1. Introduction

In the past decade, metamaterial is a kind of artificially structured composite materials with many exotic properties that cannot be obtained in nature materials. It can be made of periodic or quasi-periodic arrays of subwavelength metallic or dielectric elements. Thus they can possess a significant ability to control electromagnetic waves and enable the realization of many novel phenomena and functionalities from microwave to optics, such as negative refraction [1–3], electromagnetically induced transparency [4–6], and polarization converter [7–9]. It is not easy for these structures to change operating frequency or working intensity if non-tunable materials are employed. The electromagnetic behaviors of conventional metamaterials can only be adjusted by changing the dimension of the unit cell or the dielectric property of the embedded medium. So such devices in conventional metamaterials lack real-time modulations, and it strongly restricts the suitability for practical applications.

One possible method to overcome this limitation is to use tunable materials, such as liquid crystal [10,11], graphene [12–14], and reconfigurable metal [15,16]. Among various tunable materials in the field of active photonics, phase change materials have attracted remarkable attention due to its exceptional electrical and optical properties [17–26]. A typical example of phase change materials is vanadium dioxide (VO₂) [27–30]. It exhibits a dramatic change in dielectric permittivity due to a reversible structural phase transition between an insulating monoclinic phase and a conducting tetragonal phase around ∼340 K. This change can be actively manipulated by external stimuli, such as electric field, temperature, and optical pulse. The process of phase transition occurs on a time scale of some femtoseconds. Several fascinating applications using VO₂ have been proposed and experimentally demonstrated in active or reconfigurable photonic components, including modulator [31], filter [32], and switch [33]. In the terahertz range, there is little research on the dynamic operation of composite metamaterials with multifunctional performances. In this work, a switchable hybrid metamaterial is designed at terahertz frequencies. It is realized by incorporating a VO₂ film into the multilayer structure. By triggering the insulator-metal phase transition of VO₂, the designed system can be switched from an absorber to a transparent conducting metal.

2. Design and method

As shown in Fig. 1, the designed switchable metamaterial consists of six parts. Each part from top to bottom is metallic ring, silica (SiO₂) layer, VO₂ film, SiO₂ layer, subwavelength metallic mesh, and silicon (Si) substrate. The geometric parameters are adjusted in order to obtain the best performance. They are set as follows: period $P = 80\;\mu m$, side length of metallic ring $L = 70\;\mu m$, thicknesses of SiO₂ ($V{O_2}$) ${t_1} = 9\;\mu m$ and ${t_3} = 12\;\mu m$ (${t_2} = 2\;\mu m$), thicknesses of metallic ring and metallic mesh $0.5\;\mu m$, line widths of metallic ring and metallic mesh $5\;\mu m$. The frequency-dependent complex dielectric permittivity of $V{O_2}$ is described by Drude model $\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }}$ in the terahertz range, where ${\varepsilon _\infty } = 12$ is the dielectric permittivity in the infinite frequency, ${\omega _p}(\sigma )$ is the plasma frequency dependent on conductivity and $\gamma$ is the collision frequency [34–36]. In addition, $\omega _p^2(\sigma )$ and $\sigma$ are proportional to free carrier density. The plasma frequency at $\sigma$ can be approximately defined by $\omega _p^2(\sigma ) = \frac{\sigma }{{{\sigma _0}}}\omega _p^2({\sigma _0})$ with${\sigma _0} = 3 \times {10^5}\;S/m$, ${\omega _p}({\sigma _0}) = 1.4 \times {10^{15}}\;rad/s$, and $\gamma = 5.75 \times {10^{13}}\;rad/s$ which is independent of $\sigma$. The phase-transition process of $V{O_2}$ is accompanied by great changes in both conductivity and dielectric permittivity. In the calculation process, different permittivities of $V{O_2}$ are adopted for different phase states. In our simulation, the conductivity of $V{O_2}$ is assumed to be $2 \times {10^5}$ S/m (0 S/m) for the conducting (insulating) state. The relative dielectric permittivity of the insulating $V{O_2}$ is set to 12. These two assumptions can simulate the phase-transition process of $V{O_2}$. Metal is assumed to be gold with the conductivity of $4.561 \times {10^7}$ S/m. SiO₂ (Si) is modeled as a lossless dielectric material with $\varepsilon = 3.8$ (11.7) [37,38]. The thickness of Si is considered to be infinite in simulation to avoid Fabry-Pérot resonance.

 

Fig. 1. 3D schematic of the proposed switchable metamaterial.

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3. Results and discussions

The proposed system is simulated for numerical calculation by the finite element method. The computational domain is a single element in calculation, and unit cell boundary condition is applied to simulate the periodic structure in the X and Y directions. The designed structure is illuminated by an incident plane wave. In order to evaluate the performance of the designed absorbers, Absorbance (A) is calculated as $A = 1 - R - T = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$ when VO₂ is in the conducting state, where $R = {|{{S_{11}}} |^2}$ and $T = {|{{S_{21}}} |^2}$ are reflectance and transmittance. Transmission (${S_{21}}$) is nearly zero because the thickness of VO₂ is larger than skin depth. So the best absorption can be achieved by minimizing the reflection. As shown in Fig. 2(a), there is an obvious absorption peak at the frequency of 0.638 THz. Thus a narrowband metamaterial absorber is realized with three layers of metallic ring, SiO₂, and VO₂ film, and it is caused by the localized magnetic resonance which is formed by opposite currents on the metallic ring [Fig. 2(b)] and VO₂ film [Fig. 2(c)]. The whole thickness is $11.5\;\mu m$, and the ratio between working wavelength (0.638 THz, $470.2\;\mu m$) and thickness is ∼41.

