Oblique Incident Plane Wave Research Articles

The currents on a cylinder illuminated by a general obliquely-incident plane wave

A relation is presented that determines the total current induced by a general plane wave obliquely incident or a perfectly electrically conducting cylinder of arbitrary cross section from the total current induced by a normally incident plane wave. Remarkably, this same relation ran also be used to determine the physical optics (PO) and nonuniform (NU) currents for oblique incidence directly from the PO and NU currents, respectively, for normal incidence.

Discontinuity waves cannot describe evanescent waves

The problem of oblique incidence of plane waves on a boundary between two linear media is examined in detail especially in connection with generation of evanescent waves. It is shown that, unlike plane waves, evanescent waves are fully determined by two functions, which are to be chosen as the Hilbert transform of each other so as to guarantee an appropriate behavior of the solution at infinity. When such an approach is contrasted with the theory of discontinuity waves, it turns out that the usual information about discontinuities does not suffice for calculating evanescent waves. In conclusion, the oblique incidence problem does not admit a consistent answer within the sole framework of discontinuity waves.

Diffraction of an oblique-incidence plane wave on a reflection grating

Diffraction of an oblique-incidence plane wave on a reflection grating

Generalized WKB Approximation for Stratified Isotropic Chiral Media with Obliquely Incident Plane Wave

The WKB method and its generalization are extended to stratified chiral media for waves with oblique incidence. Wave propagation in chiral media inhomogeneous in one space coordinate is considered through normalized wave fields, a certain combination of the electric and magnetic fields, which are slightly coupled in slightly inhomogeneous media. Omitting the coupling leads to the WKB solution for waves propagating without reflection. The reflection effect is obtained as a first order correction to the WKB solution. For sufficiently slowly varying media, the reflection dyadic due to the stratification can be expressed in closed integral form.

Frequency spectrum of dynamic COD.

Dynamic crack opening displacement (DCOD) of a two-dimensional finite crack to the oblique incidence of an elastic plane wave is computed based on the elastodynamic theory for the fundamentals of ultrasonic wave scattering analysis. The formulations can be done through the Fredholm integral equations of the second kind. Infinite integration of the kernel is transformed to a finite one. Then, it is expanded into the Neumann series of the Bessel functions. This expansion enables us to estimate the kernel easily because the Bessel functions can be calculated by the recurrence relation of their order. The numerical results of the DCOD are plotted in three-dimensional graphic form and their frequency dependencies are shown in perspective.

Oblique scattering from lossy strip structures with one-dimensional periodicity

The intentional addition of loss to a periodic structure can be used as a technique to alter its scattering characteristics. The problem of an oblique plane wave incident on an array with one-dimensional periodicity is examined. The unit cell of the array is composed of a number of thin resistive strips. The obliqueness of the incident plane wave combined with the lossy nature of the structure causes the transverse electric (TE) to z and the transverse magnetic (TM) to z fields to couple. To analyze the described problem, two coupled electric field integral equations that have as unknowns the equivalent surface currents on the strips in the unit cell are derived. The integral equations are discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Green's function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the TE/TM coupling behavior as strip resistance is increased for representative structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Prediction of bending resonances on elastic spheroids due to oblique incident plane waves from exact beam theory and comparison to T-matrix calculations

Exact beam theory predicts the presence of “bending” or flexural resonances from oblique incident plane waves. In an earlier paper, Timoshenko theory, which assumes a constant moment of inertia along the beam, was employed to derive an approximate theory to predict flexural resonances. Good agreement was found (for the lower modes) with the exact T-matrix calculations based on exact 3-D elastodynamics. It is possible to solve the exact beam equation using phase matching techniques to predict “bending” resonance locations. Such calculations are performed for spheroids for aspect ratios from 1.5 to 10, with extremely good agreement between beam theory and the exact T-matrix calculations for all modes.

Optical multistability and solitonlike intensity distribution in a nonlinear superlattice for oblique incidence

The optical transmission properties of a nonlinear superlattice structure for oblique incidence of TE-polarized plane waves are investigated. A simple characteristic matrix method using the slowing varying envelope approximation is developed to obtain the reflection and transmisson coefficients from such structures. The nonlinear system is shown to possess a multistable output with total transmission states characterized by a solitonlike distribution of intensity in the layers.

Analytical method of a multilayered meander-line polarizer plate with normal and oblique plane-wave incidence

Simple empirical formulas for perpendicular and parallel polarization susceptances for a meander-line grating plate are given. The numerical results compared favorably with experimental data and published data. Simple transmission-line model in terms of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -type mode and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -type mode for multilayered meander-line polarizer plate is presented for plane wave incidence at normal and oblique angles. Numerical results for design examples are given for practical application.

