## 3 Results and Discussion
The real \(Ez\) in Figure 2(b\({}_{2}\)) is mainly distributed in the surface (or edge) of the metallic array, while the real \(Ez\) shown in Figure 2(c\({}_{2}\)) not only distributed in the surface (or edge) of the metallic array but also the four corners of the unit cell. The real \(Ez\) distribution of the third mode demonstrates that its absorption performance could be tuned by changing the period of the triple-band light absorber, while the performance changes of the first two resonance modes should be neglected because their real \(Ez\) values are mainly focused on the surface (or edge) of the metallic array. Generally, the sensing performance is a very important index for evaluating the narrow-band absorber. Here we first analyze the dependence of the absorption spectra on the refractive index change of the surrounding. As shown in Figure 3a, we observed that frequency and absorbance changes of the first resonance peak can be neglected, while the absorption performance of the last two modes has a large dependence on the change of the surrounding index. Different from the second peak having only frequency change, the third peak not only has the characteristics of frequency shift but also absorbance decrease. Figure 3b gives the resonance frequency and absorbance of the third peak as the function of the refractive index of the surrounding. The results show that the resonance frequency and absorbance of the third peak are both approximately linearly decrease with the increase of surrounding index. When the refractive index of the surrounding is changed from 1.00 to 1.10, the frequency change range of the third absorption peak can reach 0.305 THz, and the linearly fitted bulk sensitivity of the frequency change of the third resonance mode is 3.05 THz per refractive index, which is respective 2.440 and 12.200 times larger than that of the second peak (1.25 THz per refractive index) and the first peak (0.25 THz per refractive index). If converted into the FOM (figure of merit, for the definition of FOM the reader can refer to References [35; 36; 37; 38; 39; 40]), the FOM value of the third peak can be up to 40.667, which is 5.205 and 39.853 times as much as the second (7.813) and the first (1.020) peaks, respectively. These results demonstrate that sensing performance of the high-order resonance response is much greater than that of the fundamental mode resonance. In other words, these studies provide us with a new way to design high sensitivity sensors. Moreover, we found that the variation range of the absorbance of the third peak can be as high as 64.63% when the refractive index is changed from 1.00 to 1.10. The linearly fitted sensitivity of the absorbance change of the third mode is 646.6% per refractive index, which is far greater than that of the first two resonance peaks, and even previous works. We also investigated the dependence of the absorption spectra on the overlayer thickness change of the triple-band absorber. It can be seen from Figure 4a that the frequencies of the three peaks are all blue-shift with the increase of the overlayer. The frequency changes of these peaks are due to the increase of the capacitance of the absorber. Besides the frequency shifts, the absorbances of these peaks are also decreased when the overlayer thickness is increased. For example, the variation ranges of the absorbances of the second and the third peaks are respective 11.45% and 53.19% when the thickness of the overlayer is changed from zero to 8 \(\upmu\)m. Furthermore, we found that the refractive index of overlayer also affect the absorption performance of the triple-band absorber, see Figure 4b. These results prove that the designed triple-band absorber can be used for sensor applications by adding thickness (or changing the refractive index) of the overlayer. The main research focus of this paper is mainly on the three-band absorption and the analysis of its sensing performance.