Krzysztof A. Michalski

Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces. >

Multilayered media Green's functions in integral equation formulations

A compact representation is given of the electric- and magnetic-type dyadic Greens functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.

Extrapolation methods for Sommerfeld integral tails

A review is presented of the extrapolation methods for accelerating the convergence of Sommerfeld-type integrals (i.e. semi-infinite range integrals with Bessel function kernels), which arise in problems involving antennas or scatterers embedded in planar multilayered media. Attention is limited to partition-extrapolation procedures in which the Sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real-axis tail segment (/spl alpha/,/spl infin/) of the integration path, where /spl alpha/>0 is selected to ensure that the integrand is well behaved. An analytical form of the asymptotic truncation error (or the remainder), which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods, is derived. Several extrapolation algorithms deemed to be the most suitable for the Sommerfeld integrals are described and their performance is compared. It is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points /spl rho/ and by the choice of the subinterval break points. Furthermore, it is found that some well-known extrapolation techniques may fail for a number of values of /spl rho/ and ways to remedy this are suggested. Finally, the most effective extrapolation methods for accelerating Sommerfeld integral tails are recommended.

Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. II. Implementation and results for contiguous half-spaces

For pt.I see ibid., vol.38, no.3, p.335-44 (1990). In pt.I, three mixed-potential electric field integral equations (MPIEs) for conducting surfaces of arbitrary shape residing in plane-stratified dielectric media with an arbitrary number of layers were formulated. One of the MPIEs (formulation C) was found to be particularly well suited for the application of the method of moments (MM). In pt.II, formulation C is specialized to the important case of a scatterer or antenna of arbitrary shape residing in contiguous half-spaces. This MPIE is solved by the MM employing a triangle-patch model of the surface of the object. Sample numerical results for several cases of interest are presented. >

Closed-Form Green's Functions in Planar Layered Media for All Ranges and Materials

An important extension of the two-level discrete complex image method is proposed to eliminate any concerns on and shortcomings of the approximations of the spatial-domain Greens functions in closed form in planar multilayered media. The proposed approach has been devised to account for the possible wave constituents of a dipole in layered media, such as spherical, cylindrical, and lateral waves, with the aim of obtaining accurate closed-form approximations of Greens functions over all distances from the source. This goal has been achieved by judiciously introducing an additional level into the two-level approach to pick up the contributions of lateral waves in the spatial domain. As a result, three different three-level algorithms have been proposed, investigated, and shown that they work properly over all ranges of distances from the source. In addition to the accuracy of the results at all distances, these approaches also proved to be robust and computationally efficient as compared to the previous algorithms, which can be attributed to the fact that the sampling of the spectral-domain Greens functions in the proposed approaches gives proper emphasis to the associated singularities of the wave types in the spectral domain. However, the judicious choices of the sampling paths may not be enough to get accurate results from the approximations unless the approximating functions in the spectral domain can provide similar wave natures in the spatial domain. To address this issue, the proposed algorithms employ two different approximations; the rational function fitting methods to capture the cylindrical waves (surface waves), and exponential fitting methods to capture both spherical and lateral waves. It is shown and numerically verified that a linear combination of exponential functions in the spectral domain represent the lateral waves at the interface of the involved layers.

Rigorous analysis of open microstrip lines, of arbitrary cross section in bound and leaky regimes

The problem of an open microstrip line of arbitrary cross section is solved by an integral equation technique in conjunction with the method of moments. The approach is general and can handle, as special cases, multiple strips and strips of finite or infinitesimal thickness. It applies to both the fundamental and higher order modes, whether in the bound or the leaky regime. Computed dispersion curves and modal current distributions are presented for several cases of interest and, where possible, are compared with published data. >

Analysis of microstrip resonators of arbitrary shape

A space-domain approach based on a mixed-potential integral equation formulation is developed for efficient computation of complex resonant frequencies of laterally open microstrip-pitch resonators of arbitrary shape. The effects of the substrate-which may consist of any number of planar, possibly uniaxially anisotropic, dielectric layers-are rigorously incorporated in the formulation by means of the vector and scalar potential Greens functions. The current distribution on the conducting patch is approximated in terms of vector basis functions defined over triangular elements. Computed resonant frequencies, quality factors, modal currents, and far-field radiation patterns are presented for several microstrip resonators. For patches of simple, regular shapes, the results are in agreement with published data obtained by specialized techniques, which, unlike the method presented here, are not easily extendible to arbitrary shapes. >

On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium

It is demonstrated that one can choose the form of the magnetic vector potential to render the scalar potential of a single point charge associated with a horizontal, time-harmonic dipole in a layered medium identical to that associated with a vertical dipole, provided that the source and observation points are within the same layer. This proves the existence of the so-called mixed-potential electric field integral equation for objects of arbitrary shape in layered media.

The Sommerfeld half-space problem revisited: from radio frequencies and Zenneck waves to visible light and Fano modes

The classical Sommerfeld half-space problem is revisited, with generalizations to multilayer and plasmonic media and focus on the surface field computation. A new ab initio solution is presented for an arbitrarily oriented Hertzian dipole radiating in the presence of a material half-space with arbitrary horizontal stratification. The solution method combines the vector potential approach and the spectral domain transmission line analog of the medium, which results in the most compact formulation and facilitates the inclusion of any number of layers in the analysis. Following Sommerfeld, the solution is first expressed in terms of the Fourier–Bessel transforms, also known as Sommerfeld integrals. Analytical properties of the integrands in the complex plane are then investigated, including the location of the Sommerfeld pole, which gives rise to the Zenneck wave (ZW) or surface plasmon polariton (SPP), and alternative field representations are developed by a deformation of the integration path and analytic continuation of the integrand functions, using hyperbolic and vertical branch cuts. Closed-form expressions for the asymptotic surface fields are also derived and the rôle of the ZW and SPP is elucidated. Numerical examples are included to illustrate the theory, from radio frequencies to visible light.

Rigorous analysis of open microstrip lines of arbitrary cross-section in bound and leaky regimes

The problem of a microstrip line of arbitrary cross-section is solved by an integral equation technique in conjunction with the method of moments. The approach is general and can handle as special cases multiple strips and strips of finite or infinitesimal thickness. It applies to both the fundamental and the higher-order modes, whether in the bound or leaky regime. Computed dispersion curves and modal current distributions are presented for several cases of interest and, where possible, are compared with published data.<<ETX>>