Absorption of longitudinal and shear waves and generation of heat in soft tissues

The author analysed the oblique incidence of a longitudinal plane wave and the generation of a shear wave at a boundary between a soft tissue and a gas, considering a viscoelastic model (Voigt solid) of the medium. From the data measured by Frizzell et al. (J. Acoust. Soc. Am. 60, 1409-1411) for shear waves, the average velocity 30 m/s and the average absorption coefficient 7.7 X 10(3) cm-1 at the frequency of 5 MHz were assumed for calculations. The amplitude and the intensity of the generated shear wave were obtained and hence the rate of heat production per unit volume was determined. At the boundary, this quantity was found to be of the same order of magnitude for the generated shear wave as for the incident longitudinal wave. In the case of the shear wave, which propagates almost perpendicularly to the boundary, it decreases rapidly with the distance. Therefore, the temperature increase caused by shear waves was negligible in respect to longitudinal waves in spite of the extremely high absorption coefficient. This conclusion could be confirmed by solving the inhomogeneous equation of heat conductivity for the case under consideration.

Sound transmission through a flexible plate with porous layers mounted directly on its surfaces.

The equation of motion for a flexible plate with porous layers mounted directly on its surfaces is derived by taking account of the interaction between the solid frame of porous material and the fluid in the pores. In the derivation of the equation of motion, the effects of transverse shear defbrmation and rotary inertia of the solid material itself and of rotary force by the in-plane motion of the fluid in the pores are neglected. By the use of the obtained equation of motion, the fbrmula fbr the sound transmission coefficient through the composite plate is deduced for the oblique incident plane wave. Some discussions are made upon the increases of transmission loss by the application of the porous layers on the core plate and upon the reversibility in spatial arrangement of the plate for sound transmission.

Shielding Properties of Thick Conducting Cylindrical Shells with an Obliquely Incident Plane Wave

The shielding properties of a thick circular cylindril shell of finite conductivity is analyzed for the case of an obliquely incident plane wave. The results show that the apparent radius of the cylinder is contracted as compared to the normal incidence case.

Thin-film reflection properties of an anisotropic plasma slab immersed in a static magnetic field normal to the plane of incidence †

Abstract The reflection and transmission properties of an anisotropic plasma slab immersed in a static magnetic field normal to the plane of incidence are studied for the case of oblique incidence of a parallel-polarized plane wave. The emphasis is on ‘ the thin-film reflection properties ’, namely, the oscillations in the reflection coefficient due to constructive interference of internally reflected waves from the front and back surfaces of the slab geometry. The effect of the slab width, the angle of incidence and the strength of the magnetic field on the nature of the oscillations in the power reflection coefficient are discussed. The general nature of variation of power reflection coefficient for the slab can be predicted from the nature of the characteristic root q1. In the range of real q1 the power reflection coefficient ρ is oscillatory and the oscillations with increasing amplitude will be more and more crowded as q1 increases, finally giving rise to an infinite number of oscillations around the...

Reflection at oblique incidence of an impulsive transverse magnetic plane wave from a cold, lossy, semi‐infinite plasma

Branch‐cut integrals are used to calculate the reflection of transient pulses from the surface of a cold, lossy, semi‐infinite plasma. For the case considered in detail, small to moderate losses and an impulse‐incident waveform with transverse magnetic polarization, the reflected waveform is oscillatory for small losses (collision rate much less than the plasma frequency) but decays monotonically for a collision rate of half the plasma frequency. The reversal of polarity of the initial half cycle of the reflected waveform observed as the incidence angle increases through 45° is interpreted as a Brewster‐angle phenomenon.

Modelling The Poro-elastic-acoustic-elasticLayer Interactions: A Finite Element Method

Porous materials are widely used as effective sound absorbers in both industrial as well as in architectural applications. In most cases, the frame of the porous materials is not rigid. It is well-known that Biot's theory* models effectively the behaviour of such materials. Analytical solutions to Biot's theory^ are restricted to simpler geometrical shapes. In the present paper, a finite element method based on the Galerkin approach is presented to model the poro-elastic medium and its interactions with elastic medium as well as surrounding fluid medium. The boundary conditions are effectively brought out in the process. Modelling the interaction between two porous layers is also discussed in the present paper. Finally, comparisons are made with the analytical solutions exisiting in the literature for both normal as well as oblique incident plane waves.

Excitation of Fabry-Perot Resonator III. Wave Incidence through Semi-Transparent Mirror

The excitation problem is theoretically analysed for the plane wave incident through a semi-transparent mirror of the resonator. The authors' foregoing analysis of the forced excitation of a resonator with perfect mirrors is extended in this paper, using the additional boundary condition across a dielectric mirror. The formulation is generally made for an oblique incidence of plane wave on the dielectric mirror. The analysis in the case of free oscillation yields the one-transit loss which equals the ordinary diffraction loss plus half the transmission coefficient. For the normal incidence input characteristics and amplitude and phase distributions of the field are computed for some transmission coefficients of the mirror. Similar computations are made approximately for the oblique incidence and the field distributions are represented as the contour maps, where rotationally asymmetric modes are more excited as the incident angle increases.

Amplitude and phase scintillations of waves scattered from ionospheric irregularities

The basic statistics of fluctuations of an electromagnetic wave after scattering from ionospheric irregularities are derived in this paper for the oblique incidence of a primary plane wave. The irregularities are assumed to be enclosed within a layer of finite thickness which is placed at a certain height above the ground. The spatial autocorrelation function of refractive index fluctuations is described by anisotropic Gauss and isotropic Bessel functions. The results obtained are compared with the conclusions of both diffraction and scattering theory so far achieved.