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Abstract
A three-dimensional origami-structured absorber based on ${{\rm VO}_2}$ is designed. The unit structures of the origami absorber are folded from both sides to the middle, and a cavity is formed. After simulation, it is found that this absorber possesses insensitivity to polarized electromagnetic waves and stability at large incident angles. In addition, the origami absorber exhibits good absorption performance at low frequencies. An absorption band with absorptivity over 0.9 at 0.61–6.5 THz can be formed in TE mode. The coverage of the absorption band exceeds 10 octaves, and the relative bandwidth is 165.7%. In TM mode, the absorption band is located at 0.68–6.5 THz, which exceeds 9.5 octaves, and the relative bandwidth is 162.1%. We demonstrate the absorption mechanism by analyzing the electric field, surface current, and magnetic field distribution.
© 2022 Optica Publishing Group
1. INTRODUCTION
Metamaterials, a periodic array of sub-wavelength unit structures, are a sort of artificial material with peculiar properties. Metamaterials are widely regarded because of their regulable electrical response and magnetic response. The past decade has seen rapid development of metamaterials in many fields, for instance, antennas [1,2], cloaking [3], sensors [4,5], and absorbers [6,7]. A nearly perfect electromagnetic absorber, made up of a piece of metal line and a square split ring, was designed and manufactured by Landy et al. in 2008 for the first time, which predicted that absorption achieves approximately 96% [6]. Due to the narrow bandwidth of these absorbers, their applications in practical scenarios are limited. Many measures have been taken to optimize the performance of the absorber. One approach is to design absorbers with multiple absorption peaks through structures of multiple resonances. For example, Ma and his colleagues proposed an absorber composed of two square resonators [7]. It achieves two absorption peaks due to strong magnetic resonance. Hu and his workmates developed a multi-band absorber composed of dielectric spacers, a metal cross, and a metal rectangular ring with inwardly extending branches [8]. The values of the four absorption peaks at 0.68 THz, 1.27 THz, 2.21 THz, and 3.05 THz are respectively achieved at 98%, 97%, 98%, and 97%. Absorbers with multiple absorption peaks work well in applications such as detectors because of their high detection sensitivity. However, due to its narrow absorption band, there are many limitations in practical applications.
Therefore, many effective measures to achieve broadband absorption are put forward to break through the limitations of narrowband absorption. An effective method is to obtain broadband absorption by stacking multi-layer structures in the same unit cell. Xiong and his colleagues came up with a structure made up of three vertical layers of split metal square rings [9]. Through the combination of adjoining anti-reflection peaks caused by destructive interference, an absorption band located at 8.31–21 GHz is formed, which is above 90%. Sun and his workmates proposed a multi-layer structure consisting of three gradually changing split resonance rings stacked vertically on top of each other, which forms ultra-wideband absorption with a bandwidth approaching 60 GHz [10]. Another effective strategy is to obtain significant broadband absorption by arranging unit structures of different sizes with continuous absorption peaks along the wave vector [11]. Absorbers that broaden the absorption band through these methods have drawbacks such as being too thick, not easy to manufacture, and requiring precise parameters of every unit structure. Furthermore, the frequency selective surface is also a way to enhance the absorption intensity and broaden the absorption band due to its frequency-selective properties for electromagnetic waves [12–14]. The absorption band can be widened by utilizing materials that have properties of strong ohm loss, such as resistive patches [15–17]. Advantages of being more efficient, easier to achieve broadband absorption, lighter in weight, and easier to fabricate are shown intuitively in this way. But it is not practicable to load lumped elements in the THz band as well. In recent years, graphene has been widely used in the THz band due to its tunability [18–20]. A multi-layer graphene structure was proposed by Liu and his co-workers, which can form an absorption band with absorptivity greater than 0.9 at 1.12–3.78 THz [21]. By changing the Fermi level of graphene, the bandwidth and intensity of the absorption band can be controlled. Similarly, the bulk Dirac semimetal (BDS) has attracted much attention because its electrical conductivity can be controlled by doping [22] and biasing [23,24]. Due to their peculiar properties, many double-controlled absorbers [25,26] have been designed. For example, a terahertz absorber based on Dirac semimetals and water is proposed by Xiong et al., which can control the bandwidth and absorption rate of the absorption band in the range of 3.05–6.35 THz by temperature and Fermi level [26]. It can be seen that the relative bandwidth of these absorbers is not wide enough, and it is difficult to form an absorption band at low frequencies. In addition, the absorptivity for obliquely incident electromagnetic waves tends to drop significantly.