 

Fig. 2. The simulated results of absorptance (a) when VO₂ is in the conducting state. The distributions of electric current on the top of metallic ring (b) and VO₂ (c).

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When VO₂ is in the insulating state, it can be found in Fig. 3 that transmittance is 95.8% at the frequency of 0.398 THz. This result is very noticeable since transmittance through the structure without the top metallic ring is only 45.4%. The designed structure at 0.398 THz obtains a ∼2.1 times transmittance enhancement compared to the structure without the top metallic ring. So by putting square metallic rings on top of the subwavelength metallic mesh, one can make an optically opaque object transparent. The transparent behavior can be explained by scattering cancellation scheme [39]. More concretely, the presence of the top metallic ring can generate the scattering to cancel those contributed by the subwavelength metallic mesh and the semi-infinite Si substrate. It means that the multiple reflections and transmissions in the metamaterial coating, are responsible for the reduction of reflection and enhancement of transmission [40].

 

Fig. 3. The simulated results of transmittance with metallic ring (red line) and without metallic ring (blue line) when VO₂ is in the insulating state.

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The above results are calculated under normal incidence. But the dependences of polarization angle and incident angle on the performances of absorptance and transmittance are worthy to investigate. Figures 4(a) and 4(d) show the evolution contour of absorptance and transmittance with polarization angle from ${0^\circ }$ to ${90^\circ }$. The calculated results clearly manifest that absorptance and transmittance under normal incidence is totally independent on polarization angle. This is caused by the symmetry of the designed system. The absorptance and transmittance spectra of the proposed design with different incident angles are plotted in Fig. 4 for transverse electric (TE) and transverse magnetic (TM) waves. As shown in Figs. 4(b) and 4(e) under TE wave, absorptance and transmittance are rather stable within the incident angle ${40^\circ }$. When incident angle is larger than ${40^\circ }$, the intensities of absorptance and transmittance will become to decrease and the bandwidths become narrower. As can be seen in Figs. 4(c) and 4(f) under TM wave, absorptance and transmittance is over 90% within the incident angle ${60^\circ }$. When incident angle is larger than ${60^\circ }$. The corresponding intensity becomes to deteriorate. Thus, the performances of the designed absorber and transparent conducting metal for both conducting and insulating phases of VO₂ are stable over a wide range incident angle.

 

Fig. 4. Absorptance (a) and transmittance (d) as a function of frequency and polarization angle under normal incidence. Absorptance (b and c) and transmittance (e and f) for TE wave (b and e) and TM wave (c and f) as a function of frequency and incident angle.

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In the above analysis, the length ($L$) of metallic ring and the thickness (${t_1}$) of the top SiO₂ are fixed at $70\;\mu m$ and $9\;\mu m$, respectively. In this part, the influences of L and ${t_1}$ on absorptance and transmittance are investigated to evaluate the importance of geometrical parameters. Firstly, L is changed to study absorptance and transmittance, keeping other structural parameters unchanged. As shown in Figs. 5(a) and 5(c), with the increase of L from $35\;\mu m$ to $75\;\mu m$, the curves of absorptance and transmittance show a trend of red shift. The intensity of absorptance increases continuously. As shown in Fig. 5(b), when ${t_1}$ is changed from $3\;\mu m$ to $18\;\mu m$, the intensity of absorptance fluctuates obviously. The perfect absorptance can be obtained when ${t_1}$ is $9\;\mu m$. Deviation from the optimized thickness leads to a degraded performance of absorptance. A smaller or larger thickness results in a smaller absorption level. As can be seen from Fig. 5(d), with the increase of ${t_1}$ from $3\;\mu m$ to $18\;\mu m$, the peak of transmittance has a little red shift in transparent center frequency (wavelength) from 0.398 THz ($753.77\;\mu m$) to 0.374 THz ($802.14\;\mu m$). Because of the small ratio (${t_1}/\lambda \approx 0.00398\sim 0.0224$) between ${t_1}$ and wavelength, this shift is not obvious. To some degree, the design is robust against the slight change of ${t_1}$.

 

Fig. 5. Absorptance (a and b) and transmittance (c and d) curves of the system with different structure parameters L and ${t_1}$ when VO₂ is in the conducting (a and b) and insulating (c and d) states.

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4. Conclusions

To summarize, a hybrid metamaterial with the switchable function is proposed at terahertz frequencies. It can be switched from an absorber to a transparent conducting metal. When VO₂ is in the conducting state, the designed system acts as an absorber. It is caused by the localized magnetic resonance. When VO₂ is in the insulating state, the designed system acts as a transparent conducting metal. The performances of absorption and transparency are insensitive to polarization direction under normal incidence and incident angle. The influences of geometric structures on the performances of absorption and transparency are also discussed. Our design may provide potential applications in the fields of terahertz energy harvesting and transparent conducting devices. Different methods, including thermal method [41], electrical method [42], and optical method [43], have been proposed to change the phase state of VO₂ in practice. According to recently experimental works about VO₂ deposited on SiO₂ [44–46], our design is realizable based on currently experimental conditions. It may be beneficial for possible applications in modulating and filtering. The future design can be expected to realize perfect absorption and high transparency at the same frequency. Meanwhile, the concept of the proposed terahertz device can be easily extended to other frequency ranges.