A terahertz band multifunctional metamaterial transmission–absorption switching device based on vanadium dioxide

Abstract

In this paper, a vanadium dioxide (VO₂)-based terahertz device is proposed to realize the conversion between broadband absorption and broadband transmission functions, including the VO₂ bottom layer, dielectric layer and VO₂ pattern layer in a three-layer structure. With the change of the VO₂ conductivity, the terahertz metamaterial device can switch between broadband absorption and broadband transmission. When the device exhibits broadband transmission, it has a high transmittance of 90% for terahertz waves in the 5.6 THz to 8.7 THz frequency band. When the device exhibits broadband absorption, it has a high 90% absorption of terahertz waves in the 3.66 THz to 9.98 THz frequency band. Furthermore, with increasing VO₂ conductivity, the peak transmittance of the device decreases from 93.8% to 0% and the absorption increases from 1% to 99.5%. The impedance matching theory is invoked and the physical mechanism of the device is elucidated by analyzing the surface electric field of the device. By studying the absorption characteristics for different incidence and polarization angles, the device is insensitive to polarization and has good absorption performance over large incidence angles. Compared with other absorbers of terahertz metamaterials, the device structure proposed in this study has a unique design and diverse functions and can play an important role in various fields such as communications, electromagnetic stealth, sensors, and thermal emission devices.

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1. Introduction

Terahertz waves occupy a position between microwaves and infrared waves within the electromagnetic spectrum and operate at frequencies between 0.1 THz and 10 THz.^1–3 Recent advancements in THz radiation sources and detection technologies have enabled widespread application of terahertz systems in wireless communications,^4,5 imaging,⁶ sensing,^7,8 and other domains.^9,10 However, the limited electromagnetic response of natural materials at THz frequencies has hindered the development of functional terahertz devices essential for practical systems. This challenge has been addressed by the emergence of metamaterials,¹¹ artificially engineered sub-wavelength periodic structures that exhibit extraordinary electromagnetic properties absent in natural materials, such as negative permittivity and negative refractive indices.¹² Due to their unique electromagnetic characteristics and sub-wavelength dimensions, metamaterials can strongly interact with THz waves, enabling effective modulation of THz radiation. With the continuous application of metamaterials in terahertz technology, various kinds of terahertz metamaterial devices have been proposed, among which the terahertz metamaterial absorber¹³ can realize high absorption efficiency for the incident electromagnetic wave and thus has important application prospects in electromagnetic stealth,¹⁴ thermal imaging,¹⁵ sensing,¹⁶ modulation,¹⁷etc., which has been paid great attention by researchers. Meanwhile, with the continuous development of terahertz metamaterial absorbers, a series of absorbers, including single-band,¹⁸ multi-band,¹⁹ wide-band²⁰ and ultra-wide-band²¹ absorbers, have gradually appeared. However, most of the absorbers mentioned above have a narrow absorption bandwidth, and with the determination of the structure, it is impossible to regulate the absorption rate of electromagnetic waves or the dynamic regulation range is small, which can't meet the needs of people to solve the complex electromagnetic environment. Therefore, the design of a terahertz metamaterial absorber that has a large range of absorptivity dynamic modulation and a wide absorption bandwidth has become a new research direction.

Ge₂Sb₂Te₅ (GST) and VO₂ are two important optical phase change materials. Compared to sulfur-based phase change materials such as GST, VO₂ exhibits unique dynamic modulation advantages in the terahertz band.^22,23 VO₂ has a significantly lower phase change temperature (68 °C), which makes it more engineered for room temperature modulation scenarios. In contrast, GST's surface oxidation, volumetric expansion, and roughness degradation during the phase change process are different, bringing limitations to the application.^24–26 In addition, VO₂ can realize a reversible phase transition under the stimulation of physical conditions such as heat, light, electricity, etc., and its conductivity will undergo a drastic leap of four orders of magnitude with the phase transition, thus realizing the regulation of the absorption rate of electromagnetic waves. Based on the above properties, VO₂ is an ideal candidate as a terahertz metamaterial absorber to modulate terahertz waves. Recently, numerous VO₂-based absorbers have been reported. In 2018, Zhao et al. presented a terahertz-perfect absorber with over 90% absorption bandwidth switchable between 0.1 THz and 0.13 THz.²⁷ In 2022, Yang et al. designed a wideband absorber with an absorbance tunable between 4% and 100% and an absorption bandwidth of 2.45 THz.²⁸ In 2023, Wang et al. proposed a broadband adjustable absorber that has an absorption bandwidth of 4.26 THz and an adjustable absorption range between 4% and 100%.²⁹

