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Abstract
Metamaterial absorbers deliver potential applications in the field of civil and military products. Herein, we proposed a dual-band metamaterial absorber in a range of terahertz (THz) frequency based on numerical simulations. A novel design of swastika-shaped microslots in aluminum film is introduced that displays two high absorbance peaks at the resonant frequencies of 2.77 THz and 3.42 THz, respectively. The microslots enhance the efficiency of the device by accumulating most of the energy inside the symmetrical organized micro-gaps. Impressively, high absorbance in the range of 100–60% is recorded for a wide range of angle of incidence (0°–70°) of the electromagnetic wave. Furthermore, the calculated absorbance considerably remains insensitive (>80%) to any angle of polarization. To achieve relatively easy and cost-effective fabrication of metamaterial absorbers, the proposed absorber is simply designed with micrometer scale slots that are simply ingrained along only the vertical and horizontal directions in the aluminum film.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial made subwavelength structures, which are extensively studied due to their peculiar electromagnetic (EM) behavior [1,2]. Fascinating aspect of metamaterial arises because of negative index of refraction (negative permittivity and negative permeability), which is impossible to observe in naturally existing materials [3]. Recently, metamaterial absorbers are widely researched and introduced in various range of the EM spectrum, for example, in visible [4], infrared [5] and microwave [6]. Metamaterial absorbers have potential applications in civil and military products, for example, in the form of thermal detectors [7–9]. In principle, metamaterial absorber provides high absorbance in a certain range of frequency. Therefore, reflectance and transmission through the absorber should be minimum which are possible to achieve by impedance matching condition [10]. In most of the cases, the frequency of interest is within the terahertz (THz) region because it is difficult to find resonant absorbers in this part of the EM spectrum [11]. The recent surge in the study of metamaterial has introduced many kinds of absorbers based on design and performance. Few example are; circular-sectors [12], thin wires [13], pyramid structure [14], interlaced fishnet layers [15], crossed-shaped [16], split ring resonator [17,18], I-shaped resonators [19] and dual-band absorbers [20–23]. Furthermore, tunable absorbers, e.g., [24,25], are also studied by applying various methods (see [26–32]). Apart from that different chiral metamaterials containing swastika-shaped structures are also studied to explore the phenomenon of optical activity [33–36]. One of the advantages of metamaterial absorber in the terahertz range is the size in micrometer scale, which makes its fabrication relatively easy for practical usage.
In this work, we proposed a dual-band metamaterial absorber in terahertz frequency range based on numerical simulations. Two absorbance peaks are observed at the frequencies of 2.77 THz and 3.42 THz, respectively. The metamaterial absorber consists of novel design of swastika-shaped microslots in aluminum (Al) film with symmetrical arrangements. The proposed structure shows promising results by keeping the absorbance high, for example the maximum 100% and minimum 60% absorbance values are recorded for a wide range of incidence angles (0° – 70°). In the same vein, absorber provides a relatively high absorbance for any angle of polarization of the incident wave. It is noticeable that the microslots in the aluminum film contain most of the energy in the gaps and thus provide a relatively high insensitivity for the incident electromagnetic wave. Furthermore, such kind of microslots in the aluminum film are feasible to pattern by applying laser surface texturing method (e.g., [37]) which is simple and fast in practice unlike to the commonly used advanced lithographic techniques. The design of the structure is simple with only a thickness of 3 µm, for example it consists only micro-gaps in the metallic layer which are aligned only along the vertical and horizontal directions, and therefore are relatively easy to fabricate in comparison with the complicated structures (e.g., round shaped features).
2. Design and theory
A schematic illustration of the proposed metamaterial absorber is shown in Fig. 1. Swastika-shaped microslots are ingrained in a film of Al in the xy-plane. The thickness of the Al layer is 50 nm which is deposited on the TiO2 thick layer (2.75 µm). The microslots are designed in such a way that the polarization state of the incident electromagnetic wave has a minimum effect on the structure’s absorbing ability. A detailed discussion on the performance of the structure in terms of the polarization state and the angle of incidence of the incoming field is discussed in later section. A parametric study is performed for optimizing the device dimensions. The optimized parameters of the microslot-features are given in the caption of the figure. In Fig. 1, the EM wave (blurred red color) that is propagating in the negative z-direction impinges at the structure. A second layer of the Al with a thickness of 200 nm is deposited at the bottom of TiO2 which blocks any possible transmission of energy through the metamaterial absorber device. The second layer of the Al is not shown in the figure. The overall thickness of the device is 3 µm. The dimension of the unit cell, length (L) × width (W), is 22 µm × 22 µm. The material properties, e.g., optical permittivity, of Al and TiO2 are adopted from Lorentz-Drude model [38] and DeVore 1951 [39], respectively. The permittivity value of the TiO2 is high in the used terahertz frequency range which indicates the high absorbance ability of the material [40].