In this paper, different from previous absorbers that arrange unit structures periodically on the same plane, we design a kind of absorber similar to an origami structure, which greatly optimizes the performance of the first designed plane absorber. It exhibits good stability under the irradiation of incident waves and polarized waves at different angles and forms ultra-broadband absorption at extremely low frequencies in the THz band. For TE and TM waves, the plane absorber can achieve an absorption band with absorptivity greater than 0.9 in the range of 0.608–2.06 THz, longer than three octaves, and the relative bandwidth is 108.8%. In TE mode, the absorptivity of the origami absorber in the 0.61–6.5 THz range is greater than 0.9. It can be calculated that the relative bandwidth is 165.7%, and the absorption range is longer than 10 octaves. In TM mode, the absorption band is formed at 0.68–6.5 THz, and the relative bandwidth is 162.1%. The effects of different incidence and polarization angles on absorption performance are also discussed. At the same time, we analyze the mechanism of absorption by calculating the electric field, surface current, and magnetic field distribution.
2. STRUCTURE
The geometric structure of the plane absorber is displayed in Fig. 1. The structure is made up of two parts: a backplane and a ${{\rm VO}_2}$-based hemispherical resonant structure perpendicular to it. The bottom of the plane absorber is depicted in Fig. 1(a). As portrayed in Fig. 1(b), the hemispherical resonant structure is composed of a single unit structure rotated at an equal angle of 45°. The unit structure is composed of split resonance rings formed by two 1/4 concentric cylinders, as portrayed in Fig. 1(c). The backplane is made of a gold square, and the central area of the backplane is hollowed out and connected to a bowl-shaped ${{\rm VO}_2}$ hemispherical, gradually spherical shell structure. The conductivity of the gold is ${6.5} \times {{10}^7}\;{\rm S}/{\rm m}$. Figure 1(d) displays the front view of the bottom plate, and Fig. 1(e) shows the external display of the plane absorber. It can be seen that the resonant structure is embedded in the substrate. Figure 1(f) portrays the bottom view and the cross section of the bowl-shaped ${{\rm VO}_2}$ hemispherical, spherical shell structure. Except for Fig. 1(e), in other figures, we hide the silicon dioxide substrate to better show the rest of the structure. Triggered by a change in temperature, ${{\rm VO}_2}$ will undergo a phase transition from an insulating phase to a metallic phase [27], and its electrical conductivity will change dramatically. In this paper, we chose to set its conductivity to ${2} \times {{10}^5}\;{\rm S}/{\rm m}$ [28]. The dielectric substrate uses silicon dioxide, and the other detailed structural specification are listed in Table 1.
Fig. 1. Display of the plane absorber: (a) bottom view of the plane absorber, (b) front view of the plane absorber, (c) unit resonant structure, (d) front view of the bottom plate (e) external view of the plane absorber, and (f) bottom view and cross-section view of the bowl-shaped ${{\rm VO}_2}$ hemispherical, spherical shell structure.
Table 1. Structural Specification of the Absorbers
After the performance of the plane absorber is simulated and analyzed, we propose a new structure (exhibited in Fig. 2) to enhance the absorbing properties. Similar to the situation in Fig. 1, we also hide the substrate to better show the structure of the absorber. The unit structure of the horizontal and periodic arrangement on the left and right sides is folded 70° from both sides to the middle. We also extended the branches of the middle part of the split resonance ring. The three-unit components [shown in Fig. 2(b)] are named B, A, and C, and the slits [displayed in Fig. 1(a)] of the vertical split resonance ring are marked as I, II, and III. The scales of unit components A, B, and C are set to one, 0.8, and 0.95, respectively. In this paper, the commercial software High Frequency Structure Simulator (HFSS) is used to calculate the properties of the absorber. The electromagnetic wave of normal incidence propagates in the ${-}z$-axis direction. According to the definition of TE mode, the electric vector is along the $y$ axis, and the magnetic vector is along the $x$ axis. According to the definition of TM mode, the electric and magnetic vectors are parallel to the $x$ axis and $y$ axis. The absorptivity can be calculated by $A(\omega) = {1} - R(\omega) - T(\omega) - P(\omega)$, where $R(\omega)$, $T(\omega)$, and $P(\omega)$ stand for reflectance, transmissivity, and polarization conversion rate, respectively. ${S_{11}}$ and ${S_{21}}$ are defined as the reflection coefficient and transmission coefficient of the scattering parameters, severally, where $R(\omega) = |{S_{11}}{|^2}$, $T(\omega) = |{S_{21}}{|^2}$. Therefore, the above formula can be expressed as $A(\omega) = {1} - |{S_{11}}{|^2} - |{S_{21}}{|^2} - P(\omega)$ also.