Based on the above analysis, the current research on terahertz metamaterial absorbers mainly focuses on broadening the absorption bandwidth, improving the tunable range and absorption rate. On this basis, a terahertz metamaterial device is proposed in this paper, which is capable of switching between broadband absorption and broadband transmission modes using the phase transition of VO₂. Different from the conventional metal-dielectric–metal absorber, our device adopts a VO₂–SiO₂–VO₂(metamaterial–dielectric–metamaterial) three-layer structure. Simulation results show that when σ(VO₂) is 200 S m⁻¹, the structure of the device is equivalent to a dielectric–dielectric–metamaterial (dielectric) structure, and at this time the device exhibits strong transmission of the incident electromagnetic wave. When σ(VO₂) is 2 × 10⁵ S m⁻¹, the structure of the device changes to a metaldielectric–metamaterial (metal) structure, at which time the device exhibits high absorption of incident electromagnetic waves, with over 90% absorption in the 6.32 THz frequency range. The peak absorption of the device as a metamaterial absorber can be dynamically adjusted between 1% and 99.5% as the VO₂ conductivity is varied. In addition, we not only discuss the theoretical principles of the device as a metamaterial absorber, but also explore the influence that the incidence angle and polarization angle of the electromagnetic wave exert on the absorber's absorption performance. The broadband transmission and broadband absorption switchable terahertz metamaterial device proposed in this paper has a novel structure, excellent performance, and low limitations in practical applications, which can have a dramatic impact in areas such as communications, electromagnetic stealth, sensors and thermal emission devices, and bring new research ideas to related fields.

2. Design and simulation

In the model presented in this paper, the conductivity alteration of VO₂ enables the realization of its phase transition effect. The device designed in this paper is shown in Fig. 1(a) as a three-layer structure of VO₂–SiO₂–VO₂ grouped layers. The thickness of the underlying VO₂ is 0.5 um, and this thickness ensures that when σ(VO₂) is 2 × 10⁵ S m⁻¹, it has a thickness that greatly surpasses the skin depth of terahertz waves, and when the σ(VO₂) is 200 S m⁻¹, it allows as much of the terahertz waves to pass through as possible. SiO₂ is used as the dielectric layer and its permittivity is 2.13, which can be considered as an ideal medium.³⁰ The top metamaterial patterning layer is a periodic structure composed of VO₂ arranged along the x, y direction. In this paper, we use the commercial simulation software comsol to simulate the devices through the finite element analysis method, in which the frequency domain solver is employed and the tetrahedral adaptive mesh dissection is used in the simulation process. The parameters were optimized by simulation and the best parameters obtained are as follows: t = 0.04 μm, h = 7 μm, m = 0.5 μm, r = 14 μm, w = 30 μm, a = 2 μm.

Fig. 1 (a) Diagram of the device structure array; (b) top-view illustration of the cell; (c) side-view representation of the cell.

The Drude model can represent the permittivity of VO₂ in the terahertz frequency range:^31,32

where ε_∞ = 12 s is the permittivity in the high frequency limit. γ = 5.75 × 10¹³ s⁻¹ is the collision frequency. ω is the terahertz angular frequency. ω_p(σ) is the plasma frequency, which can be approximated as , where σ₀ = 3 × 10⁵ S m⁻¹ and ω_p²(σ) = 1.4 × 10¹⁵ s⁻¹.

