest are also deduced.

Plane wave refraction on convex and concave angles in geometric acoustics approximation

An exact analytical solution to the eikonal equation for a plane wave refracted on a boundary comprising both convex and concave obtuse angles has been built. Under the convex angle summit the solution has a line of discontinuity in the ray vector field and in the first derivatives of the first arrival times, and under the concave angle it has a cone of waves diffracted on this angle. This cone corresponds to the Keller diffraction cone in the geometric diffraction theory. The relation between the eikonal equation and the resultant Hamilton–Jacoby equation for arrival times of downward waves and the ray parameter conservation equation is investigated. Solutions to these equations coincide for pre-critical incidence angles and differ for super-critical angles. It is shown that the arrival times of maximum amplitude waves, which are of the greatest practical interest, coincide with the times calculated from the ray parameter field for the ray parameter conservation equation. The numerical algorithm proposed for calculation of these times can be used for arbitrary speed models.

Negative refraction and superresolution by a steel-methanol phononic crystal

Negative refraction and the associated lensing effect of a two-dimensional (2D) phononic crystal (PC) in the MHz regime were studied both experimentally and numerically. The PC consists of a hexagonal array of steel cylinders (r = 0.4 mm, a = 0.5 mm) in a methanol matrix for use in an aqueous medium. FEM simulations of the pressure field show negative refraction of plane waves through a prism shaped crystal and superresolution lensing through a rectangular crystal. These phenomena were observed with hydrophone scans of the transmitted pressure fields through the steel-methanol PC in a water tank.

The plane wave refraction on convex and concave obtuse angles in geometric acoustics approximation

The plane wave refraction on convex and concave obtuse angles in geometric acoustics approximation

Reflection and Refraction of Plane Waves at the Interface of Two Visco-thermoelastic Liquid Layers in Presence of Magnetic Field and Compressional Stress, with the Outer Core Inside the Earth as a Model

This paper is devoted to investigate the effects of viscosity, magnetic field and compressional stress on reflection and refraction of plane waves while propagating through the interface of two visco-thermoelastic liquid layers. The basic dynamical equations of motion for visco-thermoelastic liquid medium in presence of magnetic field and the heat conduction equation in the context of Green–Lindsay theory have been solved to derive the wave equations for the reflected and refracted P, SV and thermal waves. Using appropriate boundary conditions, equations containing the ratios of amplitude of various reflected and transmitted components to that of incident wave have been obtained in matrix form. These amplitude ratios have been computed numerically for P-wave incidence only and results obtained are presented graphically.

Reflection/refraction at the interface of an elastic solid and a partially saturated porous solid containing liquid filled bound pores and a connected pore space saturated by two-phase fluid

The phenomena of reflection and refraction of plane waves incident obliquely at a plane interface between uniform elastic solid half-space and porous solid containing liquid filled bound pores and two-phase fluid in connected pores has been analyzed. The amplitude ratios of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used further to derive the expressions for the partition of incident energy among the reflected and refracted waves. Partition of incident energy among the reflected and refracted waves is studied for incidence of P and SV waves. The conservation of the energy across the interface is verified. The effect of gas saturation, wave frequency, capillary pressure and bound liquid film on the amplitude ratios and energy partitions are studied in the numerical example.

Dual-Phase-Lag Model of Wave Propagation at the Interface Between Elastic and Thermoelastic Diffusion Media

A dual-phase-lag diffusion model, augmenting the Fick law by the inclusion of the delay times of the mass flow and the potential gradient at the interface between two media into it, is proposed. The effects of reflection and refraction of plane waves at the interface between an elastic and a thermoelastic diffusion media were investigated with the use of this model. It was established that the ratios between the amplitudes and energies of the waves reflected and refracted at the interface between the indicated media are determined by the angle of incidence of radiation on this interface, the frequency of the incident wave, and the thermoelastic and diffusion properties of the media. Expressions for the ratios between the energies of different reflected and refracted waves and the energy of the incident were derived. The variation in these ratios with change in the angle of incidence of radiation on the indicated interface was calculated numerically and represented graphically.