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Abstract
In this work, we propose a multi-functional broadband terahertz polarization converter based on graphene-VO2 hybrid metamaterial, which can switch between transmissive linear-to-linear conversion and reflective linear-to-circular conversion. The function of the metamaterial can be controlled by both the temperature and the Fermi energy of the graphene. At 298K, the metamaterial converts the y-polarized wave into x-polarized wave in 0.39-1.22THz. In the meanwhile, changing the Fermi energy of graphene, the converted polarization angle can be tuned from 90° to 45°. Increasing the temperature to 358K, the incident linearly polarized wave is reflected into circularly polarized wave. On this condition, tuning the Fermi energy, the metamaterial can separately convert the linear polarization wave into left-circularly polarized wave in 1.57-2.74THz and right-circularly polarized wave in 1.13-1.59THz. Such a switchable multi-functional broadband polarization converter may achieve potential applications in compact terahertz devices and integrated terahertz circuits.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The traditional methods to realize polarization conversion are based on birefringent crystals or Faraday effect [1, 2], which have the drawbacks of large block size not conducive to integration, and limited working frequency rarely suitable for terahertz band [3,4]. Metamaterials composed of artificial subwavelength structures can break the limits of the traditional materials [5]. Till now, various polarization conversion metamaterials in terahertz band have been proposed, achieving high efficiency [6] and broad working band [7,8].
In recent years, active materials have been introduced into metamaterial due to the demand for multi-functional devices to construct integrated and miniaturized optical system [9–25]. Graphene is one of the widely utilized active materials due to its excellent photoelectric properties. Below the damage voltage, the conductivity of graphene changes gradually with the external voltage, which can continuously tune the optical response of metamaterials, such as working frequency [12], amplitude [26], phase [16] and polarization [19,20,27]. Different from graphene, VO2 undergoes reversible insulator-metal phase transition as the temperature varies, whose conductivity changes about 5 orders of magnitude due to the phase change (at about 340 K) [28]. Therefore, VO2 has been widely used to design switchable metamaterials [14,15].
Taking advantages of both graphene and VO2, multi-functional polarization converters have been proposed. The phase change of VO2 helps the metamaterials to switch between different functions, for example, from transmission to reflection [15,21], from linear-to-linear polarization conversion to linear-to-circular polarization conversion [15], and from absorber to polarization converter [22,23,29]. In the meanwhile, the controllable Fermi energy of graphene can tunes the polarization conversion efficiency [9], the working frequency [24] or the amplitude of the emitted wave. Consequently, the combination of graphene and VO2 increases the functional diversity and integration of the devices.
In this paper, we present a switchable multi-functional broadband terahertz polarization converter based on graphene-VO2 hybrid metamaterial. It consists of a three graphene gratings with VO2 patterns on the top layer and a thin VO2 plane in the middle. Controlling the temperature, the metamaterial can switch from transmissive linear-to-linear converter to reflective linear-to-circular converter. In the meanwhile, changing the Fermi energy of the graphene, the working states of the metamaterial can be tuned. The proposed graphene-VO2 hybrid metamaterial with multiple functions and multiple control means possesses the advantages of versatility and wide operating band, which has potential applications in integrated polarization manipulation devices for terahertz communications, such as active wave plate, multichannel imaging and switchable polarization sensor.
2. Structure design
The multi-functional polarization converter consists of three graphene gratings separated by dielectric spacers, with the thin VO2 plane inserted into the dielectric spacer and the VO2 rectangular patterns on the top graphene gratings. The unit cell of the structure is shown in Fig. 1. The material of the dielectric spacer is cyclic olefin copolymer (COC) with low birefringence and heat resistance. The top and bottom graphene gratings are monolayer graphene gratings perpendicular to each other, with the same geometric parameters. The middle graphene grating is oriented at 45° with respect to the top grating, which includes two monolayer graphene gratings with an interlayer of SiO2. Such a bi-layer grating shows strong optical anisotropy due to the effect of local field enhancement between the two graphene layers [12]. In terms of experimental realization, the total fabrication process is similar with those of the multilayer metal gratings [7], replacing the standard photolithographic methods by high-speed femtosecond laser plasmonic lithography to fabricate the graphene gratings, whose orientation can be controlled by the laser polarization direction. For the convenience of description, we set up two rectangular coordinate systems with an included angle of 45°, labelled as x-y axis and u-v axis. The geometric parameters in Fig. 1 are lv = 37 µm, wv = 18 µm, wg1 = 24 µm, dg1 = 11 µm, wg2 = 16 µm, dg2 = 8.75 µm, h1 = 20 µm, h2 = 9.8 µm, h3 = 30 µm, tv1 = 1 µm, tv2 = 0.2 µm, ts = 0.1 µm, and the period of the structure is p = 70 µm.
