Sergio A. Matos

Anisotropy without tensors: a novel approach using geometric algebra

The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.

Circular Polarization Wide-Angle Beam Steering at Ka-Band by In-Plane Translation of a Plate Lens Antenna

A simple mechanical beam steering antenna concept is proposed for ground mobile terminals of Ka-band satellite and high altitude platform (HAP) providing broadband access services. The wide-angle elevation beam steering is achieved by in-plane translation of a thin offset flat lens in front of a stationary primary feed while full azimuth coverage is obtained by simple 360° rotation of the lens. A new strategy is also proposed to reduce the effective F/D of the focusing system and consequently the total antenna height without increasing beam distortion: a second small flat lens is added on top of the primary feed to create a virtual focus located well below the feed phase center. The challenge is to conciliate high gain both with wide beam scanning and reduced antenna height. Design rules are presented for this antenna concept along with a 27.3-dBi gain fabricated example for the up-link Ka-band (29.5-30 GHz), with circular polarization, 0° to 50° elevation scan, better than 2.8-dB scan loss and an effective F/D of only 0.55. Both lenses are 3.35-mm thick, formed by a suitable assembly of phase shifting unit cells with less than 0.4 dB of transmission loss in simulation. The main lens dimensions are 195 mm × 145 mm and its weight is 215 g. Total antenna height, including the feed is 84 mm.

Minkowskian Isotropic Media and the Perfect Electromagnetic Conductor

The perfect electromagnetic conductor (PEMC) was introduced as an observer-independent “axion medium” that generalizes the concepts of perfect electric conductor (PEC) and perfect magnetic conductor (PMC). Following the original boundary definition, its 3-D medium definition corresponds to a 4-D representation that is, actually, observer-dependent (i.e., it is not isotropic for the whole class of inertial observers), leading to a nonunique characterization of the electromagnetic field inside. This characterization of the PEMC, then, violates the boundary conditions-unless some extraneous waves, called “metafields,” are surgically extracted from the final solution. In this paper, using spacetime algebra, we define the PEMC as the unique limit of the most general class of isotropic media in Minkowskian spacetime, which we call Minkowskian isotropic media (MIM). An MIM is actually a “dilaton-axion medium.” Its isotropy is a Lorentz invariant characterization: It is an observer-independent property, contrary to isotropy in 3-D Gibbsian characterization. Hence, a more natural definition of a PEMC is herein presented: It leads to a unique electromagnetic field in its interior; it corresponds, though, to the same original boundary definition. This new approach is applied to the analysis of an air-MIM interface that, as a particular case, reduces to an air-PEMC interface.

A Geometrical Approach to Duality Transformations for Tellegen Media

Duality transformations are of key importance in the study of Tellegen (i.e., achiral and nonreciprocal biisotropic) media: they often can reduce electromagnetic problems with both Tellegen media and simple isotropic media (SIMs), to simpler problems just with SIMs. Here, we generalize known results and derive the most general classes of Tellegen media that can be reduced, under the same duality transformation, to SIMs. Furthermore, it is shown that a family of isorefractive Tellegen media can be completely mapped onto the Riemann sphere where duality transformations are conformal mappings. Depending on their geometrical action in the Riemann sphere the duality transformations are then classified as: 1) generalized rotations; 2) Lorentz boosts; or 3) Galilean boosts. Applications include a wide range of structures containing Tellegen media: from (open and closed) waveguides to photonic crystals.

A spacetime algebra approach to moving bi-isotropic media

In summary, this communication has three main contributions: i) we have shown how spacetime algebra can be used to analyze moving bi-isotropic media; ii) we have also shown how vacuum form reduction can be applied to Tellegen media; iii) finally, with this analysis, a new perspective about the discussion concerning the existence of Tellegen media was brought up. In fact, by analyzing a moving Tellegen media, the nonreciprocal effect cannot be reduced to an equivalent moving reciprocal isotropic medium.

A new framework based on geometric algebra for the analysis of materials and metamaterials with electric and magnetic anisotropy

Few studies address media with both electric and magnetic anisotropy. However, the advent of metamaterials has prompted a fresh look into the old problem of anisotropic media in electromagnetics. In this communication we have presented a new general approach to solve this problem by using the grammar of geometric algebra. In fact, with this novel approach, we have shown how geometric algebra can provide a mathematical framework for general anisotropy that is far better than plain tensors and dyadics: through the direct manipulation of coordinate-free objects such as vectors, bivectors and trivectors, geometric algebra reveals itself as the most natural setting to study anisotropy by providing a deeper physical and geometrical insight while avoiding cumbersome calculations. We have shown that general anisotropy can be understood through a new function zeta that plays a central role: when zeta is uniaxial (biaxial) the medium is uniaxial (biaxial). Furthermore, a generalization of uniaxial and biaxial media has revealed new features when compared with media with only electric or magnetic anisotropy (but not with both). We have also defined a new state of anisotropy that we have called pseudo-isotropy. This state, although stemming from both electrical and magnetic anisotropy, corresponds to an isotropic zeta. In summary: we have shown that general anisotropy does not depend on the mathematical form that each constitutive function (either epsiv or mu) separately assumes but rather on a new single constitutive function: zeta = epsiv-1(mu).

Focal-Plane Multi-Beam Dual-Band Dielectric Lens for Ka-band

A shaped double-shell dielectric lens is evaluated as a primary feed for a multibeam single-reflector system operating in the satellite uplink and downlink Ka-bands, complying with gain and edge-of-coverage (EoC) directivity requirements. An assembly of dual-band printed feeds is integrated at the base of a single lens, each feed producing a virtual focus far behind the lens base and coincident with the reflector focal arch. The used double-shell lens approach, instead of a single-material lens, allows an extra degree of freedom to accommodate an aberration mitigation condition. This primary feed system is proposed as a low-complexity solution to enable fitting more beams per solid angle than conventional single-feed-per-beam systems based on a cluster of focal-plane horns. A proof-of-concept lens prototype with 87 mm diameter and 62 mm height, fed by a linear arrangement of five dual-band printed feeds, was fabricated and tested at the Ka-band. The lens measured radiation patterns were post-processed to evaluate the combined performance of the lens with an offset

Prototype of a compact mechanically steered Ka-band antenna for satellite on-the-move

F/D

A geometric algebra approach to anisotropic media

≈ 1 reflector system designed for 45-dBi EoC directivity. It is shown that it duplicates the reflector aperture efficiency compared to horn-fed systems with same feed separation.

Phase-Delay Versus Phase-Rotation Cells for Circular Polarization Transmit Arrays—Application to Satellite Ka-Band Beam Steering

We present a functional prototype of a SOTM user terminal antenna based on a planar offset Fresnel lens that implements a new mechanical steering concept previously proposed by the authors. The beam scanning is achieved by inplane translation of the feed (for zenith scanning) and axial rotation of the antenna (for azimuth scanning). The feed is as assembly of a circular polarization patch and a small planar lens. The goal of the small lens is two-fold : to adjust the primary feed directivity for a proper illumination of the main lens and to shift backwards the phase center of the patch, allowing reducing the antenna height. In the developed prototype the measured gain is 27 dBi at 30 GHz with a scan loss of 3 dB for an elevation scanning range between 18° and 53° for full azimuth. The antenna provides good circular polarization, with a cross polarization level below -14 dB. The side lobe level is below -10 dB for all beams positions. The antenna weight is less than 500 grams.