Fig. 1. Schematic illustration of the unit cell of proposed metamaterial absorber. The optimized parameters of swastika-shaped microslots are; a = 4 µm, b = 9 µm, c = 21 µm and d = 0.5 µm. The thickness of the device is 3 µm with L = W = 22 µm.
In theory, an ideal metamaterial absorber should produce a 100% absorbance by minimizing reflectance (R) and transmission (T) through the structure. The reflectance of the incident EM wave becomes zero at the impedance matching condition wherein the impedance of the metamaterial structure becomes equal to the impedance of the free space. On the other hand, transmission of the energy can be blocked by applying a material which possesses a high value of imaginary part of the refractive index at a certain range of frequencies. Therefore, ultimately, entire amount of energy that impinges on the device is absorbed by the metamaterial structure at a frequency of interest. Usually, the transmission through the metamaterial absorber is hindered by placing a second metallic layer at the bottom of the device. The reflectance and transmission coefficients are achievable by calculating S-parameters [41], for example, S11 and S21 [20].
3. Simulations and results
In our model, a whole unit cell, as shown in Fig. 1, is simulated by employing a finite element method (COMSOL Multiphysics). A port boundary condition is applied in a xy-plane to excite the incident EM wave. According to the orientation of the electric field, perfect electric and magnetic boundary conditions are applied along the x- and y-axis. The used conductivity value of Al is 37 × 106 S/m. The absolute values of S-parameters abs(S11)2 and abs(S21)2, which are reflection and transmission coefficients, respectively, are calculated. In Fig. 2, the calculated reflectance is shown in a black color. The reflectance is 0.1 and 0 at frequency of 2.77 THz and 3.42 THz, respectively. This behavior of reflectance indicates a high dual-band absorbance because of the resonance at those values of frequency. A detailed discussion on the absorption mechanism is discussed in a later section. The red solid horizontal line represents the transmission through the metamaterial absorber, which gives a zero value, as expected, due to the presence of the Al layer at the bottom of the device. The incident angle θ, as given in Fig. 2, is the angle between the wave vector of the incident wave and the normal to the surface. The incident electric field is polarized along the y-axis (TE mode).
Fig. 2. Calculated reflectance of the incident electromagnetic wave in a frequency range of 1.5 THz – 4.5 THz. The angle θ represents the angle of incidence. The red solid line depicts the transmission.
To further analyze the performance of the proposed absorber at the resonant frequencies we plotted the distribution of electric field intensity inside the microslot structures. The results are shown in Fig. 3. The incident electric field is oriented along the y-axis or TE mode (see axis in Fig. 1). In Fig. 3(a), intensity is plotted for the resonant frequency of 2.77 THz. It is worth to notice that most of the energy is accumulated at the center along the x-axis. The active region is highlighted with a white color ellipse in the figure. Only a tiny amount of energy is stored in upper-left and bottom-right slots. The amount of the stored energy is relatively high as well as it is distributed differently at 3.42 THz as shown in Fig. 3(b). For example, energy modes are aggregated in the upper-left and bottom-right slots which are shown with white circles in the figure. This enhancement of intensity at 3.42 THz could be attributed to the perfect matching of impedance at this frequency, which was discussed in our earlier work [42]. However, in general, the response of the metamaterial absorber is promising with respect to the energy storing ability at the resonant frequencies. Similar behavior, which is not shown here, is observed for the polarized incident field along the x-axis (TM mode). However, in this case the accumulating behavior of the stored energy in the microslots is opposite to the TE mode. This trend of the field distribution indicates insensitivity of the metamaterial absorber against the polarization state of the incident EM wave.
Fig. 3. Distribution of the electric field intensity inside the microslots at resonant frequencies of (a) 2.77 THz and (b) 3.42 THz. In (c) and (d), current density is plotted for the same frequencies. The incident electromagnetic wave is polarized along the y-axis.
Figures 3(c) and (d) represent the distribution of current density (small white arrows) inside the slots at 2.77 THz and 3.42 THz, respectively. Akin to Figs. 3(a) and (b), most of the charges are settled inside the slots at the center for 2.77 THz while charges are stored in upper-left and bottom-right slots at 3.42 THz. Although, the charges are also stored in other regions of the structure, nevertheless the amount is smaller in comparison to the active slots. Overall, the behavior of the device is symmetric for the incident EM field that is polarized either along the y- or x-axis.