Fig. 1. (a) The schematic diagram of the polarization converter. (b) Top graphene grating with VO2, (c) middle graphene grating, and (d) bottom graphene grating in a unit cell. (e) Side view of the structure.
In simulation, the refractive index of SiO2 is set as n1 = 1.95, and that of COC is n2 = 1.53. In terahertz band, the conductivity of monolayer graphene can be approximated as [30]
3. Simulation results and discussions
3.1 Transmissive linear-to-linear polarization conversion
For the y-polarized incident wave, we quote the Stokes parameters [18] to describe the polarization state, which are
At room temperature 298K, the VO2 is in the insulator phase, which is transparent to the terahertz wave. Set the Fermi energy of all the three graphene gratings as 1.0 eV, the calculated transmission coefficients under linear polarization incidence are shown in Fig. 2(a). The cross-polarization coefficient |txy| reaches above 0.7 in the frequency range of 0.39THz-1.22THz, and in the meanwhile, the PCRx reaches above 0.9, indicating that the y-polarized wave is almost converted into x-polarized wave. In contrast, |txx| and |tyx| are both below 0.2, suggesting low transmission of the x-polarized incident wave. Similar to metallic grating, graphene grating also allows the linearly polarized waves perpendicular to it and prevent the parallel one. Therefore, only y-polarized wave can pass the top graphene grating. Then, the y-polarized wave can split into two linearly polarized waves with equal intensity, along u- and v-axis respectively. As shown in Fig. 2(b), the u-polarized wave is reflected back and forth between the top and middle gratings, and the v-polarized wave passes through. Similar processes occur between the middle and bottom graphene gratings to allow the transmission of the x-polarized wave, which finanlly results in the y-to-x polarization conversion.
Fig. 2. (a) The transmission coefficients and PCRx. (b) The schematic of the transmission process in the metamaterial. (c) The cross-polarization and (d) co-polarization transmission coefficients of incident wave related to the polarization angle, with the same colorbar.
The propagating process in multilayer system can be conveniently described by the transfer matrix. For the graphene grating between two media A and B, the propagating field follows
For the incident wave with different polarization angles related to y-axis, we calculate the cross-polarization and co-polarization transmission coefficients. As shown in Fig. 2(c) and Fig. 2(d), the metamaterial can maintain a high cross-polarization transmission coefficient in the broadband frequency range when the polarization angle is smaller than 30°. With the increase of the polarization angle, both the cross-polarization and co-polarization transmission coefficients gradually decreases to zero, indicating low transmission. Therefore, the metamaterial can work as a broadband linear-to-linear converter only for the polarization angles below 30°.
Keeping the Fermi energy of the top and bottom graphene gratings as 1 eV and tuning that of the middle graphene grating, the transmission coefficients under y-polarization is shown in Fig. 3(a). When the Fermi energy is 0 eV, no polarization conversion is achieved as |txy| is zero, and the transmitted wave is completely y-polarized with low transmission in the frequency range of 0.39THz-1.22THz. On this condition, the polarization conversion cannot be achieved without the middle graphene grating. As the Fermi energy increasing, the total transmittance gradually increases, accompanied by the increase of the |txy| and the decrease of |tyy|. When the Fermi energy is higher than 0.4 eV, the PCRx keeps above 0.9 in the broadband frequency range and hardly varies with the Fermi energy. Consequently, the y- to x-polarization conversion can be effectively achieved at relatively low Fermi energy, and further improving the Fermi energy can achieve higher transmittance. In addition, set the middle grating as monolayer graphene grating at 1 eV, the related PCRx is given in Fig. 3(b) as well. Although polarization conversion can still be realized, both the polarization conversion efficiency and the bandwidth are obviously reduced. Consequently, bi-layer graphene is employed for the middle grating. Then, we have tuned the Ef of the bottom and top gratings to be 0 eV, respectively, with the other graphene layer at 1 eV. When the bottom graphene is 0 eV, the metamaterial converts the y-polarized wave into u-polarized wave due to the selective transmission of the subwavelength graphene gratings, as shown in Fig. 3(c). On the other hand, when the top layer graphene is 0 eV, the transmission coefficients are small for the y-polarized wave. On this condition, the u-to-x polarization conversion is efficiently achieved, as shown in Fig. 3(d). Therefore, the polarization conversion can take place when only the two adjacent gratings works, and the rotation angle is 45°.
