1. Introduction

Terahertz metamaterial absorbers have attracted the research interest of a wide range of researchers due to their great potential value and market vacancy. Different types of metamaterial absorbers with different frequency bands, absorption widths and numbers of absorption peaks have been proposed one after another [1–5]. Most of the currently available metamaterial-based structures for electromagnetic wave absorbers are passive, and their performance is determined once they have been prepared. This means that they have one obvious disadvantage: their resonant frequency and absorption intensity cannot be tuned flexibly. The increasingly complex electromagnetic applications require active, tunable electromagnetic metamaterial absorbers. Tunable metamaterial absorbers are far superior to non-tunable metamaterial absorbers in practical applications [6–7]. Due to the good market prospects of tunable metamaterial absorbers, more and more workers are devoting themselves to tunable metamaterial absorbers [7]. However, in the terahertz band range, most researchers have mainly focused on metamaterial absorbers with tunable absorption strength [8–13]. There is a lack of research on absorbers with high performance in terms of absorption form (broadband, narrowband) conversion. Therefore, there is a need to develop metamaterial absorbers with adjustable absorption forms and a large adjustment range in practical applications.

To achieve tunable functionality of the absorber in the terahertz band, we use the phase change material vanadium dioxide (VO₂). VO₂ has significant optical variation properties in the terahertz band, as well as a distinct infrared active phonon vibration peak in the 7-11 THz band [14–15]. The phase change properties of VO₂ are fundamental to its application in the terahertz band. And they were first observed in the laboratory by Morin in 1959: when the oxides of vanadium metal were heated, the lower valence oxides of vanadium could be converted from the semiconductor state to the metallic state [16]. The phase transition temperature of VO₂ is close to room temperature at around 68 degrees Celsius. There are virtually no limitations in terms of experimental and practical applications. Therefore, VO₂ has gained widespread interest as a room temperature, high speed phase change material [17].

VO₂ can undergo a phase change from an insulating state at room temperature to a stable, high loss metal state at higher temperatures. And the process of this phase change is reversible. The phase change from insulator to metal is accompanied by a steady increase in the conductivity of VO₂, which can vary in the range of 200 S/m to 200000 S/m [18–20]. VO₂ crystals have also changed their internal structure from monoclinic to tetragonal. Based on these properties, the optical properties of the VO₂ film can be changed by heating or cooling the film to a temperature near the phase change temperature. The phase change properties of VO₂ are well suited to the need for harmony in metamaterial absorbers. By exploiting the modulation properties of VO₂, tunable metamaterial absorbers based on the phase change material VO₂ can be fabricated [21–22]. As in 2020, Song et al. [23], designed a multilayer structure of absorber that allows switching between broadband and narrowband absorption using thin films and rings composed of VO₂ and metal crosses. The absorber achieves narrow-band absorption at 0.677 THz and an average absorption greater than 90% over a wide spectral range of 0.393 THz - 0.897 THz. In 2021, Wu et al. [24], achieved more than 90% absorption in the 2.34 THz to 5.64 THz range with an ultra-broadband perfect absorber composed of a VO₂ resonant ring. And the intensity of the absorption peak could be tuned up to 100% from 4% when the conductivity of the VO₂ was varied. However, terahertz absorbers that combine broadband absorption and narrowband absorption with a wider band and a simple structure have rarely been reported.

This paper proposes a tunable ultra-broadband terahertz absorber consisting of four VO₂ discs and a metal ring. By adjusting the temperature to vary the conductivity of the VO₂, it was found that the absorber allowed flexible switching between ultra-broadband and narrowband absorption. As the VO₂ disc is tuned to the metallic state (T=72 °C), a perfect absorption is achieved in the ultra-broadband range of 8.5 THz to 11 THz with an average absorption of >99%. The absorber also achieves a high average absorption of >95.8% in the huge range of 7.5 THz to 11 THz. This is far superior to previous reports of VO₂ based absorbers. As the VO₂ disc is adjusted to the insulated state (T=61 °C), a perfect absorption of >99.9% is achieved by the absorber at f=7.44 THz. A narrow band absorption is formed which has a high quality factor of 74.4. The absorption mechanism of the absorber is analyzed through plotting the electric field and current intensity distribution at different frequencies. We have also investigated the effect of different parameter variations on the absorption performance. Finally, we also demonstrate the process of metallic and insulating phase transitions in VO₂ by varying the absorption layer pattern. In conclusion, this combination of ultra-broadband and narrowband tunable terahertz metamaterial perfect absorbers is of great value in practice. Such as terahertz modulators, sensing, energy harvesting, switchable fields in the field of thermal emission, etc [25–28]. Our design also offers a wider range of ideas for tunable metamaterial absorbers.

