Electric Field Dyadic Green Research Articles

Surface-Volume-Surface EFIE for Electromagnetic Analysis of 3-D Composite Dielectric Objects in Multilayered Media

The surface-volume-surface electric field integral equation (SVS-EFIE) is generalized for the case of scattering problems on the composite nonmagnetic dielectric objects situated in planar nonmagnetic layered medium. The piece-wise homogeneous regions of the scatterer can be arbitrarily positioned with respect to the layers of stratification. The SVS-EFIE being a class of single-source integral equations is formed by restricting the surface single-source electric field representation in each distinct region of the scatterer through the volume-EFIE (V-EFIE) enforced on the boundary of that region for only the tangential component of the total field. As a result, the SVS-EFIE utilizes only the electric field dyadic Green's functions. This allows for its cast into the mixed-potential form using classical Michalski-Zheng's formulation and method of moments (MoM) discretization featuring easily computable integrals with singularities no stronger than 1/R, R being the distance from the source to the observation point in such integrals. The matrices of MoM discretization are represented inhierarchical form (as H-matrices) enabling solution of the scattering problems in multilayered media with O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> log N) CPUtimeand memory complexities, where α is a geometry-dependent constant ranging from 1 to 1.5 depending on the shape of the scatterer. While the MoM surface and volume meshes discretizing the regions of the scatterer are constructed to ensure that no mesh element crosses interfaces between the layers, the clusters of both the surface and volume elements in their respective recursive partitionings in the process of H-matrix construction are allowed to span multiple layers of the medium. Upon computation of the layered medium Green's function kernels with the discrete complex image method allowing clusters of elements to cross dielectric interfaces between the layers is shown to preserve compressibility of the corresponding H-matrix blocks.

Efficient and Accurate Computation of Electric Field Dyadic Green’s Function in Layered Media

Concise and explicit formulas for dyadic Green's functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper. First, the electric and magnetic fields in the spectral domain for the half space are expressed using Fresnel reflection and transmission coefficients. Each component of electric field in the spectral domain constitutes the spectral Green's function in layered media. The Green's function in the spatial domain is then recovered involving Sommerfeld integrals for each component in the spectral domain. By using Bessel identities, the number of Sommerfeld integrals are reduced, resulting in much simpler and more efficient formulas for numerical implementation compared with previous results. This approach is extended to the three-layer Green's function. In addition, the singular part of the Green's function is naturally separated out so that integral equation methods developed for free space Green's functions can be used with minimal modification. Numerical results are included to show efficiency and accuracy of the derived formulas.

A generalized Debye source approach to electromagnetic scattering in layered media

The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency ω, evaluation of the electric field using this Green's function exhibits numerical instability. In this short note, we provide an alternative approach which is immune from this low-frequency breakdown as ω → 0. Our approach is based on the generalized Debye source representation of Maxwell fields. Using this formulation, the electric and magnetic fields gracefully decouple in the static limit, a behavior similar to that of the classical Lorenz-Debye-Mie representation of Maxwell fields in spherical geometries. We derive extensions of both the generalized Deybe source and Lorenz-Debye-Mie representations to planar geometries, as well as provide equations for the solution of scattering from a perfectly conducting half-space and in layered media using a Sommerfeld-like approach. These formulas are stable as ω tends to zero, and offer alternatives to the electric field dyadic Green's function.

Time-domain electromagnetic computations using a modified EFIE kernel and field-source equilibrium relations

A form for the electric-field dyadic Green's function for free space is derived that allows explicit time evolution of the modified electric-field integral equation (EFIE) applied to surface scattering. The modified EFIE kernel, here called a "source function," has an integrable singularity in the source region, and is shown to be equivalent, in the frequency domain, to the standard dyadic Green's function. With definitions of "local" and "non-local" fields at a conductor surface, both electric and magnetic versions of the relations between non-local fields and equilibrium surface sources (currents and charges) are derived. These field-source equilibrium (FSE) relations are exact if all the non-local fields are included: the interaction fields, as well as the usual incident fields from distant sources. When the interaction fields are neglected, the magnetic-field version of the FSE relations becomes the usual physical optics approximation. Source functions and the FSE relations were used in two three-dimensional, time-domain numerical simulations to compute radiation patterns from a conical helical antenna driven at a fixed frequency, and scattering of a CW plane wave by a perfectly conducting sphere. This surface-scattering simulation was explicit but remained stable. Excellent agreement between the computed and known results validated the approach.