Fig. 3. (a) The transmission coefficients and (b) the PCRx related to different Ef of the middle graphene grating, where the solid lines indicate the results of bi-layer grating and the dash-dot line indicates that of the monolayer grating. (c) The transmission coefficients when Ef of the bottom graphene grating is 0 eV. (d) The transmission coefficients when Ef of the top graphene grating is 0 eV.
3.2 Reflective linear-to-circular polarization conversion
At 358 K, the VO2 is in metal phase. On this condition, the 0.2µm-thick VO2 plane acts as a perfect reflective mirror [15,21]. Illuminating the structure with u-polarized wave, the top VO2 nanostructures can be regarded as diagonally patterned metallic strips, with the rotation angle of 45° respect to the u-axis, which satisfies the geometric symmetry principle of linear-to-circular polarization conversion metasurface [33]. We employ the reflection coefficients |rxu| and |ryu| to describe the reflective wave in x-y axis, and phases φxu and φyu to describe the corresponding phases, respectively. Therefore, the Stokes parameters in the reflection case can be achieved by analogy with Eq. (3), and the ellipticity χ=V/I can be used to characterize the linear-to-circular polarization conversion capability. When the Fermi energy of the top graphene grating is 0 eV, the simulation results are shown in Fig. 4(a). In the frequency range of 1.57-2.74THz, the reflection coefficients |rxu| and |ryu| are approximately equal to each other, and the phase difference defined as $\Delta\varphi=\varphi_{xu}-\varphi_{yu}$ is about π/2. As a result, the corresponding ellipticity χ in Fig. 4(b) is larger than 0.9, indicating that the u-polarized wave is reflected into left circularly polarized (LCP) wave.
Fig. 4. (a) The reflection coefficients and phase difference when Ef =0 eV. (b) The ellipticity when Ef=0 eV at high temperature. (c) The ellipticity χ related to the conductivity of VO2. (d) The ellipticity χ related to the Fermi energy of graphene.
During the phase change process of the VO2, the conductivity varies dramatically. We have calculated the ellipticity corresponding with the conductivity, as shown in Fig. 4(c). The ellipticity reduces greatly with the conductivity of VO2, suggesting that the metamaterial can behave as a broadband linear-to-circular conversion only when VO2 completes the phase transition, with the conductivity being large enough. In addition, tuning the Fermi energy, the variation of the ellipticity is shown in Fig. 4(d). When the Fermi energy reaches 0.6 eV, the ellipticity χ is smaller than -0.9 in the frequency range of 1.2-1.59THz, imply the conversion from linear polarization to right circular polarization (RCP). With the Fermi energy increasing, the χ keeps around -1 with the frequency range red-shift. Therefore, controlling the Fermi energy can change the function of the structure, switching the polarization of reflection wave between LCP and RCP in two different bands.
