## 3 Simulation Results and Discussion
### Ring-Type Cutoff Probe (RCP)  
Figure 2a shows the S\({}_{21}\) spectra with various \(\alpha\) (normalized width of the detecting antenna) at fixed \(\beta\) and \(\gamma\). An increase in \(\alpha\) led to a slight elevation of the S\({}_{21}\) level. This was because of an increase in the capacitive coupling between the radiating and detecting antenna. Furthermore, the S\({}_{21}\) had several resonance frequencies at its extremes. Except for the lowest resonance frequency, with an increase in \(\alpha\), the resonance frequencies shifted toward lower values. When \(a\) increased, as shown in Figure 2d,g, the low-frequency shift became enlarged. The origin of the resonance frequencies will be analyzed later. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Type** & \multicolumn{2}{c}{**Ring-Type Probe**} & \multicolumn{2}{c}{**Type**} & \multicolumn{2}{c}{**Bar-Type Probe**} \\ \hline
**Number** & \(\alpha\) (\(\equiv d/a\)) & \(\beta\) (\(\equiv b/a\)) & \(\gamma\) (\(\equiv c/a\)) & **Number** & \(\alpha\) (\(\equiv f/e\)) & \(\beta\) (\(\equiv h/e\)) & \(\gamma\) (\(\equiv g/e\))** \\ \hline \#1 & 1 & 4.5 & 0.5 & \#8 & 4 & 4.5 & 0.5 \\ \#2 & 2 & 4.5 & 0.5 & \#9 & 6 & 4.5 & 0.5 \\ \#3 & 4 & 4.5 & 0.5 & \#10 & 10 & 4.5 & 0.5 \\ \#4 & 1 & 5.5 & 0.5 & \#11 & 4 & 5.5 & 0.5 \\ \#5 & 1 & 7.0 & 0.5 & \#12 & 4 & 7.0 & 0.5 \\ \#6 & 1 & 4.5 & 1.0 & \#13 & 4 & 4.5 & 1.0 \\ \#7 & 1 & 4.5 & 1.5 & \#14 & 4 & 4.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation conditions with various \(\alpha\), \(\beta\), \(\gamma\), and probe diameters. Parameters \(a\)–\(g\) are given in Figure 1.  
Figure 2b plots the S\({}_{21}\) spectra with several \(\beta\) (normalized antenna distance), with results showing that the overall S\({}_{21}\) signal level reduced with increasing \(\beta\) due to a decrease in the capacitive coupling between the antennae [23]. Besides, an increase in \(\beta\) led to a low frequency shift of the resonance frequencies. Compared with the effect of \(\alpha\), increasing \(\beta\) more clearly shifted the resonance frequencies toward lower values. As shown in Figure 2c, an increase in \(\gamma\) (normalized dielectric thickness) did not change the resonance frequencies. The signal levels changed with \(\gamma\), while there was no trend compared with the \(\alpha\) and \(\beta\) effects. This might have resulted from a characteristic impedance mismatching between the radiation and detecting antennae, since they had no symmetry with each other. Impedance matching might deteriorate at \(\gamma=1.0\). To figure out the origin of the resonance frequencies as shown in Figure 2, the electric field on the detecting antenna surface was examined, the direction of which was normal to the antenna surface (z-axis as shown in Figure 1). Figure 3 exhibits the normalized electric field as a function of the normalized antenna length (\(\hat{\theta}\)-axis as shown in Figure 1) at resonance (2.61, 5.17, and 7.71 GHz) and non-resonance (3.90 and 6.50 GHz) frequencies of the \(\#6\) condition at \(a=3.0\) mm. The simulation result showed that the oscillation amplitude at the resonances was larger than that at the non-resonances. Furthermore, the wavelength at the three resonances was one, two, and three times the antenna length. Based on these two facts, the resonance frequencies resulted from the SW resonances of the electric field on the detecting antenna [20,24]. Due to this SW resonance, electric field energy was strongly localized on the detecting antenna surface such that it could not propagate toward the Signal Out (Figure 1); the S\({}_{21}\) value at the resonances, therefore, dramatically decreased, as shown in Figure 2.  
Figure 2: S\({}_{21}\) spectra of the RCP from various (**a**,**d**,**g**) antenna widths, (**b**,**e**,**h**) antenna distances, and (**c**,**f**,**i**) dielectric thickness at various antenna diameters: (**a**–**c**) \(a=2.0\) mm, (**d**–**f**) \(a=2.5\) mm, and (**g**–**i**) \(a=3.0\) mm.