# Dual-Band Light Absorption Enhancement in Hyperbolic Rectangular Array
## 3 Results and Discussion  
Figure 3 shows optical properties of the HRA, and the structural parameters are the same as those in Figure 1a. As can be seen in Figure 3a, dual-band absorption enhancement with a peak efficiency of \(\sim\)95% are obtained at 712.2 nm and 835.4 nm, which are denoted as peak 1 and peak 2, respectively. The absorption bandwidths of peak 1 and peak 2 are 34.6 nm and 28.0 nm, respectively. Comparing with many previous HMMs-based absorbers, which were mainly designed to achieve broadband absorption enhancement in different wavelength regions [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27], the absorption response of the HRA shows the property of narrowband absorption enhancement. In addition, the sideband level of the absorption  
Figure 2: Real parts of the \(\varepsilon_{\perp}\) and \(\varepsilon_{\parallel}\) of dielectric permittivity of the HRA calculated by using the EMT. spectra is low and flat as wavelength is varied. Thus, the HRA possesses good selective absorption performance with double channels. To better understand the selective absorption properties of the HRA, the equivalent impedances of the structure are studied by using the impedance theory. According to the impedance theory [35], the input impedance \(Z_{in}(\omega)\) and the scattering parameters of the HRA can be generated by:  
\[Z_{in}(\omega)=\pm\sqrt{\frac{\left(1+S_{11}\right)^{2}-S_{21}^{2}}{\left(1-S_ {11}\right)^{2}-S_{21}^{2}}} \tag{5}\]  
\[s_{21}=s_{12}=\frac{1}{\cos(nkD)-\frac{i}{2}\left(Z_{in}(\omega)+\frac{1}{2} \right)\sin(nkD)} \tag{6}\]  
\[s_{11}=s_{22}=\frac{i}{2}\bigg{(}\frac{1}{Z_{in}(\omega)}-Z_{in}(\omega)\bigg{)} \sin(nkD) \tag{7}\]  
where \(S_{11}\), \(S_{21}\), \(S_{12}\), \(S_{22}\) are scattering parameters; \(k\) is the wavevector, and \(n\) is the effective refractive index of the HRA. Therefore, the reflection of the HRA can be calculated as:  
\[R=\big{[}\frac{Z_{in}(\omega)-Z_{0}}{Z_{in}(\omega)+Z_{0}}\big{]}^{2} \tag{8}\]  
where \(Z_{0}\) is the impedance of the free space, and \(Z_{0}=\sqrt{\mu(\omega)/\varepsilon(\omega)}=1\). Obviously, to reduce the reflection of the HRA, the input impedance \(Z_{in}(\omega)\) should be matched with the impedance of the free space \(Z_{0}\) for both two absorption bands. Figure 3b shows reflection response and input impedance of the HRA. As can be seen in Figure 3b, both the real and imaginary parts of \(Z_{in}(\omega)\) are varied abruptly around the absorption bands so as to meet the impedance matching condition. In particular, the real part of \(Z_{in}(\omega)\) approaches 1, and the imaginary part of \(Z_{in}(\omega)\) tends to 0 at the wavelengths of peak 1 and peak 2, which confirms the preceding theoretical analysis on dual-band absorption enhancement of the HRA. In order to evaluate the validity of the EMT for estimating absorption performance of the HRA, the absorption spectra of the HRA and the equivalent structure are shown in Figure 4, where the equivalent structure is shown in the figure inset. As can be seen in Figure 4, the absorption response calculated using the EMT shows a similar curve to the HRA. The absorption peaks of the EMT are slightly deviated from those of the HRA. This is mainly because the number of film stacks is assumed to be infinite (\(N=\infty\)) in the EMT approximation. However, the properties of dual-band absorption enhancement of the HRA can be well demonstrated using the EMT. Figure 3: Optical properties of the HRA. The parameters are the same as those in Figure 1a. (a) Absorption response of the HRA. (b) Reflection response and input impedance of the HRA. To investigate the physical origin of the dual-band light absorption enhancement of the HRA, near field distributions of the \(E_{z}\) and \(H_{y}\) components at peak 1 and peak 2 are calculated. Figure 5 shows field distributions of the HRA associated with the two absorption peaks.