Conducting Half Plane Research Articles

Pulsed Electromagnetic Diffraction by a Semi-Infinite Sheet With Conductive and Dielectric Properties

The 2-D diffraction of a pulsed electromagnetic (EM) plane wave by a semi-infinite sheet with conductive and dielectric properties is analyzed analytically with the aid of the Wiener–Hopf technique and the Cagniard–DeHoop technique. Novel exact analytical expressions describing the time-domain (TD) EM field in the presence of the conductive half-plane are derived. Moreover, closed-form approximate TD expressions are arrived at via Koiter’s approximate method of factorization. Illustrative numerical examples are presented.

Modified Theory of Physical Optics Approach to Diffraction by an Interface between PEMC and Absorbing Half-Planes

The scattering of electromagnetic plane waves by an interface, located between perfect electromagnetic conductor and absorbing half-planes is investigated. The perfect electromagnetic conductor half-plane is divided into perfect electric conductor and perfect magnetic conductor half-screens. The same decomposition is done for the absorbing surface. Then four separate geometries are defined according to this approach. The scattered fields by the four sub-problems are obtained with the aid of the modified theory of physical optics. The resultant scattering integrals are combined in a single expression by using key formulas, defined for the perfect electromagnetic conductor and absorbing surfaces. The scattering integral is asymptotically evaluated for large values of the wave-number and the diffracted and geometric optics fields are obtained. The behaviors of the derived field expressions are analyzed numerically.

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Diffraction by an interface between perfect electromagnetic conductor and conductive surfaces

The interaction of electromagnetic plane waves by a planar interface between conductive and perfect electromagnetic conductor half-planes is investigated. The method of transition boundary is used for the solution of the problem. The geometry, under consideration, is divided into two parts by using a relation, obtained for a perfect electromagnetic conductor half-plane. After obtaining the diffracted fields for sub-problems, they are combined into a single field for the co- and cross-polarized waves. The behaviors of the total field and its components are analyzed numerically.

Physical optics approach to wave diffraction by a perfect electromagnetic conductor half-plane

The scattering of electromagnetic plane waves by a perfect electromagnetic conductor is investigated. The method of physical optics is used for the analysis of the problem. The reflected fields by a whole-plane are taken into account. The surface electric and magnetic current densities are constructed with the aid of the incident wave and the reflected field from the whole-surface. The scattering integrals are obtained for the electric and magnetic vector potentials. The scattered electric and magnetic fields are expressed in terms of the vector potentials. The scattering integrals are evaluated asymptotically for large values of the wave-number. Some numerical results are given.

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Diffraction by an anomalously perfect reflecting metasurface half-plane

The scattering process of plane waves by a half-plane, composed of anomalously perfect reflecting surfaces, is investigated. The solution of the problem is obtained in an original way. The boundary condition of the problem is also taken into account in the construction of the edge diffracted field. The limiting case of the problem is the diffraction of waves by a perfect electric conductor half-plane. The obtained field expression are analyzed numerically.

Wave diffraction by a perfect magnetic conductor half-plane between free space and anisotropic plasma

The diffraction of magnetic polarized electromagnetic plane waves by a perfect magnetic conductor half-screen, located between free space and anisotropic plasma, is studied. The method of transition boundary is used for the solution of the problem. The scattered GO wave is obtained. The diffracted fields are derived with the aid of the scattered GO wave. The uniform expressions of the edge diffracted waves are derived. The behaviors of the evaluated fields are investigated numerically.

Scattering of waves by a perfect electric conductor half-screen in an anisotropic medium

The scattering process of electromagnetic plane waves by a perfect electric conductor half-plane, in an anisotropic medium, is studied. The technique, used for the solution of the problem, is the method of transition boundary. The values of an unknown function, which constructs the diffracted wave, are found at the reflection and shadow boundaries. The function is determined by applying a factorization process with the reciprocity principle. A new diffraction field is derived by the mentioned method. Some numerical results are given.

Comparison of diffraction methods for lunar occultations

The only analytical method, which is used for the mathematical analysis of lunar occultations, is the Fresnel diffraction. The Fresnel integral is derived from the diffraction integral of Kirchhoff under some approximations. This paper aims to compare this method with the exact solution of Sommerfeld, which is obtained for a perfect electric conductor half-plane. The geometrical optics and diffracted fields are expressed separately. Numerical simulations are given for the comparison of two different total and diffracted waves.

