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Abstract
A multifunctional design based on vanadium dioxide (VO2) metamaterial structure is proposed. Broadband absorption, linear-to-linear (LTL) polarization conversion, linear-to-circular (LTC) polarization conversion, and total reflection can be achieved based on the insulator-to-metal transition (IMT) of VO2. When the VO2 is in the metallic state, the multifunctional structure can be used as a broadband absorber. The results show that the absorption rate exceeds 90% in the frequency band of 2.17 - 4.94 THz, and the bandwidth ratio is 77.8%. When VO2 is in the insulator state, for the incident terahertz waves with a polarization angle of 45°, the structure works as a polarization converter. In this case, LTC polarization conversion can be obtained in the frequency band of 0.1 - 3.5 THz, and LTL polarization conversion also can be obtained in the frequency band of 3.5 - 6 THz, especially in the 3.755 - 4.856 THz band that the polarization conversion rate is over 90%. For the incident terahertz waves with a polarization angle of 0°, the metamaterial structure can be used as a total reflector. Additionally, impacts of geometrical parameters, incidence angle and polarization angle on the operating characteristics have also been investigated. The designed switchable multifunctional metasurfaces are promising for a wide range of applications in advanced terahertz research and smart applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1 Introduction
Terahertz waves are between infrared light and microwaves in the electromagnetic spectrum, with the frequencies in the band of 0.1 to 10 THz. In recent years, terahertz science and related technologies have developed rapidly, showing promising applications in communication, sensing, imaging, and nondestructive testing [1]. These applications require not only efficient terahertz sources but also high-performance terahertz devices [2,3]. Presently, materials capable of manipulating terahertz waves are relatively scarce in nature, and in order to make more use of terahertz sources, researchers have developed materials that are not found in nature-metamaterials. Metamaterials [4] are artificially designed composite material systems with periodic arrangements of artificial microstructure units, which break the boundaries of traditional materials, enable the fabrication of electromagnetic functional structures with novel functions and easier preparation by existing technologies. Metamaterials have broad applications and development prospects in infrared imaging [5], energy harvesting [6], filters [7], electromagnetic stealth [8], sensors [9], modulators [10,11], etc., which have attracted strong interest in the scientific community. To this end, a lot of researches have been conducted in terahertz devices, and various metamaterial-based terahertz absorbers [13,14] and polarization converters [15–17] have been proposed. Most of the previously reported metamaterials are not easy to change their dimensions after being fabricated, which severely limits their practical applications. So far, most of the designed metamaterials exhibit a single function. Therefore, in order to achieve tunability or reconfigurability, functional materials such as graphene [16–19], VO2 [12,13,15–17], liquid crystals [11], GeSbTe [20], and other materials have been introduced combined with metamaterials, which can achieve multiple functions in a single metamaterial device. As an excellent material for optoelectronic functions, the conductivity of VO2 can vary by 4 - 5 orders of magnitude and the phase change can be completed within a few picoseconds [13]. This change can be stimulated by external, electric field, temperature and light pulses [22]. Therefore, VO2 is widely used in metamaterials [23], optical storage devices [24], nanoantennas [25], temperature sensors [26], and rewritable devices [27].
Up to now, there is a simple function for the majority of the designed in metamaterials. Although there are different terahertz absorbers and polarization converters based on metamaterials that have been proposed previously, these designs provide resemble functions. Liu [28] et al. proposed a broadband tunable absorber by treating VO2, which can achieve 5% - 90% absorption modulation in the frequency range of 1.2 - 3.2 THz. Zheng [29] et al. proposed a reflective wide-band polarization converter based on the fractal structure with a polarization conversion rate (PCR) of more than 90% from 8 to 23 GHz. Zhu [30] et al. designed a switchable broadband and multiband absorber based on graphene and VO2, with absorption up to 90% in the range of 1.06 - 2.58 THz when VO2 is in the insulating state. And when VO2 is in metallic state, the absorber is converted from broadband to multiband. Tang [31] et al. designed a spiral slot structure to achieve complete conversion of line polarization waves to cross-polarized waves in the dual-band with a PCR of more than 90% from 9 to 10.4 THz.
