Terahertz metamaterials for broadband, high modulation depth modulator, and tunable dual-band absorber based on metal-vanadium dioxide hybrid structure

Researchers have shown a growing interest in the potential of terahertz technology since terahertz frequency band, which ranges between the microwave and visible spectrums, is still underutilized.^1–3 Over the years, terahertz technologies have rapidly developed with applications reported in various fields such as high-speed communication, spectral detection of biological samples, radar imaging, and safety detection.^4–6 However, since few natural materials have been found that respond directly to terahertz waves, functional devices including terahertz modulators, switches, detectors, and waveguides are highly desirable and need to be further investigated and exploited. Recently, metamaterials have attracted tremendous attention due to their capability of manipulating incident electromagnetic waves. By constructing artificial designed materials, efficient modulation of terahertz waves can be achieved, which provides a feasible method for the realization of functional devices.^7–9 

For practical applications, it is desirable to have dynamic control over terahertz manipulation. Therefore, active approaches have been introduced to adjust the response of the metamaterial.¹⁰ Many controllable materials, such as graphene,¹¹ semiconductors,¹² liquid crystal,¹³ and GeSbTe,¹⁴ are exploited in metamaterial devices to realize dynamic responses through external stimulus. Vanadium dioxide (VO₂) is a typical phase-change material. This material undergoes an insulator-metal transition under external thermal, optical, or electrical stimuli.^15,16 Its conductivity can be drastically adjusted during the phase-change process. Therefore, by integrating the VO₂ film with the metamaterial, a dynamic terahertz response may be obtained.

Currently, many tunable metamaterial designs based on VO₂ film have been proposed and analyzed for the manipulation function of terahertz waves. For instance, Ding et al. presented switchable THz metasurfaces with diversified functionalities, showing reflective and absorptive states switching through the insulator-metal transition in VO₂ film as a function of temperature.¹⁷ Zhao et al. proposed a broadband and switchable THz metamaterial absorber by utilizing a stacked structure composed of a VO₂ periodic array, a dielectric layer, and a VO₂ film.¹⁸ Lv et al. theoretically demonstrated a metamaterial for thermal-controlled chirality using a hybrid structure consisting of 90° twisted E-shaped resonators and an embedded VO₂ film.¹⁹ Zhang et al. realized a terahertz bifunctional absorber with switchable characteristics of broadband absorption and multiband absorption based on a multilayer metamaterial containing both VO₂ and graphene.²⁰ Qi et al. proposed a structural-insensitive, switchable, and broadband metamaterial absorber that consists of several gold rods and a VO₂ ground plane separated by a dielectric spacer.²¹ 

In this paper, we propose and investigate hybrid terahertz metamaterials comprised of a periodic array structure of metals and VO₂ films. The terahertz transmittance of the metamaterial is modulated by changing the conductivity of the VO₂ film by promoting an insulator-metal phase transition via external excitation. The calculation results show that the maximum modulation depth is 92% in the investigated frequency range, and the bandwidth with modulation depth exceeding 60% is 142%. Additionally, by increasing the dielectric thickness and integrating a metal ground plane, the broadband, high modulation depth modulator can be switched to a controllable dual-band absorber. The normalized equivalent impedance of the metamaterial is calculated to explain the absorbing mechanism. Due to the rotational symmetry of the unit structure in the metamaterial, the modulation performance and absorption effect exhibit polarization-insensitive characteristics, which is beneficial for potential practical applications.

The schematic diagram of the proposed hybrid metamaterial and the top view of a unit cell are shown in Fig. 1. The metamaterial is composed of three layers, a circular metal patch, a vanadium dioxide cross strip, and a silicon dioxide medium. The material of the circular patch is gold with a thickness of 200 nm, and the radius of the circular patch is R = 25 µm. The thickness of the silicon dioxide layer is t = 2 µm, and the VO₂ film is h = 400 nm thick. The structure is arranged as an array, with the periodic size equal to the unit side length p = 65 µm. The width of the VO₂ strip is w = 15 µm. Since the VO₂ film exhibits a grid-like connection in its overall structure, the mesh film may be heated by applying an external current. Therefore, the phase transition can be excited and the VO₂ conductivity can be controlled.

