IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 (b) 5 Frequency [ GHz ave transmission across a flat metal surface.(b)TM surface-wave transmission across a two-layer high- impedanc ission across a two-layer high-impedance surface. The strong fluctuations are due to multipath inter (b)and (c) charge. The lowest TE mode is a sheet of current that is surface wave. Another method for coupling to surface waves, continuous in space, but oscillating at the lC resonance which is more practical at microwave frequencies, is to use frequency, at the origin of k-space. The te band slopes very small probe. A point source launches all wave vectors smoothly upward in frequency, crossing through the light line thus, a small antenna brought near the surface is capable of at some point. At the highest TE mode, at the Brillouin zone coupling to surface-wave modes. The antenna geometry can boundary, transverse currents flow in opposite directions on be tailored to distinguish surface-wave polarization each row of protrusions In TM surface waves, the electric field forms loops that ex- In the other upper bands, the electric field is primarily tend vertically out of the surface. TM waves can be measured concentrated in the region below the capacitor plates. The using a pair of small monopole antennas oriented normally modes in these bands resemble the modes in a parallel-plate with respect to the surface, as shown in Fig. 11(a). The vertical waveguide. The first of these modes occurs at about the electric field of the probe couples to the vertical electric field requency where one half-wavelength fits between the rows of the TM surface waves In TE surface waves, the electric of metal vias field is parallel to the surface. They can be measured with a pair of small monopole probes oriented parallel to the sheet, MEASURING SURFACE PROPERTIES as shown in Fig. 11(b). The horizontal electric field of the antenna couples to the horizontal electric field of the Te wave On a flat metal sheet, a TM surface-wave measurement pro- Since surface waves cannot generally couple to external duces the results shown in Fig. 12(a). The surface under test plane waves, specialized methods must be used to measure was a 12-cm- sheet of flat metal. The measurement represents them. At optical frequencies, surface plasmons are often the transmission between a pair of monopole probes oriented studied using a technique called prism coupling [8]. A prism is vertically at the edges of the metal sheet. (A TE surface- placed next to the surface, and the refractive index of the prism wave measurement produces no significant signal because any is used to match the wave vector of a probe beam to that of a antenna that excites te waves is shorted out on a conducting2066 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 (a) (b) (c) Fig. 12. (a) TM surface-wave transmission across a flat metal surface. (b) TM surface-wave transmission across a two-layer high-impedance surface. (c) TE surface-wave transmission across a two-layer high-impedance surface. The strong fluctuations are due to multipath interference. The forbidden bandgap is shown for cases (b) and (c). charge. The lowest TE mode is a sheet of current that is continuous in space, but oscillating at the resonance frequency, at the origin of -space. The TE band slopes smoothly upward in frequency, crossing through the light line at some point. At the highest TE mode, at the Brillouin zone boundary, transverse currents flow in opposite directions on each row of protrusions. In the other upper bands, the electric field is primarily concentrated in the region below the capacitor plates. The modes in these bands resemble the modes in a parallel-plate waveguide. The first of these modes occurs at about the frequency where one half-wavelength fits between the rows of metal vias. VI. MEASURING SURFACE PROPERTIES A. Surface Waves Since surface waves cannot generally couple to external plane waves, specialized methods must be used to measure them. At optical frequencies, surface plasmons are often studied using a technique called prism coupling [8]. A prism is placed next to the surface, and the refractive index of the prism is used to match the wave vector of a probe beam to that of a surface wave. Another method for coupling to surface waves, which is more practical at microwave frequencies, is to use a very small probe. A point source launches all wave vectors, thus, a small antenna brought near the surface is capable of coupling to surface-wave modes. The antenna geometry can be tailored to distinguish surface-wave polarization. In TM surface waves, the electric field forms loops that ex￾tend vertically out of the surface. TM waves can be measured using a pair of small monopole antennas oriented normally with respect to the surface, as shown in Fig. 11(a). The vertical electric field of the probe couples to the vertical electric field of the TM surface waves. In TE surface waves, the electric field is parallel to the surface. They can be measured with a pair of small monopole probes oriented parallel to the sheet, as shown in Fig. 11(b). The horizontal electric field of the antenna couples to the horizontal electric field of the TE waves. On a flat metal sheet, a TM surface-wave measurement pro￾duces the results shown in Fig. 12(a). The surface under test was a 12-cm sheet of flat metal. The measurement represents the transmission between a pair of monopole probes oriented vertically at the edges of the metal sheet. (A TE surface￾wave measurement produces no significant signal because any antenna that excites TE waves is shorted out on a conducting