In this paper, based on the phase transition properties of VO2, we propose a switchable multifunctional metamaterial structure to realize the broadband absorption, polarization conversion and total reflection. When VO2 is in the metallic state, the designed device can work as a broadband absorber consisting of a VO2 patch array, an upper polyimide (PI) dielectric layer, a metal grating and a VO2 film from top to bottom. When VO2 is in the insulated phase, the device can be used as a polarization converter consisting of a VO2 patch array, an upper PI dielectric layer, a metal grating, a VO2 film, a lower PI dielectric layer, and a metal substrate. In this case, when the polarization angle of the incident terahertz waves is 45°, the structure can realize the LTC and LTL polarization conversion in different frequency band. When the polarization angle is 0°, the metamaterial structure can achieve total reflection. Moreover, the influences of structure parameters, polarization angle and incidence angle on the absorption and polarization conversion performances have also been investigated. The switchable multifunctional metamaterial device designed in this paper exhibits the advantages of flexible and adjustable, simple structure, demonstrating broad application prospects for future miniaturization and integration of terahertz systems.
2 Structure and methodology
The schematic structure of the metamaterial unit cell based on VO2 metamaterials and the specific parameter distribution are given in Fig. 1. The unit cell structure from top to bottom is six-sided VO2 patch array, PI (ɛPI = 3.5 + 0.00945i) [40], metal grating, VO2 film, PI and bottom metal backing. The geometric sizes are optimized through numerical calculation, and the selection of the values is as follows: P = 100 µm, b = 16 µm, a = 26 µm, g = 26 µm, h3 = 10.5 µm, and h1 = 10.5 µm. The thicknesses of sides of six-sided VO2 patch array, metal grating, and bottom metal (σAu = 4.561 × 107 S/m) [13] are 0.1 µm [32], 0.6 µm and 0.6 µm, respectively.
Fig. 1. Schematic diagram of the designed switchable metamaterial, (a) 3D schematic view (b) side view.
To investigate the operation properties of the VO2-based switchable multifunctional metamaterial device designed in this paper, the structure is numerically simulated in the 0.1 - 6 THz frequency band using the commercial simulation software CST. The unit cell boundary conditions are selected for the x- and y-axes to simulate the infinite arrays, and the open boundary conditions are selected for z-axis. The linearly polarized plane waves propagate along the -z direction throughout the structure. In the terahertz frequency, the optical dielectric constant of VO2 can be described by Drude model [32,33]: $\mathrm{\varepsilon }(\mathrm{\omega } )= {\varepsilon _\infty } - \frac{{\omega _\rho ^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }}$, where ɛ∞ = 12 represents the dielectric constant with high frequency, ωp(σ) represents the plasma frequency related to conductivity, and γ represents the collision frequency. Furthermore, there is a proportional relationship between the ωp2(σ), the σ and the free carrier density. $\omega _\rho ^2 = \frac{\sigma }{{{\sigma _0}}}\omega _\rho ^2({{\mathrm{\sigma }_0}} )$ can be used to express the plasma frequency at σ[4], where σ0 = 3×103Ω-1cm-1, ωρ(σ0) = 1.4×1015rad/s, and γ = 5.57×1013 rad/s. The relative dielectric constant of the insulating VO2 is set as 12. The phase-transition process of VO2 demonstrates significant variations in both conductivity and dielectric constant. In our investigation, the VO2 conductivities of 2 × 105 S/m and 20 S/m are selected to define the metallic and insulating state, respectively [34]. These two values can simulate the phase change process of VO2.
3 Results and discussion
3.1 When VO2 is metal, the proposed switchable metamaterial works as a broadband absorber
As given in Fig. 1, the proposed switchable metamaterial device is a typical broadband absorber when VO2 is in the metallic state. The finite element method is treated in the simulation to investigate the absorption properties of the metamaterial structure. The reflection coefficient (S11) and transmission coefficient (S21) of the designed structure are achieved through simulation, then the terahertz absorption rate (A) of this device can be calculated from the expression:
Fig. 2. (a)Absorption of the designed metamaterial device with VO2 patches (orange) and without VO2 patches (green), and (b) plots of relative impedance and absorption curves when the thicknesses of VO2 and PI are 0.1 µm and 10.5 µm, respectively.
