## 3 Results and Discussion
### Effect of the Dielectric Properties of the Nanotip and Substrate  
The enhancement effect depends on the dielectric properties of the nanotip and the substrate according to Equations (1)-(3). Metallic nano/microstructures have long been applied in local plasma resonance enhancement studies in the visible and near-infrared wave bands to promote light-matter interaction, but do not always succeed in the THz wave band, owing to a mismatch of the plasma frequency of the metal and the THz radiation. However, the plasma resonance frequency of semiconductor materials happens to be localized in the THz wave band. The plasma property of  
Figure 3: **(a)** The electric field distribution of Au nanotip-Au substrate; **(b)** Relation between the maximum electric field amplitude \(E\) and the nanotip-substrate distance \(D\). The solid line is for the guide of eyes; **(c)** The electric field distribution along the \(y\)-axis for the Au nanotip-Au substrate system and the FWHM is marked with a dash line; **(d)** The maximum electric field amplitude \(E\) as a function of incident angle \(\theta\). semiconductor material makes the electromagnetic coupling with metal tips much stronger [20]. Hence, from the perspective of the tip and substrate materials, metal (Au) and semiconductor (InSb) are introduced in our simulations to observe the signal intensity and compare the spatial resolution. Two substrate materials are selected in our simulations: Au and InSb, for InSb material \(\varepsilon_{\text{lattice}}=15.6\), \(\omega_{\text{p}}=46\times 10^{12}\) rad/s, scattering ratio \(\gamma=0.3\times 10^{12}\) rad/s [20]. Other parameters are set as follows: \(r=10\) nm, \(D=6\) nm. Figure 4a shows the maximum electric field distribution along the \(x\)-axis for different nanotip-substrate combinations using different materials. From Figure 4a, we can see that there is a maximum enhancement effect for the InSb nanotip above the InSb substrate, while a minimum enhancement effect for the Au nanotip above the Au substrate. The variation is shown clearly in the inset with a double-logarithmic plot. The dielectric properties of the nanotip and substrate affect not only the electric field enhancement effect, but also the resonant excitation frequency. From Figure 4b, when Au is used for the nanotip, there is a strong frequency-dependent electric field enhancement observed for Au nanotip above the InSb substrate (black curve in Figure 4b) compared with Au nanotip above an Au substrate (red curve in Figure 4b) at the incident THz wave frequency range from 0.8 to 2.4 THz. The maximum electric field enhancement for Au nanotip above InSb substrate is observed at 1.6 THz. From Equations (1)-(3), the near-field signal will only depend on the dielectric constant of the substrate when the radius of the nanotip apex, the dielectric constant of nanotip and the apex-substrate distance are given. \(\beta\) is the polarization intensity of the substrate and gets its maximum when Re\([\varepsilon_{\text{s}}\left(\omega\right)]=-1\). This can be satisfied for InSb substrate at \(\omega=1.7\) THz according to the Drude model, which is in very good agreement with our simulation result of 1.6 THz from Figure 4b, but cannot be satisfied for Au substrate in the entire THz frequency range considered here. Therefore, there is a strong resonance enhancement for Au nanotip above InSb substrate and no resonance enhancement for Au nanotip above the Au substrate. The resonance enhancement stems from the interaction between the THz wave and the substrate, in that the semiconductor InSb supports strongly confined surface plasmons (SPs) in the THz frequency range, and these SPs tend to enhance the requisite light-matter interaction [20]. Figure 4: **(a)** Relation between the maximum electric field amplitude \(E\) and the nanotip-substrate distance \(D\) when using Au, InSb as nanotip and substrate materials; **(b)** Relation between the maximum electric field amplitude and the incident frequency for Au nanotip above an Au and InSb substrates, respectively, at 0.8–2.4 THz.