The absorptivity of the device in this paper can be described by the equation A(ω) = 1 − R(ω) − T(ω) = 1 − |S₁₁(ω)|² − |S₂₁(ω)|², where R(ω) = |S₁₁(ω)|² is the device reflectivity and T(ω) = |S₂₁(ω)|² is the device transmittance.^33,34 When the skin depth of the incident wave in the metal film is much smaller than the thickness of the underlying metal, the transmittance T(ω) approaches zero, and the device absorptivity becomes A(ω) = 1 − R(ω) = 1 − |S₁₁(ω)|². When R(ω) is 0, A(ω) will be 1, then perfect absorption of the incident electromagnetic wave is achieved.^35–37

3. Results and discussion

The absorption spectra and transmission of the device are illustrated in Fig. 2(a) and (b), respectively, as the conductivity of VO₂ is progressively raised from 200 S m⁻¹ to 2 × 10⁵ S m⁻¹. Fig. 2(a) shows that the transmittance of the device to the incident terahertz wave decreases with increasing VO₂ conductivity, with the peak transmittance decreasing from 93.8% to 0%. This indicates that along with the change in VO₂ conductivity, the device structure is transformed from a dielectric–dielectric–dielectric to a classical metamaterial absorption structure (metal–dielectric–metamaterial), which results in a change from a strong transmission to a strong absorption of the incident terahertz wave.³⁸ When the device exhibits terahertz broadband transmission, it has more than 80% transmission for terahertz waves in the frequency range from 3.6 THz to 10 THz, reaching more than 90% from 5.6 THz to 8.7 THz. In addition, because the conductivity of VO₂ is not exactly zero, there is a partial ohmic loss when electromagnetic waves are incident on the insulating VO₂, which prevents 100% transmission of incident terahertz waves. Fig. 2(b) shows that when the σ(VO₂) is 200 S m⁻¹, the device absorption is very low, up to only 1%, which exhibits a very low absorption rate. However, when the σ(VO₂) becomes 2 × 10⁵ S m⁻¹, the peak absorption rate of the device is as high as 99.5%, which basically realizes the complete absorption of the incident terahertz wave. The above shows that the transmission and absorption of terahertz waves can be regulated by the conductivity of the device.³⁹ As observed in Fig. 2(b), the absorption spectrum resonance centers of the devices undergo continuous shifts as the VO₂ component transitions progressively towards the metallic state. Furthermore, as the conductivity of the VO₂ increases, the magnitude of these resonance centers decreases. Fig. 2(c) and (d) depict the changes in the real and imaginary components of the VO₂ permittivity with respect to conductivity. The imaginary component of the VO₂ permittivity increases drastically as the conductivity increases. Whereas the imaginary component of the permittivity is related to the loss of the incident terahertz wave, the real component of the permittivity is related to the resonant frequency. Therefore, the loss of VO₂ to the incident electromagnetic wave is increasing, and the device structure changes from very low loss (dielectric)–dielectric–very low loss (dielectric) to the classical metamaterial absorption structure (metal–dielectric–metal). In addition, it can be seen from the figure that the change in the imaginary component of the VO₂ permittivity is much larger than that in the real component of the VO₂ permittivity, which is the reason why the magnitude of the change in the centre of the resonance of the absorption spectra of the device decreases with the gradual increase in the VO₂ conductivity, while the absorption efficiency changes significantly.

Fig. 2 (a) Transmission spectrum of the device; (b) absorption spectrum of the device; (c and d) are the real and imaginary components of the permittivity of VO₂, respectively.

Fig. 3(a) illustrates the absorption, transmission and reflection spectral plots when the THz wave is incident in the vertical direction and the device exhibits broadband absorption. By observing the absorption spectra, we can clearly see that the device has over 90% absorption efficiency in the frequency range from 3.66 THz to 9.98 THz. Especially at the three frequency points f₁, f₂, and f₃, it exhibits obvious absorption peaks. In addition, the device is able to perfectly absorb terahertz waves from 4.39 THz to 4.62 THz and from 7.77 THz to 8.10 THz. In addition, both the TE and TM polarized incident terahertz waves exhibit identical absorption spectra, which indicates that the designed devices are polarization insensitive, because the surface pattern of the devices designed in this paper is highly symmetric.^40,41 In addition, the transmittance of the metamaterial perfect absorber can be seen as 0 from the transmission spectrogram, verifying that the VO₂ thickness is much larger than its skin convergence depth at terahertz waves.⁴² In this paper, the principle of wave absorption of the device as a metamaterial absorber is illustrated by impedance matching theory. The equation for relative impedance is given by:^43–45

