Impedance Wedge Research Articles

A Rigorous Solution to Electromagnetic Wave Diffraction by Junctions of Impedance and Semitransparent Surfaces

Recent studies of surface-wave-based waveguides for terahertz (THz) imaging and spectroscopy have displayed some interest in investigating surface-wave diffraction by junctions of surfaces with different boundary conditions. Generally, many practically applicable surfaces for THz surface waveguides can be described using nontransparent or semitransparent impedance boundary conditions. In this communication, we find rigorous solutions to electromagnetic wave diffraction by the junction of a nontransparent impedance wedge and a semitransparent half-plane, as well as the junction of two semitransparent half-planes. Generalized semitransparent boundary conditions characterize these semitransparent surfaces.

DIFFRACTION RADIATION OF PARTICLE PASSING BY IMPEDANCE WEDGE

The diffraction radiation field generated by the charged particle passing by the perfectly conductive or impedance wedge is considered. With perfect conductivity, the wedge rotation around the edge fixed along with the straight particle motion line, does not change the total radiated energy. When the motion to the edge is almost parallel to a face of wedge then an increase of impedance from zero increases the radiated energy.

Diffraction by a right angle impedance wedge between left- and right-handed media

ABSTRACTAn analytical solution for the diffraction of plane waves by a right angle impedance wedge which is lying between double negative and positive materials is investigated. In order to satisfy the boundary conditions and shifted shadow boundary, the diffracted fields are divided to subfields. As a result, an anomalous shift of shadow boundary is observed towards to lower surface of the wedge. In addition, geometric optics fields are determined by using the geometry of the problem. Also, the behavior of the fields is investigated numerically.

Wave diffraction by an impedance wedge

A new diffraction field expression is proposed for a wedge with different face impedances. The modified theory of physical optics based diffraction coefficient is taken into account. The reflection coefficients are expressed in terms of the split functions that occur in the double integral solution of the resistive half-plane problem. The effects of wedge’s each faces are represented separately. The uniform field expression is obtained and compared with the literature for a right-angled impedance wedge numerically.

Scattering of acoustic waves from a point source over an impedance wedge

In this work we study diffraction of a spherical acoustic wave due to a point source, by an impedance wedge In the exterior of the wedge the acoustic pressure satisfies the stationary wave (Helmholtz) equation and classical impedance boundary conditions on two faces of the wedge, as well as Meixner’s condition at the edge and the radiation conditions at infinity. Solution of the boundary value problem is represented by a Weyl type integral and its asymptotic behavior is discussed. On this way, we derive various components in the far field interpreting them accordingly and discussing their physical meaning.

Application of instantaneous spectral analysis and acoustic impedance wedge modeling for imaging the thin beds and fluids of fluvial sand systems of Indus Basin, Pakistan

Fluvial sand frameworks have magnificent oil and gas reservoirs far and wide. The reservoir sands are exceedingly compartmentalized by the broadened fault framework. So, to distinguish the thin beds of gas-bearing facies is an assessment for band-limited stratigraphic investigation. To conquest this issue, we execute the progressed seismic ascribe methods to the 3D seismic information of the Miano area of the Indus Basin, SW Pakistan. Apparatuses, for example, the seismic amplitude and coherence are discovered less exact for reservoir description. Sweetness analysis indicates the gas-bearing reservoir facies, which are compartmentalized by the NNW–SSE oriented normal fault system. Yet, the continuous wavelet transforms (CWT) of spectral decomposition (SD) separates the thick and thin sand beds of channel sand and point bars, which were not unsurprising utilizing the band-limited seismic properties. 22 Hz demonstrates the best amplitude tuning cube, which recognizes the profitable clastic (sand-filled barrier bars) sequences. The net-to-gross (N/G) examination uncovers the barrier bars as the chief hydrocarbon-bearing facies. 22 to 37 Hz frequencies confirm the occurrence of hydrocarbon sands. The acoustic impedance (AI) wedge model settles the thin beds of barrier bars sands, which are encased inside the shales, and affirm the suggestions for gas-bearing stratigraphic traps.