In practice, the EM wave can incident on the structure at random angles other than the normal angle of incidence. Therefore, we calculated the absorbance, A = 1 – R, for a wide range of incidence angles, i.e., 0° – 70°. The results are shown in Fig. 4. In Fig. 4(a), the incident electric field is oriented along the x-axis (TM). At θ = 0°, the proposed metamaterial absorber gives ∼90% and ∼100% absorbance at the frequencies of 2.77 THz and 3.42 THz, respectively. The relatively high absorbance at 3.42 THz corresponds to the high-energy storage ability of the slots at this frequency as it was discussed earlier in Fig. 3(b). The absorbance starts decreasing as the angle of incidence increases. For example, at an extreme angle of 70° the absorbance drops to 60% and 65% at the respective resonances of 2.77 THz and 3.42 THz, respectively. The reduction in absorbance for the large incidence angles, e.g., θ ≥ 70°, can be attributed to the significant mismatch of impendences at the large angles of incidence [42].
Fig. 4. Calculated absorbance as a function of a wide range of angle of incidence θ = 0° – 70°. In (a), the incident electric field is oriented along the x-axis while in (b) it is polarized along the y-axis. The insets of the figure, TM and TE modes of the incident wave are defined where E, B and k represent electric field, magnetic field and wavevector, respectively. The angle θ lies between k and normal to the surface.
In Fig. 4(b), the incident electric field is polarized along the y-axis (TE). At large θ = 70°, absorbance drops to 75% and 80% at the resonant frequencies of 2.77 THz and 3.42 THz, respectively. The absorbance of a perfect absorber is expected to remain at high values irrespective of changing the incident angle of the EM wave. However, control over small variations in absorbance and frequency is a challenging task in the field of metamaterial absorbers [43]. These small variations in the absorbance and frequancy are manifested in the calculations performed in this study. From Fig. 4, one can clearly observe the fluctuations in calculated absorbance as well as the slight shift in the resonance frequency as the angle of incidence increases. Theses fluctuations correspond to the slight mismatch of the impedances at the large angles. Nevertheless, the overall response of the device is promising by showing a maximum of ∼100% and a minimum of 60% absorbance in a wide range of incidence angles for either TM or TE mode. In other words, the designed metamaterial absorber remains relatively independent on wide range of incidence angles of the impinging EM field.
To further analyze the response of the proposed metamaterial absorber against the polarization of the incident EM wave, we calculated the absorbance as a function of angle of polarization φ. The results are shown in Fig. 5. The φ is defined as the angle between the x-axis and the electric field E as demonstrated inside the figure. The angle of incidence θ of the EM wave is zero for these calculations. Due to the symmetric nature of the microslots, only a range of angles φ = 0° – 90° is considered for calculating the absorbance. Clearly, it can be noticed that absorbance at 2.77 THz (in red color) is around 90% for any angle of the polarization. The absorbance decreases slightly at the large values of φ, e.g., 70° – 90° which can be attributed to the mismatch of impedances. A similar trend of the absorbance is observed for resonant frequency of 3.42 THz and it is shown in dark blue color in the figure. As it was expected from the Fig. 3, the absorbance is little higher (∼10%) than that of the frequency of 2.77 THz. Furthermore, the absorbance almost remains constant (∼100%) for a range of incident angle of polarization φ = 0° – 90°. This behavior of absorbance as a function of φ appears due to the symmetric nature of the swastika-shaped microslots which are enable to store the same amount of the incident energy for any angle of polarization. It is noticeable the overall absorbance is more than 80% (dotted black line) for the both resonant frequencies. This promising result displays the relatively high insensitivity of the metamaterial absorber against the any state of polarization of the incoming electromagnetic wave in terahertz.
Fig. 5. Absorbance as a function of angle of polarization φ at resonant frequencies of 2.77 THz and 3.42 THz. The inset of the figure demonstrates the definition of φ.
Although, the fabrication of the proposed metamaterial absorber is not a part of this work, however, due to the used materials (Al and TiO2) and size of the device in microscale, it is feasible to manufacture such kind of structures by employing a laser surface texturing method. Furthermore, the design of the microslots is simple in a way that gaps or slots are aligned only along the vertical and horizontal directions on the Al film.
4. Conclusions
In summary, we proposed a simple design of a dual-band metamaterial absorber composed of swastika-shaped microslots. The absorbance spectra extracted based on numerical simulations have shown high resonances at two frequencies, 2.77 THz and 3.42 THz. The simulations were performed based on the finite element method (FEM). From the impressive results obtained based on the calculated angle and polarization dependent absorbance, the absorber has displayed considerably high insensitivity to a wide range of incidence as well as polarization angles. We envisage that the simple design coupled with the used materials will ease the fabrication process of the structure. The current study only focuses on the theoretical simulations and gives technical insight into the design and possible fabrication of the proposed metamaterial absorber. Experimental demonstrations are currently outside the scope of this study.
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