Unit Cell Design and Full-wave Simulations
Based on the above parametric study, it can be concluded that in order to obtain a greatly extended impedance bandwidth of the coated monopole, the coating requires a high ?rz with a value around 8 to 10, near-unity ?rx and ?ry, and a proper radius. However, no known natural materials have such high-contrast anisotropy with low loss at microwave frequencies. Hence, a custom-designed MM must be synthesized, which would respond to electromagnetic waves as if it were an effective homogeneous anisotropic material with the required properties. The unit cell of such an MM coating is illustrated in Fig. 1.2(a), which comprises two identical I-shaped copper patterns printed on both sides of a Rogers Ultralam 3850 substrate. The thicknesses of the substrate (ds) and the copper (dc) are 51 |im and 17 |im, respectively. Using this thin flexible substrate, the nominally planar MM structure can be easily rolled into a cylindrical configuration. In the simulation setup for the MM unit cell, periodic boundary conditions were assigned to the walls in the y- and z-directions. A TE/TM-polarized plane wave, with the E-field/H-field oriented along the z-direction, is assumed to be incident from the left half-space at an angle of ф (0° < ф < 90°) with respect to the x-axis. An anisotropic inversion technique presented in Ref.  was employed to extract the effective permittivity and permeability tensor quantities from the scattering parameters calculated at different angles of incidence using ANSYS HFSS (high frequency structure simulator).
Figure 1.2 (a) Geometry and dimensions of the unit cells of the anisotropic
MM coating. All dimensions are in millimeters: a = 2.5, ds = 0.051, dc = 0.017, w = 2, b = 10, c = 1.5, g = 0.8, and l = 8. (b) Real parts of the retrieved effective anisotropic permittivity tensor parameters (srx, ?ry, ?rz). The imaginary parts are extremely small and are thus not shown.
The retrieved real parts of the effective permittivity tensor parameters are shown in Fig. 1.2b. Their imaginary parts are near zero (not shown) over the entire band of interest. It can be seen that none of the parameters exhibit a resonant response below 5 GHz, resulting from the subwavelength size of the I-shaped elements, which corroborates previously reported results on I-shaped unit cells utilized for broadband microwave transformation optics devices . The retrieved effective ?rx and ?ry have values near unity throughout the band, whereas ?rz exhibits a large value, which is attributed to the inductance provided by the central bar in the I-shaped elements and the capacitance associated with the gaps between the stubs of adjacent unit cells in the z-direction. The three effective permeability tensor parameters (not shown here) have unity values with very low loss, indicating that the MM does not have any effect on the radiated magnetic field.
When the actual MM coating is integrated with the monopole, two concentric layers are employed, each having four unit cells in the z-direction, as shown in Fig. 1.3(a). The inner and outer layers contain eight and sixteen unit cells along their circumference, respectively, in order to approximate a circular outer periphery. The outer radius of the MM coating is only 5 mm, i.e., about A0/24 at 2.5 GHz, ensuring that the ultra-thin subwavelength coating is compact in the radial direction. The entire structure was simulated using HFSS. To examine the effect of the MM coating on the impedance bandwidth of the monopole and the efficacy of the anisotropic effective medium model, we compare the simulated for three cases: monopole alone, monopole with the actual MM coating, and monopole with the anisotropic effective medium coating (see Fig. 1.3b).
The monopole alone has an 511 < -10 dB bandwidth of 0.4 GHz, from 2.3~2.7 GHz, with a resonance at 2.5 GHz. In contrast, with the actual MM coating present, the 511 < -10 dB bandwidth is remarkably broadened to 2.3 GHz, spanning a range from 2.1 to 4.4 GHz. The fundamental resonance shifts down slightly to 2.35 GHz, while the second resonance is located at 3.85 GHz. The current distribution is the same as that of the fundamental mode at this second resonance, leading to a well-maintained radiation pattern . When a homogeneous anisotropic effective medium coating with the retrieved dispersive material parameters is employed, the 511 exhibits a similar behavior to that of the actual MM coating.
This indicates that the assumed homogeneous anisotropic effective medium model is a valid approximation for the actual curved MM, primarily due to the fact that a sufficient number of unit cells were used to form the cylindrical coating such that every MM unit cell still maintains local flatness.
Figure 1.3 (a) Configuration of the quarter-wave monopole antenna with
ultra-thin flexible anisotropic MM coating. Reprinted, with permission, from Ref. 44, Copyright 2011, IEEE. All dimensions are in millimeters: di = 5, do = 2d,, and h1 = 40. The dielectric is 51 mm thick Rogers Ultralam 3850 (er = 2.9, dtan = 0.0025). (b) Simulated 5n of the monopole alone, the monopole with the actual MM coating, and the monopole with the anisotropic effective medium coating.