Homogeneous Dielectric Half-space Research Articles

Pulsed Electromagnetic Excitation of a Narrow Slot Between Two Dielectric Halfspaces

The transient electromagnetic (EM) excitation of a narrow slot in a perfectly electrically conducting (PEC) screen that separates two homogeneous dielectric halfspaces, a simplified model of a typical feeding structure of leaky lens antennas, is analyzed numerically in the time domain (TD). The problem is formulated using the TD reciprocity theorem of the time-convolution type and subsequently solved with the aid of the Cagniard-DeHoop method of moments (CdH-MoM). Numerical results are validated using a general-purpose EM-field solver.

Two Solution Techniques for the Problem of Diffraction of a Plane Wave by a Revolution Body Located in a Dielectric Half-Space

Two techniques for calculation of the problem of diffraction of a plane wave by a dielectric revolution body located in a homogeneous dielectric half-space are suggested. The case, in which the permittivity of the medium inside the body is the coordinate function independent of the angular coordinate in the cylindrical coordinate system, is considered. When the first technique is used (in the case of a homogeneous medium of the body), the discrepancy of the boundary condition on the contour of the axial section of the body is constructed. Two methods are compared using the example of the problem of the plane wave scattering by a homogeneous sphere and circular cylinder of finite dimensions that are located in a half-space. The results of calculation of the field scattering pattern are presented for the case of diffraction by a finite circular cylinder having variable material characteristics.

Electromagnetic Scattering From a Buried Cylinder Using a Multiple Reflection Approach: TM Case

A simple, fast, and accurate analytical method is introduced to obtain the EM scattered fields due to an infinite circular cylinder buried in a homogeneous dielectric half-space, illuminated by a normally incident transverse magnetic (TM) plane wave. The method is applied to perfect electric conducting (PEC) and dielectric cylinders of complex permittivity with the host dielectric medium being lossy or lossless. The accuracy of this method is verified using a finite-difference time-domain code (FDTD) on a wide frequency range and the results are presented discussing the range of validity of this approach.

Errata to "Improved Formulation for Investigation of Proximity-Coupled Microstrip Antenna in Homogeneous Dielectric Half Space" [Apr 08 927-932

In the above titled paper (ibid., vol. 56, no. 4, pp. 927-932, Apr. 08), two errors occurred in equation (30). The correct equation is presented here.

Improved Formulation for Investigation of Proximity-Coupled Microstrip Antenna in Homogeneous Dielectric Half Space

Analytical evaluation of asymptotic part of the Green's function, in product with piece-wise sinusoidal, entire domain, and travelling wave mode basis functions, is presented. The Sommerfeld type double integral in spectral domain is solved and reduced into a single integral in spatial domain with very short integration range. The derived results lead to develop a computational efficiency improved code, which has been found 27 times faster than the earlier validated common method of moments code.

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton–Chu method [2] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.

Moderately rough dielectric interface profile reconstruction via short-pulse quasi-ray gaussian beams

A new technique for estimating the coarse-scale profile of a moderately rough interface between air and a homogeneous dielectric halfspace is presented. The proposed approach is based on space-time sparsely sampled reflected field observations and uses a quasi-ray Gaussian beam fast-forward model, coupled with a compact parameterization of the surface profile in terms of B-splines, from which the profile estimation problem is posed as a nonlinear optimization problem. Numerical experiments are presented to assess accuracy, reliability, and computational efficiency. The proposed approach finds applications in adaptive schemes for rough surface underground imaging of shallowly buried targets via ultra wide-band ground penetrating radars.

Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms of B-splines. The profile estimation problem is posed as a parameter optimization problem, which is solved using a multiresolution continuation method via frequency hopping. Numerical experiments establish that the algorithm is efficient and yields accurate reconstructions throughout most of the illuminated region even in noisy environments, losing accuracy only in regions with very weak illumination.

