Flexible Terahertz Metamaterials Absorber based on VO₂

Abstract

Terahertz (THz) metamaterials have attracted great attention due to their widely application potential in smart THz devices; however, most of them are fabricated on rigid substrate and thus limit the exploration of flexible THz electronics. In this paper, a flexible THz metamaterial absorber (MMA) incorporated with phase change material vanadium dioxide (VO₂) is proposed. The simulation results indicate that two absorption peaks at around 0.24 THz (marked as A) and 0.46 THz (marked as B) can be observed by designing a I-shaped metamaterial combined with split ring structure. The strong absorption over 92% at 0.24 THz is bending-insensitive, but the absorption at 0.46 THz is bending-sensitive, across the bending angle in the range of 0–50 degrees. Moreover, dynamic modulation of the absorption can be achieved across the insulator-metal phase transition of VO₂. Particularly, the absorption of the A-peak can be tuned from 99.4% to 46.9%, while the absorption of the B-peak can be tuned from 39.6% to 99.3%. This work would provide significance for the design of flexible THz smart devices.

1. Introduction

Terahertz (THz) wave are located between 0.1–10 THz range and has been widely investigated due to its great application potential in next-generation communication, imaging technology [1], space remote sensing [2], non-destructive testing [3], etc. Particularly, the development of THz technology strongly leads to the development of THz wave manipulation devices, including switches [4], modulators [5], filters [6], absorbers [7], and polarizers [8], etc.; however, the weak response between THz waves and natural materials severely limits their development. Fortunately, metamaterials composed of subwavelength unit structures with supernatural properties that conventional materials do not possess provide a new way to solve the problem [9].

THz MMAs can efficiently absorb electromagnetic waves due to the tunable electromagnetic properties of artificially designed unit structures. Although the MMAs reported can achieve high absorptivity, most of them still have many drawbacks, such as single wave band, narrow receiving angle, fixed resonant frequency and absorption intensity, which greatly limit their practical applications [10,11,12,13,14]. Additionally, most of the MMAs can only achieve static electromagnetic absorption; once the processing is completed, their absorbing performance will be fixed. To address this issue, tunable dielectric materials are incorporated into the structure of the MMA to achieve dynamic manipulation of THz waves [15,16,17,18]. For example, Liu et al. propose a broadband-tunable THz absorber based on VO₂. This absorber can achieve a maximum tunable range of 5% to 100% by external thermal excitation, and it achieves more than 80% absorption in the 2.0 THz bandwidth [19]. Mou et al. propose a flexible, thermally convertible THz metasurface, whose structure can achieve ultra-broadband absorption from 0.398 THz to 1.356 THz when the ambient temperature reaches 358 K. Additionally, it achieves more than 90% absorption with a relative absorption bandwidth of 109.2% [20].

VO₂ is a thermally induced phase transition metal oxide that undergoes a reversible transformation from a low-temperature insulating phase to a high-temperature metallic phase near 340 K, accompanied by reversible changes in its optical, electrical, and magnetic properties [21]. Therefore, by inducing the phase transition of VO₂ through temperature modulation and altering its conductivity, dynamic control of THz waves can be achieved. In addition, the reports on phase-change-material-integrated THz components are mostly limited to rigid substrates, which cannot meet the flexible and lightweight requirements of some application scenarios. Flexible metamaterials offer the potential to be flexible, stretchable and reversible, which helps to manipulate electromagnetic waves according to specific requirements. Flexible metamaterials can therefore be used for curved surfaces in a range of devices or installations, which makes them promising for a wide range of innovative applications, including mobile and wearable devices [22], stealth [23], smart skin [24], etc. Additionally, by integrating metamaterials onto flexible substrates, flexible metamaterials can be realized. For example, Wang et al. created a stretchable, microwave-invisible photonic skin made of rigid scales using pangolin-inspired metamaterial design [25]. A flexible spiraling elastic metasurface has been used to build a generic haptic interface, which is capable of distinguishing various tactile sensations by locally amplifying both incoming displacements and forces in a wide range of elastic waves [26]. Such compelling achievements provide superb boilerplates for flexible THz MMAs. Xiao et al. propose a flexible and ultra-wideband THz wave absorber that keeps an average power absorptance over 98.9% from 0.1 to 2.5 THz and that can function well in bended states and after 300 times bending cycles [27]. This MMA is expected to be applied to wearable devices, wireless communications and biological sensing due to the flexibility, high-absorptance performance and ultra-wideband operation of the device. Nowadays, how to fabricate flexible and tunable THz MMAs with a uniformly high absorptance across the entire THz band merely based on traditional bulk materials is still a challenging but meaningful task.

