Effects of Parameter Variations on Metasurface Characteristics
Figures 2.17b,c show how the anisotropic surface reactances change as the patch length and width change. In general, the frequency response of the surface reactances shifts to lower frequencies when either the patch width or length is increased, with length having a stronger effect. In all cases, XTE remains nearly zero, while X™ varies from a large negative value toward zero. These characteristic curves provide insight for the design of metasurfaces optimized for a specific frequency band.
Figure 2.17 Unit cell geometry (a) and surface reactances for varying patch length (b) and width (c). For (b), the width was fixed at 2.0 mm, and for (c), the length was fixed at 2.3 mm. In all cases, t = 5.2 mm, s = 0.4 mm, and p = 3.0 mm. Reprinted, with permission, from Ref. 16, Copyright 2013, IEEE.
Metasurfaces in Cylindrical Waveguides
Figure 2.18a shows a section of cylindrical waveguide lined with the metasurface under consideration. Importantly, the field distributions in a hybrid-mode cylindrical waveguide are determined by the anisotropic surface impedances on the waveguide walls . Of interest here is the fact that the aperture field magnitude becomes independent of azimuth angle and no cross-polarized field exists when the following relationship is satisfied:
where n0 is the wave impedance in a vacuum. This relationship can be satisfied either by XTE x XTM = -h0 , or with both terms on the left of Eq. (2.18) being zero. The former is the balanced hybrid condition presented earlier, which can be satisfied by dielectric-loaded horns [7, 8, 31]. The latter is the definition of a soft surface and can be realized by appropriately sized corrugations or by many of the metasurfaces presented in this chapter. The metasurface of Fig. 2.17 provides a soft surface with an easily designed operating frequency band, and proved an ideal candidate for creating hybrid modes in a metasurface-lined circular waveguide. The connecting strip of width s becomes a circular ring, while the vias connect from the patches radially outward to the waveguide wall. The eigenmode solver in HFSS was used to create the dispersion diagrams and mode patterns shown in Figs. 2.18b,c. These characteristics of the metasurface provide more insight into how the surface behaves in the context of a cylindrical waveguide or horn than is possible with plane wave models used for the previously presented horn designs. The calculated mode patterns verified the operation of the metasurface as a soft surface, exhibiting tapered field distributions and nearly perfect linearly polarized electric fields. Also of note is the fact that metasurfaces with smaller patches lead to a higher cutoff frequency and more confined mode patterns, while larger patches lower the cutoff frequency further.
Figure 2.18 (a) Schematic of a section of metasurface lining a cylindrical
waveguide. йг = 30.4 mm and D2 = 20.0 mm. (b) Dispersion diagram for metasurfaces with varying dimensions. The dispersion of a cylindrical waveguide with an inner diameter of 20.0 mm is shown for reference, and the plane wave behavior is indicated by the dash-dotted line. (c) Electric field mode patterns for the three metasurface-lined waveguides at 12 GHz. Reprinted, with permission, from Ref. 16, Copyright 2013, IEEE.