In order to better understand the physics behind this phenomenon, we have checked the distributions of the electric field and corresponding currents on the lower surface of the VO2 pattern and the upper surface of the VO2 plane, as shown in Fig. 5. The electric field and current distributions at 1.8THz are displayed in the row I. Under both x- and y-polarized waves, the currents on the surface of the VO2 pattern are parallel to those on the VO2 plane, producing the electric moment p1 and p2, manipulating the amplitude and phase of the reflected electric field along x- and y-axis, respectively. The conversion from u-polarized wave to LCP wave occurs when the reflective electric intensity along x- and y-axis are approximately the same and their phase difference is π/2. The electric field and current distributions at 2.2THz is shown in row II. Under x- and y-polarized waves, the currents on the surface of the VO2 pattern are parallel and untiparallel to those on the VO2 plane, respectively, result in the electric moment p3 and magnetic moment m1. On this condition, p3 and m1 manipulating the reflected electric field along x- and y-axis, respectively, to achieve the approximately same intensity with phase difference of π/2, leading to the conversion from u-polarized wave to LCP wave. Similar process occurs at the frequencies in the range of 1.57-2.74THz, making the metamaterial a broadband linear-to-left circular polarization converter. The field and current distributions at 1.4THz is shown in row III. The induced m2 and p4 manipulating the reflected electric field along x- and y-axis, respectively, causing the approximately same intensity with phase difference of -π/2. As a result, u-polarized wave is converted to RCP wave. Consequently, the electric or magnetic momoents induced by the electric field distributions help to form artificial birefringence of the metamaterial, result in the linear-to-circular polarization conversion.
Fig. 5. The distributions of the electric field and corresponding currents under x-polarized wave (the first two columns) and y-polarized wave (the last two columns). The rows labelled as I and II display the electric field distributions at 1.8THz and 2.2THz when the Fermi energy is 0 eV, and row III shows those at 1.4THz when the Fermi energy is 1 eV. The first and third columns present the electric field distributions on the lower surface of VO2 pattern, and the second and fourth columns show those on the upper surface of VO2 plane. In the last column, the red arrows indicate the equivalent electric moment and the blue ones indicate the equivalent magnetic moment induced by the currents.
When designing the metamaterial, we have swept the geometric parameters to see their affections and select the optimized combination. At 298 K, keeping the thickness of the dielectric spacers as h3 = h1 + tv2 + h2, the variation of the thickness h3 affects the transmission efficiency and the working bandwidth via tuning the phase induced by the optical path, as shown in Fig. 6(a). The width of the graphene ribbons in every grating layers, both wg1 and wg2, has an influence on the bandwidth as well, as shown in Figs. 6(b) and 6(c), which tunes the phase induced by the grating. In order to realize the broad working band, the phase dispersion induced by the dielectric spacer should eliminate that induced by the graphene grating. Consequently, the optimized combination of the geometric parameters is achieved by satisfying the phase dispersion compensation and the compromise between the transmission efficiency and the bandwidth. At 358 K, the thickness of the dielectric spacer h1 affects the bandwidth obviously by tuning the propagating phase, as shown in Fig. 6(d). On the other hand, the width wv and length lv influence the working band by changing the geometric phase induced by the VO2 patterns. As shown in Figs. 6(e) and 6(f), smaller width or larger length increases the aspect ratio, which increases the phase difference. The propagating phase and the geometric phase work together to achieve the broadband linear-to-circular polarization conversion. As a result, the balance between the propagating phase and the geometric phase leads to the optimized combination of the geometric parameters.
Fig. 6. The transmission coefficients and PCRx vary with (a) the dielectric layer thickness h3, (b) the width wg1 and (c) the width wg2 of the graphene ribbons, in which |Exy|, |Eyy| and PCR are described by the solid lines, dash lines, and dash-dot lines, respectively. The reflected phase difference and ellipticity vary with (d) the thickness h1, (e) the width wv and (f) the length lv of the VO2 patterns at 358 K.
Finally, we compared this work with the active multi-functional polarization converters in terahertz band reported recently. As shown in Table 1, our work has certain advantages in not only the functional diversity, but also the bandwidth for both linear-to-linear and linear-to-circular polarization conversions.
Table 1. The comparison between references and our work
4. Summary
In summary, we propose a multi-functional broadband terahertz polarization converter based on graphene-VO2 hybrid metamtaterial. Controlling the temperature, the metamaterial can switch between transmissive linear-to-linear converter and reflective linear-to-circular converter. At 298K, the metamaterial converts the linear polarization wave into its cross-polarization in the frequency range of 0.39-1.22THz. In this case, changing the Fermi energy of the graphene, the working state of the converter can be tuned. At 358K, the metamaterial is reflective. Tuning the Fermi energy of graphene, it can separately convert the linear polarization wave into LCP wave in 1.57-2.74THz and RCP wave in 1.13-1.59THz. The switchable multi-functional metamaterial we proposed has advantages of active adjustment, rich functions, and wide working band, which is significance for the development of polarization manipulation terahertz devices.
