The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

This is a book review of 'The Micro-Doppler Effect in Radar' by V. C. Chen. Artech House, 16 Sussex Street, London, SW1V 4RW, UK. 2011. 290pp + diskette. Illustrated. £90. ISBN 978-1-60807-057-2.

'The Micro-Doppler Effect in Radar' by V.C. Chen

Hyperuniform states of matter

This paper explains the basic characteristics of dielectric resonator antennas (DRAs), with emphasis on the effect of the form factor on their resonance (operating) frequencies. It is followed by discussions on their recent developments in higher order mode, circularly polarized, dual function, and transparent designs over the last few years. The idea of using glass DRAs as decoration antennas is proposed and demonstrated for the first time.

Dielectric Resonator Antennas: From the Basic to the Aesthetic

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties.

Hyperuniform States of Matte

Using OpenMP to further accelerate the pure MPI parallel MLFMA, an efficient and flexible parallel multilevel fast multipole algorithm (MPI-OpenMP-MLFMA) is proposed. Compared with previous MPI parallel schemes, the MPI-OpenMP-MLFMA improves the load-balance and scalability greatly. The computational capability of the proposed MPI-OpenMP-MLFMA is demonstrated by computing scattering from two extremely large targets: a sphere with a diameter of 1200 wavelengths, modeled by 1,063,706,700 unknowns, and an airplane model with the largest dimension of 1600 wavelengths, involving 288,151,344 unknowns.

Solving Problems With Over One Billion Unknowns by the MLFMA

In this letter, a rectangular dielectric resonator antenna (DRA) structure fed by two vertical strips with quadrature in phase is studied. Both the fundamental TE111 and the higher order TE113 modes can be simultaneously excited to generate a wideband circular polarization. The measured 10-dB impedance bandwidth is 32.8% from 2.7 to 3.76 GHz, under which the axial ratio is less than 4 dB. The radiation pattern and antenna gain are also studied.

A Dual-Mode Quadrature-Fed Wideband Circularly Polarized Dielectric Resonator Antenna

A novel antenna design is proposed to enhance the gain and reduce the radar cross section (RCS) of a patch antenna by using metamaterial surface. A polarization-dependent metamaterial surface composed of blocks of slotted electromagnetic bandgap (EBG) structures are adopted in this letter. The layout pattern of the slotted EBG elements is designed to enhance the gain of the antenna. Chessboard configuration is further equipped for scattering cancellation. The induced currents on the EBG are studied, resulting in the mechanism of the gain enhancement by the EBGs clearly explained for the first time. This enables the strategy of designing a high-gain and low-RCS antenna by using EBGs. Full-wave simulations validate that high gain in the operating frequency band and low-RCS in a broad frequency band for normal incidence are achieved by the proposed antenna.

Gain Enhancement and RCS Reduction for Patch Antenna by using Polarization-Dependent EBG Surface

The hybrid method of the finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation/scattering problems. A domain decomposition algorithm (DDA) of FE-BI-MLFMA is presented in this paper by using the finite element tearing and interconnecting method (FETI). The formulation of DDA-FE-BI-MLFMA is presented and analyzed in detail. The numerical performance of DDA-FE-BI-MLFMA is investigated by numerical experiments from many aspects. It includes the convergence speed versus types of domain decomposition, number of subdomains, types and inhomogeneity of dielectrics involving in solved problems, and the scalability of DDA-FE-BI-MLFMA. The comparison of DDA and previous algorithms of FE-BI-MLMFMA is also carried out. Finally, the capability of DDA-FE-BI-MLFMA is shown for large inhomogeneous problems.

Parallel Domain-Decomposition-Based Algorithm of Hybrid FE-BI-MLFMA Method for 3-D Scattering by Large Inhomogeneous Objects

The asymptotic waveform evaluation (AWE) technique has been widely used in the method of moment (MoM), the finite element method (FEM), and the hybrid finite element–boundary integral method (FE-BI) for fast computation over a wide frequency band. However, how to apply AWE to the multilevel fast multipole algorithm (MLFMA) still remains challenge. This paper proposes an efficient and robust approach to apply AWE to the hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE-BI-MLFMA). The validity of the proposed approach is verified by numerical examples for scattering problems. Numerical experiments show that the application of AWE to FE-BI-MLFMA can greatly improve the efficiency of FE-BI-MLFMA for computation of scattering over a wide frequency band.

Xin-Qing Sheng

Papers

Solving Problems With Over One Billion Unknowns by the MLFMA

A Dual-Mode Quadrature-Fed Wideband Circularly Polarized Dielectric Resonator Antenna

Gain Enhancement and RCS Reduction for Patch Antenna by using Polarization-Dependent EBG Surface

Parallel Domain-Decomposition-Based Algorithm of Hybrid FE-BI-MLFMA Method for 3-D Scattering by Large Inhomogeneous Objects

Application of Asymptotic Waveform Evaluation to Hybrid FE-BI-MLFMA for Fast RCS Computation Over a Frequency Band