Physical optics-based diffraction coefficient for a wedge with different face impedances.

A new diffraction field expression is introduced with the aid of the modified theory of physical optics for a wedge with different face impedances. First, the scattered geometrical optics fields are determined when both faces of the wedge are illuminated by the incident wave. The geometrical optics waves are then expressed in terms of the sum of two different fields that occur for different impedance wedges. The diffracted fields are determined for the two cases separately, and the total diffracted field is obtained as a sum of these waves. Lastly, the uniform field expressions are obtained, and the resultant fields are numerically compared with the solution of Maliuzhinets.

Scattering of an Electromagnetic Surface Wave from a Hertzian Dipole by the Edge of an Impedance Wedge

In this paper, extensions of the results obtained in our previous paper devoted to the diffraction of waves from a Hertzian dipole (point source) located over an impedance wedge are presented. The surface waves components and the edge wave, produced by a surface wave from a point source coming to the edge, are discussed. The geometric optics laws for the surface waves reflected by and transmitted across the edge are also addressed.

Comparison of Solution Options for Line-Source Generated Short-Waves in a Wedge with Neumann and Robin Conditions on Respective Faces: Application to Waves on a Plane Beach

High-frequency waves generated by a moving oscillatory line source over a plane beach are examined in the context of a linear non-hydrostatic theory. The work complements a recent study by the author of low-frequency wave generation in a similar environment (Q. Jl. Mech. Appl. Math.68 (2015) 421–460) and provides a special case of a wider class of problems to which belong also a number of problems on electromagnetic diffraction by impedance wedges currently of considerable interest. The latter are generally treatable only by numerical techniques and the opportunity is seized here to examine a comparison between such numerically generated solutions and analytic solutions which can be and are derived and evaluated for the water wave problem. In common with the electromagnetic problems, the water-wave solution is formulated in terms of an inverse Kontorovich–Lebedev transform the inversion of which is considered both by direct quadrature and by residue composition while the spectral function of the transform is also determined in two different ways namely as (i) (for special wedge angles) a semi-closed form entire function and (ii) a numerical solution of a singular integral equation (as commonly encountered in the electromagnetic problems) valid for more general wedge angles. It is concluded that the residue composition technique can be fraught with difficulties and, where spectral function structure allows, should be replaced by the strategy of direct numerical inversion. For the water-wave problem, the anticipated resonances at edge wave frequencies are shown to exist and their strengths prove to be consistent with the well-known findings of Ursell though the process of successfully detecting these purely from the numerical model is shown to be somewhat error prone.

The Weyl–Van Der Pol Phenomenon in Acoustic Diffraction by a Wedge or a Cone with Impedance Boundary Conditions

The paper deals with the asymptotic description of a diffraction pattern similar to the classical Weyl–Van der Pol phenomenon (the Weyl–Van der Pol formula). The latter arises in the problem of diffraction of waves generated by a source located near an impedance plane. An incident wave illuminates an impedance wedge or cone. The singular points of the wedge’s (the edge points) or cone’s (the vertex of the cone) boundary play the role of an imaginary source, giving rise to a specific boundary layer in some neighborhood of the corresponding impedance surface, provided that the surface impedance is relatively small. From the mathematical point of view, the description of the phenomenon is given by means of the far field asymptotics for the Sommerfeld integral representations of the scattered field. For small impedance of the scattering surface, the singularities describing the surface wave, which propagates from the edge (or from the vertex) along the impedance surface, may be located in a neighborhood of saddle points. The latter are responsible for a cylindrical wave from the edge of the wedge (or for a spherical wave from the vertex of the cone). As a result, the asymptotics of the Sommerfeld integral are uniformly represented by a Fresnel type integral for the wedge problem or by a parabolic cylinder type function for the cone problem.

