Conducting Half Plane Research Articles

Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium

The Sommerfeld’s problem of plane wave diffraction by a perfectly conducting half-plane is considered for the general case of an absorbing medium and an inhomogeneous incident wave, whose the constant phase planes are not parallel to the constant amplitude ones. The exact solution is represented in terms of parameters of incident wave propagation in the coordinate axes, but not in terms of angular variables, as usually. We adduce the original derivation of this solution, which use generalized functions and admits complex values for propagation parameters. Our approach is based on calculation of diffraction integrals by the method of transformations on the real axis without using a complex argument of integration. The results of diffraction field computation for the cases of an absorbing medium and of a decaying incident wave in a transparent medium are presented.

"Shadowing" of the electromagnetic field of relativistic charged particles

In radiation processes such as a transition radiation, diffraction radiation, etc. based on relativistic electrons passing through or near an opaque screen, the electron self-field is partly shadowed after the screen over a distance of the order of the formation length γ2λ. This effect has been investigated on coherent diffraction radiation (DR) by electron bunches. Absorbing and conductive half-plane screens were placed at various distances L before a standard DR source (inclined half-plane mirror). The radiation intensity was reduced when the screen was at small L and on the same side as the mirror. No reduction was observed when the screen was on the opposite side. It is worth noting that absorbing and conductive half-plane screens produce the same shadowing effect. The shadowing effect is responsible for a bound on the intensity of Smith-Purcell radiation.

Wiener-Hopf Analysis of Plane Wave Diffraction by an Impedance Strip Attached on a Perfectly Conducting Half-Plane

In this article, diffraction of a plane wave by an impedance strip on a perfectly conducting half-plane, which represents a metallic half-plane with a material coating near its edge, is investigated rigorously. In order to obtain an analytical solution to such a problem, where the lateral boundary conditions are different in the three-part mixed boundary-value problem, the Fourier transform and spectral iteration technique is applied. The diffracted field is analyzed numerically with respect to the surface impedance of the strip and the strip width. The results are illustrated graphically.

TM and TE Diffraction by a Perfectly Conducting Half-Plane in Presence of a Perfectly Conducting Strip: Solution by Exponentially Converging Nystrom and Galerkin Methods

We study TM and TE diffraction by a perfectly conducting half-plane in presence of a perfectly conducting flat strip of finite width and infinite length; the edges of the strip are parallel to the edge of the half-plane. The relevant integral equations with unknowns the induced current densities on the strip are solved by a Nystrom and a Galerkin method that fully account for the singular nature of the kernels and the singularities of the solution at the edges. The proposed algorithms are highly accurate, and appear to converge exponentially as shown by detailed numerical examples and case studies. The Nystrom method is the most efficient of the two methods because of its simple formulation, fast computer implementation, and much less effort in computing the matrix elements. When the strip is coplanar to the half-plane, an additional formulation method in terms of equivalent surface magnetic currents is possible in the framework of the field equivalence principles. This alternative method is applied in order to validate the algorithms and test their accuracy.

Diffraction by an imperfect half plane in a bianisotropic medium

A general theory to study the electromagnetic diffraction by imperfect half planes immersed in linear homogeneous bianisotropic media is presented. The problem is formulated in terms of Wiener‐Hopf equations by deriving explicit spectral domain expressions for the characteristic impedances of bianisotropic media, which allow one to exploit their analytical properties. In the simpler case of perfect electric conducting and perfect magnetic conducting half planes, the Wiener‐Hopf equations involve matrices of order 2, which can be factorized in closed form if the constitutive tensors of the bianisotropic material are of special form. Four of these special cases are discussed in detail. In order to deal with the more general problem, a technique to numerically factorize the Wiener‐Hopf matrix kernels is presented. Our numerical approach is discussed on one example, by considering the previously unsolved problem of a perfect electric conducting half plane in a gyrotropic medium. The reported numerical results show that the diffracted field contribution is obtained by use of the saddle point integration method.

Phase Space Gaussian Beam Summation Analysis of Half Plane Diffraction

The canonical problem of scattering of an ultrawideband (UWB) plan wave by a perfectly conducting half plane is analyzed via the UWB frame-based Gaussian beam summation (GBS) formulation of . The scattered field is described as a sum of isodiffracting-Gaussian beams (ID-GB) that emerge from the edge in a discrete frequency-independent lattice of directions, plus beams that describe the geometrical optics reflections. Asymptotic expressions for the diffracted beams excitation amplitudes are derived, interpreted, and validated via a comparison with an exact numerical calculations. The beams that are strongly excited are those associated with the geometrical optics and the edge diffracted rays. As discussed in the conclusions to this paper, the quality of the present GBS scheme deteriorates for grazing incidence and/or observations, hence we propose an alternative GBS scheme that is expected to be more useful for edge diffraction problems. This issue will be presented in a future publication.