2. Modeling and manufacturing methods

The tunable absorber we have designed is composed of three layers, as illustrated in Fig. 1. They form the reflector layer, the dielectric layer and the absorption layer of the absorber respectively. As can be seen in (b) of Fig. 1, the bottom metal layer is a thin gold (Au) film of height h1. The middle layer is a dielectric layer of height h2, which consists of silicon dioxide. The permittivity is equal to 2.13. The top layer consists of a Au ring and four VO₂ discs, which have a uniform height of h3. And the ring remains tangent to the discs. The internal and external radii of the ring are R1 and R2, respectively, and the radius of the disc is R3. When the VO₂ discs are metallic, the VO₂ discs together with the Au ring form the resonator of the absorption layer. The absorption layer is formed by the metal ring alone as the VO₂ is insulated. At this point the four VO₂ discs can be treated as a dielectric layer. The structural parameters of the absorber have been optimised using the finite element method via the COMSOL simulation platform. The final optimisation parameters are as follows: a = 35 μm, h1 = 8 μm, h2 = 5.75 μm, h3 = 0.1 μm, R1 = 12 μm, R2 = 13.5 μm and R3 = 4.77 μm.

 

Fig. 1. Structure of the tunable absorber. (a) Periodic units. (b) Front view of the absorber. (c) Top view of the absorber.

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The structure of the absorber unit repeats periodically in the xy-plane. We achieve this infinite array arrangement by setting periodical boundary terms in both X and Y directions. And a perfect match layer (PML) is set in the Z-direction. Due to the special nature of metamaterials, resonances of specific frequencies will occur when electromagnetic waves are incident on the absorber surface. The Drude model allows us to characterize VO₂ and Au optically in the terahertz range [28–29]. The dielectric constant of Au ${\mathrm{\varepsilon }_{Au}} = \frac{{1 - {\mathrm{\omega }_{p1}}^2}}{{\mathrm{\omega }({\mathrm{\omega } + \textrm{i}{\mathrm{\omega }_{\textrm{t}1}}} )}}$ where the bulk plasma frequency ${\mathrm{\omega }_{p1}} = 1.37 \times {10^{16}}{\textrm{s}^{ - 1}}$, and the collision frequency ${\mathrm{\omega }_{t1}} = 1.23 \times {10^{14}}{\textrm{s}^{ - 1}}$ [30]. In the terahertz range, the dielectric constant of VO₂ ${\mathrm{\varepsilon }_{V{O_2}}} = {\mathrm{\varepsilon }_\infty } - \frac{{{\mathrm{\omega }_{p2}}^2}}{{\mathrm{\omega }({\mathrm{\omega } + \textrm{i}{\mathrm{\omega }_{\textrm{t}2}}} )}}$. And ${\mathrm{\varepsilon }_\infty } = 12$ is the permittivity of VO₂ at infinite frequency and ${\mathrm{\omega }_{p2}}^2 = \frac{\sigma }{{{\sigma _0}}}{\mathrm{\omega }_{p0}}^2$. The conductivity σ can vary with the phase transition of VO₂, ${\sigma _0} = 3 \times {10^5}\;\textrm{S}/\textrm{m}$.