When terahertz wave is incident perpendicular to the device surface, the impedance matching theory can be treated to study the intrinsic mechanism of the absorption characteristics. Both the real and imaginary parts of the relative impedance of the metamaterial structure can be calculated based on the S-parameter inversion method. The absorption rate and relative impedance can be expressed as [32–34]:
As depicted in Fig. 2(b), the relative impedance of the structure matches the free space, and the real part approaches 1 in the range from 2.17 to 4.94 THz, and the imaginary part is close to 0 in this band, achieving the perfect absorption in the corresponding frequency band.
In order to better understand the capability of the metamaterial structure, the geometric sizes (a, b, h3) of the metamaterial structure are researched and illustrated in Fig. 3. In Fig. 3(a), as the distance a between the diagonals increases, the overall absorption bandwidth increases and the first absorption peak is red-shifted toward lower frequencies, and it can be observed that the absorption intensity between the first and second resonant peaks inclines to decrease significantly with the grow of a. In Fig. 3(b), the absorption bandwidth widens slightly with the increase of the upper and lower hexagonal side lengths b. When b is larger than the optimized value, the absorption rate will be lower than 90%. In Fig. 3(c), the influences of the upper dielectric spacer thickness h3 on the absorption performances is studied when the h3 increases from 6.5 µm to 13.5 µm with a step of 2 µm. With the increase of h3, the bandwidth of the overall absorption increases and red-shifted, and the absorption band is changed from double band to triple band. When the dielectric thickness increases to 14.5 µm, the broadband effect weakens and the absorption bandwidth becomes significantly smaller. In summary, it can be seen that the absorption efficiency achieves the optimal results when the parameters are a = 26 µm, b = 16 µm and h3 = 10.5 µm.
Fig. 3. The absorption spectrum varies with (a) the distance of a, (b) the lengths of b in the upper and lower sides of six-sided VO2 patch array and (c) thickness h3 of PI dielectric layer when σ = 2 × 105 S/m.
For further understanding the operating mechanism of the broadband absorber in detail, the electric field distributions of the designed broadband absorber at 2.5 THz, 3.7 THz and 4.8 THz are investigated with TE-polarized incident terahertz wave. Since the electric field distributions are the same for the three absorption amplitudes, we only put the front-view of the electric field distribution with a frequency of 2.5 THz, as shown in Fig. 4(a). At this frequency, the absorber achieves strong field restraint around VO2 patch, resulting in highly efficient terahertz capture and absorption. These three resonant areas are superimposed to realize wide-band absorption. Figure 4(b) depicts the distribution of the electric field in the side view confirming the foregoing results. At 2.5 THz, because of the absorption caused by the interaction between VO2 film and VO2 patch, there will be a large amount of energy confinement at the margin of the periodic substrate. In addition, it is the type of resonance caused by the proposed metamaterial structures that is the plasma excitonic resonance, which can significantly raise the absorption produced by the Fabry-Perot cavity from the metamaterial structure and the reflector.
Finally, the effects of incidence angle and polarization angle on the absorber performance are investigated for practical application requirements, and Fig. 5(a) depicts the relationship between the absorption rate and the variation of the incidence angle. The designed absorber still exhibits a stable absorption rate and a wide operating bandwidth with high incident angle tolerance in the large incident angle range of 0° - 50°. When the angle of incidence is more than 50°, the bandwidth of its main absorption peak becomes narrower as the incidence angle increases. Therefore, the absorber is able to provide good absorption characteristics even at larger incidence angles. Figure 5(b) gives influence of the polarization angle on the absorption performance when the terahertz wave is incident vertically on the metamaterial structure surface. Due to the asymmetric structure of the design, the absorption rate has almost no great effect in the range of 0° - 45° as the polarization angle increases, but when the incident angle is larger than 43°, some higher order diffraction phenomena appear and the absorption spectrum bandwidth becomes narrower. The absorber has a simple structure and can be applied in terahertz modulation, thermal emitters and electromagnetic energy collect.
