Windowed Green Function method for layered-media scattering

This paper introduces a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which is based on use of smooth windowing functions and integral kernels that can be expressed directly in terms of the free-space Green function, does not require evaluation of expensive Sommerfeld integrals. The proposed approach is fast, accurate, flexible and easy to implement. In particular, straightforward modifications of existing (accelerated or unaccelerated) solvers suffice to incorporate the WGF capability. The mathematical basis of the method is simple: the method relies on a certain integral equation posed on the union of the boundary of the obstacle and a small flat section of the interface between the penetrable media. Numerical experiments demonstrate that both the near- and far-field errors resulting from the proposed approach decrease faster than any negative power of the window size. In the examples considered in this paper the proposed method is up to thousands of times faster, for a given accuracy, than a corresponding method based on the layer-Green-function.Comment: 17 page

Scattering of a plane wave from a perfectly conducting sphere buried in a lossy soil

İletken bir kürenin gömülü olduğu iletken topraktan, lineer-polarizasyonlu düzlemsel bir dalganın saçılması kesin bir metodla çözülmüştür. Alanlar düzlemsel dalgaların integralleriyle ifade edilmiştir. Alanlara ait bilinmeyen 2n saçılma katsayısının oluşturduğu sonsuz sayıda lineer denklem elde edilmiştir. Bu denklemler, ortam sabitlerini, frekansı, kürenin yarıçapını ve derinliğini içerir. Toprak yüzeyine paralel bir düzlemde, geri-saçılan alanın analizi yapılmıştır ve bu alanın gönderilen alana dik bir bileşeninin olduğu saptanmıştır. Düzlemsel ince anten dizileri ile bu bileşenin dedekte edilmesi sonucu, hedefin varlığı ve konumu tespit edilebilir. Sonsuz sayıdaki denklem sistemi istenen hassasiyeti sağlayacak belli bir sayıda kesilip ve toprağın iletkenliği, dielektrik sabiti, ve kürenin yarıçapı parametreleri ve üç frekans için, sonuçlar sunulmuştur.Anahtar Kelimeler: Saçılma, gömülü küre.A rigorous method has been developed to determine the scattering of a linearly polarised plane wave above a conducting ground, in which a perfectly conducting (PEC) sphere is buried. The method is simply based on expressing the fields as the integrals of plane waves. Using this method, an infinite linear system of equations is obtained for the unknown scattering coefficients of the field components. The result is two equations. Each of these equations includes a summation with 2n unknown coefficients bn, cn and .  appears in Bessel functions and Legendre polinomials of various orders. Therefore, for the solution of these equations orthogonality relations cannot be applied. The back scattered field is analysed at a plane which is parallel to the surface of the earth. It is found that this field includes a cross-polarised component. In a z=constant plane the magnitude of the cross-polarised component has one minimum at the center and four maxima around this minimum. By making a planar array of linear antennas, the cross-polarised field can be detected and thus the presence and the position of the target is revealed. A truncation of the set of equations is applied depending on the desired level of accuracy. Some numerical results are presented for various parameters such as conductivity and permittivity of the soil and radius of the sphere for three frequencies. Keywords: Scattering, buried sphere

Optical microscopy in the nano-world

Scanning near-field optical microscopy (SNOM) is an optical microscopy whose resolution is not bound to the diffraction limit. It provides chemical information based upon spectral, polarization and/or fluorescence contrast images. Details as small as 20 nm can be recognized. Photophysical and photochemical effects can be studied with SNOM on a similar scale. This article reviews a good deal of the experimental and theoretical work on SNOM in Switzerland

Windowed Green function method for the Helmholtz equation in the presence of multiply layered media

This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871–1898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals

Enhancements to and Characterization of the Very Early Time Electromagnetic (VETEM) Prototype Instrument and Applications to Shallow Subsurface Imaging at Sites in the DOE Complex - Final Report

Field tests and deployments of VETEM is a flexible and highly effective new system for electromagnetic imaging that offers significant new 3D electromagnetic imaging capabilities in the shallow subsurface. Important new numerical modeling techniques have been produced, which are applicable to electromagnetic subsurface imaging, and suggest further research and development. In addition, this research has also produced a flexible, fast, and fully functional prototype VETEM system that has produced some remarkable subsurface images, has bridged the gap between pure research and applications, and is now available for use at DOE sites that have shallow subsurface imaging needs

Arbitrarily Oriented Perfectly Conducting Wedge over a Dielectric Half-Space: Diffraction and Total Far Field

Complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field. In this paper, we describe a complete procedure to study this problem with possible developments in radar technologies (like GPR), antenna development, or electromagnetic compatibility (tips near substrates). The diffraction of an incident plane wave by a perfectly conducting (PEC) wedge over a dielectric half-space is studied using generalized Wiener-Hopf equations (GWHEs), and the solution is obtained using analytical and numerical-analytical approaches that reduce the Wiener-Hopf (WH) factorization to integral equations (IEs). The mathematical aspects are described in a unified and consistent theory for angular and layered region problems. The proposed procedure is valid for the general case and the paper focuses on E-polarization at normal incidence. The solutions are given in terms of geometrical/uniform theory of diffraction (GTD/UTD) diffraction coefficients and total far fields for engineering applications. This paper presents several numerical test cases that show the validity of the proposed method

Modelling of interconnects in 3DIC based on layered green functions

As traditional CMOS scaling pace gradually slows down, three-dimensional (3D) integration offers another dimension of in the ”More-than-Moore” era. In this dissertation, a number of investigations were conducted to better model interconnects in 3D integrated circuit (IC), to evaluate electrical behavior including delay, power consumption, signal integrity (SI), and power integrity (PI) for 3D ICs. Partial Element Equivalent Circuit (PEEC) method with layered Green’s function is studied here, since it consumes less computational resources and provides better physical insight to model the interconnects in 3DIC for high-speed digital circuits. The work is organized as a series of papers. The first paper reviewed the fundamental methods to derive layered Green’s function in spectral domain using discrete complex image method (DCIM) and analyzed the effects of each Green function terms to model silicon interconnects. The second paper proposed a unique method to extract poles near branch cut in complex kp plane, to accurately extract surface wave effects. The last paper proposed a new equivalent circuit model for coplanar waveguide (CPW) structure on 3DIC. The silicon effects on series inductance were also studied by employing the modified Green functions with semiconductor images at a complex distance from spectral-domain analysis. --Abstract, page iii