Fig. 2. Structure display of the origami absorber: (a) front view, (b) bottom view, and (c) perspective view.
3. RESULTS AND DISCUSSION
Figure 3 shows the absorptivity curves of the plane absorber at normal incident angles. In addition, the reflection, transmission, and polarization conversion spectra are also given in the figure. Because of the bottom plate, the electromagnetic wave is prevented from passing through, so the transmittance is zero. Therefore, the formula will change to $A(\omega) = {1} - R(\omega) - P(\omega) = {1} - |{S_{11}}{|^2} - P(\omega)$, which can be demonstrated from the curves plotted in Fig. 3. By definition, the relative bandwidth can be calculated by the formula $BW = {2}$(${f_H} - {f_L})/({f_H} + {f_L})$ [29], where ${f_H}$ can be interpreted as the upper limit frequency, and the meaning of ${f_L}$ is the lower limit frequency.
From the curves depicted in Fig. 3, it can be proved that the plane absorber can form an absorption rate exceeding 90% in the range of 0.608–2.06 THz in TE and TM modes, approximately 3.4 octaves. Its relative bandwidth is 108.8%. To enhance the absorbing quality of the plane absorber, we propose the origami absorber. The absorption band of the origami absorber [depicted in Fig. 4(a)] is located at 0.61–6.5 THz in TE mode, with a relative bandwidth of 165.7%, which exceeds 10 octaves. TM mode is displayed in Fig. 4(b). The absorptivity in the 0.68–6.5 THz range is above 90%. Furthermore, the absorption band is greater than 9.5 octaves, and its relative bandwidth is 162.1%.
Due to the characteristics of split resonant rings, absorbers using this resonant structure are usually sensitive to obliquely incident electromagnetic waves [30]. In practice, however, the direction of electromagnetic radiation is usually tilted. Therefore, the absorptivity of the origami absorber for incident waves and polarized waves at different angles is also simulated and analyzed. Figure 5(a) shows the circumstances in TE mode. When the incident angle ($\theta$) is 20°, the absorptivity at low frequencies declines slightly, and the absorption rate greater than 0.9 is divided into two parts: 0.602–0.716 THz and 0.758–6.5 THz. When $\theta = {40}^\circ$, a narrow absorption peak appears at 0.563–0.617 THz with the highest absorptivity of 0.99, and the absorptivity is greater than 0.9 in the range of 0.773–6.5 THz. When $\theta = {60}^\circ$, the initial absorption band becomes many narrow bands, and there is an absorption peak at 0.536–0.566 THz with the highest absorption rate of 0.98. The absorption rates in frequency bands of 1.175–1.445 THz, 1.55–2.07 THz, 2.357–2.477 THz, 2.534–2.636 THz, 2.735–3.308 THz, and 3.455–3.5 THz are all greater than 0.9. When $\theta = {80}^\circ$, the absorption performance deteriorates drastically, and there is an absorption peak with the highest absorption rate of 0.97 at 2.321–2.345 THz. As depicted in Fig. 5(b), the curves for the TM wave do not change with $\theta$. When the incident angles gradually increase, the absorptivity curves at low frequencies slightly move forward. Therefore, a conclusion can be drawn that the origami absorber greatly enhances the performance of the plane absorber proposed at the beginning of the paper, and it has good incident angle stability and can be adapted to various application scenarios. Physically, it can be considered from the following aspects: (1) the given absorber has a symmetrical structure, so it exhibits good stability for electromagnetic waves incident at different angles; (2) when electromagnetic waves with different incident angles are irradiated, one of the three-unit structures of this absorber is approximately normal incidence; (3) the three-unit structures of the absorber form a U-shaped resonant cavity. The incident electromagnetic wave has a long optical path, so multiple reflections and transmission will occur.
Fig. 5. Absorption spectra of the origami absorber for (a) TE and (b) TM waves at oblique incident angles.
