Printed-Patch Balanced Hybrid Metasurface
Many horn antennas operate in the ^,-band, where wavelengths range from 1.7 to 2.5 cm. Metamaterial surfaces thus require features on the scale of 0.1 mm, which can easily and inexpensively be achieved using standard printed circuit board (PCB) technology. Moreover, the required substrate thicknesses also fall within typical PCB ranges. These properties make the ^,-band an ideal candidate for testing metasurfaces and metahorns.
The soft- and hard-surface examples in the previous section satisfy the balanced hybrid condition only over a narrow bandwidth. This means that, although they can be useful over a broadband when lining a single-polarization horn, they would only allow low cross-polarization over a narrow band when lining a dual-polarized horn. In order to achieve broadband operation in a dual-polarized communication system, a metasurface was optimized using the combination of Eqs. (2.15) and (2.17), resulting in an approximately soft metasurface that also met the balanced hybrid condition. The optimization incorporated a single conducting via in each unit cell, as well as several constraints, including symmetry across the x-z plane to reduce cross-polarized reflections from the metasurface and restrictions on diagonally connected pixels for reasonable fabrication. The substrate material was chosen to be Rogers 5880LZ, which has a low dielectric constant of 1.96 and a loss tangent of 0.002. A lower substrate dielectric constant leads to larger operating bandwidths. Removing some unnecessary pixels from the optimized structure to simplify manufacturing yielded the geometry shown in Fig. 2.4, which also shows its simulated properties for a unit cell periodicity p = 0.134A, thickness t = 0.134A, w1 = 0.074A, w2 = 0.045A, s1 = 0.060A, and s2 = 0.060A, where l is the wavelength at 12 GHz.
Figure 2.4 Printed-patch metasurface geometry (a), surface reactances (b), effective index of refraction (c). Although it is not shown, the unit cell geometry includes a substrate material between the top patch and the ground plane beneath. Note that XTM is significantly less than zero across the band, and that the hybrid-mode condition is approximately satisfied across the band. Also note that the imaginary component of the effective index is essentially zero, indicating minimal intrinsic loss in the metasurface.
The simulated properties in Fig. 2.4 correspond to an obliquely incident plane wave at an angle approaching 90°. TM-polarized waves at these oblique angles interact with the conducting via, leading to an effective surface reactance appropriate for soft operation. Although both the TE and TM surface reactances are dispersive across the band, their product remains in the vicinity of one, approximately satisfying the balanced hybrid condition across the ^,-band. The remaining plot in Fig. 2.4 shows the effective refractive index achieved by the metasurface. Note that across the band of interest, the refractive index is below unity; i.e., the metasurface acts as a low-index metamaterial. Moreover, the imaginary component of the refractive index remains on the order of 0.001, indicating minimal intrinsic loss across the ^„-band.