This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features. Expressions are presented for wire, surface, and volume elements but emphasis is given to the surface elements. In this case, the new hierarchical basis leads to a near-orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge. In addition, all higher order terms in the expansion have two vanishing moments. In contrast to existing formulations, these properties allow the use of very high-order basis functions without introducing ill-conditioning of the resulting MoM matrix. Numerical results confirm that the condition number of the MoM matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions. As a consequence of the excellent condition numbers, we demonstrate that even very high-order MoM systems, e.g., tenth order, can be solved efficiently with an iterative solver in relatively few iterations.

The scattering-parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is that related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function). It is shown that the method has no ambiguity for the sign of the wavenumber and intrinsic impedance. While the method indeed yields two signs for the intrinsic impedance and thus the wavenumber, the signs are dependent. Moreover, both sign combinations lead to the same permittivity and permeability, and are thus permissible. This observation is in distinct contrast to a number of statements in the literature where the correct sign of the intrinsic impedance and wavenumber resulting from the scattering-parameter method is chosen by imposing additional physical requirements, such as passivity. The scattering-parameter method is reviewed through an investigation of a uniform plane wave normally incident on a planar slab in free space. The severity of the branch ambiguity is illustrated through simulations of a known metamaterial realization. Several approaches for proper branch selection are reviewed, and the suitability to metamaterial samples is discussed.

A shared aperture antenna for simultaneous operation at L- (1525 to 1661 MHz) and Ka-band (19.7 to 20.2 GHz and 29.5 to 30.0 GHz) is demonstrated. This stacked antenna consists of a Ka-band reflectarray antenna with a frequency selective surface (FSS) ground-plane above an L-band patch array antenna. The reflectarray is based on the concentric dual split-loop element backed by a concentric dual-loop FSS element. The reflectarray comprises 80 × 80 elements and it is printed on a 40 ×40 cm² Rogers 5880 substrate, while the L-band antenna is a 2 × 2 patch array. The reflectarray antenna has been manufactured at the Technical University of Denmark (DTU) and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility. The reflectarray provides a maximum directivity of 36.4 and 38.5 dBi at 20.0 and 29.8 GHz, respectively, and an aperture illumination efficiency in the two frequency bands up to 57% and 48%, respectively. There is very little degradation in the L-band patch array performance due to the reflectarray, and it provides a minimum directivity of 11.8 dBi over the L-band.

This letter documents the design, manufacturing, and testing of a single-layer dual-band circularly polarized reflectarray antenna for 19.7-20.2 and 29.5-30.0 GHz. The reflectarray is designed using the concentric dual split-loop element and the variable rotation technique that enables full 360 ° phase adjustment simultaneously in two separate frequency bands. The elements have been optimized to suppress cross-polar reflection. Thereafter, the element data is included in a design tool that computes the reflectarray layout and the associated radiation patterns. The reflectarray is composed of 80 × 80 elements printed on a 40 × 40-cm² Rogers 5880 substrate. The antenna has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility. The peak gain is 35.8 and 40.0 dBi at 20.0 and 29.8 GHz, respectively, and the aperture illumination efficiency is in the range of 53%-63% over the two frequency bands.

A complete antenna pattern characterization procedure for spherical near-field antenna measurements employing a high-order probe and a full probe correction is described. The procedure allows an (almost) arbitrary antenna to be used as a probe. Different measurement steps of the procedure and the associated data processing are described in detail, and comparison to the existing procedure employing a first-order probe is made. The procedure is validated through measurements.

An accurate and efficient direct optimization technique for the design of contoured beam reflectarrays is presented. It is based on the spectral domain method of moments assuming local periodicity and minimax optimization. Contrary to the conventional phase-only optimization techniques, the geometrical parameters of the array elements are directly optimized to fulfill the contoured beam requirements, thus maintaining a direct relation between optimization goals and optimization variables, and hence resulting in more optimal designs. Both co- and cross-polar radiation patterns of the reflectarray can be optimized for multiple frequencies, polarizations, and feed illuminations. Several contoured beam reflectarrays, that radiate a high-gain beam on a European coverage, have been designed and compared to similar designs obtained using the phase-only optimization technique. The comparisons show that the designs obtained using the proposed direct optimization technique are superior in performance, both for multi-frequency and dual-polarization designs. A reflectarray breadboard has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility to validate the proposed technique. An excellent agreement of the simulated and measured patterns is obtained.