where z and z₀ describe the effective impedance and the impedance in free space of the device, respectively. z_r = z/z₀, which represents the relative impedance of the device; S₁₁(ω) and S₂₁(ω) can be obtained with the comsol parameter. The formula demonstrates that an absorber's equivalent impedance perfectly matches the impedance of free space when its relative impedance (z_r) is equal to 1 and the incident terahertz wave is immobilized in the surroundings and enters completely into the inner part of the device, and at this time, R(ω) is equal to 0, so as to realize the complete absorption.⁴⁶Fig. 3(b) demonstrates the imaginary and real curves of relative impedance when the VO₂ is in the metallic state. From the figure, it could be observed that Re(z_r) is equal to 1 and Im(z_r) can be approximated as 0 at frequencies f₁ and f₂, which meets the condition of perfect absorption, which corresponds to the perfect absorption peaks at f₁ and f₂. Re(z_r) of the absorption peak at frequency f₃ is not equal to 1, thus failing to realize perfect absorption.⁴⁷

Fig. 3 (a) Spectrum of absorption, reflection and transmission of the device (b) Re(z_r) and Im(z_r) of the device. Here the σ(VO₂) is 2 × 10⁵ S m⁻¹.

To delve deeper into the physical processes underlying the device's wideband absorption characteristics, we depicted the distribution of the E-field at different peak frequencies (at frequencies f₁, f₂ and f₃). Fig. 4(a)–(c) show the normalized |E| distribution of the VO₂ patterned layer at the resonance frequencies of the three absorption peaks. The E-field at the three frequencies is mainly distributed in the forked slit and the periphery of the VO₂ disk, which shows that different polarities of charges are distributed on the surface of the VO₂, causing a localized surface equipartition excitation resonance, so that the external electromagnetic wave is fixed around the VO₂ and enters into the inner part of the device.⁴⁸ And finally, it is absorbed perfectly by the loss of the surface and the bottom VO₂ layer and by the multiple reflections localized in the SiO₂ layer.^49,50 The E-field strength of the patterned layer in Fig. 4(b) and (c) is smaller than that in Fig. 4(a), which suggests that there are other reasons for forming high absorption at frequencies f₂ and f₃. The Ez components at the resonant frequencies of the three absorption peaks are presented in Fig. 4(d)–(f). The E-field in Fig. 4(d) is particularly strong in the upper half of the four sectors. Unlike Fig. 4(d), the E-field in Fig. 4(e) and (f) is stronger in the lower half of the four sectors, which also suggests that charges of opposite polarity are distributed in the VO₂ surface layer thereby forming an electric dipole resonance, which leads to perfect absorption of the device at the absorption peak.^51,52Fig. 4(g)–(i) depict the distribution of the E-field in the yz direction, revealing that the E-field is concentrated primarily within the SiO₂ layer. This indicates that, upon entering the device, the terahertz wave is predominantly confined within the dielectric layer, aligning with the previous analysis. In addition, Fig. 4(h) and (i) show the distribution of the electric field at the boundary of the VO₂ surface layer and the SiO₂ layer in contrast to the distribution at the boundary of the VO₂ bottom layer and the SiO₂ layer, which in turn forms currents in the opposite direction between the VO₂ surface layer and the VO₂ bottom layer, which in turn excites the magnetic resonance, which is another physical mechanism that leads to the two resonant frequencies at f₂ and f₃ to become absorption peaks.^53,54 All in all, the physical source of the perfect absorption at the absorption peaks is attributed to the different polar charges distributed on the VO₂ surface layer, thereby inducing localized surface plasmon resonance and magnetic dipole resonance, and hence perfect absorption.

