The previous examples deal with trying to increase the level of isolation for a single direction, but sometimes isolation in all directions is required. A design that has a square unit cell will need to employ capacitive loading on all its sides, which consequently increases both the size and the complexity of the underlying structure. To reduce these effects, the underlying unit cell was chosen to have a hexagonal geometry. The underlying base structure design is depicted in Fig. 4.16. The hexagonal unit cells have a periodicity of 9 mm, a separation between patches of 1.5 mm, a length for each of the sides of the patches of 4.1858 mm, a via radius of 12 mil, and a 1.52 mm thick Rogers RO3203 substrate. To reduce the amount of capacitors being optimized, a configuration with eight distinct capacitor values was chosen, as represented by the color scheme present in Fig. 4.16. This arrangement of the capacitors was selected because the energy traveling across the surface (0°) and at 60° will detect the same set of capacitors values. To optimize for all directions, only two critical angles are needed for this setup. First is the 0° angle, representing the worst case scenario with propagation parallel to the capacitors, and the second is the 30° angle, representing the angle away from the parallel that encounters the first set of the capacitors. A comparison between the port reduction optimization design and a full-wave simulation for the unloaded and an arbitrary capacitively loaded metasurface is shown in Fig. 4.17. There are some minor discrepancies between the full-wave simulation results and the optimization methodology; however, these are not significant enough as to have an impact on the optimization process.

Figure 4.16 Omnidirectional base structure design. Each color represents a distinct capacitance value used in the optimization scheme.

Figure 4.17 Comparison between the port-substitution method and the full- wave simulation for the omnidirectional design.

Figure 4.18 Optimization results for the omnidirectional metasurface design to maximize the broadband response for both the 0° and 30° angle cases.

This underlying structure was used in the design of a broadband metasurface. For the optimization, the values of capacitance were continuously varied from 0.1 to 1 pF and the cost function used attempted to minimize isolation bandwidth for both the 0° and the 30° cases. Figure 4.18 shows the results of this optimization. The unloaded metasurface has less than -20 dB of transmission from 4.8 to 6.1 GHz (bandgap of 1.3 GHz), while the continuously capacitively loaded optimized metasurface has a stopband from 3.25 to 5.95 GHz (bandgap of 2.7 GHz).