Full-Wave Analysis of an Imperfectly-Conducting Stripline

In this paper, the discrete principal-mode propagation constant of an imperfectly-conducting stripline field applicator is investigated. Specifically, a complex correction to the ideal (i.e., perfectly-conducting) propagation constant is sought using a full-wave spectral-domain analysis. First, the electric-field dyadic Green's function for a general three-dimensional (3D) current source immersed within an imperfectly-conducting stripline background environment is determined with the aid of Hertzian-potential impedance boundary conditions. These boundary conditions, which are developed in the paper, follow from a Leontovich boundary condition and include important coupling terms that are absent in the perfectly-conducting case. Next, the stripline structure is realized by specializing the general 3D current to a 2D current flowing in an imperfectly-conducting center strip. Boundary conditions are subsequently enforced on the center strip, leading to an electric field integral equation (EFIE). The complex propagation constant for the imperfectly-conducting stripline is found through solution of the EFIE via formulation of a non-Galerkin's method-of-moments (MoM) technique. In particular, Chebyshev expansion and testing functions of the first and second kind are implemented to closely model the strip current, to accelerate convergence and to allow resulting spatial integrals to be performed in closed form. The advantage of this full-wave analysis over the standard perturbation method is discussed and various numerical results are given for the attenuation and phase constant of the principal-mode.

Analysis of finite grid structures with lenses in quasi-optical systems

A full-wave moment-method technique developed for the analysts of quasi-optical (QO) systems is used to model finite grid structures in a lens system. This technique incorporates an electric-field dyadic Green's function for a grid centered between two lenses. This is derived by separately considering paraxial and nonparaxial fields. Results for the driving point reflection coefficient of a 3/spl times/3 and 5/spl times/5 grid in the lens system are computed and compared with measurements.

Full-wave analysis of quasi-optical structures

A full-wave moment method implementation, using a combination of spatial and spectral domains, is developed for the analysis of quasi-optical systems. An electric field dyadic Green's function, including resonant and nonresonant terms corresponding to coupling from modal and nonmodal fields, is employed in a Galerkin routine. The dyadic Green's function is derived by separately considering paraxial and nonparaxial fields and is much easier to develop than a mixed, scalar and vector, potential Green's function. The driving point impedance of several antenna elements in a quasi-optical open cavity resonator and a 3/spl times/3 grid in free space are computed and compared with measurements.

The dyadic Green's function as an inverse operator

It is shown that the integral of the scalar product of the current density with the electric field dyadic Green's function can be carried out without difficulty by allowing the observation point to be an arbitrarily located point within a small spherical volume and using an appropriate representation for the Green's dyadic function obtained from the eigenfunction expansion. On the basis of this result it is established that the integral operator using the Green's dyadic function is the correct inverse operator for the vector wave equation provided the integration is taken over the whole volume (the support of the current density).

DYADIC GREEN'S FUNCTION EXPANSIONS IN SPHERICAL COORDINATES

ABSTRACT The complete eigenfunction expansion of the electric field dyadic Green's function in spherical coordinates is presented with particular attention given to the significance of the longitudinal eigenfunctions in this expansion. It is shown that the spectrum of the transverse eigenfunctions contribute zero frequency static like modes that cancel the longitudinal modes outside the source region. Inside the source region the cancellation is not complete but the non-cancelling part can be expressed as a delta function contribution in full agreement with the results obtained by Tai by a different method. Various representations for the dyadic Green's function in free space and in a spherical cavity are presented. The paper includes a brief historical survey of the development of the eigenfunction expansion method for the dyadic Green's function in order to highlight some of the early difficulties that were encountered.