Fig. 4 E-field distributions at frequencies f₁, f₂ and f₃ for the metallic state of the VO₂. (a–c) show the |E| distribution in the x and y directions; (d–f) show the distribution of Ez in the x, y plane; (g–i) show the E-field distribution in the y and z cross-sections.

Through optimizing various parameters of the structural unit when the device is used as an absorber of metamaterials, the effective impedance of the device can be adjusted, thus enabling the device to show excellent absorption performance. Therefore, in the design process of the device, the optimization of geometric parameters occupies a crucial position.⁵⁵ In this paper, the other structural parameters are fixed on the basis of one-by-one adjustment of a single structural parameter, so as to comprehensively optimize the structural characteristics of the device.⁵⁶Fig. 5(a)–(d) show the absorption spectra of the VO₂ belonging to the metallic state for different individual cycle widths w, circle radius r, fork-shaped short edge a and thickness m of the underlying VO₂, respectively. Fig. 5(a) illustrates a gradual decline in the device's absorption capacity with increasing values of w. This suggests that as the width (w) increases, the effect of coupling between the VO₂ layer and the dielectric layer diminishes, resulting in the narrowing of the absorption bandwidth. Fig. 5(b) presents the increasing bandwidth of the device as the radius of circle r increases. However, the absorption intensity at the center resonance frequency gradually decreases as the absorption bandwidth increases. Therefore, the r-radius of the circle should be around 14 μm to maintain a broad absorption bandwidth while increasing the absorption efficiency of the device. In Fig. 5(c), the absorptive capacity of the device is increasing as the short side a of the fork decreases. When a increases from 1.5 μm to 2.0 μm, the absorption bandwidth has a little decrease but the absorption intensity at the center resonance frequency gradually increases, and the peak-to-peak absorption rate also increases, so that the absorber absorption effect is more when a is 2 μm. Fig. 5(d) indicates that the transmittance is 0 when the thickness of the VO₂ is varied between 0.5 μm and 2.5 μm. To reduce the absorption of terahertz waves when the device is used as a transmissive, the thickness of m is chosen to be 0.5 μm.

Fig. 5 The absorption spectra for various structural parameters when VO₂ is in the metallic state. (a) Individual cycle width w. (b) Circle radius r. (c) Forked short edge a. (d) Bottom VO₂ thickness m.

In the next step, next, this study investigates the influence of varying SiO₂ dielectric layer thickness (h) and VO₂ surface layer thickness (t) on the device's broadband absorption performance. As shown in Fig. 6(a), increasing the SiO₂ layer thickness (h) enhances absorption at the first resonance peak and the central frequency but reduces absorption in the high-frequency regime, accompanied by a blue shift in peak positions. To achieve both wide bandwidth and high peak absorption, the optimal SiO₂ thickness is determined to be h = 7 μm. Fig. 6(b) demonstrates that increasing the VO₂ surface layer thickness (t) in the range of 0.04 μm to 0.07 μm broadens the absorption bandwidth and enhances the overall absorption intensity. Notably, the second absorption peak (f₂) remains stable in resonance frequency, while its absorption rate diminishes. This phenomenon arises because f₂ originates from magnetic dipole resonance, whose frequency depends on the effective length of the top metallic structure. Since the VO₂ surface layer thickness does not alter this effective length, the resonance frequency remains unchanged.⁵⁷ However, thicker VO₂ layers weaken the counter-propagating currents between the surface and bottom layers, thereby suppressing magnetic resonance and reducing the peak absorption intensity.⁵⁸ This is to show that too thin a VO₂ layer will allow a lower match between the impedance of the free-space and the effective impedance of the device, thus leading to a lower absorption bandwidth. In addition, the absorption bandwidth decreases when the VO₂ surface layer changes from 0.04 μm to 0.03 μm. This suggests that a VO₂ layer that is too thin reduces the impedance matching between the free space and the device, resulting in a narrower absorption bandwidth.

Fig. 6 (a) The absorption spectra for SiO₂ layers with different thicknesses; and (b) the absorption spectra for VO₂ layers with varying thicknesses. Here σ(VO₂) is 2 × 10⁵ S m⁻¹.

