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Abstract
We propose a metal-vanadium dioxide (VO2) metamaterial with broadband and functionality-switchable polarization conversion in the terahertz regime. Simulation results show that the function of the proposed metamaterial can be switched from a half-wave plate (HWP) to a quarter-wave plate (QWP) over a broad bandwidth of 0.66–1.40 THz, corresponding to a relative bandwidth of 71.8%. The HWP obtained when VO2 is in the insulating state has reflection of 90% and linear polarization conversion ratio exceeding 98% over the bandwidth of 0.58–1.40 THz. By transiting the phase of VO2 into the conducting state, the obtained QWP can convert the incident linearly-polarized wave to circularly-polarized wave with an ellipticity of 0.99 over 0.66–1.60 THz. Additionally, results show that the proposed broadband switchable HWP/QWP has a large angular tolerance. We expect that this broadband and switchable multi-functional wave plate will find applications in polarization-dependent terahertz systems including sensing, imaging, and telecommunications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The manipulation of the polarization state of electromagnetic waves is of great interest in both fundamental physics and a diverse range of applications such as sensing, imaging and telecommunications. Among the various polarization converters, half-wave plates (HWPs), which shift the polarization direction of linearly polarized light, and quarter-wave plates (QWPs), which convert linearly polarized light into circularly polarized light and vice versa, are two common types of wave plates. Conventionally, these wave plates are realized based on birefringence or total internal reflection effects in crystals or polymers, which cause phase retardation between the two orthogonal polarization components [1]. Recently, metamaterials and metasurfaces have been widely used to tailor the polarization state of light because of their appealing advantages such as compactness, flexibility, broad bandwidth and easy integration [2–6].
Driven by practical applications, wave plates with broad bandwidths and dynamically tunable functionalities have been the focus over the years. Since 3D chiral metamaterials [7] suffer from the difficulty of fabrication, Yu et al. [8] demonstrated a optically thin QWP based on a metasurface in 2012, and Pors et al. [9] demonstrated a broadband HWP using a multi-layered metmaterial in 2013. After that, various planar structures or multi-layered ones have been proposed or demonstrated for achieving broadband terahertz HWPs [10–13] or QWPs [11,14–19]. The relative bandwidth, defined as the ratio of the bandwidth to the central frequency, can reach more than 80% [11]. However, these metamaterials or metasurfaces are made of metals or dielectrics, and thus their functionalities cannot be dynamically tuned, limiting their applications.
By incorporating tunable materials such as graphene, or phase-changing materials including vanadium dioxide (VO$_2$) and Ge$_2$Sb$_2$Te$_5$, metamaterials or metasurfaces can be designed with switchable functionalities [20,21]. For example, by changing the chemical potential of graphene in metamaterials, Zhang et al. [22] and Tavakol et al. [23] respectively proposed switchable QWPs, of which the polarization state of the output wave can be dynamically switched among linear, left- and right-handed polarization. By applying biased electric field to liquid crystals sandwiched between two graphene gratings, Ji et al. [24] also proposed a broadband switchable QWP to switch between linear-to-linear and linear-to-circular polarization states over a bandwidth of 0.35 THz. By changing the phase of VO$_2$ in metasurfaces from the insulating state into the conducting state, Wang et al. [25] demonstrated a tunable QWP of which the operating frequency can be tuned from 0.47 THz to 0.50 THz, Ding et al. [26], Song and Zhang [27] and He et al. [28] demonstrated switchable functionalities from a broadband perfect absorber to a broadband polarization converter, respectively. Nakata et al. [29] demonstrated a switchable QWP operating at 0.617 THz by designing a VO$_2$-based anisotropic checkerboard metasurface. Jiang et al. [30] proposed a frequency-tunable HWP in the mid-infrared regime based on a graphene-silicon hybrid metasurface. Quite recently, tunable metamaterials with functionality switching between an HWP and a QWP have also been proposed. Zhang et al. [31] proposed functional switch from a QWP to an HWP within 4.80–5.10 THz based on a graphene metasurface. The relative bandwidth was calculated to be 6%. Li et al. [32] proposed a metasurface based on the phase-changing material Ge$_2$Sb$_2$Te$_5$ and showed that its function can switch from a QWP to an HWP over 10.3–10.9 $\mu$m, corresponding to a relative bandwidth of 6%. Zhao et al. [33] also proposed a switchable terahertz metamaterial that can be switched between an HWP and a QWP over 2.09–2.27 THz, corresponding to a relative bandwidth of 8%. In other words, the bandwidths of these switchable QWPs/HWPs are very narrow (no more than 8%).