In this paper, we proposed a flexible VO₂-based THz-tunable MMA. The I-shaped metamaterial combined with split ring structure achieves nearly perfect absorption at 0.24 THz and another absorption at 0.46 THz at normal incidence. The absorber is bending-insensitive at 0.24 THz and bending-sensitive at 0.46 THz before the phase transition of VO₂. Moreover, the tunable absorption can be achieved by triggering the phase transition of VO₂. This work would provide significant insights for the development of flexible THz smart devices.

2. Materials and Methods

The microstructure of the proposed metamaterial array is shown in Figure 1. The absorber continues the basic metal–dielectric-metal structure. The top and bottom metal layers are both gold, and the thickness is 0.3 μm and 2 μm, respectively. The main function of the bottom metal plate is to prevent THz wave transmission through the sample. The middle layer is mica with a dielectric constant of 6.7 and a thickness of 40 μm. The top layer is a periodic gold unit array incorporated with VO₂. The unit is composed of an I-shaped resonator and split ring. The VO₂ is embedded in both sides where the split ring meets the metal bar.

To confirm transmission variations, the designed MMA structure in Figure 1 was simulated by finite element simulation using the commercial software CST Microwave Studio. In the calculation, the x-direction and the y-direction is the unit cell condition, and the z-direction is open (add space) using. THz waves are incident on the absorber along the angle between the plane of incidence and the z-axis, and the electric field of the incident wave is polarized along the y direction, and the magnetic field is polarized along the x direction. Two metallic layers of this MMA were modeled as lossy metal gold with a frequency-independent conductivity (r) of 4.56 × 10⁷ S/m. We calculate the THz reflectivity (R), transmissivity (T), and absorptivity (A) in detail. The absorptivity A can be calculated by the equation A = 1 − R − T = 1 − |S₁₁|² − |S₂₁|², where S₁₁ and S₂₁ are reflection coefficients and transmission coefficients, respectively. At this time, the thickness of the metal film is far greater than the skin depth of the incident electromagnetic wave, and the metal film used can completely prevent the transmission of the incident beam. In addition, by selecting an appropriate dielectric layer thickness to match the impedance of the metamaterial with that of the air, the absorbance A can be simplified as A = 1 − |S₁₁|². When S₁₁ is very small, even close to zero, A becomes infinitely close to 1.

3. Results and Discussion

Figure 2a illustrates the absorption curves of the proposed MMA at optimal structural parameters and normal incidence. At a temperature of about 323 K, below the phase transition temperature, VO₂ can be considered an insulator with a conductivity of 10 S/m. The simulation results show that on a normal incidence of 0 degrees, the designed MMA can produce two resonant peaks (marked as A and B) with frequencies of 0.24 THz and 0.46 THz and absorptivity of 99.4% and 39.6%, respectively.

To understand the absorption mechanism of this absorber, we calculate the electric field distribution, surface current density and magnetic field distribution of absorption peaks A and B; the results are shown in Figure 2b–g. For the resonance peak A at 0.24 THz, the electric field distribution is weak, while the current on the vertical metal bar is opposite to the current on the bottom metal plate. The I-shaped metallic resonators can be modeled as a LC circuit, in which the capacitance (C) result from the electric field distribution in the gaps between the adjacent periodic I-shaped metallic resonators, and the inductance (L) is related to the current distribution in the metallic wires, and leads to a strong LC resonance. In addition, the magnetic field distribution in Figure 2d also provides further evidence. The magnetic field is mainly concentrated on the vertical metal rod. Strong magnetic field aggregation can also be found in the insulating medium layer under the metal arrays and non-metal array. Different from the field distribution characteristics of resonance peak A, the electric field distribution of peak B focuses on the gap of the split ring. The magnetic field is mainly distributed in the metal area of the split ring, and strong magnetic field accumulation can be found in the insulating dielectric layer under the metal array.