The electrical conductivity of VO₂ varies at different temperatures [31–32]. And the sudden change in conductivity is reversible, as shown in Fig. 2. It can be seen from the graph that the temperature rise curve is ahead of the temperature drop curve by a certain temperature. There is a thermal hysteresis line for the sudden change in conductivity of VO₂. In this paper conductivity σ is taken as: 200 S/m, 1000 S/m, 5000 S/m, 10000 S/m, 50000 S/m, 100000 S/m, 200000 S/m [31–32]. The plasma frequency of VO₂ has an initial value of ${\mathrm{\omega }_{p0}} = 1.45 \times {10^{15}}{\textrm{s}^{ - 1}}$ and a collision frequency of ${\mathrm{\omega }_{\textrm{t}2}} = 5.75 \times {10^{13}}{\textrm{s}^{ - 1}}$ [33–34].

 

Fig. 2. Variation of VO₂ with temperature. (a) Curve of conductivity of VO₂ with temperature. (b) Phase transition of VO₂ in the metallic and insulating states.

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The absorptance, reflectance and transmittance of the absorber in Fig. 1 were simulated using finite element analysis. No transmission will occur if the thickness is greater than the maximum skinning depth of the metal in the terahertz range. In the structural design, the thickness h1 of the underlying metal is bigger than the maximum skin depth. The underlying metal is a good barrier to the transmission of electromagnetic waves. The transmittance of the absorber $\textrm{T}(\mathrm{\omega } )= 0$, so we just need to consider the reflectance and absorption. The absorption equation $\textrm{A}(\mathrm{\omega } )= 1 - \textrm{T}(\mathrm{\omega } )- \textrm{R}(\mathrm{\omega } )$ is simplified to $\textrm{A}(\mathrm{\omega } )= 1 - \textrm{R}(\mathrm{\omega } )$ [35–38]. $\textrm{A}(\mathrm{\omega } )$, $\textrm{T}(\mathrm{\omega } )$ and $\textrm{R}(\mathrm{\omega } )$ above are the absorptance, transmittance and reflectance of the absorber respectively. They are all functions of the electromagnetic wave frequency $\mathrm{\omega }$. To achieve 100% absorption in our absorber, the reflectivity must be infinitely close to zero. From the impedance matching principle, we know that no reflection of electromagnetic waves occurs in the absorber when the overall impedance of the absorber is matched to the free space [39–41]. For this reason, we can adjust the impedance of the absorber by adjusting each parameter of the absorber to finally achieve the effect of perfect absorption. In order to make the absorber polarization insensitive, we designed the absorber to have a highly symmetrical structure. In addition to this, the absorber has been designed as a three-layer thin structure in order to reduce the difficulties in the actual production process. And the pattern of the absorption layer is very simple and not very difficult to process. It can be achieved by a dry etching process [42–44] on the silica substrate.

3. Results and discussion

Through simulation, we calculated the absorption of the absorber at different polarization modes (TE, TM) and different temperatures (phase change of the VO₂ disc with temperature), respectively, as shown in Fig. 3. From Fig. 3(a), it can be seen that the absorber has an average absorption of more than 95.8% in the ultra-broadband range of 7.5-11 THz. The absorption bandwidth is 3.5 THz and the absorber has the advantage of polarization insensitivity. It can be seen from Fig. 3(b) that the absorber can achieve a harmonizable perfect absorber integrating ultra-broadband and narrowband when the VO₂ disc undergoes phase transition. The absorber can be flexibly switched between narrow-band absorption and ultra-broad-band absorption through temperature regulation. When the VO₂ disc is metallic (T=72 °C, σ = 200000 S/m), the absorber achieves an average absorption rate greater than 99% in the ultra-broadband range of 8.5 to 11 THz. When the dioxide disc is in the insulating state (T=61 °C, σ = 1000 S/m), the absorber will form a narrow band absorption peak with a high quality factor. The absorber achieves an absorption of >99.9% at the electromagnetic frequency f = 7.44 THz with a quality factor of 74.4.

 

Fig. 3. Absorption curves of the absorber. (a) Absorption curves of the absorber in TE and TM modes. (b) Absorption curves of the VO₂ disc at different temperatures.