In this work, we propose a broadband and switchable terahertz HWP/QWP based on a tunable metamaterial composed of multi-layered metal-VO$_2$ structures. The operation principle will be elaborated. Simulation results will show that when the phase of VO$_2$ transits from the insulating state to the conducting state, the function of the proposed metamaterial can be switched from a broadband HWP with polarization conversion ratio (PCR) exceeding 98% over 0.58–1.40 THz, into a broadband QWP with ellipticity of $0.99$ over 0.66–1.6 THz. These switchable functionalities share the same broad bandwidth of 0.66–1.40 THz, corresponding to a broad relative bandwidth of 71.8%. Moreover, the effects of the incident angles and geometric parameters will also be investigated.
2. Design and simulation of metamaterial
Figure 1 illustrates the unit cell of the proposed metal-VO$_2$ metamaterial, which is composed of multi-layered structures. A gold film, a cyclic olefin copolymer (COC) layer, and a VO$_2$ film are deposited in sequence on a silicon substrate (not shown for clarity). Double-L-shaped gold resonators are then patterned on top, followed by the deposition of a second layer of COC film. Finally, double-T-shaped VO$_2$ resonators with orientation angle of $45^\circ$ with respect to the $y$ axis are patterned on top. Both the gold film and the gold resonators have thickness of $t_1=0.2~\mu$m. The VO$_2$ film and the VO$_2$ resonators have thicknesses of $t_2=0.2~\mu$m and $t_3=1~\mu$m, respectively. The bottom and the top COC films have thicknesses of $t_\textrm {d1}=34~\mu$m and $t_\textrm {d2}=40~\mu$m, respectively. The unit cell has periods of $p=122~\mu$m in both the $x$ and $y$ directions. The double-L-shaped gold resonators have length of $l_1=69~\mu$m, width of $w_1=9~\mu$m, and distance from the unit boundary of $d=11~\mu$m. The double-T-shaped VO$_2$ resonators have length of $l_2=46~\mu$m, widths of $w_2=4~\mu$m and $w_3=2~\mu$m, and gap of $g=56~\mu$m.
Fig. 1. Schematic of the proposed metamaterial composed of multi-layered metal-VO$_2$ hybrid structures. (a) When VO$_2$ is in the insulating state, it acts like dielectric, denoted by VO$_2$ (D) and indicated by the blue block, the metamaterial functions as an HWP converting linear $y$ polarization into linear $x$ polarization. (b) When VO$_2$ is in the conducting state, it acts like metal, denoted by VO$_2$ (M) and indicated by the red block, the metamaterial functions as a QWP converting linear $y$ polarization into LCP. (c) Geometric parameters of the unit cell of the multi-layered metamaterial.
The operation principle of the proposed metamaterial, which is illuminated by terahertz plane wave with $y$ polarization, is as follows. At room temperature, VO$_2$ is in the insulating state, as illustrated in blue in Fig. 1(a), thus the VO$_2$ film and resonators have little influence on the interactions between terahertz waves and the gold metamaterial, which function as an HWP. At the high temperature of 87$^\circ$C, however, VO$_2$ is in the conducting state, as illustrated in red in Fig. 1(b), the VO$_2$ resonators and the VO$_2$ film now acts like the corresponding metal structures. Thus the proposed metamaterial can function as a QWP that converts the linear $y$ polarization into left-handed circular polarization (LCP). Therefore, by adjusting the phase of VO$_2$ from the insulating state to the conducting state or reversely, we expect that the functionality of the proposed metamaterial can switch between an HWP and a QWP. In order to achieve broadband performance, we adopt double-L-shaped gold resonators for the HWP inspired by [12,17], and adopt oriented double-T-shaped VO$_2$ resonators for the QWP inspired by [34,35].