To better interpret the formation mechanism of absorption peaks, we decompose the unit structure into an I-shaped structure and split ring structure, and analyze their electromagnetic characteristic in detail. As shown in Figure 3a, the I-shaped structure induces a resonant peak with an amplitude of 0.90 at 0.26 THz. It can be ascribed to the LC resonance [28] according to:

$$f=\frac{1}{2\pi \sqrt{LC}}$$

(1)

where f decreases when L or C increases. To better explain the mechanism of the resonance curve, we simulate the distribution of the electric field, surface-current density, and magnetic field of the I-shaped structure at the formant. The surface-current density distribution at 0.26 THz in Figure 3c shows that the current flow on the vertical metal rod is in the opposite direction to the current flow on the metal base plate. Since no loop will be formed, resonance will eventually occur, which can also prove the LC resonant characteristics of this structure. It can be seen from Figure 3d that the strong magnetic field is mainly concentrated on the metal vertical pole. Figure 3e is the absorption spectrum of the THz waves normal incidence to the split ring. It can be seen that there is an absorption peak at 0.46 THz with an absorptivity of 38.25%. At this time, VO₂ is insulating, the magnetic field concentrates mainly on the sides of the split ring and generates a large amount of current in the opposite direction to the base. There is almost the same peak intensity and position for both resonant frequency structures as for the whole structure in Figure 2a, providing evidence that the two absorption peaks from the MMA are independently contributed by the I-shaped and split ring. For the peak positions, the small difference is due to the loading effect when the two resonators are combined. This means that each absorption peak responds to the contribution of a different sub-element that constitutes the unit cell of the MMA structure. Thus, the overall absorption spectrum appears as a superposition of the contributions of each sub-element [29].

Most traditional THz absorbers use inflexible metamaterials, which limits their application prospects. Since the overall thickness of the proposed structure is only 42.3 μm, it can be flexibly bent and easily to conform to the curved target. For cylindrical objects covered with absorbing material, when the plane electromagnetic wave irradiates to the surface of the object, it can be equated to the oblique incidence of the electromagnetic wave at different angles [30]. Thus, we use the incidence angle to simulate its bending state. Next, we will analyze the effects of different incidence angles on the performance of the designed MMA. Additionally, the results are shown in Figure 4a, where Figure 4b is the dot plot of the variation in absorptivity at different incident angles for 0.24 THz and 0.46 THz. It can be seen from Figure 4a that peak A still has near-perfect absorptivity (more than 92%) after scanning at 0–50 degrees. When the peak resonance frequency is 0.24 THz, the absorption line width is 0.01 THz. It should be noted that the so-called absorption line width refers to the full width of the maximum half width. In this case, it refers to the span with absorption of 50%. To understand the device performance further, we have calculated the quality factor for the resonance modes. The quality factor is typically defined as

$$Q=\frac{f_{res}}{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}$$

(2)

of which f_res is the resonance frequency of the absorption peak. We can calculate that the Q value at 0.39 THz is 51.03 at an oblique incidence of 30 degrees, but 48.81 at an oblique incidence of 50 degrees, which means that the Q-factor of the resonant mode near 0.39 THz decreases as the angle of oblique incidence increases. This phenomenon can be attributed to the physics of bound states in the continuum (BICs). BICs are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away [31]. Among the many causes of metamaterial BICs in metamaterials, coupled mode theory (CMT) is a flourishing and widespread theory that is widely used in many systems [32,33,34,35]. Here, BICs and quasi-BICs come from metamaterial structures with I-shaped and split ring coupling.

Additionally, the numerical simulation results show that two resonance peaks are generated at 0 degrees of incidence with frequencies of 0.24 THz and 0.46 THz, respectively, and that four resonance peaks are generated at 50 degrees of incidence with frequencies of 0.24 THz, 0.4 THz, 0.46 THz, and 0.57 THz, with absorption rates of about 92.3%, 71.3%, 58.8%, and 33.3%, respectively. As the angle of incidence increases, the A peak ends up red shifted by 0.6 GHz and the B peak ends up blue shifted by 3.7 GHz, but their frequency points remain roughly unchanged. Additionally, as shown in Figure 4b, the amplitudes of the A and B peaks decrease with the increase in the angle, with the A peak changing by 0.07, but the amplitude intensity of the B peak changing significantly by 0.19. Therefore, it can be considered that peak A is bending-insensitive and peak B is bending-sensitive.