Funding
National Natural Science Foundation of China (11804178); National Laboratory of Solid State Microstructures, Nanjing University (M34009).
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.
References
1. D. R. Grischkowsky, S. Keiding, M. V. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]
2. T. Nose, S. Sato, K. Mizuno, J. Bae, and T. Nozokido, “Refractive index of nematic liquid crystals in the submillimeter wave region,” Appl. Opt. 36(25), 6383–6387 (1997). [CrossRef]
3. H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: Physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016). [CrossRef]
4. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
5. M. Kadic, T. Buckmann, R. Schittny, and M. Wegener, “Metamaterials beyond electromagnetism,” Rep. Prog. Phys. 76(12), 126501 (2013). [CrossRef]
6. R. H. Fan, Y. Zhou, X. P. Ren, R. W. Peng, S. C. Jiang, D. H. Xu, X. Xiong, X. R. Huang, and M. Wang, “Freely Tunable Broadband Polarization Rotator for Terahertz Waves,” Adv. Mater. 27(7), 1201–1206 (2015). [CrossRef]
7. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz Metamaterials for Linear Polarization Conversion and Anomalous Refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]
8. K. K. Xu, Z. Y. Xiao, J. Y. Tang, D. J. Liu, and Z. H. Wang, “Ultra-broad band and dual-band highly efficient polarization conversion based on the three-layered chiral structure,” Phys. E (Amsterdam, Neth.) 81, 169–176 (2016). [CrossRef]
9. Z. Y. Song, K. Wang, J. W. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018). [CrossRef]
10. Y. Y. Ji, F. Fan, X. H. Wang, and S. J. Chang, “Broadband controllable terahertz quarter-wave plate based on graphene gratings with liquid crystals,” Opt. Express 26(10), 12852–12862 (2018). [CrossRef]
11. J. J. Bai, S. S. Zhang, F. Fan, S. S. Wang, X. D. Sun, Y. P. Miao, and S. J. Chang, “Tunable broadband THz absorber using vanadium dioxide metamaterials,” Opt. Commun. 452, 292–295 (2019). [CrossRef]
12. S. N. Guan, J. R. Cheng, T. H. Chen, and S. J. Chang, “Widely tunable polarization conversion in low-doped graphene-dielectric metasurfaces based on phase compensation,” Opt. Lett. 45(7), 1742–1745 (2020). [CrossRef]
13. J. R. Zhang, K. Zhang, A. L. Cao, Y. Liu, and W. J. Kong, “Bi-functional switchable broadband terahertz polarization converter based on a hybrid graphene-metal metasurface,” Opt. Express 28(18), 26102–26110 (2020). [CrossRef]
14. H. Wang, F. Ling, and B. Zhang, “Tunable metasurfaces for independent control of linearly and circularly polarized terahertz waves,” Opt. Express 28(24), 36316–36326 (2020). [CrossRef]
15. J. Luo, X. Z. Shi, X. Q. Luo, F. R. Hu, and G. Y. Li, “Broadband switchable terahertz half-/quarter-wave plate based on metal-VO2 metamaterials,” Opt. Express 28(21), 30861–30870 (2020). [CrossRef]
16. Y. Zhang, Y. J. Feng, T. Jiang, J. Cao, J. M. Zhao, and B. Zhu, “Tunable broadband polarization rotator in terahertz frequency based on graphene metamaterial,” Carbon 133, 170–175 (2018). [CrossRef]
17. Z. T. Zhang, J. F. Wang, R. C. Zhu, Y. X. Jia, T. H. Liu, M. B. Yan, J. M. Jiang, Y. F. Li, Y. Y. Meng, and S. B. Qu, “Multifunctional full-space metasurface controlled by frequency, polarization and incidence angle,” Opt. Express 29(5), 7544–7557 (2021). [CrossRef]
18. M. Barkabian, N. Sharifi, and N. Granpayeh, “Multi-functional high-efficiency reflective polarization converter based on an ultra-thin graphene metasurface in the THz band,” Opt. Express 29(13), 20160–20174 (2021). [CrossRef]
