Surface waves at microwave frequencies excited on a zigzag metasurface

Surface waves at microwave frequencies are excited on a zigzag metasurface formed from unit cells comprised of a pair of identical, alternately oriented, rhombic-shaped metal tubes. This particular symmetry leads to diffractive excitation, with polarization selectivity of different orders, of a family of surface waves. Furthermore, the expected band gap at the first Brillouin zone boundary is absent.

Figure 1

(a) Photograph of experimental sample with coordinate system. Plane of incidence (dashed line) and a plane of mirror symmetry (dotted line) are shown. The unit cell (solid line) is formed from paired rhombic-shaped holes, side length, $l$ $=$ 7.0 mm, zigzag pitch $L$ $=$ 16.5 mm and orthogonal pitch, $S$ $=$ 9.5 mm. (b) Schematic representation of experimental setup for transmission at normal incidence. (c) Schematic representation of plane of incidence and coordinate system used.

Figure 2

Predicted time-averaged (color map) and instantaneous (arrows) $E$-field profiles calculated over a surface parallel to the $xy$ plane of the waveguide, plotted at a phase corresponding to maximum field enhancement, for the waveguide modes supported at (a) $f_1$ $=$ 18.33 GHz and (b) $f_2$ $=$ 28.71 GHz. Yellow regions (light gray) corresponds to high-field enhancement, and blue (medium gray) corresponds to a field magnitude of zero. To break the degeneracy and resolve the two modes supported at 28.71 GHz, a rhombic cross section with 60.001° corner has been modeled.

Figure 3

Experimental transmission data (grayscale) plotted on a log scale for (a) $p$- and (b) $s$-polarized incident radiation in a $xz$ plane, recorded as a function of $\theta$. Light and dark regions correspond to high and low transmissivity, respectively. The horizontal dashed lines represent the frequencies of the first ($f_1$) and second ($f_2$) supported TE waveguide modes. The solid and dashed diagonal lines represent the first- and second-order diffracted light lines, respectively. The dashed vertical lines indicate the Brillouin zone boundaries at $\pm \pi /L$ ($=$$k_{\mathrm{g}}$/2). Inset: Predicted time-averaged $E$-field profiles plotted in the $xz$ plane for ($i$) symmetric (predicted dispersion, squares) and ($ii$) antisymmetric (predicted dispersion, crosses) field solution. Yellow regions (light gray) correspond to high field enhancement, and blue (medium gray) corresponds to a field magnitude of zero.

Figure 4

Schematic representation of the instantaneous $E$-field (solid arrows) for the surface mode supported at low frequencies for (a) $s$- and (b) $p$-polarized radiation incident in a plane containing the zigzag axis. Plane of incidence (dashed line) and mirror plane (dotted line) are shown. Open arrows represent the local component of the electric vector contained in the plane of incidence.

Figure 5

(a) Predicted dispersion of the modes near the band gap centered around $k_x$ $=$ 0. (b) Time-averaged $E$-field distribution of the symmetric solution of the ($i$) high-energy (triangles) and ($ii$) low-energy band (squares) at $k_x$ $=$ 0 plotted in the $xy$ plane. Yellow (light gray) regions correspond to high field enhancement, and blue (medium gray) corresponds to a field magnitude of zero.