The polarization conversion performance of the proposed metamaterial was numerically evaluated using the frequency-domain solver in CST Microwave Studio. Unless otherwise specified, the metamaterial is illuminated by normally incident terahertz plane wave with polarization along the $y$ direction. Unit cell boundary conditions were applied in the $x$ and $y$ directions, and open boundary was set in the $z$ direction. Adaptive tetrahedral mesh refinement was used to speed up the convergence. In our simulations, the relative permittivity of COC layer was taken to be $\varepsilon = 2.1 + 0.006i$ [36]. The gold with the conductivity $\sigma$ was set to be $4.56 \times 10^7$ S/m. We adopted the Drude model to describe the frequency-dependent permittivity of VO$_2$, either in the insulating state or in the conducting state, in the terahertz regime [37],
3. Results and discussion
3.1 Functionality switching between HWP and QWP
Figures 2(a)–(c) show the reflection amplitudes and phases when the proposed metamaterial operates at room temperature. In this scenario, VO$_2$ is in the insulating state and acts as a dielectric. Figure 2(a) shows that the reflection magnitudes $|r_{uu}|$ and $|r_{vv}|$ for normally incident terahertz waves with $u$ and $v$ polarization, respectively, are almost equal and close to unity. Figure 2(b) shows that the phase difference condition $\Delta \Phi = \Phi _{vv}-\Phi _{uu} = -180^\circ$ is approximately satisfied within the frequency range of 0.58–1.40 THz. It’s worth noting that the dispersion-free of the phase difference originates from the geometrical symmetry of double-L-shaped antenna [15]. Within this broad band, Fig. 2(c) shows that the cross-polarized reflection amplitude $|r_{xy}|$ is larger than 0.9, whereas the co-polarized reflection amplitude $|r_{yy}|$ is smaller than 0.22.
Fig. 2. Simulated spectra of the (a) reflection amplitudes and (b) phases for the proposed metamaterial working at room temperature under normally incident terahertz waves with $u$ and $v$ polarization, as illustrated by the inset. (c) Simulated spectra of the co-polarization and cross-polarization reflection amplitudes under normally incident wave with $y$-polarization. (d) Calculated spectra of PCR and DoLP.
For further investigation, Fig. 2(d) shows the spectra for the polarization conversion rate (PCR) and the degree of linear polarization (DoLP), which can be calculated by,
At 87$^\circ$C, VO$_2$ is in the conducting state and VO$_2$ behaves like a metal. Figure 3(a) shows that the reflection amplitudes $|r_{uu}|$ and $|r_{vv}|$ are almost equal and close to unity for frequencies above 0.80 THz. The corresponding phase difference between $\Phi _{uu}$ and $\Phi _{vv}$ are approximate to $-270^\circ$ within the frequency range of 0.66–1.60 THz, as shown in Fig. 3(b). Therefore, within this frequency range the co-polarized reflection amplitude $|r_{yy}|$ and cross-polarized reflection amplitude $|r_{xy}|$ are approximately equal to each other, as shown by Fig. 3(c).
Fig. 3. (a)–(c) Similar as Figs. 2(a)–(c) except that the proposed metamaterial is working at 87$^\circ$C. (d) Spectra of ellipticity.