In TE and TM modes, the absorptivity spectra at different polarization angles ($\varphi$) are portrayed in Figs. 6(a) and 6(b). In TE mode, the absorptivity spectra hardly change with the increase in polarization angles. Meanwhile, the spectra at low frequencies will shift backward. When $\varphi = {80}^\circ$, the absorption curve with absorptivity greater than 0.9 will shift backward from 0.61–3.5 THz at normal incidence to 0.66–3.5 THz. Analysis in TM mode is similar to that in TE mode. Most of the spectra do not change with polarization angles, and the spectra at low frequencies will move forward with the increase in $\varphi$. When $\varphi = {80}^\circ$, the absorption curve with absorptivity greater than 0.9 will move forward from 0.656–3.5 THz at normal incidence to 0.611–3.5 THz. Therefore, the origami absorber can be considered to be polarization insensitive.
Considering the influences of parameter precision on absorption performance in the actual manufacturing process of the absorber, we calculate the variation of the absorptivity curve under different parameters. When the value of ${h_2}$ is 9 µm, 14 µm, and 19 µm, the absorption performance has in turn been enhanced. When ${h_2} = {19}$, the absorption rate in the TE mode depicted in Fig. 7(a) is above 0.95, and the relative bandwidth is 165.7%. When ${h_2}$ changes from nine to 19, the absorption rate in the range of 1.1–1.5 THz will increase from around 0.9 to more than 0.95. As exhibited in Fig. 7(b), the absorption spectra for TM waves at low frequencies shift slightly forward as ${h_2}$ increases. It can be seen that the absorption performance is greatly improved with the increase in ${h_2}$.
The ratio between units B, A, and C is also an important parameter for origami absorbers. The variations of absorption spectra with the scaling factor in TE and TM modes are depicted in Figs. 8(a) and 8(b), respectively. When the scale of C becomes larger, the absorption performance at 3.2–3.3 THz will decrease, as displayed in Fig. 8(a). When the scales of B, A, and C are 0.9, one, and 0.95, respectively, the absorption rate at 3.25 THz will drop to 0.91, but the absorption rate in the range of 0.61–6.5 THz is still above 0.9. When the proportion of B gradually increases, the absorption rate at 2.2 THz will decrease, as portrayed in Fig. 8(b). When the ratio of C increases to 0.9, the range of absorption rate greater than 0.9 will be split into two parts: 0.68–2.15 THz and 2.28–6.5 THz.
4. THEORETICAL ANALYSIS
To investigate the absorption mechanism, the electric field and surface current distributions at 1.57 THz are analyzed. The electric field distributions of components B, A, and C, and the front view of the distributions of the overall structure in TE mode are exhibited in Figs. 9(a) and 9(b), respectively. According to the labeling of the gap position in Fig. 9(a), for structure A, the electric field exists mainly at gaps I, II, and III. For gap III in TE mode, there is an electric field distribution only on elements aligned along the electric field direction. For unit structure B, the cells are distributed mainly in gaps I and II, and gap III is marked by circles; the edge parts of the four resonant rings indicated by the arrows also have electric field concentrated distribution. The electric field distribution on unit structure C is similar to the distribution on unit structure B. The electric field distributions of units B, A, and C, and the front view of the distributions of the overall structure in TM mode are exhibited in Figs. 9(c) and 9(d). For component A, the electric field is located mainly at gaps I and III of the split rings arranged along the direction of the electric field. For units B and C, the electric field exists mainly at the three slits, and the outer edge of the resonant ring is indicated by the arrows. Then the positions where these electric fields are concentratedly distributed can be considered to be equivalently distributed with some positive charges.
Fig. 9. Electric field distributions at 1.57 THz: (a) distributions of units B, A, and C in TE mode, (b) front view of distributions in TE mode, (c) distributions of units B, A, and C in TM mode, and (d) front view of distributions in TM mode.
