Tunable Dual Broadband Terahertz Metamaterial Absorber Based on Vanadium Dioxide

Abstract

With the rapid development of terahertz technology, tunable high-efficiency broadband functional devices have become a research trend. In this research, a dynamically tunable dual broadband terahertz absorber based on the metamaterial structure of vanadium dioxide (VO₂) is proposed and analyzed. The metamaterial is composed of patterned VO₂ on the top layer, gold on the bottom layer and silicon dioxide (SiO₂) as the middle dielectric layer. Simulation results show that two bandwidths of 90% absorption reach as wide as 2.32 THz from 1.87 to 4.19 THz and 2.03 THz from 8.70 to 10.73 THz under normal incidence. By changing the conductivity of VO₂, the absorptance dynamically tuned from 2% to 94%. Moreover, it is verified that absorptance is insensitive to the polarization angle. The physical origin of this absorber is revealed through interference theory and matching impedance theory. We further investigate the physical mechanism of dual broadband absorption through electric field analysis. This design has potential applications in imaging, modulation and stealth technology.

1. Introduction

Terahertz (THz) waves generally refer to electromagnetic waves with a frequency ranging from 0.1 to 10.0 THz. They have a wide range of applications in the fields of wireless communication, sensors and imaging [1,2,3]. Because of their bright future, they have aroused great interest in the past few decades. With the rapid development of THz technology, the performance requirements of related functional devices are gradually increasing. Traditional natural materials have inherent shortcomings such as performance limitations, bulky and difficulty of integration, which can no longer meet the current needs for optic applications. Metamaterials (MM) composed of periodic subwavelength antenna arrays can solve the above problems. Because MM have the advantages of high efficiency, tunability and easy integration, various functional devices based on MM have been proposed, such as optical filters, absorbers and polarization converters [4,5,6,7,8,9]. Among various devices, the metamaterial perfect absorber (MPA) has received widespread attention due to its significant role in imaging, stealth technology and sensing applications [10,11,12]. The first MPA working in the microwave band was proposed by Landy et al. in 2008 [13]. A metal–insulator–metal (MIM) configuration is used to demonstrate MPAs. The basic unit structure of MPAs usually consists of three functional layers: a patterned metal layer on the top layer, a metal layer on the bottom layer and a dielectric layer in the middle. Under the guidance of this design, many types of MPAs have been reported, and the research on them is not limited to the microwave frequency range but gradually extends to all spectra related to technology, including THz, infrared, visible light and ultraviolet ranges [14,15,16,17,18,19,20]. So far, various MM have realized absorbers that work at THz frequencies. However, once the structure of the traditional MM absorber is determined, the electromagnetic response cannot be adjusted, and it has a fixed peak frequency and absorptance, which limits their practical application.

MPAs based on semiconductors, graphene and liquid crystals have been reported to realize the dynamic tunable characteristics [21,22,23]. Vanadium dioxide (VO₂), as a phase change material, varies greatly during the phase transition from insulator to metal by changing the temperature [24]. This is caused by the transformation of the structure from the insulating monoclinic phase to the metallic tetragonal phase around 68 °C. Therefore, combining MM with VO₂ is a promising method to achieve dynamic tunable characteristics in the THz range. In 2018, Song et al. presented an active absorption device based on VO₂ metamaterials, 90% absorptance bandwidth reaches 0.33 THz with a central frequency of 0.55 THz, and absorptance at peak frequencies can be continuously tuned from 30% to 100% [25]. In order to improve operation bandwidth, in 2019, Bai et al. designed a broadband THz absorber that the bandwidth of absorption rate above 90% is 1.25 THz, and the absorption rate can be continuously tuned from 15% to 96% [26]. To achieve multi-band absorption, in 2020, Huang et al. presented a dual broadband absorber, the bandwidths with the absorption above 80% were 0.88 THz and 0.77 THz in the frequency ranges of 0.56–1.44 THz and 2.88–3.65 THz, and the absorptance can be continuously adjusted from 20% to 90% [27]. Although the performance of absorbers based on vanadium dioxide metamaterials has been improved, the characteristics of the broad bandwidth, multi-band and active control still require more research to meet the expectations of practical applications.

For the classic three-layer structure absorber, the material and the structure of the top layer design are the most critical parts. In this work, we propose a tunable dual broadband THz absorber, which consists of a VO₂ structure with two perpendicularly intersecting ellipses and a circular hole in the center, and a metal ground plane separated by a dielectric spacer. The conductivity of VO₂ can be controlled by changing the temperature, thereby inducing the transition of VO₂ from an insulator to a metal. Under thermal control, the absorptance of the two bands of the absorber can be continuously tuned. The physical mechanism of MPA is investigated by the impedance matching and interference theory. The electric field analysis is discussed to gain a deeper understanding of the absorption mechanism. Moreover, it is verified that the absorptance is independent of polarization through the incidence of different polarization angles. The influence of the geometrical parameters of the structure on the absorber is discussed. This kind of tunable dual broadband perfect absorber has considerable application prospects in the field of THz technology.