Effects of impedance wedge diffraction on backscattering from breaking waves

Electromagnetic scattering characteristics change significantly from breaking waves, which is considered to be one reason for sea spike phenomenon（HH polarization scattering intensity close to or even greater than VV polarization scattering intensity). Spiky sea clutter is often treated falsely as targets, which affects radar performance in target detection in the sea surface background. Thus the investigation on the physical mechanism of the sea spike phenomenon can help mitigate false alarms. In this paper, the authors investigate the microwave backscattering from the wedge-shaped breaking waves, which is simulated with the dihedral impedance wedge of finite length. The physical optical field of the breaking waves is calculated with the Kirchhoff approximation. Based on the Maliuzhinets method with using the precise impedance boundary condition, the impedance wedge scattering solution in spectral integral representation is presented. The spectral function is derived by the perturbation method with respect to the oblique incident angle based on the incidence normal to or grazing to the edge. After obtaining the spectral function, the asymptotic theory is used to determine the diffraction field of impedance wedge at an arbitrary skew incidence. The equivalent edge currents are derived from the uniform diffraction of impedance wedge by combining the physical optical coefficients and diffracted coefficients. Backscattering radar cross-sections（RCSs) of the diffracted field from 120 impedance wedge are calculated in both HH and VV polarizations, and the effects of frequency and permittivity on the wedge diffraction are discussed as well. The physical optical field backscattering from 135 impedance wedge is compared with the total field with considering the diffraction effects. Further calculations and analyses for backscattering from the three-dimensional extension breaking waves are presented by using the contribution of edge diffraction field to correct the physical optics field. Numerical results show that the backscattering RCS of impedance diffracted field in HH polarization is greater than that in VV polarization in the Keller cone. Therefore, the diffraction effects will make the backscattering RCS of the total field in HH polarization greater than that in VV polarization when the breaking wave grows to near-collapse stage at a small grazing angle with upwind observation. This indicates that the wedge diffraction is one of the causes of sea spike phenomenon.

Calculation of the backscattered field by the method of the physical diffraction theory in the problem of diffraction from impedance objects

A solution to the problem of diffraction by arbitrary impedance objects with edges is obtained on the basis of the physical diffraction theory (PDT). Analytical relationships necessary for calculating the diffraction field in the case of backscattering an impedance wedge are given. The diagrams of the angular field distribution provided by the irregular part of the current are presented for various values of the relative permittivity and specific conductivity of the wedge for the E and H polarizations of the incident field. The diagrams of the radar cross section (RCS) of the perfectly conducting and impedance cylinders are comparatively analyzed in the cases when they are obtained by the methods of physical optics, PDT, and by the rigorous solution based on the method of integral equations.

Solution of the diffraction problem of a plane wave by an impedance wedge (Non-stationary case. Smirnov-Sobolev method)

Using the Smirnov-Sobolev approach, we reduce the nonstationary problem of diffraction of a plane wave by an impedance wedge to the Hilbert problem on a half-plane. The index of the Hilbert problem is equal to one. The Hilbert problem is “solved in quadratures.” In another way and in another form, a similar diffraction problem was solved earlier by Popandopulos [J. Aust. Math. Soc. 1 (1), 97–106 (1961)].

Diffraction by a right-angled impedance wedge: an edge source formulation.

This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact Sommerfeld-Malyuzhinets contour integral solution for the diffracted field can be transformed to a line integral over a physical variable along the diffracting edge. This integral can be interpreted as a superposition of secondary point sources (with directivity) positioned along the edge, in the spirit of the edge source formulations for rigid (sound-hard) wedges derived by Svensson et al. [Acta Acust. Acust. 95, 568-572 (2009)]. However, when surface waves are present the physical interpretation of the edge source integral must be altered: it no longer represents solely the diffracted field, but rather it includes surface wave contributions.

