Electromagnetic waves can be reflected, transmitted, absorbed, scattered, or induce by surface electromagnetic waves (SEW) at the boundary line of two planes. Wavelengths in the \({\lambda }_{0}\) range should be considered in wave propagation analysis, and it is assumed that the surface has an average roughness \({R}_{a}\) that is much smaller than the characteristic wavelength \({R}_{a}\ll {\lambda }_{0}\), in which case scattering effects can be ignored.
Plasmons [21] and surface electromagnetic waves in general [22] may also exist on the surface. It is often described as \({L}_{p}=\frac{1}{2{k}_{2}}\), where \({k}_{2}\) is the imaginary part of the complex wave with the relation \({\tilde{k}}_{\parallel }={k}_{2}+{jk}_{2}\), and only the wave parallel to the surface is considered [23]. \({L}_{p}\) is the specific distance over which the SEW or plasmon intensity decays by \(1/e\). The plasmon emission length \({L}_{p}\), on the other hand, is an inadequate description of what needs to be quantified. In other words, the ease with which an external electromagnetic wave can be attached to the surface and propagated as SEW. To connect a radiated electromagnetic wave to a surface wave, energy (\(E=\hslash \omega\)) and momentum \(p=\hslash {k}_{1}\) must be conserved, and thus the relation \({k}_{1}={k}_{0}\) must be established, where \({k}_{0}\) is the real part of the wave vector in the environment and also \({\omega }_{0}=c{k}_{0}\), which Assuming that it is located at an arbitrary wavelength, \({\omega }_{0}=2\frac{c}{{\lambda }_{0}}\) and the merit value that includes the above discussion:
\({W}_{p}=\frac{1}{2}\frac{{k}_{2}}{{\left{k}_{1}{k}_{0}\right}^{2}+{k}_{2}^{2}}\)(1)
The merit value in Eq. (1) considers how well the radiated wave corresponds to the k 1surface scattering and the k 2surface loss for SEW propagation. \({W}_{p}\) is reduced to \({L}_{p}\) if the motion exactly matches k_1 = k_0. If k_2 is large enough, generating surface electromagnetic waves may be a loss, but as previously stated, SEW may reradiate the wave, indicating that the surface is curved. Assuming a smooth surface exists and that any SEW or plasmon decays before scattering, it can be determined that a wave can be reflected (R), transmitted (T), or absorbed (A), which are all attributed to each other via the formula Α = 1TR.
Figure 1 depicts the structure of an absorber with two layers of gold on the bottom and top and an alumina dielectric layer between these two layers. In the part of the upper metal layer, which is made of gold, a meander line structure has been created to trap terahertz waves, which is the cause of intensifying the electric field and increasing absorption in the terahertz band.
Table 1
absorber thickness parameters (dimensions: nm)
Parameter

Thickness

d1
d2
d3
a
L1
L2
L3 & L4
W1
W2
W3

1600
560
600
9800
3500
4800
2300
1000
300
500

The geometric shape of the absorber will always have an important effect on the absorber's insensitivity to the radiation angle of electromagnetic waves, or in other words, the insensitivity to the structure, in the design of electromagnetic absorbers or metamaterials. Because of the symmetry in its geometrical shape and the symmetrical curved structure in the upper layer, which receives it like a wave receiving antenna and traps the magnetic field and enhances absorption, the absorber in Fig. 1 is not sensitive to the radiation angle.
The geometric symmetry of the structure has caused its response to be independent of the angle of incidence according to Fig. 2. which has been investigated for φ = 70 and φ = 80 angles and according to that, it will be insensitive for other angles such as 60.
Since\(I=\frac{1}{2}n{\epsilon }_{0}c{E}^{2}\), the electric field is also higher in the parts where the incoming current intensity is higher, resulting in less absorption. And as the intensity of the input current decreases, the field decreases as well, resulting in more absorption.
The response of the structure for TE and TM polarizations at the radiation angle of 70 is shown in Fig. 4. In TE polarization, the magnetic field is in the Y direction, and in TM polarization, the electric field is in the Y direction. As it is evident, in both polarizations, the absorption peak of 100% has been constantly repeated in the range of 10 to almost 70 THz.
Due to the unique structure of this absorber, which is designed in the form of a meander line, absorption peaks above 90% are observed in a compact form and with a high number in the 10–70 THz range. The imaginary peak of the electrical permeability coefficient indicates the electric resonance in the structure, and the imaginary peak of the magnetic permeability coefficient indicates the location of magnetic resonances in the structure.