2. Materials and Methods

The design structure of the absorber is shown in Figure 1. It consists of a three-layer structure: VO₂ on the top layer, a dielectric layer in the middle layer and a metal substrate on the bottom layer. The period of the structural unit is p = 30 μm. The top layer is composed of VO₂ with a thickness of 0.08 μm. As is shown in Figure 1b, the pattern is composed of two perpendicularly intersecting ellipses and a circular hole in the center. The lengths of the semi-major axis and semi-minor axis of the ellipse and the radius of the inner circle are a = 14 μm, b = 9 μm and c = 6 μm, respectively. The dielectric constant of VO₂ can be expressed by the Drude model [28], which is:

$$\epsilon (\omega )={\epsilon }_{\infty }-\frac{{\omega }_{\mathrm{p}}^2\left(\sigma \right)}{\left({\omega }^2+i\gamma \omega \right)}$$

(1)

where ${\epsilon }_{\infty }$ and $\gamma$ are 12 and 5.75 × 10¹³ rad/s, respectively. The relationship between plasma frequency and conductivity is:

$${\omega }_{\mathrm{p}}^2\left(\sigma \right)=\frac{\sigma }{{\sigma }_0}{\omega }_{\mathrm{p}}^2\left({\sigma }_0\right)$$

(2)

with ${\sigma }_0$= 3 × 10⁵ S/m and ${\omega }_{\mathrm{p}}\left({\sigma }_0\right)$ = 1.4 × 10¹⁵ rad/s. The middle layer is silicon dioxide (SiO₂) with a thickness of 12 μm and a permittivity (ε) of 3.8 [29]. The bottom layer is composed of gold with a thickness of 0.2 μm and a conductivity of 4.56 × 10⁷ S/m. As shown in Figure 1a, the incident wave propagates along the Z-axis from top to bottom, and the electric field polarization direction is along the X-axis. The spectral response of the structure is calculated by the finite element method. Periodic boundary conditions are applied in the X and Y directions, and a perfect matching layer is applied in the Z direction. The absorptance can be calculated by calculating the reflection coefficient (S₁₁) and the transmission coefficient (S₂₁). The expression of absorptance is:

$$A(\omega )=1-R(\omega )-T\left(\omega \right)=1-{\left|S_{11}\left(\omega \right)\right|}^2-{\left|S_{21}\left(\omega \right)\right|}^2$$

(3)

due to the thickness of metal is significantly larger than the skin depth to ensure no transmission, $T\left(\omega \right)$= 0. The absorptance here can be expressed as:

$$(\omega )=1-R(\omega )=1-{\left|S_{11}\left(\omega \right)\right|}^2$$

(4)

3. Results

The absorption spectrum and reflection spectrum of the absorber when VO₂ patterns are in the metal phase are shown in Figure 2a. The results show that there are two absorption bandwidths of 90% absorptance reach as wide as 2.32 THz from 1.87 to 4.19 THz and 2.03 THz from 8.70 to 10.73 THz under normal incidence. Moreover, there are also four perfect absorption peaks located at 2.3 THz, 3.6 THz, 8.8 THz and 10.4 THz, respectively. Due to the influence of the polarization angle is one of the most important properties of the absorber, we simulated the absorption spectrum under different polarization angles. Figure 2b is the color map under different polarization angles. Obviously, due to the symmetry of the structure, polarization is insensitive.

The conductivity of VO₂ can be controlled by adjusting the temperature. The change of conductivity can change the dielectric constant of VO₂. Therefore, the absorptance of the absorber can be continuously tuned by changing the temperature. When the conductivity of VO₂ changes from 200 S/m to 2 × 10⁵ S/m, we can tune the absorption from 2% to 94% at the corresponding frequency range, and the central position of the peak keeps unchanged, as shown in Figure 3. When the conductivity is 2 × 10⁵ S/m, VO₂ appears as a metallic phase, and the best performance of the absorber is achieved. The absorption peaks that appear in the two absorption bands of VO₂ at low conductivity can be explained by wave interference theory. The two absorption peaks in Figure 3b are at 3.21 THz and 9.63 THz, while the corresponding vacuum wavelengths are 93 μm and 31 μm, respectively. The refractive index in the dielectric layer is $\sqrt{\epsilon }$, and the corresponding wavelengths in the dielectric layer are 48 μm and 16 μm. The thickness of the dielectric layer is d = 12 μm, and the length is precisely the corresponding 1/4 and 3/4 wavelengths, which meets the destructive interference condition between reflection and incidence. When the structural phase of VO₂ is not a metallic phase, the position of the absorption peak is determined by the thickness of the dielectric layer. The presence of VO₂ is to tune the amplitude of absorption peaks. As the conductivity increases, the dielectric constant of VO₂ changes, and the insulating phase gradually approaches the metal phase, and the absorptance gradually increases.