Impact of Coated Ground-Plane Edge Diffractions on Amplitude Patterns of Circular Apertures

The impact of finite dielectric-covered ground-plane edge diffractions on the amplitude patterns of circular apertures is investigated. The model is based on the Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD) for an impedance wedge. The circular aperture antenna is mounted on square and circular finite ground planes that are coated with a thin lossy dielectric layer. The predictions based on the GO/UTD model are validated by comparisons to experimental results and simulated data.

Numerical Simulation of Scattering by a Wedge With Periodic Anisotropic Impedance Faces

Plane wave scattering by an infinite, three-dimensional wedge whose faces are characterized by periodic anisotropic impedances is investigated. An improved hybrid of the moment method (MM) and the physical optics (PO) is proposed to calculate the equivalent electric current on the wedge surface. As for the infinite periodic wedge surface, a periodic representation of the scattering surface is used to prevent nonphysical edge effects in the scattering evaluation. The surface of the wedge is split into an MM region and a PO region. In the implementation of MM, the evaluation of the interaction matrix elements in the MM region is simplified by deriving six universal series. Moreover, the PO-current is modified by a diffracted current to improve its accuracy. The accuracy and effectiveness of the proposed approach is validated and demonstrated by using series solution, the method in [T. B. A. Senior, “Solution of a class of impedance wedge problem for skew incident,” Radio Sci., vol. 21, no. 2, pp. 185-191, 1986], and the two-dimensional improved MM-PO approach under several canonical two-dimensional wedge cases. At last, the proposed approach is applied to analyze the scattering from the wedges with periodic anisotropic impedance faces, and the numerical results are presented.

High-frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder at grazing incidence

We shall derive new results for the electromagnetic scattered far wave field produced when a high frequency plane E-polarized wave is at grazing incident on an imperfectly conducting rectangular cylinder. The solution to the problem is obtained by using the geometrical theory of diffraction, multiple diffraction methods, the canonical solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with a novel analytic approach.

On the Accuracy of Asymptotic Solutions for TM Waves Diffracting on an Impedance Wedge

The contribution focuses on the accuracy of two asymptotic solutions aimed at representing the electromagnetic field scattered by penetrable wedges. One is a heuristic manipulation of the solution for the perfect electrical conductor, and the other one is a more rigorous coefficient based on approximate boundary conditions. The results presented here extend those proposed by other authors by illustrating the accuracy of such solutions at the edge of validity of the uniform theory of diffraction. In particular, they show that the heuristic formulation can be freely applied in similar conditions, while the other might not always lead to accurate predictions.

Diffraction by Canonical Metallic and Material-Coated Structures: A Review

Keller's landmark paper in 1962 formulated the Geometrical Theory of Diffraction (GTD). This was the beginning of a long process that brought the Geometrical Theory of Diffraction into practice, making it one of the most ubiquitous analysis methods in electromagnetics. This paper provides a personal historical trace of the Geometrical Theory of Diffraction: in particular, its further development in the 1970s and 1980s, and its realization into computer codes. The latter provided the first step for the analysis of complex realistic structures. The second half of the paper discusses the historical development of diffraction coefficients for impedance wedges using first- and higher-order generalized impedance boundary conditions.

Heuristic Physical Theory of Diffraction for Impedance Polygon

A heuristic physical theory of diffraction (PTD) for an acoustic impedance wedge is proposed. This method is based on Ufimtsev's three-dimensional PTD, which is derived for an acoustic soft or hard wedge. We modify the original PTD according to the process of physical optics (or the Kirchhoff approximation) to obtain a 3D heuristic diffraction model for an impedance wedge. In principle, our result is equivalent to Luebbers' model presented in electromagnetism. Moreover, our approach provides a useful insight into the theoretical basis of the existing heuristic diffraction methods. The derived heuristic PTD is applied to an arbitrary impedance polygon, and a simple PTD formula is derived as a supplement to the physical optics formula.