Vanadium dioxide is a typical phase-change material. The insulator-metal phase transition can be excited under heat, light, and electricity excitation with lattice structure changes. Therefore, a conductivity increase of up to 3–4 orders of magnitude can be achieved. Generally, the Drude model can be adopted to describe the conductive characteristics of the VO₂ film. Since the working frequency band studied in this work is 0.2–1.2 THz, the conductivity of the VO₂ film is frequency-independent in the investigated range. Therefore, the conductive characteristics can be directly modeled by using different conductivity and dielectric constants in the insulator and metallic states according to Refs. 22–25. In the calculation, the dielectric constant is set to 12. The conductivity of the VO₂ film in the insulator state and metal state is 200 and 200 000 S/m, respectively.²⁶ 

The terahertz response of the proposed metamaterial is calculated using the electromagnetic simulation software CST. The unit cell boundary is utilized in the x and y directions of the unit structure, while the open boundary is used in the z direction. The excitation mode is set to Floquet mode. In the initial state, the terahertz wave is normally incident on the surface of the metamaterial, and the polarization direction of the electric field is the y direction.

Figure 2 displays the terahertz transmission spectra of the proposed metamaterials under different states of vanadium dioxide film. It can be observed from Fig. 2(a) that when vanadium dioxide film is in the insulator phase, the transmission coefficient maintains a value higher than 0.8 in the whole frequency band, revealing a transmissible state. By contrast, when vanadium dioxide film is in the metal phase, the transmission coefficient is lower than 0.2 in the investigated frequency range, exhibiting an isolation state. It is obvious that a large-scale terahertz modulation effect occurs with the phase-change process of the VO₂ film. As mentioned earlier, the phase transition could be induced using external current excitation by adding bias voltage according to the experimental results in Ref. 26. Furthermore, the terahertz modulation performance could be quantitatively evaluated using modulation depth expressed as T_MD = |T_max − T_min|/T_max.²⁷ The terahertz modulation depth of the metamaterial is calculated and plotted as shown in Fig. 2(b). It can be seen that the modulation depth exceeds 80% in the range of 0.2–0.8 THz, while the bandwidth of the modulation depth exceeds 60% and reaches 142%. The bandwidth of high modulation depth is greater than that of the metamaterials based on VO₂ or graphene reported in previous studies.^28–33 The maximum value of the modulation depth reaches 92% at 0.2 THz. The results manifest that broadband, high modulation depth modulation can be realized based on the metamaterial designed in this work. It is noted that by applying continuous external current such as square wave excitation, the terahertz transmission of the metamaterial can be continuously modulated.³⁴ The modulation speed offered by this proof-of-concept metamaterial is limited to millisecond timescales.²⁶ 

In order to analyze the mechanism of the high depth modulation, the electric field distributions on the metamaterial are calculated when the VO₂ film is in the insulator phase and metal phase, respectively. Figure 3 shows the field distributions on the surface of the metamaterial at a frequency of 0.7 THz. The amplitude scale of surface currents is fixed in different figures for accurate comparison. As can be seen from Fig. 3(a), when VO₂ is in the insulator phase, there are strong electric fields located on the edge of the circular metal patch and between the patches. The incident terahertz electromagnetic wave passes through the metamaterial through the space between the circular patches, thus causing a high transmission coefficient. When VO₂ is in the metal phase, it can be seen from Fig. 3(b) that the strength of the electric fields on the edge of the circular patch and between the patches is drastically weakened. Because the VO₂ film leads to the electrical connections for the metal patches, the overall structure could be considered a conductive grid, and the incident waves can no longer be transmitted between the patches. As a result, the transmission coefficient decreases significantly, which results in a high modulation depth.