4. Discussion

Impedance matching theory can be used to explain the phenomenon of perfect absorption. The effective impedance of the MPA can be expressed as [30]:

$$Z_{eff}=\sqrt{\frac{{\mu }_{eff}}{{\epsilon }_{eff}}}=\sqrt{\frac{{\left(1+S_{11}\right)}^2-S_{21}^2}{{\left(1-S_{11}\right)}^2-S_{21}^2}}$$

(5)

where ${\mu }_{eff}$ and ${\epsilon }_{eff}$ are the effective permeability and effective permittivity, respectively. It is well known that impedance matching can be achieved as both of them reach the same. The real and imaginary parts of the impedance are derived from the S parameter. As is shown in Figure 4, when the VO₂ conductivity is 2 × 10⁵ S/m, the real parts of the impedance are close to 1, and the imaginary parts of the impedance are close to 0 in the frequency range from 1.87 to 4.19 THz and from 8.70 to 10.73 THz. This means that the impedance of the absorber gradually matches with free space, which is the typical perfect absorber feature [27].

To further understand the physical mechanism of the absorber, we conducted an electric field analysis. Figure 5 shows the electric field distribution at the four resonance peaks. The first resonance peak is located at 2.3 THz, as shown in Figure 5a; the electric field is mainly concentrated in the gap between the long axis of the ellipse of the two structural units. The second resonance peak is located at 3.6 THz, as shown in Figure 5b; the electric field is mainly concentrated at the long axis of the ellipse and the edge of the inner ring of the unit structure. The combination of the overlapping regions of the two resonance spectra provides a guarantee for high-efficiency broadband absorption [31]. The third resonance peak is located at 8.8 THz, as shown in Figure 5c; the electric field is mainly concentrated in the inner ring and the junction of the two perpendicular ellipses. The fourth resonance peak is located at 10.4 THz, as shown in Figure 5d; the electric field is mainly concentrated at the junction of two ellipses and the gap area of the corresponding unit. Both resonance spectra provide the basis for the second broadband absorption. Due to the symmetry of the structure, similar phenomena also apply when the structure is under the Y-polarized incident wave.

To illustrate the importance of geometric structure parameters, it is necessary to verify the influence of geometric structure parameters on the absorber. Figure 6 shows the influence of the major axis of the ellipse a, the minor axis of the ellipse b, the radius of the inner circle c and the thickness of the medium d on the absorptance of the absorber. As shown in Figure 6a, when the major axis of the ellipse becomes longer, the absorption bandwidth becomes wider; however, the absorption efficiency decreases. When the major axis of the ellipse becomes shorter, the absorption bandwidth becomes narrower, but the absorption becomes higher. In Figure 6b, it is obvious that the minor axis of the ellipse has the same changing law. In Figure 6c, conversely, when the radius of the inner circle becomes shorter, the absorption bandwidth becomes wider, and the absorption efficiency decreases. When the radius of the inner circle becomes longer, the absorption bandwidth becomes narrower, and the absorption becomes higher. The position of the resonance peak varies with the change of the major axis and minor axis of the ellipse or the radius of the inner circle. The absorptance and bandwidth will change with the change of the resonance peak position. As shown in Figure 6d, when the thickness of SiO₂ increases, the absorption peak gradually shifts to low frequencies. At the same time, the number of absorption peaks increases and the bandwidth narrows. When the thickness of SiO₂ decreases, the absorption peak gradually shifts to high frequency, and the bandwidth becomes larger. However, the number of absorption peaks and the absorptance decrease. The position of the resonance peak is affected by the thickness of the medium. The position of the resonance peak and the absorptance of the entire absorber are affected by the SiO₂ and VO₂. VO₂ and SiO₂ determine the impedance of the proposed system and have a significant influence on the absorptance and bandwidth. The results further confirmed the important role of geometrical structure parameters in absorber performance. After optimizing the structural parameters, a high-performance tunable dual broadband terahertz absorber is obtained.

5. Conclusions

In conclusion, we propose a tunable dual broadband THz metamaterial absorber. Two VO₂ ellipses that intersect perpendicularly with a circular hole dug out of the center are used as the top structure, the middle layer is SiO₂, and the top layer is gold. Based on interference theory and impedance matching theory, we obtained a tunable absorber with which two bandwidths of 90% absorption reach as wide as 2.32 THz from 1.87 to 4.19 THz and 2.03 THz from 8.70 to 10.73 THz under normal incidence. By changing the conductivity of the VO₂, dynamic absorption control from 2% to 94% can be achieved. Moreover, due to the symmetry of the structure, the absorptance is insensitive to the polarization angle. We envision that our high-performance, tunable, dual broadband absorber may have potential in a vast range of applications in imaging, modulation and stealth technology.