# Cascaded Nanorod Arrays for Ultrabroadband, Omnidirectional and Polarization-Insensitive Absorption
## 3 Absorption Performance Analysis
It is interesting to note that although several metal/dielectric multilayers are required for the CNA-based absorber, its physical mechanism for ultrabroadband absorption is fundamentally  
Figure 2: Absorption performance of different CNA-based structures. The parameters are: \(P=300\) nm, \(N=5\), \(h=140\) nm, \(t_{b}=30\) nm, \(t_{m}=10\) nm, \(t_{d}=33\) nm, \(D_{1}=140\) nm, and \(D_{2}=276\) nm. (**a**) Absorption of total structure, total structure with \(D_{1}=D_{2}=276\) nm, and total structure without Ti rods. (**b**) Absorption of CNA-based absorber, and absorption distributions of different parts of the structure. different from the tapered metal/dielectric multilayer-based absorbers associated with the intrinsically slow-light mode [35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49]. That is, these metal/dielectric multilayer-based absorbers can be equivalent to the anisotropic metamaterials with tapered width, and each metal/dielectric/metal layer acts as an independent slow light waveguide to stop and consume the light energy of a particular wavelength. In order to figure out the link between the ultrabroadband absorption performance and the related electromagnetic parameters of the CNA-based metasurface, we also investigate the input impedances of the structure by using the impedance theory. By using the impedance theory [63; 64], the impedance \(Z\) of the CNA-based metasurface can be expressed as  
\[Z\ =\ \pm\sqrt{\frac{\left(1+S_{11}\right)^{2}-S_{21}^{2}}{\left(1-S_{11} \right)^{2}-S_{21}^{2}}} \tag{4}\]  
\[S_{11}\ =\ S_{22}\ =\ \frac{i}{2}(\frac{1}{Z}-Z)\sin(nkd) \tag{5}\]  
\[S_{21}\ =\ S_{12}\ =\ \frac{1}{\cos(nkd)-\frac{i}{2}(Z+\frac{1}{2})\sin(nkd)} \tag{6}\]  
where \(S_{11}\), \(S_{21}\), \(S_{12}\), and \(S_{22}\) are \(S\) parameters; and \(n\), \(k\), and \(d\) are the effective refractive index, the wave vector, and thickness of the structure, respectively. Therefore, the relation between the theoretically calculated reflection of CNA-based structure and the impedance \(Z\) can be simplified as \(R=[(Z-Z_{0})/(Z+Z_{0})]^{2}\), where \(Z_{0}\) is the impedance of free space. Figure 4a shows the reflection response and impedance of the CNA-based metasurface. The parameters are the same as those in Figure 2b. As shown in Figure 4a, the real part of \(Z\) approaches one and the imaginary part of \(Z\) tends to zero in the wavelength range of 0.38-2.5 \(\upmu\)m, resulting in the ultrabroadband antireflection with \(R\approx 0\) in this wavelength region. Figure 4b shows the FDTD and the theoretical results of the absorption response of the CNA-based metasurface. Herein, the theoretical results are calculated by using the retrieved input impedances, which show excellent agreement with the FDTD results. Figure 3: Electric field and Poynting vector distributions of CNA-based absorber at three resonance absorption peaks. (**a**) \(\lambda\) = 0.524 \(\upmu\)m; (**b**) \(\lambda\) = 1.001 \(\upmu\)m; (**c**) \(\lambda\) = 1.952 \(\upmu\)m. The parameters are the same as those in Figure 2b, the arrows indicate the Poynting vector direction.