The electric field distributions of the proposed MMA at different incidence angles of 0.24 THz and 0.46 THz are given in Figure 5. From Figure 5a–d, it can be seen that as a symmetric structure, the electric field at 0.24 THz also remains symmetric, the electric field intensity gradually increases, and the position remains constant when the incidence angle increases. Additionally, from Figure 5e–h, it can be seen that the electric field at 0.46 THz is not symmetric; the electric field intensity gradually decreases; and scattered distribution, when the incidence angle increases, and the absorption characteristics are affected by it. Therefore, from the combined absorption spectrum shown in Figure 4, it can be considered that peak A is bending-insensitive and peak B is bending-sensitive.

The electric field distribution, surface current density, and magnetic field distribution of the four peaks at 50 degrees oblique incidence are given in Figure 6a–l, and their formation mechanisms are revealed. For the resonance peak A at 0.24 THz, the distribution of the electric field and magnetic field is roughly similar to peak A at normal incidence. The distribution of electric field is strengthened and evenly distributed on the two transverse bars of the I-shaped structure. The current is mainly distributed on the metal structure, and the current on the vertical metal bar is opposite to the current on the bottom metal plate and produces LC resonance. The magnetic field is mainly concentrated on the vertical metal bar, but it is weaker than at normal incidence. The electric and magnetic fields at 0.39 THz are mainly concentrated on the left side of the split ring, so there is also a small current on the left side of the split ring and the I-shaped resonator. When the electric field of resonance peak B in Figure 6 is weakened, a strong magnetic field appears on the split ring and a large current gathers; the magnetic response is enhanced. For the resonant peak at 0.57 THz, the distribution of the magnetic field is the opposite of the peak at 0.39 THz. It is concentrated just to the right of the split ring, and the current is also concentrated to the right of the split ring and on the I-shaped resonator.

In practical applications, efficient and flexible absorbers not only need to absorb as much radiation as possible but also need to achieve tunable functionality. Therefore, we also evaluate the performance of the absorber during the phase transition at different incident angles, and the results as shown in Figure 7, where (b) and (c) are plots of absorptivity variation with the conductivity of VO₂ for different incident angles at 0.24 THz and 0.46 THz, respectively. When the THz wave is normally incident on the MMA, a blue shift of 4.8 GHz occurs in the A-peak with a peak drop from 99.4% to 46.9% after the complete phase transition of VO₂, while for the B-peak, a red shift of 0.48 GHz occurs with a peak increase from 39.6% to 99.3%. When the conductivity is 1000 S/m, the frequency points of the absorption peaks remain unchanged, but most of its resonance peak intensities decrease. For peak A, the absorptivity decreases from 92.6% to 79.5% when the incident angle increases from 0 to 50 degrees, with a red shift of 0.6 GHz at the frequency point of 0.24 THz. For peak B, the absorptivity rises from 61% to 81.3% when the incident angle increases from 0 to 50 degrees, with a blue shift of 4.1 GHz at the frequency point of 0.46 THz. It can be seen from Figure 6a that when the conductivity reaches 10,000 S/m, there are only two peaks with frequencies of 0.25 THz and 0.46 THz, respectively. The absorptivity decreases from 46.9% to 34% when the incident angle increases from 0 to 50 degrees, with a red shift of 0.6 GHz at the frequency point of 0.25 THz; however, the second peak B is stronger, and the absorptivity decreases from 99.3% to 89.3% when the incident angle increases from 0 to 50 degrees, with a blue shift of 4.4 GHz at the frequency point of 0.46 THz.

Figure 8 shows the electric field distribution, surface current density and magnetic field distribution at 0.24 THz and 0.46 THz with the conductivity of 1000 S/m. The electric field and surface current density are unchanged, but the magnetic field strength has weakened. The same is true for the electric field and surface current density of peak B, and the magnetic field strength on the split ring is slightly strengthened, so the absorption peak increases by about 0.22. Meanwhile, there is a transition from insulator phase to metallic phase in VO₂, and some molecular particles inside it will first undergo phase change; as the temperature increases further, the number of molecular particles of phase change will gradually increase, and metallic structure will appear inside VO₂ material. The absorption spectra have a clear change, which is easy to be understood and has been discussed in many reported literature [36]. Additionally, since the phase change material VO₂ is used, we can modulate this absorber by triggering the phase transition of VO₂ incorporated in the metamaterials. To quantify the modulation efficiency, we extract the modulation depth as [37]

$$MD=\left|\left({T\left(f\right)}_{max}-{T\left(f\right)}_{min}\right)/{T\left(f\right)}_{max}\right|$$