Diffraction of waves by a perfect electromagnetic conductor half-plane between isorefractive media

In this study, diffraction of waves by a perfectly electromagnetic conductor half-plane which is lying at the boundary of isorefractive media is investigated. The diffracted field expressions are constructed by using the relation between scattered geometrical optics fields and the transition boundaries. The high frequency asymptotic expressions of diffracted fields reach infinite magnitude values at the transition boundaries. The uniform expressions of fields are obtained by using the uniform theory of diffraction method in order to obtain the finite magnitude values at the transition boundaries and the results are analyzed numerically for different set of parameters.

Wave interaction with a perfect electromagnetic conductor half-plane between two dissimilar media

The interaction of electromagnetic plane wave by a perfect electromagnetic conductor half-plane, located between two media with different electromagnetic properties, is investigated. The diffracted waves, related with the z components of the electric and magnetic fields are obtained by considering the structures of the geometric optics fields, which are expressed in terms of the waves excited by soft and hard surfaces. The diffraction fields are extended in order to satisfy the boundary conditions on the interface between two media. Some numerical results are also given.

Wave diffraction by a conductive half-plane between two different media

The scattering of waves by a conductive half-screen, which reflects some portion of the incident energy and transmits the remaining part, between two media with different electromagnetic properties is investigated. First of all the scattered geometric optics waves are obtained. Then the diffracted fields are determined by using a relation between the geometric optics and diffraction waves at the transition boundaries. The behaviors of the total field and its components are studied numerically.

Corrections to “Relativistic Aspects of Plane Wave Scattering by a Perfectly Conducting Half-Plane With Uniform Velocity Along an Arbitrary Direction” [Sep 17 4759-4767

In a recent paper [1] , there was a typo in (13), which should read as a scalar equation for the $ {z}$ -component of $\tilde {\mathbf {E}}\{\tilde {\mathbf {H}}\}$ in the form \begin{equation*} \tilde {E}_{ {z}} \{\tilde {H}_{ {z}}\} = F(\tilde {\xi }^{i}) \, \tilde {E}_{ {z}}^{i} \{\tilde {H}_{ {z}}^{i}\} + F(\tilde {\xi }^{r}) \tilde {E}_{ {z}}^{r} \{\tilde {H}_{ {z}}^{r}\} \end{equation*} from which the remaining field components may be obtained. The full vector equation for the electric field is then given by \begin{align*} \tilde {\mathbf {E}}=&F(\tilde {\xi }^{i}) \tilde {\mathbf {E}}^{i} + F(\tilde {\xi }^{r}) \tilde {\mathbf {E}}^{r} + \frac {e^{i \pi /4}}{\sqrt { 2 \pi \tilde {k} \tilde {\rho } \sin \tilde {\theta }_{0} }} e^{i \tilde {k} (\tilde {\rho } \sin \tilde {\theta }_{0} -\tilde { {z}} \cos \tilde {\theta }_{0})} \\[3pt]&\times \bigg \{ \cos \frac {\tilde {\phi }-\tilde {\phi }_{0}}{2} \left [{ \left ({ \tilde {\mathbf {E}}^{i}_{0} \cdot \hat {\tilde { {z}}} }\right) \hat {\tilde { {z}}} - \tilde {\mathbf {E}}^{i}_{0} }\right ] +\sin \frac {\tilde {\phi }-\tilde {\phi }_{0}}{2} \, \hat {\tilde { {z}}} \times \tilde {\mathbf {E}}^{i}_{0} \\[4pt]&+\,\cos \frac {\tilde {\phi }+\tilde {\phi }_{0}}{2} \left [{ \left ({ \tilde {\mathbf {E}}^{r}_{0} \cdot \hat {\tilde { {z}}} }\right) \hat {\tilde { {z}}} - \tilde {\mathbf {E}}^{r}_{0} }\right ] +\sin \frac {\tilde {\phi }+\tilde {\phi }_{0}}{2} \, \hat {\tilde { {z}}} \times \tilde {\mathbf {E}}^{r}_{0} \bigg \} \end{align*} where $\tilde {\mathbf {E}}^{i,r}_{0}$ denotes the incident (reflected) electric field amplitude at the edge of the half-plane in frame $\tilde {S}$ . In addition, $Z \tilde {B}_{h}$ in (24) should read as $\tilde {B}_{h}$ , yielding \begin{align*} \tilde {\bar {\bar {F}}}_{re}=&\dfrac {\tilde {Q}}{c} \\&\times \! \begin{bmatrix}\! 0 \!&\quad \! -\!\tilde {B}_{e} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! \tilde {B}_{e} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \tilde {B}_{e} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \!&\quad \! 0 \!&\quad \! -\tilde {B}_{h} \sin \dfrac {\tilde {\phi }}{2} -\tilde {B}_{e} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \!&\quad \! 0 \!&\quad \! \tilde {B}_{h} \cos \dfrac {\tilde {\phi }}{2} 0 \!&\quad \! \tilde {B}_{h} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! -\tilde {B}_{h} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \end{bmatrix}\!. \end{align*} None of the above-mentioned remarks affect the calculations and results presented in [1] .