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Compared with absorbers of the same type, our design offers clear advantages and improvements, as shown in Table 1. Our absorber not only has a much wider bandwidth, but also absorbs much better. Although the designed absorber is slightly shorter in bandwidth for broadband absorption compared to that reported [45], our absorber is simpler in structure. The composition of only three structural layers means that our absorber is much easier to implement in practice.

Table 1. Some of the VO₂-based terahertz absorbers of recent years. a.VO₂-based broadband and narrowband switchable terahertz absorber; b.VO₂-based broadband terahertz absorber.

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In Fig. 4, we can see the process of the optimal development of the absorber structure parameters. This also shows that the geometric parameters have a non-negligible influence over the absorber's absorption performance. The ambient temperature is 72 °C and the VO₂ disc is in its metallic state. Its electrical conductivity corresponds to 200000 S/m [18–20]. In the following four discussions (a), (b), (c) and (d), one parameter is varied and the other parameters are held constant. As can be seen in Fig. 4(a), the absorption effect receives a certain influence as the outer diameter R2 of the Au ring increases. In the high frequency band part, the absorption effect can still be maintained at a high level. In the low frequency band part, the absorption effect changes relatively more. This is because as the radius of the outer ring increases, the interaction between the Au ring and the metallic VO₂ discs is weakened and the resonance effect is reduced. The change in the outer diameter of the Au ring, R2, has a smaller effect on the equivalent impedance of the absorber in the high frequency band and a larger effect on the equivalent impedance in the low frequency band. As can be seen in Fig. 4(b), the absorption intensity increases as the radius of the VO₂ disc, R3, increases. This is because the radius of the VO₂ discs determines the spacing between the discs. As the radius of the VO₂ disc gradually increases, the spacing between the discs decreases and the coupling between the discs increases. More electric dipoles are excited between the discs and cause electromagnetic resonance, thus increasing the absorption efficiency [24–25]. In Fig. 4(c) we plot the effect of different thicknesses of the dielectric layer on the absorption effect. When the thickness of the dielectric layer h2 is varied in the range of 5.50 μm to 6.50 μm, the absorption curve has a significant red-shift phenomenon. The absorption effect of the absorber in the high frequency band decreases and the absorption effect in the low frequency band increases. This is due to an increase in the thickness of the dielectric layer causing the equivalent impedance of the resonator in the top layer to change relative to free space [44–45]. As the thickness of the dielectric layer increases, the impedance matching condition in the high frequency section is gradually broken and the impedance in the low frequency section gradually matches the free space match [46–47]. The absorption of the absorber is still able to maintain good results over a wide range. In Fig. 4(d), the overall absorption of the absorber is minimally affected when the thickness h3 of the VO₂ disc is varied from 0.05 - 0.20 μm. At T = 72°C, the VO₂ disc is in the metallic state. At this point the VO₂ disc is present as part of the top resonator. At a thickness of 0.25 μm, the overall impedance of the absorber is out of phase with the free-space matching and the absorption effect is finally reduced. As the thickness of the resonator is varied in the range 0.05-0.20 μm, the resonator can effectively excite magnetic dipole oscillations throughout the absorber. Thus, the absorber is still able to maintain a high level of absorption over a wide range as we can see in the figure.

 

Fig. 4. Optimization process of each structural parameter of the absorber at ambient temperature T=72 °C. (a) Influence of the outer radius R2 of the Au ring on the absorption rate. (b) Influence of the radius R3 of the VO₂ disc on the absorption rate. (c) Effect of the thickness of the dielectric layer h2 on the absorption rate. (d) Effect of the thickness of the VO₂ disc h3 on the absorption rate.

