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Anisotropic MM Lens for Crossed-Dipole Antenna

High-gain circularly polarized (CP) and dual-polarized (DP) antennas have widespread applications as feeds for reflector antennas. Such a feed has specific gain requirements to maintain complete coverage over the entire reflector and maximize aperture efficiency. A typical solution for a large reflector uses horn antennas whose aperture size and mode distribution is selected to produce the required reflector illumination. These waveguide-fed horns represent substantial mass and volume investments, especially for multi-feed reflectors. An AZIM lens with both electric and magnetic resonances can be used for aperture enhancement while reducing the form factor to achieve a compact feed for reflector antennas.

Configuration and unit cell design

The collimating properties of AZIM lenses, as previously described for the leaky-wave AZIM antenna with embedded slot feed, can also be used for cases where the feed is not embedded into the MM slab. The MM slab, for example, may be used as a focusing lens in concert with a radiating source. A near-zero-index uniaxial lens acts as an angular-selective spatial filter that passes only plane wave components that are propagating within a small angular tolerance of zero degrees while all other plane wave components are reflected [52]. This property allows an AZIM lens placed in front of a low-gain radiating element to demonstrate very high aperture efficiencies. A corollary of this property is that by placing an AZIM lens over a highly collimated source, little or no improvement in beam characteristics will be produced. When used in isolation, such a lens may show a very uniformly illuminated aperture, but much of the incident energy would be reflected from the back surface and result in very low realized forward gain due to high reflection losses. As a partially reflective surface, the AZIM lens and feed arrangement may be backed with a conductive ground plane to form a Fabry-Perot cavity antenna, which improves the realized gain and return loss of the system. An illustration of the MM slab placed over the feed antenna is shown in Fig. 1.13 a.

Using an AZIM slab as the partially reflective surface of a Fabry-Perot cavity produces improved behavior over either of the constituent cases of a lens illuminated by a feed-in free space, or a non-MM dielectric slab for the top surface of the cavity. Both the cavity and the AZIM MM act to distribute the energy from the subfeed more evenly throughout the aperture to improve gain, while the combination of both effects improves the response even more [52, 53].

Illustration of anisotropic ZIM lens placed over feed antenna and ground plane to form a Fabry-Perot-type cavity

Figure 1.13 Illustration of anisotropic ZIM lens placed over feed antenna and ground plane to form a Fabry-Perot-type cavity. The left side shows the lens constructed with a PEC ground plane, and the right shows the profile reduction possible when using an AMC ground plane. (b) Representative illustration of cubic AZIM unit cell. (c) Representative illustration of AMC unit cell. Reprinted, with permission, from Ref. 53, Copyright 2014, IEEE.

For a single-polarization configuration, either a near-zero- permittivity electric MM or a near-zero-permeability magnetic MM, oriented in the proper direction, can be sufficient to achieve substantial gain improvements. For a CP or DP antenna with requirements for a cylindrically symmetric radiation pattern, the MM requires both magnetic and electric properties. Although the behavior is identical at normal incidence for single-ZIM electric or magnetic lenses, off-normal responses and the resulting beam symmetry degrade if only one component is included. The AZIM lens for free-space beam collimation requires that the optical axis of the uniaxial material be parallel to the desired direction of propagation, which in turn requires, for the dual-polarization case, that the electric and magnetic properties be aligned on the same axis. For the following discussion, the optical axis is the z-axis, while the lens resides in the x-y plane.

A microwave-range MM implementation for the magnetodielectric AZIM described above requires a combination of appropriately oriented magnetic and electric resonators tuned to operate at the same frequency with approximately the same unit cell dimensions. Although SRRs are the easy choice for the magnetic MM, there is no single electric resonator that has the same beneficial properties of the SRR across a wide frequency range. In general, an SRR operating at a given frequency can be smaller than an equivalent electric resonator for the same frequency. The properties desired in an electric resonator include matched resonance frequency to an equivalent-sized magnetic resonator, a square unit cell boundary, strong coupling efficiency to the z-oriented electric field, low bianisotropy (magneto-electric coupling), and minimal, symmetric response in the x-y plane.

Selections for electric MM resonators generally focus on variations of dipole configurations. However, dipole resonators are electrically large (half-wavelength) at resonance; without additional miniaturization, dipole elements alone would be much larger in comparison to their SRR counterparts. Several variations, including the ELC resonator and the ELDR elements, allow the length of the dipole to be reduced while remaining resonant. Planar electric resonators, such as the complimentary SRR (CSRR), which operate according to the Babinet principle for symmetrical electrical operation with the SRR [54], have limited bandwidth and strong bianisotropic tendencies. All other options for planar electric resonators require orientation parallel to the z-axis. The ELC uses lumped or distributed inductance and capacitance to promote resonance for electrically compact unit cells, but has limited field coupling area, which reduces the bandwidth of the resonant response and thus the operational ZIM band. The ELDR has a lower resonant frequency compared to an ELC of the same physical size due to a larger coupling region for the electric field, which helps to generate a stronger, broader resonance. The ELDRs function much better for the creation of a broadband magneto-dielectric response than other elements. For either unit cell, the electric resonators must be oriented vertically, parallel to the x-z or y-z planes. A set of four vertically oriented resonators can be arranged in a square to form a unit cell that will have a symmetric electric response in the x-y plane.

While the electric ELD resonators were reduced in size as far as possible relative to their resonant wavelength, it is necessary to increase the size of the SRRs such that the electric and magnetic unit cells are the same size. Using symmetric, square resonators with two splits in each resonator increases the electrical size to A0/7.5 to match the minimum electric resonator dimensions. Two copies of the SRR and four of the ELDRs are arranged to fit on the six interior faces of a hollow dielectric cube, with the SRR elements on the top and bottom and the ELD on the sides. This resonator arrangement within the unit cell creates a vertically oriented magnetic resonance and a vertically oriented electric resonance, which can be aligned at the same frequency through appropriate tuning of the resonator dimensions. Figure 1.13b illustrates the structure of a representative AZIM unit cell.

The anisotropic effective MM parameters were extracted during the design process and after finalizing the design using the scattering-parameter inversion method [55]. After simulating the scattering response from a periodic tiling of the unit cells, the effective response can be computed. The z-components of the permittivity and permeability show strong resonant behavior that produces a simultaneous zero-index band at 7.5 GHz. Although there are antiresonance responses in the tangential permeability [56], the tangential permittivity and permeability are not significantly dispersive over the zero-index band.

 
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