# Dual-Band Light Absorption Enhancement in Hyperbolic Rectangular Array
## 3 Results and Discussion
As can be seen in Figure 5a,b, surface plasmon resonance (SPR) is excited at the interface of the film stack, and the electric-field energy is mainly confined in the HRA. In Figure 5c,d, the magnetic field is also greatly enhanced, and the magnetic-field energy is trapped by the HRA as well. The SPR shows a slightly higher electric-field distribution at 835.4 nm compared with 712.2 nm, thus the absorption bandwidth of peak 2 is smaller than that of peak 1. By observing the magnetic-field distribution of the HRA, the absorption enhancement at peak 1 and peak 2 can be identified as second-order and first-order PSP modes, respectively [36]. The influence of the width and the number of film stack on absorption response of the HRA is also studied. As can be seen in Figure 6, the dual-band absorption enhancement of the HRA is very  
Figure 4: Absorption response of the HRA with parameters the same as those in Figure 1a, and absorption response of the equivalent structure. Figure 5: Field distributions of the HRA associated with the absorption peaks. (**a,b**) are the near field distributions of \(E_{z}\) at 712.2 nm and 835.4 nm, respectively. (**c,d**) are the near field distributions of \(H_{y}\) at 712.2 nm and 835.4 nm, respectively. robust to the variations of \(W\) and \(N\). In Figure 6a, it shows that both the two absorption peaks shift to the longer wavelength as \(W\) is increased. The increase of \(W\) increases the length of the anisotropic metamaterial waveguide, resulting in the redshift of the absorption peak of the HRA [37]. Figure 6b shows absorption response of the HRA as a function of \(N\) with the fixed \(f\) and \(D\), and the absorption response of the HRA is calculated by using the EMT. As seen in Figure 6b, the absorption response of the HRA approaches that of the EMT as \(N\) is increased, and it almost coincides with that of the EMT as \(N=64\). In Figure 6c,d, it can be seen that the \(\lambda_{peak}\) difference between the HRA and the EMT is reduced as \(N\) is increased, indicating that the accuracy of the EMT can be improved by increasing the number of film stack. Finally, we showed that the HRA can be functioned as the refractive index sensor due to the robust performance of dual-band absorption. In general, various techniques have been investigated for sensing a special change of the refractive index. These techniques include nonlinear plasmonic sensing [38], guided-mode resonance [39], Mach-Zehnder interferometers [40], and whispering gallery mode resonators [41]. Here, we evaluate the refractive sensing capabilities of the HRA with sensitivity \(S=\Delta\lambda_{peak}/\Delta n\) and figure of merit (FoM) = _S/FWHM_, where \(\Delta\lambda_{peak}\) is the peak wavelength change with the refractive index change \(\Delta n\), and _FWHM_ is the half-width of the absorption band [42]. As can be seen in Figure 7a, both the two absorption peaks of the HRA redshift as the refractive index of the background is increased, and the low sideband level of absorption response can be kept almost the same. As shown in Figure 7b,c, the slope of the curves in the figures show that the sensitivity reaches 200 nm/RIU and 101 nm/RIU for peak 1 and peak 2, respectively. The sensitivity of peak 1 is larger, although the SPR of peak 1 shows a slightly lower field distribution. This may be because the field  
Figure 6: Influence of the width and the number of film stack on absorption response of the HRA. Other parameters are the same as those in Figure 1a. (**a**) Absorption response of the HRA as a function of \(W\). (**b**) Absorption response of the HRA as a function of \(N\) with the fixed \(D\) and \(f\); absorption response of the HRA calculated by using the EMT. (**c**) Location of peak 1 for different \(N\) comparing with that of the EMT. (**d**) Location of peak 2 for different \(N\) comparing with that of the EMT. energy of peak 1 is less localized by comparison with peak 2, and more field energy of peak 1 penetrates into the background, resulting in larger sensitivity.