Scattering of Electromagnetic Waves by Rough Interfaces and Inhomogeneous Layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Transient excitation of two coupled wires over an interface between two dielectric half spaces

The transient excitation of two identical, straight, thin wire antennas above a plane interface between two homogeneous dielectric half spaces is analyzed. The two wires are located parallel to each other and to the interface, and one of them is excited by a voltage source. By applying symmetry considerations, the problem is decomposed into two single‐wire problems, for which a method of solution is available from previous work by the authors [Rubio Bretones and Tijhuis, 1995]. The problem is solved in two steps. First, the configuration of two wires in a homogeneous medium is studied. The electric field integral equation for the total current on the wires is derived directly in the time domain and subsequently solved by using the continuous‐time discretized‐space approach. This results in a linear system of equations of a fixed dimension which is solved by marching on in frequency. Subsequently, we consider the complete configuration. As in our previous work, the field reflected by the interface is treated as a secondary incident field in the integral equation for the currents on the two wires. This leads to an integral equation of a form similar to the one describing the currents on the two wires in free space. In this equation the response of a pulsed dipole source in the two‐media configuration occurs as a Green's function. The spatial Fourier inversion involved is carried out with the aid of a fixed composite Gaussian quadature rule. This again leads to a system of equations of a fixed dimension, which can be solved by marching on in frequency. Finally, some representative numerical results are presented and discussed.

Transient excitation of a straight thin wire segment over an interface between two dielectric half spaces

The transient excitation of a straight thin wire segment parallel to a plane interface between two homogeneous dielectric half spaces is analyzed by the continuous‐time, discretized‐space approach. The analysis is carried out in three steps. First, the subproblem of a single wire embedded in a homogeneous dielectric medium, excited by a voltage source and an incident electric field, is studied with the aid of a time domain integral equation. This equation is discretized in space and transformed to the frequency domain. This procedure results in a system of linear equations of a fixed dimension which is solved by marching on in frequency. Second, the subproblem of a horizontal, pulsed dipole over the interface between two homogeneous dielectric half spaces is considered. The reflected field in the upper medium is computed by spectral techniques. With the aid of a time domain Weyl representation, a fixed, composite Gaussian quadrature rule is derived for the semi‐infinite integral involved. The angular integral is evaluated in closed form. Third, for the complete problem, the reflected field in the upper medium is expressed as a superposition of contributions from dipole sources on the wire axis, and subsequently treated as a secondary incident field in the integral equation for the current on the wire. This integral equation is then solved by combining the techniques developed for the two subproblems. Representative numerical results are presented and discussed.

The Born–Rytov controversy: I Comparing analytical and approximate expressions for the one-dimensional deterministic case

The applicability and domains of validity for the Born and the Rytov methods in scattering theory are established, with mathematical rigor, by comparing successive terms of the Born and the Rytov series calculated for wave propagation in a homogeneous dielectric half-space and a homogeneous dielectric slab for which the permittivities are assumed to have a low contrast over that of free space. While the (first-order) Rytov approximation is superior to the (first-order) Born approximation when it is applied to estimate the scattered field in the homogeneous dielectric half-space, both approximations are inapplicable to estimate the scattered fields when the dielectric slab is thick.

Representation of vector electromagnetic beams

The propagation of a vector electromagnetic beam in a linear homogeneous dielectric half-space is considered using the Whittaker potentials for the electromagnetic fields. A relation between the Whittaker potentials and the vector and scalar potentials of the electromagnetic theory is obtained. The polarization properties of the beam are discussed in the paraxial approximation and beyond.

Design of dielectric-covered resonant slots in a rectangular waveguide

A summary is given of the effects of a dielectric cover upon the resonant frequency, the resonant conductance of a longitudinal shunt slot, and the power coupled out of a waveguide by a pair of near circularly polarized crossed slots. Typical data curves are presented which illustrate these changes due to variations in the dielectric constant and thickness of the cover. A simple modification of Stevenson's free-space theory for resonant slots radiating into a homogeneous dielectric half-space is used in conjunction with the plane-wave reflection coefficient to predict bounds on the conductance and power variations for dielectric thicknesses greater than about one-quarter wavelength. The accuracy of this simple theory in predicting measurements on dielectric-covered slots is similar to the accuracy of Stevenson's free-space theory within about 9 percent for the shunt slots and about 15 percent for the cross slots.