In order to quantify the performance of the obtained QWP, we calculate the ellipticity defined as $\chi \equiv S_3/S_0$, where the Stokes parameters $S$ are expressed as [14],
When $\chi$ equals to 1 or $-1$, the polarization state of the output terahertz wave is LCP or RCP, respectively. Figure 3(d) shows that $\chi >0.99$ at the frequency range 0.66–1.60 THz, suggesting that the proposed metamaterial acts as a broadband QWP that converts linear $y$ polarization into LCP. Moreover, Fig. 3(d) also shows that the matamaterial converts linear $y$ polarization into right-handed circular polarization (RCP) at 0.50 THz.3.2 Physics mechanisms
In order to understand the physics underlying the broadband performance of the designed HWP/QWP, in Fig. 4 we plot the current distributions on the top surfaces of double-L-shaped gold resonators and on the gold film in the $u-v$ coordinate system. Here we choose three resonant frequencies, 0.60 THz, 0.85 THz, and 1.25 THz, for which $|r_{yy}|$ reaches the minimum, as shown by Fig. 2(c). Figures 4(a)(b) show that at 0.60 THz the currents on the gold resonators have the opposite direction as those on the gold film, thus magnetic resonances are produced under both the $u$-polarized and $v$-polarized incidences. Figures 4(c)(e) show that at 0.85 THz and 1.25 THz, magnetic resonances are generated because the currents on the top surface have opposite direction to those induced on the gold film under the $u$-polarized incidence. Under the $v$-polarized incidence, however, the induced currents on the top surface of the gold resonators are parallel to those on the gold film, forming an equivalent electric resonance and a current loop in the dielectric layer, as shown by Figs. 4(d)(f).
Fig. 4. Surface current distributions (arrows for the directions and colors for the strengths) on the top surfaces of the gold resonators (the $1^\textrm {st}$ and $3^\textrm {rd}$ columns) and of the gold film (the $2^\textrm {nd}$ and $4^\textrm {th}$ columns) at the three resonant frequencies of (a)(b) 0.60 THz, (c)(d) 0.85 THz, and (e)(f) 1.25 THz when VO$_2$ is in the insulating state at room temperature. The $1^\textrm {st}$ and $2^\textrm {nd}$ columns are for the $u$-polarized incidence, and the $3^\textrm {rd}$ and $4^\textrm {th}$ columns are for the $v$-polarized incidence. The black arrows indicate the dominant current directions.
The electric and magnetic resonances manipulate the magnitudes and phases of the reflected electric fields along the $u$-axis and $v$-axis. When the $u$-component and $v$-component of the reflected fields have equal magnitudes and a phase difference of 180$^\circ$, an ideal HWP will be achieved. Therefore, the broadband performance of the obtained HWP should originate from the superposition of the three resonances. This multi-resonance characteristic plays a crucial role in significantly improving the performance of the proposed polarization device, including the bandwidth and the transmission efficiency [39,40].
Figure 5 shows the current distributions on the top surfaces of double-T-shaped VO$_2$ resonators and on the VO$_2$ films for the two resonant frequencies of 0.54 THz and 1.32 THz at 87$^\circ$C. At these frequencies, $|r_{yy}|$ reaches the minimum, as shown by Fig. 3(c). Figures 5(a)(c) show that under the $u$-polarized incidence, for both frequencies the induced currents on the VO$_2$ resonators have opposite directions to those on the VO$_2$ film, forming a current loop in the dielectric layer and corresponding to magnetic resonances. Under the $v$-polarized incidence, Figs. 5(b)(d) show that the induced currents on the top surface of the VO$_2$ resonators have the same direction as those on the VO$_2$ film, forming an equivalent electric resonance. Similar to the HWP, when the $u$-component and $v$-component of the reflected fields have equal magnitudes and a phase difference of 90$^\circ$ or 270$^\circ$, an ideal QWP will be achieved. Therefore, the broadband performance of the obtained QWP should also originate from the superposition of multiple resonances.
Fig. 5. Surface current distributions (arrows for the directions and colors for the strengths) on the top surfaces of the VO$_2$ resonators (the $1^\textrm {st}$ and $3^\textrm {rd}$ columns) and of the VO$_2$ film (the $2^\textrm {nd}$ and $4^\textrm {th}$ columns) at the two resonant frequencies of (a)(b) 0.54 THz and (c)(d) 1.32 THz when VO$_2$ is in the conducting state at 87$^\circ$C. The $1^\textrm {st}$ and $2^\textrm {nd}$ columns are for the $u$-polarized incidence, and the $3^\textrm {rd}$ and $4^\textrm {th}$ columns are for the $v$-polarized incidence. The white dashed boxes are zoomed-in views. The black arrows indicate the dominant current directions.