Polarization effects caused by diffraction of the radiated of an arbitrarily oriented electric dipole at the edge of a perfectly conducting half plane

Diffraction of the field radiated by an electric dipole at the edge of a perfectly conducting half plane is considered. The uniform representation of the field in the far zone is applied to analyze the polarization of the field depending on the orientation and position of the dipole relative to the edge. The analysis is performed in the entire observation space. It is shown that the linearly polarized radiation of the dipole with the axis perpendicular to the edge of the half plane is transformed into the elliptically polarized radiation.

Alternative separation of Laplace's equation in toroidal coordinates and its application to electrostatics

The usual method of separation of variables to find a basis of solutions of Laplace's equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate θ (rather than the toroidal coordinate η or the azimuthal coordinate ψ ) . Applying these solutions to electrostatics leads to solutions, given as infinite sums over Legendre functions of the second kind, for (i) an arbitrary charge distribution on a circle, (ii) a point charge between two intersecting conducting planes, (iii) a point charge outside a conducting half plane. In the latter case, a closed expression is obtained for the potential. Also the potentials for some configurations involving charges inside a conducting torus are found in terms of Legendre functions. For each solution in the basis found by this separation, reconstructing the potential from the charge distribution (corresponding to singularities in the solutions) gives rise to integral relations involving Legendre functions.

Diffraction by a black half plane: Modified theory of physical optics approach

The scattered fields from a black half plane which absorbs all the incoming electromagnetic energy are evaluated by defining a new modified theory of physical optics surface current. This current eliminates the reflected fields, coming from the first stationary point of the reflection integral and only creates a reflected diffracted field. The incident scattered fields are found from the same integral, written for the perfectly conducting half plane. The scattered fields are evaluated by using the stationary phase method and edge point technique. The evaluated fields are plotted numerically.

Modified theory of physical optics

A new procedure for calculating the scattered fields from a perfectly conducting body is introduced. The method is defined by considering three assumptions. The reflection angle is taken as a function of integral variables, a new unit vector, dividing the angle between incident and reflected rays into two equal parts is evaluated and the perfectly conducting (PEC) surface is considered with the aperture part, together. This integral is named as Modified Theory of Physical Optics (MTPO) integral. The method is applied to the reflection and edge diffraction from a perfectly conducting half plane problem. The reflected, reflected diffracted, incident and incident diffracted fields are evaluated by stationary phase method and edge point technique, asymptotically. MTPO integral is compared with the exact solution and PO integral for the problem of scattering from a perfectly conducting half plane, numerically. It is observed that MTPO integral gives the total field that agrees with the exact solution and the result is more reliable than that of classical PO integral.

Diffraction radiation from ultrarelativistic particles passing through a slit. Determination of the electron beam divergence

In the present article the available formulas for diffraction radiation (DR) by an electron near a perfectly conducting half plane are generalized to any direction of the electron velocity, using Lorentz transformation. This allows to take into account electron beam divergence in an exact way. A new method for determining both horizontal and vertical beam divergence using one slit DR radiator, but two optical wavelengths, is proposed.

Diffraction of an obliquely incident plane wave by a two‐face impedance half plane: Wiener‐Hopf approach

The problem of diffraction of plane electromagnetic waves at an imperfectly conducting half plane with different impedances on upper and lower faces for oblique (skew) incidence either leads to a Wiener‐Hopf equation with a 4×4 Fourier symbol matrix for the tangential field components or to two formally decoupled Wiener‐Hopf equations with 2×2 symbol matrices of the Daniele‐Khrapkov form for the electric and magnetic field components perpendicular to the diffracting edge. The higher‐order edge singularity of the normal field components leads to undetermined constants in the classical Wiener‐Hopf solution that are used to eliminate “unphysical” leaky wave poles that appear in the final solution by the residue calculus technique. The interrelation between both formulations involves an analytic family of polynomial transformation matrices. Consideration of the range restriction of this mapping is shown to be equivalent to the pole elimination procedure.