(3)

where $MD$ denotes the modulation depth at frequency $f$, ${T\left(f\right)}_{max}$ and ${T\left(f\right)}_{min}$ denote the transmission coefficients at frequency $f$, the maximum and minimum values, respectively. At this point, the modulation depth at 0.24 THz is 6.88%, while the modulation depth at 0.46 THz is higher, at 35.12%.

When the conductivity reaches 10,000 S/m, VO₂ achieves a phase transition, and significant change in the absorption spectrum occur. The higher the carrier concentration, the smaller the real part of the dielectric constant, and the larger the imaginary part, the more metallic and stronger the ion resonance intensity. The change of the resonance arises from the significant decrease in the real part of the permittivity of VO₂ when it transforms to its metallic state. As can be seen from Figure 9a–c, for the absorption peak A, a stronger electric field than at a conductivity of 1000 S/m gathers in VO₂. The magnetic field starts to weaken, and the current appears only in the vertical metal rods, which means that the LC resonance of the I-shaped structure is weakening; however, the second peak is strengthening, as can be seen in Figure 9d–f. At this point, the electric field and magnetic field are mainly concentrated in the open loop body and VO₂. This is because VO₂ has completed the phase transition from the insulating state to the metallic state. The magnetic field distribution at 0.46 THz shows a strong coupling between the I-shaped structure and the split ring (Figure 9f). This is the coupling between the metallic state formed by the VO₂ after completing the phase transition and the metal rod between them. Thus this coupling and the dipole resonance on the split ring together enhance the absorption amplitude of the B peak. Now, the modulation depth at 0.24 THz has improved significantly, reaching 52.93%, while the modulation depth at 0.46 THz is higher, at 60.12%. This is mainly due to the stronger electromagnetic response of the THz MMA to THz waves at this time.

Table 1. Comparison of the present MMA with others.

Ref.	Material	Frequency (THz)	Absorption	Layer	Thickness (μm)	Flexible
[19]	polyimide, copper	0.72, 1.4, 2.3	89%, 98%, 85%	three-layer	16.2	yes
[29]	VO2	1.96	Nearly 100%	three-layer	26	no
[38]	VO2, graphene	0.75–1.15; 2.5–4.5	94%, 90%	five-layer	49.6	no
[39]	VO2	93.01–7.27	90%	three-layer	7.4	no
[40]	Silicon, polyimide, copper	0.33, 0.62, 0.82	98%, 96%, 98%	four-layer	69	no
[41]	VO2, graphene	1.2	99.3%	three-layer	30.7	no
[42]	Si, SiO2, Au, graphene	-	41.7%	three-layer	0.94	no
Our paper	VO2, mica, gold	0.24, 0.46	99.7%, 99.3%	three-layer	42.3	yes

gives a comparison of our proposed structure with some published works [19,29,38,39,40,41,42], we find that the performance of our proposed structure not only fully combines the advantages of MMAs and flexible materials, but the performance is also much better when compared with existing work and can have many innovative applications in future THz systems, such as electromagnetic cloaking and wearable and implantable applications.

4. Conclusions

To sum up, a flexible and tunable THz MMA is proposed based on VO₂. The simulation results indicate that the I-shaped metamaterials combined with split ring structure present two resonant absorption peaks at 0.24 THz and 0.46 THz at normal incidence. By contrast, the absorption at 0.24 THz is nearly insensitive to bending, but the absorption at 0.46 THz is bending-sensitive, across a bending angle of 0–50 degrees. Moreover, the THz absorption amplitude can be tunable by triggering the phase transition of VO₂ incorporated in the metamaterials. Particularly, the absorption amplitude at 0.24 THz can be tuned from 99.4% to 46.9%, while the absorption amplitude at 0.46 THz can be tuned from 39.6% to 99.3%. The research results have important research significance for the development of THz flexible devices, which can be applied to perfect intelligent flexible electronic devices application in future studies.