19. H. Zhang, Y. Liu, Z. Liu, X. Liu, and Y. Shen, “Multi-functional polarization conversion manipulation via graphene-based metasurface reflectors,” Opt. Express 29(1), 70–81 (2021). [CrossRef]
20. J. Li and R. Yang, “Dynamically tuning polarizations of electromagnetic fields based on hybrid skew-resonator-graphene meta-surfaces,” Opt. Express 28(4), 4950–4961 (2020). [CrossRef]
21. C. H. Yang, Q. G. Gao, L. L. Dai, Y. L. Zhang, H. Y. Zhang, and Y. P. Zhang, “Bifunctional tunable terahertz circular polarization converter based on Dirac semimetals and vanadium dioxide,” Opt. Mater. Express 10(9), 2289–2303 (2020). [CrossRef]
22. Z. Y. Song and J. H. Zhang, “Achieving broadband absorption and polarization conversion with a vanadium dioxide metasurface in the same terahertz frequencies,” Opt. Express 28(8), 12487–12497 (2020). [CrossRef]
23. D. X. Yan, M. Meng, J. S. Li, J. N. Li, and X. J. Li, “Vanadium dioxide-assisted broadband absorption and linear-to-circular polarization conversion based on a single metasurface design for the terahertz wave,” Opt. Express 28(20), 29843–29854 (2020). [CrossRef]
24. X. Q. Chen, Q. Meng, W. Xu, J. F. Zhang, Z. H. Zhu, and S. Q. Qin, “Electrically tunable absorber based on a graphene integrated lithium niobate resonant metasurface,” Opt. Express 29(21), 32796–32803 (2021). [CrossRef]
25. Y. Fu, Y. Wang, G. Yang, Q. Qiao, and Y. Liu, “Tunable reflective line-to-circular-polarization dual-band with opposite handedness based on graphene metasurface,” Opt. Express 29(9), 13373–13387 (2021). [CrossRef]
26. J. X. Zhao, J. L. Song, T. Y. Xu, T. X. Yang, and J. H. Zhou, “Controllable linear asymmetric transmission and perfect polarization conversion in a terahertz hybrid metal-graphene metasurface,” Opt. Express 27(7), 9773–9781 (2019). [CrossRef]
27. X. Gao, W. L. Yang, W. P. Cao, M. Chen, Y. N. Jiang, X. H. Yu, and H. O. Li, “Bandwidth broadening of a graphene-based circular polarization converter by phase compensation,” Opt. Express 25(20), 23945–23954 (2017). [CrossRef]
28. Y. Nakata, K. Fukawa, T. Nakanishi, Y. Urade, K. Okimura, and F. Miyamaru, “Reconfigurable Terahertz Quarter-Wave Plate for Helicity Switching Based on Babinet Inversion of an Anisotropic Checkerboard Metasurface,” Phys. Rev. A 11(4), 044008 (2019). [CrossRef]
29. X. B. Liu, Q. Wang, X. Q. Zhang, H. Li, Q. Xu, Y. H. Xu, X. Y. Chen, S. X. Li, M. Liu, Z. Tian, C. H. Zhang, C. W. Zou, J. G. Han, and W. L. Zhang, “Thermally Dependent Dynamic Meta-Holography Using a Vanadium Dioxide Integrated Metasurface,” Adv. Opt. Mater. 7(12), 1900175 (2019). [CrossRef]
30. T. Guo and C. Argyropoulos, “Broadband polarizers based on graphene metasurfaces,” Opt. Lett. 41(23), 5592–5595 (2016). [CrossRef]
31. S. X. Wang, L. Kang, and D. H. Werner, “Hybrid Resonators and Highly Tunable Terahertz Metamaterials Enabled by Vanadium Dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017). [CrossRef]
32. J. H. Li, Y. T. Zhang, J. N. Li, J. Li, Y. Yang, J. Huang, C. Q. Ma, Z. Z. Ma, Z. Zhang, L. J. Liang, and J. Q. Yao, “Frequency-switchable VO2-based coding metasurfaces at the terahertz band,” Opt. Commun. 458, 124744 (2020). [CrossRef]
33. Y. N. Jiang, L. Wang, J. Wang, C. N. Akwuruoha, and W. P. Cao, “Ultra-wideband high-efficiency reflective linear-to-circular polarization converter based on metasurface at terahertz frequencies,” Opt. Express 25(22), 27616–27623 (2017). [CrossRef]
