John L. Tsalamengas

Radiation from a dipole in the proximity of a general anisotropic grounded layer

The radiation from a dipole in the presence of a grounded general gyromagnetic-electric (gyrotropic) layer is investigated. The use of matrix methods in conjunction with Fourier transformation techniques greatly facilitates the formulation of the boundary-value problem, reducing the algebraic complexity to a minimum, and provides a closed-form representation of the electromagnetic field over the anisotropic region. Numerical results in plots, related to the radiation pattern of the structure, are also included for various cases.

Exponentially Converging Nystrom Methods in Scattering From Infinite Curved Smooth Strips— Part 1: TM-Case

Low-order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required. High order modeling, on the other hand, can fill the need for enhanced accuracy but at the expense of greater implementation cost. To supplement such methods, this paper presents Nyström techniques, both easily implemented and highly accurate, relevant to TM scattering by arbitrarily shaped smooth infinite curved strips. The analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges; as a result, the proposed solutions are exponentially converging. In addition, by eliminating inner product integrals, closed form analytical expressions are obtained for all matrix elements; thus our algorithms have very low implementation and computational cost. Detailed numerical examples and case studies amply demonstrate the efficiency, stability, and extremely high accuracy of the algorithms. These algorithms apply uniformly from electrically small to electrically large conducting screens. With only slight modifications the present analysis can be also used to obtain exponentially converging Galerkin solutions.

Plane wave scattering by an array of bianisotropic cylinders enclosed by another one in an unbounded bianisotropic space : Oblique incidence

We consider the following scattering problem: An arbitrarily polarized plane wave, propagating in an unbounded bianisotropic space, is obliquely incident on an array of parallel bianisotropic cylinders which are enclosed by another bianisotropic cylinder. The boundary value problem is formulated in terms of a set of two coupled second order differential equations. The solution technique combines the method of separation of variables with the translational addition theorem. The matrix elements of the resulting linear algebraic system are given by single-term analytical expressions. Numerical examples are presented for several cases along with comparisons with previously published results.

Radiation from a dipole in the presence of a grounded gyromagnetic slab

Radiation from dipoles in the presence of a grounded gyromagnetic slab is considered. The Green’s function for an arbitrarily oriented elementary dipole source is derived first, assuming that the static magnetic field applied to the gyromagnetic slab is either vertical or parallel to the slab surface. A plane‐wave Fourier representation is employed to expand the field in and out of the slab. Several symmetry relations are exploited to reduce the complexity of the solution. Radiation properties of the grounded slab, such as the surface wave launching and the far‐field behavior, are then investigated. It is shown that the far‐field amplitude and phase can be controlled by varying the external static magnetic field. Numerical results are presented for several cases.

Direct singular integral equation methods in scattering from strip-loaded dielectric cylinders

Two powerful direct singular integral equation techniques (DSIET) are applied to the analytical solution of TM/TE scattering by dielectric cylinders loaded with flat or curved strips. In all cases characteristic-currents-theory is also applied as an alternative method of solution. The emphasis here is on demonstrating the high accuracy and efficiency of the proposed algorithms by detailed numerical examples and by comparisons with available results.

Direct and efficient solutions of integral equations for scattering from strips and slots

Singular integral or integro‐differential equations (SIE or SIDE) are often used for the analytical formulation of two‐dimensional boundary‐value problems. The methods for solving them depend primarily on the complexity of their kernel and on the kind (first or second) of the SIE itself. First‐kind SIEs with a Laplacian kernel are characteristic in electrostatics. A successful method for solving them is a regularization approach based on the transformation of the SIE to an equivalent Fredholm regular integral equation of the second kind. Well‐known inversion formulas are essential to this approach. In electromagnetics, a Hankel‐type kernel complicates matters considerably; inversion formulas and regularization techniques end up as cumbersome indirect procedures making necessary the recourse to a more direct method. Such a method is developed in this paper in combination with a very suitable expansion of the Bessel function, that multiplies the logarithmic singularity of the Hankel kernel, into a series of...

Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods

We present n-point Gauss-Gegenbauer quadrature rules for weakly singular, strongly singular, and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain. Each rule has two different expressions involving Legendre functions and hypergeometric functions, respectively. Numerical examples amply demonstrate the accuracy and stability of the proposed algorithms. Application to the solution of a singular integral equation is exemplified.

Plane wave scattering by slots on a ground plane loaded with semicircular dielectric cylinders in case of oblique incidence and arbitrary polarization

Plane wave scattering by single or double slots loaded with semicircular dielectric cylinders is investigated in the most general case of oblique incidence and arbitrary polarization. To this end, systems of singular integral-integrodifferential equations of the first kind are constructed and discretized on the basis of recently developed algorithms. Several internal tests and extensive comparisons with available results were made in order to validate the numerical codes. Plotted results both for the surface magnetic current densities and the radar cross sections reveal how the scattering properties may be controlled by changing several physical and geometrical parameters of the structure.

Exponentially Converging Nyström Methods in Oblique Diffraction of Arbitrarily Polarized Waves by Bianisotropic/Chiral Cylinders With Arbitrary Smooth Cross Section

We study oblique diffraction of arbitrarily polarized plane waves by a uniform homogeneous bianisotropic cylinder with arbitrarily shaped smooth boundary. Following a boundary integral equations formulation we develop a 4 × 4 system of combined field integral equations and another 4 × 4 system of Müller-type Fredholm integral equations. Both these systems, having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns, are of the second kind and uniquely solvable. Efficient discretization via simple and rapidly converging Nyström algorithms enables one to obtain highly accurate results even for electrically large objects. The proposed solution technique: a) fully accounts for the singular nature of the kernels; b) yields simple closed form expressions for all matrix elements; and c) appears to converge exponentially versus matrix size. The analogous diffraction problem for an arbitrarily shaped smooth chiral cylinder may be treated as a simple special case of the present analysis.

Radiation and Receiving Characteristics of Parallel Plate-Fed Slot Antennas Loaded By a Dielectric Cylinder: Te-Case

In this paper, we present an exact analysis of parallel plate-fed slot antennas loaded by a dielectric cylinder. The primary excitation is taken to be either a TE incident mode of the parallel-plate waveguide or an incident E-polarized plane wave. The followed formulation technique leads to singular integral or integrodifferential equations of the first kind which are discretized using quasi-analytical methods. The matrix elements of the resulting system of linear algebraic equations are given either in closed form or via rapidly converging single series. This, in conjunction with the small matrix size required, enables one to obtain very accurate results with low computational cost. Typical numerical results are presented to bring to light the effect of the cylindrical load on the characteristics of the antenna.