As shown in Fig. 10, the current distribution on the metal backplane in TE and TM modes is at 1.57 THz. As shown by the positions of the circles in the figures, the current is concentrated mainly in the four corners of each square metal plate, and the current flow direction is marked by the arrows in the figure. In TE mode, the current flows in the direction of the $y$ axis. In TM mode, the current flows in the direction of the $x$ axis. So its direction is regulated by the electric field. These places where the current is concentrated on the bottom plate can be equivalent to some negative charges. When the origami absorber is excited by normally incident electromagnetic waves, the absorption mechanism can be elaborated as follows: the ${{\rm VO}_2}$-based hemispherical resonant structure and the metal plate can be equivalent to electric dipoles, and the energy is consumed by the magnetic resonance caused by the electric dipoles. Obviously, when the electromagnetic wave is incident to two wires, different kinds of surface current distributions can be obtained. If the two wires maintain an anti-parallel current, magnetic resonance can be formed. In such a case, it also can be looked at as the positive and negative charges being concentrated at both ends of the two wires [31]. So the electric dipole causes the magnetic resonance.
Fig. 10. Distribution of surface currents at 1.57 THz: (a) center and left metal plates in TE mode; (b) center and right metal plates in TE mode; (c) center and left metal plates in TM mode; (d) center and right metal plates in TM mode.
Furthermore, the cross section of the magnetic field distribution of the $x {-} z$ plane ($y = {0}$) at 1.57 THz and 2.03 THz are displayed in Fig. 11. In TE mode, the magnetic field distribution at 1.57 THz is displayed in Fig. 11(a). As shown by the circles marked in the figure, for components B and C, most of the magnetic field exists at gaps I and II. For component A, the magnetic field presents mostly at the lower half of the split resonant ring. In TM mode, the magnetic field occurs mostly at gaps II and III, as displayed in Fig. 11(b). Furthermore, some magnetic field distribution can be found above the origami absorber and in the cavity, as marked by the ellipses. The analysis at 2.03 THz is similar to that at 1.57 THz. The metal base plates of the two side unit structures and the middle unit structure form a cavity, and the incident electromagnetic wave will be reflected back and forth between the metal base plates on both sides. These two reflectors together with the intervening ${{\rm VO}_2}$ resonant structure and the silicon dioxide dielectric substrate form a low Q-factor lossy Fabry–Perot (FP) cavity, causing broadband light absorption due to the FP resonance [32–34]. In addition, multiple reflections and transmissions and dielectric losses are also important factors leading to broadband absorption. The magnetic field exists mostly in the cavity formed by the origami structure, and the magnetic field in the cavity at 1.57 THz is weaker than that at 2.03 THz, so the cavity resonance at 1.5 THz is weaker than that at 2.03 THz. Therefore, the ultra-broadband low frequency absorption of the origami electromagnetic absorber is caused mainly by magnetic resonance and cavity resonance.
Fig. 11. Cross-sectional view of the magnetic field distribution on the $x {-} z$ plane at 1.57 THz in (a) TE and (b) TM modes. Cross-sectional view of the magnetic field distribution on the $x {-} z$ plane at 2.03 THz in (c) TE and (d) TM modes.
5. CONCLUSION
A ${{\rm VO}_2}$-based plane absorber is designed first, which can form ultra-wideband absorption at low frequencies. For TE and TM waves, the absorption bands located at 0.608–2.06 THz can be formed by the plane absorber, and its relative bandwidth is 108.8%. Subsequently, to optimize its performance, we designed the origami absorber, which is obtained by folding the horizontally periodically arranged unit structure on both sides of the plane absorber 70° to the middle. In TE mode, an absorption band in the range of 0.61–6.5 THz can be formed, and its relative bandwidth is 165.7%. In TM mode, the absorption rate in the range of 0.68–6.5 THz is above 90%, and the relative bandwidth is 162.1%. It can be seen that the performance of the origami absorber has been greatly improved compared with the plane absorber. After analyzing its absorption spectra at different incident angles ($\theta$), it is found that its absorptivity in TE mode can remain stable until the value of $\theta$ reaches 60°. In TM mode, the absorption curve is invariant with the incident angles. At the same time, the absorption band will shift forward with the increase in the value of $\theta$, and it is found that the origami electromagnetic absorber has the property of polarization insensitivity. By analyzing the electric field diagram, the surface current diagram, and the magnetic field diagram, it is known that when the electromagnetic wave excites the origami absorber along the ${-}z$-axis direction, the energy will be lost by the magnetic resonance, cavity resonance multiple reflections and transmissions, and dielectric losses. The origami absorber will have far-reaching research significance and application value in the fields of sensing, electromagnetic stealth, electromagnetic compatibility, imaging, etc. Since its metal base plate is hollowed out, it may be able to work in harsh environments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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