As can be inferred, the VO₂ film plays an important role in the broadband modulation effect. Here, we study the influence of its width and thickness on the terahertz coefficient. As can be seen from Fig. 4(a), when the thickness of the VO₂ film increases from 0.1 to 0.4 µm, the terahertz transmission of the metamaterial when the VO₂ is in the metal phase is significantly reduced, while the transmission coefficient of the metamaterial when the VO₂ is in the insulator phase changes very slightly. Therefore, increasing the thickness of the VO₂ film could enhance the modulation performance of the metamaterial to a certain degree. However, from the point of practical application, due to the limitations of preparation technology, it is difficult to fabricate much thicker vanadium dioxide films while maintaining the performance of phase transition. Therefore, we further investigate the transmission spectra with varying widths of vanadium dioxide films. As can be seen from Fig. 4(b), a similar influence on the terahertz modulation can be achieved by increasing the width of the vanadium dioxide film. The terahertz transmission of the metamaterial when the VO₂ is in the metal phase is significantly decreased. This approach may lead to noticeably higher transmission loss in the higher frequency range when VO₂ is in the insulator phase.

In addition to terahertz modulation performance, the absorbing capability can also be realized by simply adjusting the design of the proposed metamaterial. As shown in Fig. 5, by increasing the medium thickness t and adding a layer of metal ground plane, the terahertz metamaterial absorber can be obtained. Figure 6 shows the simulated absorbing curves of the presented metamaterial when VO₂ is in the metal phase. It can be seen that dual-band absorption is obtained, and the absorption at 0.86 and 1.28 THz reaches 0.68 and 0.91, respectively. Meanwhile, it can be found that when vanadium dioxide is in the insulator phase, the absorbing performance of the metamaterial is switched off, and very low absorption can be observed. This may be attributed to the effective impedance variation of the entire metamaterial caused by the conductivity change of the VO₂ film in phase transition. The effective impedance of the metamaterials exhibits a mismatch with the free space impedance, which consequently leads to increasing reflection and dropping absorption.

Obviously, the thickness of the medium is a crucial factor that affects the absorption effect. Here, the absorption spectra as a function of frequency are simulated when the thickness of the dielectric t varies from 160 to 180 µm, as shown in Fig. 8. It can be observed that with the increase in dielectric layer thickness, the absorption peak undergoes significant changes, and the dual absorption bands shift toward the low-frequency range. Terahertz absorption primarily stems from electromagnetic wave loss caused by multiple reflections between the metamaterial top surface and the metal ground. Hence, the frequencies corresponding to the maximum loss decrease as the medium thickness increases. Consequently, the absorption peaks shift toward the lower frequency range.

The unit structure of the proposed hybrid metamaterial modulator is notable for its rotational symmetry. This feature results in the insensitivity of the modulation and absorption characteristics to the incidence polarization direction. Figure 9 illustrates how the terahertz modulation depth and absorption effect vary with the polarization angle ϕ when the incident wave is vertically incident. It is evident that the terahertz modulation depth spectra of the metamaterial undergo unnoticeable slight changes with various polarization angles. Likewise, the dual-band absorption spectra of the metamaterial nearly remain invariable with increasing polarization angle. Consequently, the terahertz modulation and absorption effects proposed in this work exhibit significant polarization stability. This attribute is highly desirable in practical application scenarios.

This paper proposes a terahertz metamaterial design based on a metal-vanadium dioxide hybrid structure. The metamaterial is composed of a metal circular patch array, a cross mesh VO₂ film, and a silicon dioxide substrate. By applying an external current stimulus or other feasible excitation, the insulator-metal phase transition of the VO₂ film can be induced, resulting in a significant increase in VO₂ conductivity, which regulates the transmission characteristics of the entire metamaterial structure. The simulation results indicate that broadband absorption can be achieved, and the bandwidth of the modulation depth exceeding 60% reaches 142%. Additionally, by increasing the thickness of the substrate and incorporating a metal ground plane, the switchable dual-band absorption effect can also be achieved. The absorbing mechanism is analyzed by calculating the normalized equivalent impedance of the metamaterial. It is worth mentioning that the modulation and absorption effects of the metamaterials are both insensitive to the polarization angle. These results exhibit potential applications in terahertz communication and detection.

This work was supported by the National Natural Science Foundation of China (No. 62101565) and the Hunan Provincial Natural Science Foundation of China (No. 2022JJ20045).

The authors have no conflicts to disclose.

Chenxi Liu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Yanlin Xu: Conceptualization (equal); Funding acquisition (supporting); Supervision (equal); Validation (equal); Visualization (equal). Ruiqi Huang: Supervision (equal); Visualization (equal). Song Zha: Supervision (equal); Validation (supporting).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.