A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

Simple and efficient numerical methods are developed for treating electromagnetic problems of scattering and radiation from surfaces. Special consideration is given to the treatment of edges so that rather arbitrary geometrical configurations may be handled. For the conducting body problems considered, an electric field integral formulation is used, and the method of moments is applied using pulse expansions to represent both the current and the charge. It is demonstrated that proper placement of the current and charge subdomains relative to edges not only is important in treating edges but also yields a convenient numerical procedure. A simple testing scheme is used which is almost as efficient as point-matching. Numerical results indicate that the approach is free of anomalies in the behavior of current near edges and of other previously observed numerical instabilities. Problems considered include conducting strips (both TM and TE), a bent rectangular plate, and both material and conducting bodies of revolution.

Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces

Starting from the equivalence theorem any composite metallic and dielectric structure can be analyzed by using SIE (surface integral equations). Such integral equations are usually solved by MoM (method of moments). Most of the existing MoM methods for solving SIE are developed for BORs (bodies of revolution). There are only few such methods that can handle structures of arbitrary shape. These methods use sub-domain basis functions defined over triangles, requiring a very large number of unknowns even for the simplest problems. This paper presents a new MoM method for electromagnetic modeling of composite metallic and dielectric structures. The method uses entire-domain basis functions defined over bilinear surfaces, resulting in a remarkably small number of unknowns.

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Electromagnetic Modeling of Composite Metallic and Dielectric Structures

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies

Among the most popular approaches used for simulating plasmonic systems, the discrete dipole approximation suffers from poorly scaling volume discretization and limited near-field accuracy. We demonstrate that transformation to a surface integral formulation improves scalability and convergence and provides a flexible geometric approximation allowing, e.g., to investigate the influence of fabrication accuracy. The occurring integrals can be solved quasi-analytically, permitting even rapidly changing fields to be determined arbitrarily close to a scatterer. This insight into the extreme near-field behavior is useful for modeling closely packed particle ensembles and to study "hot spots" in plasmonic nanostructures used for plasmon-enhanced Raman scattering.

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Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures

A surface integral equation (SIE) technique is developed to analyze the scattering properties of arbitrarily-shaped lossy dielectric bodies of revolution. Two coupled vector integral equations formulated via Maxwell's equations, Green's theorem, and the boundary conditions are used. The unknown surface currents (both electric and magnetic) are calculated by, first, Fourier decomposition, and then, the moment method, Galerkin's procedure. The far scattered field and radar cross section (RCS) are then readily determined from the reciprocity theorem and the measurement matrix concept. For a dielectric sphere good agreement is obtained between the SIE and exact solutions. Solutions of a thick dielectric cylinder are next used to demonstrate the arbitrary geometry capability of the SIE method. This method is suitable for homogeneous dielectric bodies and only the axially incident plane wave is considered here. The method also applies for a wide range of dielectric parameters (with ∈r from 1.44 to 80 and conductivity σ from 0 to 103 mho/m).

Scattering from arbitrarily-shaped lossy dielectric bodies of revolution

The shielding properties of a thick cylindrical shell of finite conductivity is presented. The analysis uses straightforward separation of variables methods via cylindrical harmonic functions. The results show that significant attenuation of the incident fields are achieved for thick cylindrical shields thus demonstrating that the resonances noted in earlier work using thin shell models can be alleviated.

Shielding Properties of Thick Conducting Cylindrical Shells

Transient shielding properties of a conducting cylindrical shell with; an EMP incident plane wave are obtained through numerical Fourier transforms of the frequeny domain solution. Anomilous resonances noted in the frequiency doman now convert to-time domain oscillations which may have significace for vulnerability studies.

Time Domain Shielding Properties of Conducting Cylindrical Shells

The shielding properties of general, two dimensional, finitely conducting shells with vanishingly thin walls are analyzed by the integral-equation method. For the circular cylinder case, a field plot throughout the shield interior reveals that, at the 'no shielding' frequencies found by Schieber, fields are attenuated greatly, except near the center. The influence of slots in the shell walls is also assessed for both circular and rectangular cylinders. Due to focusing effects, the field at the shield center is even stronger than the incident field at certain resonant frequencies for the slotted cylindrical shells.

Low-Frequency Shielding Properties of Conducting Cylindrical Shells of Arbitrary Cross Section

The shielding properties of a thick circular cylindril shell of finite conductivity is analyzed for the case of an obliquely incident plane wave. The results show that the apparent radius of the cylinder is contracted as compared to the normal incidence case.

Te-Kao Wu

Papers

Scattering from arbitrarily-shaped lossy dielectric bodies of revolution

Shielding Properties of Thick Conducting Cylindrical Shells

Time Domain Shielding Properties of Conducting Cylindrical Shells

Low-Frequency Shielding Properties of Conducting Cylindrical Shells of Arbitrary Cross Section

Shielding Properties of Thick Conducting Cylindrical Shells with an Obliquely Incident Plane Wave