3.3 Tolerance of incident angle and geometric sizes
We now consider the incident angular tolerance of the designed switchable HWP/QWP under TE-polarized incidence (the electric field is polarized along the $y$ direction). Figure 6(a) shows that when the proposed metamaterial functions as an HWP, $\textrm {PCR}>90\%$ holds within a broadband spectral range of 0.58–1.40 THz over a relatively small angular range of 0$^\circ$–20$^\circ$, as indicated by the black dashed box; within a bandwidth of 0.83–1.30 THz, the angular range can be as large as 0$^\circ$–40$^\circ$, as indicated by the white dashed box. Similarly, when the metamaterial functions as a QWP, Fig. 6(b) shows that $\chi >0.98$ holds within a broadband spectral range of 0.66–1.60 THz over a relatively small angular range of 0$^\circ$–20$^\circ$, as indicated by the black dashed box; within a bandwidth of 0.66–1.12 THz, the angular range can reaches 0$^\circ$–40$^\circ$, as indicated by the white dashed box. We should note that the angular-dependent spectra of PCR and ellipticity for the metamaterial under TM-polarized incidence (the electric field is polarized in the $x-z$ plane), as shown in Figs. 6(c)(d), are very similar to those under TE-polarized incidence, consistent with the literature [41,42].
We also investigate the tolerance of the performance of the designed HWP/QWP under normal incidence on some key geometric parameters. For the obtained HWP, Fig. 7(a) shows that for too small $d$ of 6 $\mu$m, the bandwidth of $\textrm {PCR}>0.98$ is smaller than those for $d=11~\mu$m and 16 $\mu$m, and that for too large $d$ of 21 $\mu$m, PCR decreases a lot. Figure 7(b) shows that as $t_\textrm {d1}$ increases from 24 $\mu$m to 44 $\mu$m, PCR increses first and then decreases. Similarly, for the obtained QWP Fig. 7(c) shows that as $g$ increases from 16 $\mu$m to 76 $\mu$m, the ellipticity is closer to $1$ although the corresponding bandwidth decreases. Figure 7(d) shows that $t_\textrm {d2}=40~\mu$m leads to the best performance with near unitary ellipticity over the widest frequency range, and that a 5 $\mu$m difference has little impact on performance.
Fig. 6. (a)(c) PCR and (b)(d) ellipticity for the metamaterial acting as an HWP and a QWP under (a)(b) TE-polarized and (c)(d) TM-polarized incidences, respectively, as functions of incident angle and operation frequency. The black and white dashed boxes indicate the angular and spectral ranges for (a)(c) $\textrm {PCR}>90\%$ and (b)(d) $\chi >0.98$.
Fig. 7. Spectra of (a)(b) PCR and (c)(d) ellipticity for the metamaterial acting as an HWP and a QWP, respectively, as functions of the geometric parameters (in unit of $\mu$m).
4. Conclusions
In conclusions, we have proposed a broadband switchable terahertz HWP/QWP based on a metamaterial composed of multi-layered metal-VO$_2$ structures. Results have shown that when VO$_2$ is in the insulating state, the metamaterial can function as an HWP with PCR greater than 98% within a broad spectral range of 0.58–1.40 THz. By changing the phase of VO$_2$ into the conducting state, which can be done electrically, thermally or optically, results have shown that the metamaterial works as a QWP which converts $y$ polarization into LCP, and the ellipticity is larger than 0.99 over a broad bandwidth of 0.66–1.60 THz. The obtained HWP and QWP share a broad bandwidth of 0.66–1.40 THz, corresponding to a relative bandwidth of 71.8%. We have also found that the broadband and highly efficient HWP/QWP has large angular tolerance and large fabrication tolerance. We expect that the designed broadband and switchable terahertz HWP/QWP can find applications in terahertz imaging, sensing and telecommunication systems. We also expect that the design approaches based on multi-layered metal-VO$_2$ structures can be extended to other spectral regimes, for which VO$_2$ may need to be replaced by proper materials with dynamically tunable/switchable characteristics.