Fig. 5. (a) Absorption rate of broadband absorber for TE wave incidence with diverse incident angles, and (b) absorption spectra of the wide-band absorber with different polarization angles when σ=2×105 S/m.
3.2 When VO2 is in the insulating state, the proposed switchable metamaterial works as a linear circular polarization converter at 0.1 - 3.5 THz
When linearly polarized terahertz wave with a polarization angle of 45° to the x-direction is incident on the metamaterial device, the LTC is achieved when the phase of VO2 changes to the insulating state [35]. To demonstrate the polarization performance of the reflected wave, the Stokes parameter are introduced [36–38]:
The axial ratio (AR) is treated to estimate the circular polarization performance. When AR is less than 3 dB, LTC can be achieved. So, AR is defined as [19]:
where β is the ellipticity angle defined as:Besides, the LTC conversion efficiency (η) is also used to evaluate the performances of LTC, so we defined η as [36]:
In this section, we investigate the performance of reflective LTC polarizers in the THz range. The incident angle is zero, and the polarization angle is 45°. Here, the angle between the polarization orientation of the electric field and the positive x direction is called the polarization angle. As described in Figs. 6(a) and (b), the co-polarization reflection Rxx (=|rxx|2), cross-polarization reflection Ryx (=|ryx|2), φxx, φyx and Δφ (= φyx − φxx) are plotted in Orange line, green line, black line, red line, and blue dot-dashed line, respectively. When Rxx and Ryx are equal at 1.25THz, Δφ is equal to -90°. When Rxx and Ryx are equal at 2.1 THz, 2.51 THz and 3.2 THz, Δφ is equal to 90°. According to the χ formula, in these four frequencies we can obtain the perfect right-hand and left-hand circular polarization, respectively. The results show that the function of line-to-right-circular-polarization (LTRCP) can be achieved in the lower and higher frequency region, and the function of line-to-left-circular-polarization (LTLCP) can be achieved in the mid-frequency region.
Fig. 6. (a) Reflection curve (b) phases of the reflection coefficients, and (c) ellipticity (d) axial ratio and efficiency of the designed structure incident along 45° polarization angle when σ = 20S/m.
Furthermore, the stokes parameters are usually treated to describe the characteristics of the LTC converter. In Fig. 6(c), it can be found that from 1.14 to 1.335 THz and 3.566 to 3.663 THz, χ is lower than -0.9, which demonstrates that LTRCP is realized. It can be found that from 1.784 to 3.344 THz, χ is greater than 0.9, indicating that LTLCP is realized with the relative bandwidth of 60.84%. χ is close to 1 in the frequency range of 2.07-3.22 THz which demonstrates that perfect LTLCP can be achieved. In Fig. 6(d), the AR values are smaller than 3 dB in the frequency band with χ greater than 0.9 or less than -0.9. Then, the conversion efficiency η is also calculated and displayed by the green line. The energy conversion efficiency of LTC is greater than 0.9 in the frequency band with an axial ratio of less than 3 dB. The combination of these features makes this design a novel and efficient LTC polarization converter.
3.3 When VO2 is in the insulating state, the proposed switchable metamaterial works as a broadband cross polarization converter at 3.5-6 THz
Next, it can be seen from PCR that the good polarization conversion effect can be realized during the frequency 3.755–4.856 THz. Figures 7(a) and (b) show the reflection curves and the PCR extracted from the simulations. The PCR can be expressed as [37–39]:
Fig. 7. (a) Reflection curve (b) Polarization conversion rate when σ = 20 S/m, incident angle is 0° and polarization angle is 45°.
In the range of 3.755 to 4.856 THz, the co-polarized reflection part is close to 0, while the cross-polarized reflection part is greater than 0.8, with a polarization conversion rate PCR of above 0.9 and a relative bandwidth of 25.8% for polarization conversion. The PCR at resonant frequencies of 4 THz, 4.69 THz and 5.4 THz are close to 1, and the corresponding co-polarization reflection is close to 0. Compared with the conventional cross-polarization converters, the designed metamaterial structure performs the superiority of wide operating bandwidth and thin thickness, which are promising for the realization of terahertz devices.