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In Fig. 5, we plot the scanned absorption spectra of the key parameters R2, h2 that affect the effect of narrow-band absorption. At this time the VO₂ disc is in an insulating state with a conductivity σ = 1000 S/m. It can be seen from Fig. 5(a) that as the outer radius of the Au ring R2 increases, the absorption peak is red-shifted and the absorption intensity is much reduced. This is mainly due to the weakening of the current on the Au ring, and the coupling effect of the underlying metal plate is reduced, thus reducing the magnetic resonance [24–26]. As the thickness of the silica layer h2 increases, the absorption effect increases and then decreases by a small amount, as in Fig. 5(b). The position of the absorption peak is also red-shifted and has an optimal absorption value at h2 = 5.75 μm. This is because as the thickness of the dielectric layer increases, the propagation path of the electromagnetic waves propagating through it is affected, thus affecting interference cancellation [48]. The outer radius R2 of the Au ring has a much greater effect on the narrow-band absorption effect (Q-factor) than the thickness of the dielectric layer. Therefore, we need to have a precise control of the Au ring radius R2 during the production process.

 

Fig. 5. Optimization process of structural parameters of VO₂ disc at ambient temperature T=61 °C. (a) Effect of the outer radius R2 of the Au ring on the absorption rate. (During the scanning process, the inner and outer radii of the Au ring always maintain a spacing of 1.5 μm) (b) The effect of the silicon dioxide dielectric layer h2 on the absorption rate.

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Next we investigate the causes of ultra-broadband absorption in the absorber while the VO₂ disc is in its metallic state. We plotted the absorber surface current distribution as well as the internal electric field distribution at different frequencies, as shown in Fig. 6. Thanks to the highly symmetrical nature of our design, the absorber is characterized by its insensitivity to polarization [47]. In the following illustrations we have only drawn the absorber in TE mode, as the absorber in TM mode is similar. As can be seen in Fig. 6, at low frequencies, the electric field in the absorber is mainly concentrated near the Au ring. As the frequency increases from low frequencies, the field inside the absorber expands from the Au ring inwards and outwards and the current becomes more concentrated on VO₂ discs. The concentration of the electric field on the Au ring and VO₂ discs causes a large number of charges to collect on them, and the charges are of opposite polarity at opposite places. When external electromagnetic waves interact with the absorber, the opposite charges on the absorber surface form an electric dipole and resonate electromagnetically with the external electromagnetic waves [49–50]. The resonance results in an absorption peak at the corresponding frequency of the electromagnetic wave. The particular combination structure of Au rings and VO₂ discs allows the absorber to have multiple resonant frequencies in the 8.5-11 THz range, each of which produces strong absorption. Due to the close proximity of these absorption peaks, coupling between the absorption peaks occurs, resulting in a broadband absorption [51].

 

Fig. 6. Internal electric field distribution and surface current distribution of the absorber at different frequencies. (a)ƒ = 8.5 THz. (b)ƒ = 9.5 THz. (c)ƒ = 11 THz. (red arrows indicate currents, the size and direction of the arrows indicate the magnitude and direction of the currents).

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We will now analyse the reasons for the formation of narrow band absorption peaks in the absorber by using the results after transforming the absorber layer structure. The transition of VO₂ discs from the metallic to the insulating state will also be verified. Figures 7(a) and (b) show the absorption of the absorber with VO₂ discs removed and VO₂ discs structure retained at an ambient temperature of T = 61 °C. The VO₂ discs are insulated and have an electrical conductivity of 1000 S/m. As can be seen in Fig. 7, there is an absorption peak around 7.44 THz for both structures of the absorber. The first structure has an absorption peak of >95.8%. The absorber layer is formed by the Au ring alone, which is present as a resonator. When an external electromagnetic wave interacts with the Au ring, it causes an accumulation of charge on the metal ring, as shown in Fig. 8(a). The opposite charges accumulate at the ends of the Au ring, forming an electric dipole resonance [51–52]. This induced electric dipole resonance will have a coupling effect to the metal plate at the bottom, eventually leading to the formation of a magnetic dipole in the absorber. This magnetic dipole induces a strong magnetic resonance, resulting in a resonant absorption peak at f = 7.44 THz.

 

Fig. 7. Internal electric field distribution and surface current distribution of the absorber at different frequencies. (a)ƒ = 8.5 THz. (b)ƒ = 9.5 THz. (c)ƒ = 11 THz. (red arrows indicate currents, the size and direction of the arrows indicate the magnitude and direction of the currents).