Funding
Shenzhen Fundamental Research and Discipline Layout project (JCYJ20180507182444250); National Natural Science Foundation of China (11574059, 62065005); Natural Science Foundation of Guangxi Province (2018GXNSFAA050043, 2019JJD110007); Innovation Project of Guangxi Graduate Education, China (18YJPYSS23).
Disclosures
The authors declare no conflicts of interest.
References
1. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]
2. J.-M. Hao, M. Qiu, and L. Zhou, “Manipulate light polarizations with metamaterials: From microwave to visible,” Front. Phys. 5(3), 291–307 (2010). [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. J. Zhao, Y. Cheng, and Z. Cheng, “Design of a photo-excited switchable broadband reflective linear polarization conversion metasurface for terahertz waves,” IEEE Photonics J. 10(1), 1–10 (2018). [CrossRef]
5. Y. Cheng, J. Fan, H. Luo, and F. Chen, “Dual-band and high-efficiency circular polarization convertor based on anisotropic metamaterial,” IEEE Access 8, 7615–7621 (2020). [CrossRef]
6. J. Fan and Y. Cheng, “Broadband high-efficiency cross-polarization conversion and multi-functional wavefront manipulation based on chiral structure metasurface for terahertz wave,” J. Phys. D: Appl. Phys. 53(2), 025109 (2020). [CrossRef]
7. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef]
8. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef]
9. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013). [CrossRef]
10. Y. Cheng, W. Withayachumnankul, and A. Upadhyay, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105(18), 181111 (2014). [CrossRef]
11. S. Ma, X. Wang, W. Luo, S. Sun, Y. Zhang, Q. He, and L. Zhou, “Ultra-wide band reflective metamaterial wave plates for terahertz waves,” EPL 117(3), 37007 (2017). [CrossRef]
12. R. Xia, X. Jing, X. Gui, Y. Tian, and Z. Hong, “Broadband terahertz half-wave plate based on anisotropic polarization conversion metamaterials,” Opt. Mater. Express 7(3), 977–988 (2017). [CrossRef]
13. L. Peng, X.-F. Li, X. Jiang, and S.-M. Li, “A novel thz half-wave polarization converter for cross-polarization conversions of both linear and circular polarizations and polarization conversion ratio regulating by graphene,” J. Lightwave Technol. 36(19), 4250–4258 (2018). [CrossRef]
14. L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014). [CrossRef]
15. S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014). [CrossRef]
16. M. T. Nouman, J. H. Hwang, and J.-H. Jang, “Ultrathin terahertz quarter-wave plate based on split ring resonator and wire grating hybrid metasurface,” Sci. Rep. 6(1), 39062 (2016). [CrossRef]
17. Y. Jiang, L. Wang, J. Wang, C. N. Akwuruoha, and W. 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]
18. W. S. Lee, R. T. Ako, M. X. Low, M. Bhaskaran, S. Sriram, C. Fumeaux, and W. Withayachumnankul, “Dielectric-resonator metasurfaces for broadband terahertz quarter-and half-wave mirrors,” Opt. Express 26(11), 14392–14406 (2018). [CrossRef]
19. Z. Han, S. Ohno, Y. Tokizane, K. Nawata, T. Notake, Y. Takida, and H. Minamide, “Off-resonance and in-resonance metamaterial design for a high-transmission terahertz-wave quarter-wave plate,” Opt. Lett. 43(12), 2977–2980 (2018). [CrossRef]
20. Q. He, S. Sun, and L. Zhou, “Tunable/reconfigurable metasurfaces: physics and applications,” Research 2019, 1–16 (2019). [CrossRef]
21. L. Bao and T. J. Cui, “Tunable, reconfigurable, and programmable metamaterials,” Microw. Opt. Technol. Lett. 62(1), 9–32 (2020). [CrossRef]
22. Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Switchable quarter-wave plate with graphene based metamaterial for broadband terahertz wave manipulation,” Opt. Express 23(21), 27230–27239 (2015). [CrossRef]