Relativistic Aspects of Plane Wave Scattering by a Perfectly Conducting Half-Plane With Uniform Velocity Along an Arbitrary Direction

The scattering of time-harmonic plane waves by a perfectly electrically conducting (PEC) half-plane (H-P) in relativistic uniform motion is discussed. The problem is formulated using the special theory of relativity by means of the Lorentz transformation applied to the classic Sommerfeld solution. Exact fields are obtained for the 3-D vector problem of scattering of an obliquely incident and arbitrarily polarized plane wave by a PEC H-P in relativistic translational motion. The total fields are then presented as the relativistic analog of their motionless counterparts and an association with the uniform asymptotic theory of diffraction framework is inferred. In addition to recovering known features such as the relativistic Doppler effect and shadow boundary shifts, it is herein depicted a polarization coupling effect due to motion that can give rise to a 3-D scattered field with all components present even for a linearly polarized incident wave. Validating results and illustrative examples are also presented.

Diffraction of waves by a conductive half-plane

The scattering process of plane waves by a conductive half-plane is investigated. The scattered geometrical optics waves are obtained by subtracting the incident field from the total geometrical optics waves. The physical optics integral is constructed from the scattered geometrical optics fields. The diffracted waves are evaluated by the application of the edge point method to the physical optics integral. A correction field is added to the diffracted waves in order to satisfy the conductive boundary conditions on the surfaces of the half-plane. The uniform diffracted fields are evaluated and the resultant scattered waves are compared with the literature numerically.

Scattering by a conductive half-screen between isorefractive media.

The scattering process of electromagnetic waves by a conductive half-plane, located between isorefractive media, is investigated. First, the conductive sheet at the interface of isorefractive media is considered. The reflection and transmission coefficients of the plane are evaluated. The diffracted fields by the half-plane are obtained with the aid of a relation between the diffracted and scattered geometrical optics waves. The resultant field expressions are numerically examined.

Diffraction of waves on square lattice by semi-infinite rigid constraint

The problem of diffraction of a time harmonic lattice wave in a two-dimensional square lattice, by a semi-infinite rigid constraint, is investigated as a discrete analogue of diffraction by a Sommerfeld ‘soft’ half plane. The discrete Helmholtz equation, with input data prescribed on a semi-infinite row of lattice sites, is solved exactly using the discrete Wiener–Hopf method. The far-field asymptotic approximation of exact solution is provided. The scattered wave, in far field, is compared with a numerical solution of the problem for a set of frequencies in the pass band. The low frequency approximation of the exact solution is derived and it coincides with the Sommerfeld’s solution in its integral form. The results and discussion associated with the discrete Sommerfeld problem are relevant to numerical methods based on a 5-point discretization of the two-dimensional Helmholtz equation. In addition to the mechanics of waves in lattices, other physical applications of the latter concern the scattering of an E-polarized electromagnetic wave by a conducting half plane as well as its acoustic counterpart.

Exact solution of conducting half plane problems in terms of a rapidly convergent series and an application of the multiplicative calculus

The problem of cylindrical wave incidence on a conducting half plane has been considered. A modal solution for Green's function of the problem is transformed into contour integral representations in a complex plane. Some contour deformations and changes of variables are then made for the integrals. Finally, the resultant integrals are transformed back into a series, which converges rapidly to the exact solution when the observation angles are close to the reflection/shadow boundaries (RSBs) of the conducting half plane. The multiplicative calculus is employed in deriving an expression that can be used for obtaining approximate solutions when the observation angles are away from the RSBs of the conducting half plane. The derived expressions are seen to be very simple for implementing in any computational environment.

Quasi-static analysis of lightning-radiated electric field in the vicinity of sea-land structure

A quasi-static approach is presented to compute electric field radiated by a lightning return stroke above the sea-land structure modeled as a dielectric half space with a perfectly conducting half plane situated in its interface. It appears that the quasi-static approach provides a closed-form time-domain solution for the radiated electric field. The proposed approach is mainly based on the electrostatic solution of the structure. The governing Poisson's equation in the presence of the sea-land structure is solved in three dimensions, using the contributions of dielectric half space and perfectly conducting half plane. The solution, expressed in terms of image contributions, consists of two point images in physical space. The validity domain of the time-domain quasi-static approach is investigated by comparison of the obtained electric fields with full-wave results obtained using the finite-difference time-domain method. The proposed approach has a reasonable accuracy at near (200m) distance range from the lightning channel.