The effects of structural parameters (g and h1) on PCR conversion performances are investigated. Figure 8(a) illustrates the relationship between the PCR and the metal grating width g when other geometry parameters are unchanged. With the thickness g gradually raises in a step of 1 µm, the PCR bandwidth increases and exhibits a slight red-shift trend. A relatively better PCR can be obtained at 26 µm. When the metal grating width g is greater than 26 µm, the bandwidth is still widened but the PCR is significantly weakened. With the increase of g, the valley of PCR at the resonant frequency of 5.76 THz decreases, leading to a great influence on the polarization conversion performances. As depicted in Fig. 8(b), the relationship between the PCR and the thickness of the media layer h1 has been investigated by fixing the other parameters of the structure. As h1 raises from 9.5 µm to 11.5 µm, the overall resonance peak is slightly red-shifted to the lower frequencies and the PCR curve is improved, but the corresponding bandwidth keeps getting smaller. Considering the thickness of the dielectric layer, a relatively optimal PCR can be obtained for h1 = 10.5 µm.
Fig. 8. PCR changes with (a) the width of the metal grating g and (b) the thickness of the dielectric layer h1 when the incident angle is 0°, the polarization angle is 45°, and the other structural parameters are kept constant.
When the polarization angle is 0°, the co-polarization and cross-polarization reflection under normal incident linearly polarized waves are depicted in Fig. 9. The amplitude of the cross-polarization reflection coefficient (ryx) is almost zero, and the co-polarization reflection coefficient (rxx) is greater than 0.9 at most frequencies. In this case, the structure has no polarization conversion capability, and total reflection is realized [41,42].
Finally, in order to address the novelty of the structure designed here, the comparison between the proposed structure and the recently reported structures has been studied, and listed in Table 1. Most of the reported structure can only realize one or two functions in a single metamaterial structures by treating graphene or VO2. In this paper, the designed metamaterial device can realize four different functions, including broadband absorption, LTL, LTC, and total reflection. In addition, the device can achieve excellent operation characteristics for different functions, which exhibit the significant improvements.
Table 1. The comparison between references and our work.
4 Summary
In summary, a switchable metamaterial with multiple functions is proposed caused by the phase change properties of VO2. By optimizing the geometric parameters, the investigations show that the versatile switchable metamaterial can act as an absorber, a LTL polarization converter, a LTC polarization converter, and a total reflector. When the VO2 is in the metallic state, the absorption rate is all greater than 90% in the frequency band of 2.17 - 4.94 THz, and the corresponding bandwidth ratio is 77.8%. Due to the asymmetry of the structure, both the incident angle and the polarization angle have a certain degree of influence on the absorption. The metamaterial structure is designed to act as an efficient polarization converter when the VO2 is in the insulating state. In this case, when the polarization angle of incident terahertz wave is 45°, two kinds of polarization conversion functions can be obtained. Firstly, in the band of 0.1 - 3.5 THz, the linear polarized terahertz waves can be effectively converted into the circularly polarized terahertz wave, especially in the range of 1.784 - 3.344 THz, the linear polarization is almost completely converted into a LHCP. Secondly, the LTL conversion can be realized in the band of 3.75 - 4.86 THz with the PCR above 90%. In addition, when the polarization angle of the incident terahertz wave is 0°, the almost total reflection can be achieved in the interesting frequency rang. The designed metamaterial structure with simple structure and switchable various functions can be used to construct the terahertz communication systems, electromagnetic stealth, modulation, electromagnetic energy harvesting and so on.
Funding
Natural Science Foundation of Zhejiang Province (LQ20F010009); National Natural Science Foundation of China (62001444, 62175223); Fundamental Research Funds for the Provincial Universities of Zhejiang (2021YW13); State's Key Project of Research and Development Plan for National Quality Infrastructure (2021YFF0600300).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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