Plane wave scattering by edges in unidirectionally conducting screens

According to its original definition a unidirectionally electrically conducting (UEC) screen is a penetrable anisotropic surface which is perfectly conducting in one direction and perfectly insulating in the orthogonal direction. The scattering of an arbitrarily polarized plane wave obliquely incident on the edge of either a UEC half plane or a planar junction between a UEC screen and a perfectly conducting half plane is analyzed in this paper. The direction of infinite conductivity of the UEC screen is arbitrarily oriented with respect to the edge. Exact closed form expressions for the scattered field are derived, which contain the standard transition function of the uniform geometrical theory of diffraction and simple ratios of trigonometric functions. Specific attention is devoted to the phenomenon of surface wave excitation at the diffracting edge of the structures under investigation. The features of this wave guided by the anisotropic screen are discussed.

A heuristic solution for the UTD diffraction coefficients of an anisotropically loaded half plane

Heuristic UTD diffraction coefficients for an anisotropically loaded half plane illuminated at oblique incidence are obtained by generalizing the standard UTD diffraction coefficients for a perfectly conducting half plane and by neglecting the presence of surface waves. The principal axes of anisotropy can be not coincident with the edge. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 143–146, 1999.

Diffraction of electromagnetic waves by a half-plane located in a moving cold plasma

Diffraction of plane electromagnetic waves by a conductive half-plane located in a parallel flow of cold plasma is studied. The velocity of the plasma motion and the propagation direction of the incident wave are normal to the half-plane edge. A general solution of the problem is obtained using the Wiener-Hopf-Fok method. The behavior of the field is analyzed far from the half-plane edge and in its vicinity.

Diffraction by a right‐angled resistive wedge

In this paper the electromagnetic diffraction by a right‐angled resistive wedge made up by a resistive sheet and a perfectly conducting half plane is presented. The resistive wedge is normally illuminated by an E‐plane wave. The Sommerfeld‐Maliuzhinets method is used to represent the fields in the interior and exterior regions of the resistive wedge by means of two spectral functions. Four coupled functional equations are obtained for the two unknown spectral functions which can be reduced to a fourth‐order difference equation with 2π‐periodic coefficients. The solution of this difference equation is constructed using the Fourier transform method. The high‐frequency approximation of the Sommerfeld integral is obtained with the corresponding uniform diffracted field. Representative curves of the uniform total field are presented.

Diffraction of a spherical electromagnetic wave by a perfectly conducting half plane in a homogeneous biisotropic medium

The diffraction of a spherical electromagnetic wave by a perfectly conducting half plane embedded in a homogeneous biisotropic medium is considered. This is important because the point sources are regarded as reasonable substitutes for real sources. The diffracted far field is calculated using integral transforms and the asymptotic methods.

Diffraction by a sinusoidal phase screen

In order to develop computer simulations of diffraction patterns produced by scintillations, it is important to verify the simulations with examples of diffraction patterns that may be calculated analytically. One such example is classical knife‐edge diffraction from a conducting half plane. Here we present another test case based on the one‐dimensional sinusoidal phase screen first considered by A. Hewish. Using Huygens‐Fresnel diffraction theory, we derive expressions, as a function of sinusoid scale size (Λ) and maximum phase deviation (ϕ0) for (1) the intensity, (2) the horizontal wave number spectrum of the intensity pattern, and (3) the modulation index, seen by an observer situated below a one‐dimensional phase screen with an incident plane wave. Then we compare the analytic results with a computer simulation. Provided that the frequency resolution of the simulation is adequate, the simulation agrees quite well with the analytic results. Additionally, diffraction from a sinusoidal phase screen provides a case in which the influence of increasing distance from the screen on the modulation index (deviation of intensity from its mean) may be explored analytically for both weak and strong scattering.

A hybrid method based on reciprocity for the computation of diffraction by trailing edges

A procedure is developed for combining analytic and numerical methods in the computation of scattering by large surfaces. It handles near-field effects numerically and far-field effects in a high-frequency approximation. This approach is applicable to a wide variety of problems involving trailing edges. It is applied to trailing edge scattering by a conducting half plane. This method removes a singularity encountered by other numerical and seminumerical methods at grazing angle. The error is controllable, both for monostatic and for bistatic scattering. The result can be forced to converge rapidly, making this approach suitable for calculations of arbitrarily high accuracy. A short description of this method was presented in Ingham (1990).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Image solution for Poisson's equation in wedge geometry

The Poisson's equation for a dielectric wedge is solved by deriving a static image that corresponds to the potential contribution of the wedge. The problem is studied mainly in three dimensions but the solution for the analog two-dimensional problem is also provided. It appears that the use of image sources provides numerically a simple and efficient method to compute the potential inside and outside the wedge. Image sources for the exterior and interior regions consist of a line charge that decays exponentially as a function of complex angle and a set of point charges that can be interpreted as reflection or transmission images of a dielectric plane. All known closed-form solutions in terms of elementary functions are derived for an electrically and magnetically conducting half plane. >