23. M. R. Tavakol, B. Rahmani, and A. Khavasi, “Terahertz quarter wave-plate metasurface polarizer based on arrays of graphene ribbons,” IEEE Photonics Technol. Lett. 31(12), 931–934 (2019). [CrossRef]
24. 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]
25. D. Wang, L. Zhang, Y. Gu, M. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C.-W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5(1), 15020 (2015). [CrossRef]
26. F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium dioxide integrated metasurfaces with switchable functionalities at terahertz frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018). [CrossRef]
27. Z. Song and J. 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]
28. H. He, X. Shang, L. Xu, J. Zhao, W. Cai, J. Wang, C. Zhao, and L. Wang, “Thermally switchable bifunctional plasmonic metasurface for perfect absorption and polarization conversion based on VO2,” Opt. Express 28(4), 4563–4570 (2020). [CrossRef]
29. 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]
30. H. Jiang, W. Zhao, and Y. Jiang, “Frequency-tunable and functionality-switchable polarization device using silicon strip array integrated with a graphene sheet,” Opt. Mater. Express 7(12), 4277–4285 (2017). [CrossRef]
31. W. Zhang, J. Jiang, J. Yuan, S. Liang, J. Qian, J. Shu, and L. Jiang, “Functionality-switchable terahertz polarization converter based on a graphene-integrated planar metamaterial,” OSA Continuum 1(1), 124–135 (2018). [CrossRef]
32. Y. Li, J. Luo, X. Li, M. Pu, X. Ma, X. Xie, J. Shi, and X. Luo, “Switchable quarter-wave plate and half-wave plate based on phase-change metasurface,” IEEE Photonics J. 12(2), 1–10 (2020). [CrossRef]
33. Z. Jian-Xing, S. Jian-Lin, Z. Yao, L. Yi-Chao, and Z. Jian-Hong, “Switching between the functions of half-wave plate and quarter-wave plate simply by using a vanadium dioxide film in a terahertz metamaterial,” Chin. Phys. Lett. 37(6), 064204 (2020). [CrossRef]
34. M. T. Nouman, J. H. Hwang, M. Faiyaz, K.-J. Lee, D.-Y. Noh, and J.-H. Jang, “Vanadium dioxide based frequency tunable metasurface filters for realizing reconfigurable terahertz optical phase and polarization control,” Opt. Express 26(10), 12922–12929 (2018). [CrossRef]
35. R. T. Ako, W. S. L. Lee, M. Bhaskaran, S. Sriram, and W. Withayachumnankul, “Broadband and wide-angle reflective linear polarization converter for terahertz waves,” APL Photonics 4(9), 096104 (2019). [CrossRef]
36. S. Wietzke, C. Jansen, M. Reuter, T. Jung, D. Kraft, S. Chatterjee, B. Fischer, and M. Koch, “Terahertz spectroscopy on polymers: A review of morphological studies,” J. Mol. Struct. 1006(1-3), 41–51 (2011). [CrossRef]
37. S. 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]
38. H.-T. Zhang, L. Zhang, D. Mukherjee, Y.-X. Zheng, R. C. Haislmaier, N. Alem, and R. Engel-Herbert, “Wafer-scale growth of vo2 thin films using a combinatorial approach,” Nat. Commun. 6(1), 8475 (2015). [CrossRef]
39. X. Gao, X. Han, W.-P. Cao, H. O. Li, H. F. Ma, and T. J. Cui, “Ultrawideband and high-efficiency linear polarization converter based on double v-shaped metasurface,” IEEE Trans. Antennas Propag. 63(8), 3522–3530 (2015).
40. H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, “Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances,” J. Appl. Phys. 115(15), 154504 (2014). [CrossRef]
41. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014). [CrossRef]
42. L. Peng, X.-F. Li, X. Jiang, and S.-M. Li, “A novel thz half-wave polarization converter for cross-polarization conversions of both linear and circular polarizations and polarization conversion ratio regulating by graphene,” J. Lightwave Technol. 36(19), 4250–4258 (2018). [CrossRef]