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Fig. 8. Internal electric field and surface current distribution after the absorber surface structure transformation. (a) Au ring only. (b) Both Au ring and VO₂ discs are present, but VO₂ discs are in the insulated state.

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The second structure has an absorption peak of >99.9%. Since VO₂ discs in this case are in an insulating state, VO₂ discs act as the equivalent of a dielectric layer. The structure of the absorption layer is equivalent to the case when only the Au ring is present. The absorption peak can also be explained by the same principle. However the overall absorption effect of the second structure of the absorber is greater than that of the first structure. By comparing Fig. 8(a) and (b), the electric field distribution on the Au ring is similar under both structures, but the surface current density of the Au ring is more concentrated under the second structure than the first. This is because the presence of VO₂ discs corresponds to an increase in the thickness of the dielectric layer. The dielectric layer provides a useful space for the transmission of electromagnetic waves. As the thickness of the dielectric layer increases, the electric dipole coupling to the magnetic resonance increases, leading to greater absorption rates [53–55]. The final result is that the absorption effect is enhanced at all parts of the absorber. Indeed, the above results also provide indirect evidence of the phase transition of VO₂ discs from the metallic to the insulating state.

We also discuss the absorption effect of the absorber at different ambient temperatures, as shown in Fig. 9. There is a control value for the ambient temperature against the conductivity of VO₂ [56–57], as shown in Fig. 2. Therefore, here we use the conductivity of VO₂ to characterize the absorber at different temperatures. In Fig. 9, the conductivity in (a) corresponds to the temperature in (b). From the graph we can see that the absorber achieves broadband absorption in the range 8.5 to 11 THz as the conductivity σ of VO₂ discs is varied in the range 50000 to 200000 S/m. This conductivity range allows VO₂ discs to be treated as a metallic state. The absorber forms a conventional metal-dielectric-metal structure. Rational structural parameters are designed to match the impedance of our design to free space, resulting in perfect absorption of electromagnetic waves in the broadband range [58–59]. The absorber achieves narrow-band absorption around 7.44 THz as the electrical conductivity σ of VO₂ discs vary in the range 200 to 10000 S/m. The VO₂ discs can be insulated in this conductivity range and acts as a dielectric layer. The impedance matching condition of the absorber is disrupted by the VO₂ discs in the insulated state. As a result, the electromagnetic waves are strongly reflected and the absorption effect of the absorber is reduced. However, a significant local magnetic resonance is still present, constituting a narrow-band absorption peak. Therefore, it is possible to make the absorber flexible between narrow band and broadband band by regulating the temperature.

 

Fig. 9. Absorption effect of the absorber at different ambient temperatures. (a) Schematic of the absorption curve at different temperatures. (b) Contours corresponding to the absorption curves.

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4. Conclusion

This paper presents a tunable terahertz perfect absorber that combines ultra-broadband and narrowband in one. By controlling the temperature, the VO₂ discs is converted between the metallic and insulating states. This enables the absorber to switch flexibly between ultra-broadband absorption and narrowband absorption. When designed as a narrow band absorber, a peak absorption of >99.9% is achieved at f=7.44 THz with a quality factor of 74.4. When designed as a broadband absorber, a perfect absorption of >99% is achieved in the ultra-broadband range of 8.5 to 11 THz. To investigate the principle of the absorber producing broadband absorption, the electric field as well as the current distribution of the absorber at different frequencies were plotted. The metallic VO₂ discs were found to form a good resonator with the Au ring. The influence on the absorption performance of different structural parameters was also simulated and the absorber was found to have a certain process tolerance. The reason for the narrow-band absorption peak of the absorber was analyzed by varying the absorption layer structure. The process of phase transition from the metallic to the insulating state of VO₂ discs were also verified. In addition to this, the absorber was found to have the advantage of being polarization insensitive. As a result, we have designed a high-performance, coordinated terahertz perfect absorber that will play a major role in modulation, sensing, energy harvesting and switching devices.