THz-metamaterial absorbers^*

The simulation was carried out by using a finite-integration-technique package of CST Microwave Studio. The unit cell of MM is designed as in figure 1(a) [14]. The conductor is copper with an electric conductivity of 5.96 × 10⁷ S m⁻¹. The insulator is SiO₃ with a relative dielectric constant of 3.2. The geometrical parameters were a = 11.5, l_max = 9.0 and l_min = 5.5 μm. The thicknesses of SiO₂ and metallic layers are 0.2 μm and 36 nm, respectively. The EM wave is polarized such that the electric and the magnetic fields are parallel to the MM slab, and the wave vector k propagates to the front side of MM (figure 1(a)). The boundary conditions were set so that the unit cell is periodic in the E–H plane. The simulation was performed for free space. In the conventional absorber model, the absorption is calculated from the reflection and expressed by the S₁₁ parameter as $A(\omega ) = 1 - \left| {S_{11} (\omega )} \right|^2$. The operating range of EM wave was from 5 to 16 THz.

Zoom In Zoom Out Reset image size

Figure 1(b) shows the absorption spectrum of MM with highly broad-band (3.7 THz from 8 to 11.9 THz) absorption. The highest and the lowest absorption are nearly 100% at 8.58 THz ('perfect absorption') and 92.24% at 11.5 THz, respectively. It is noted that the broad-band absorption results from the combination of absorption peaks which correspond to cut-wire pair (CWP) [15] separated by SiO₂ layer. The successive arrangement of this sandwich structure along the wave-vector direction significantly reduces the EM interaction and then leads to a series of independent operations for different frequencies. However, to yield the absorption peaks at desired frequencies the lengths of CWP should be gradually reduced. This affects the absorption conditions of the structure. The impedance matching [11, 16] is not properly achieved for all the peaks. Therefore, the decrease of absorption occurs according to the resonance frequency as shown in figure 1(b). This trouble could be overcome by changing the materials for the MM, but it is a new challenge for future fabrication in the higher-frequency modes.

The EM properties are presented in figure 2 to numerically clarify the mechanism of absorption. It is known that there are conventionally two plasmonic resonances responsible for the sub-wavelength absorption: electric and magnetic [16]. In figure 2(a), the distribution of the induced current at 8.8 and 10.5 THz exhibits anti-parallel flows, indicating that the absorption is responded to by the magnetic resonances. The contour of the induced magnetic energy in figure 2(b) illustrates more clearly the magnetic plasmon. This also elucidates that the major EM energy is dissipated in the capacitor created by the magnetic dipole mode. In other words, the dielectric loss is dominant in achieving the high performance of the PA structure [16]. The distribution of the power flow of EM wave also supports the argument of magnetically induced broad-band absorption. The EM energy is focused in the substrate layer and dissipated by the dielectric loss as magnetic dipole excitations as in figure 2(c).

Zoom In Zoom Out Reset image size

We now discuss further the magnetic excitation modes inducing the dielectric loss in the MM absorption with SiO₂ substrate. It is seen that the broad-band in THz of high absorption of the MM has great potential for applications in solar energy. In particular, in this MM, the dissipation is a semiconductor (SiO₂). This shows promise for high-efficiency MM solar panels in the future. However, the operating frequency in mid-IR is a disadvantage of this broad-band absorption. In higher frequency (for example, visible range), the broad-band MM by the magnetic excitation modes is not able to guarantee in induction of the dielectric loss when the Ohmic-loss of conductor is dominant. In addition, the multilayer structure is a significant impediment in nano-fabrication.

To develop the MM absorber with semiconductor substrate, we investigated a conventional sub-wavelength absorber structure with anti-dot pattern for the IR range of EM wave [17]. The design for the unit cell of MM is depicted in figure 3(a). The geometrical parameters were set to be a = 475, r = 150, t = 68 and t_s = 15 nm. t and t_s are the thicknesses of substrate and metal layers, respectively. The conductor is silver with an electric conductivity of 6.301 × 10⁷ S m⁻¹. The insulator is silicon with a relative dielectric constant of 11.9. The boundary conditions are as aforementioned. The operating frequency range of applied plane-EM wave is 350–450 THz. The calculation of absorption and reflection from S-parameters was as in the above discussion.

Zoom In Zoom Out Reset image size

The reflection and absorption spectra are plotted in figure 3(b) in the near-IR frequency range (350–450 THz). This shows a perfect-absorption peak with nearly no reflection at 395 THz. Two conditions for PA are satisfied by employing the cavity resonance [17].

We further studied the origin of loss in the MM. The distribution of the power loss (absorption) of the THz wave was calculated for the absorption, as indicated in figure 3(c). It is concluded that the absorber can concentrate the EM wave in some specified locations (for example, in the semiconductor area), where the energy is significantly reinforced and subsequently converted into thermal energy, leading to a strong absorption. This is significant for future application to solar energy.