Due to the fact that terahertz waves in practical applications may be incident at various angles, it is important to have good wide-angle absorption and polarization insensitivity when the device is used as a perfect absorber for metamaterials, which can greatly enhance the practical application performance of the device.^59–61 From Fig. 7(a), it can be seen that under TE polarization conditions, the device has more than 90% absorption efficiency for terahertz waves from 3.8 THz to 10 THz as the incident angle varies from 0° to 30°, and it has more than 80% absorption efficiency in the range of 0° to 50°. It is clear from Fig. 7(b) that under the TM polarization conditions, the device has more than 90% absorption efficiency for terahertz waves from 4.5 THz to 9.6 THz as the incident angle varies from 0° to 50°, and it has more than 80% absorption efficiency in the range of 0° to 65°. Fig. 7(c) demonstrates the spectrum of absorption at the different polarization angles, which shows that the device is insensitive to polarization and the absorption rate is not affected by the polarization angle. It is shown by the above that due to its high symmetric structure of the device designed in this paper, it has good wide-angle absorption performance and polarization insensitivity and can adapt to more electromagnetic environments in practical applications.^62–64

Fig. 7 Variation of absorptivity with the angle of incidence and polarization for VO₂ in the metallic state. (a) TE mode; (b) TM mode; (c) TE with various polarization angles.

For the purpose of showing the significant advantages of the text-designed device over other terahertz absorbers, we present a comparison of various terahertz absorbers in terms of absorption performance and the number of structural layers in Table 1.^65–71 The comprehensive performance comparison in Table 1 reveals three key advantages of our proposed device: the first one is the bandwidth advantage. Compared to the previous VO₂-based record (ref. 70, 2.45 THz), an absorption bandwidth (ABW) of 6.32 THz is achieved at >90% efficiency, while maintaining a comparable tunable range (1.0%–99.5% vs. 4.0%–100%). The second is the simplicity of construction. Compared to other terahertz absorbers (typically 4–6 layers in ref. 65–69), our design has the lowest number of stacked layers. The third is the performance balance. Among all the listed absorbers, the device simultaneously achieves the widest ABW while maintaining a wide tenability.⁷¹ Therefore, all the above show that the device designed in this paper has significant advantages over other terahertz absorbers.

Table 1 Comparison of the performance of various terahertz absorbers

Ref.	Material	Number of layers	ABW (>90%)	Tunable range
65	Graphene	5	1.32 THz	14%–100%
66	Graphene	7	2.20 THz	—
67	Graphene and VO2	3	0.65 THz	0%–99%
68	Graphene and VO2	6	0.83 THz	7%–90%
69	VO2	4	1.25 THz	15%–96%
70	VO2	3	2.45 THz	4.0%–100%
71	VO2	5	5.3 THz	2.6%–99%
Pro.	VO2	3	6.32 THz	1.0%–99.5%

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4. Conclusion

In this paper, we propose a terahertz metamaterial device switchable between broadband transmission and broadband absorption functions, consisting of a three-layer structure with the VO₂ layer, SiO₂ layer, and VO₂ patterned layer in the order from bottom to top. The conversion of the device between high transmission and high absorption functions is realized through changing the conductivity of the VO₂. When the device is in the transmittance function, 90% transmittance is realized at the 3.66 THz–9.98 THz. When the device is a metamaterial absorber function, the 90% absorption bandwidth is 6.32 THz. In addition, the principle of wave absorption in metamaterial absorbers is illustrated by impedance matching theory, and the E-field distribution at the absorption peak is analyzed to derive that the perfect absorption is due to localized surface equipartitioning primitives and magnetic coupling resonance. The designed device possesses a high degree of structural symmetry, which makes it characterized by wide-angle absorption and polarization insensitivity. Thanks to these excellent properties, the devices proposed in this paper show a wide range of potential applications in areas such as communications, electromagnetic stealth, sensors, and thermal emission devices.

Data availability

Data are available from the corresponding author on reasonable request.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful to the support by the National Natural Science Foundation of China (No. 51606158, 11604311, 61705204, 21506257) and the Science Foundation of Zhejiang University of Technology (GYY-ZH-2023084).

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