Open Access
Add to BibSonomy
Abstract
Developing the broadband controllable or tunable terahertz (THz) polarization and phase devices are in an urgent need. In this paper, we demonstrate a broadband controllable THz quarter-wave plate (QWP) with double layers of graphene grating and a layer of liquid crystals. The double layer graphene gratings can achieve a switchable QWP to switch between linear-to-linear and linear-to-circular polarization states with over 0.35THz bandwidth in the ON or OFF state by applying biased electric field on the graphene grating or not. Moreover, this QWP based on the structure of periodic gradient grating can significantly enhance the phase difference between two orthogonally polarized components compared to that based on equal-periodic grating structure because of the additional phase distribution of the gradient structures. Furthermore, we incorporate liquid crystals into the graphene grating to form a tunable QWP, of which operating frequency can be continuously tuned in a wide frequency range by electrically controlling the molecular director of the liquid crystals. The results show that the graphene periodic gradient grating with LCs not only broadens the operating bandwidth, but also reduces the external electric field. This device offers a further step in the development of THz polarization and phase devices for potential applications in THz polarized imaging, spectroscopy, and communication.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, THz wave has been widely used in imaging, spectroscopy, sensing, and communication with the rapid development of terahertz (THz) science and technology [1–4]. For further applications and developments of THz wave, THz functional devices such as THz switches [5], filters [6], polarizers [7–9], phase shifters [10,11], and wave plates [12,13] are essential. Many natural uniaxial crystalline materials have weak responses to THz wave and have low birefringence, narrowband, large loss, huge volume, and high prices, so that conventional polarization optics devices in the THz frequency range are limited [14–16]. Therefore, developing the new THz polarization and phase devices are in an urgent need for many practical applications.
Recently, the artificial metasurfaces or metamaterials, can enable more flexible manipulation of the electromagnetic (EM) waves and provide a promising pathway towards the realizing of THz polarization and phase devices at THz frequencies [17,18]. By careful design of the geometries, the amplitude, phase, and polarization of the output wave of these single-layered or multi-layered metallic structures can be easily engineered to realize polarization converter, polarization rotation or dichroism [19–21]. However, once fabricated, most of these polarization and phase devices are neither electrically switchable nor dynamically tunable. Graphene, a novel two-dimension (2D) material, has recently attracted great attentions of the research communities due to its extraordinary mechanical, electronic and optical properties. The combination of graphene with metasurfaces has been successfully applied into the THz transmitted and reflective polarization devices to realize electrically switchable polarization manipulation [13,22–24]. Nevertheless, the reflective polarization devices always have narrow bandwidth though they have a high polarization conversion rate (PCR) [22–24]. While the transmitted polarization devices can enlarge the bandwidth, but they introduce the low transmittance due to the insertion loss in the multi-interfaces and also have difficulty in fabrication [13].
Liquid crystals (LCs) are active phase shift materials from optical down to THz frequencies, which can be employed in dynamically tunable THz polarization devices due to its large optical anisotropy and can be flexibly manipulated by thermal, electrical, optical or magnetic field [25]. However, in the THz frequency range, the high-performance LC devices, which including larger phase modulation depth and faster tuning speed under a lower external electric field, remain to be further explored and improved. Therefore, in order to realize higher PCR, lower loss, and larger bandwidth, the active LC phase shift effects within graphene metasurfaces provide a newly strategy for THz broadband tunable polarization devices.
Herein, we proposed a broadband electrically controllable quarter-wave plate (QWP) for efficient THz polarization conversion, which consists of double layers of graphene grating and a layer of LCs. The results demonstrate that the graphene grating can achieve a switchable QWP to convert a linear polarization to a left-handed circular polarization (LP to LCP) or a right-handed circular polarization (LP to RCP) in the ON state, while this device remains the same LP output in the OFF state when no biasing is applied on the graphene grating. The comparison indicates that the periodic gradient grating (PGG) structure has a larger phase difference than that of the equal-period grating (EPG) owing to the additional gradient phase distribution. Moreover, the combination of the switching characteristics of graphene and the tuning characteristics of LCs leads to a broadband tunable THz QWP based on the graphene EPG or PGG with LCs (EPGLC or PGGLC). The results show that the PGGLC not only broadens the operating bandwidth, but also reduces the tuning voltage compared with the EPGLC.
2. Switchable QWP based on graphene grating
The schematic diagram of the QWP based on graphene grating is illustrated in Fig. 1, which is composed of double monolayer graphene films structured as wire grid grating, and this double monolayer graphene films are separated by a t1 = 10μm thick silica spacing layer and a t0 = 250μm thick silica substrate. The graphene wire grids are oriented 45° with respect to the y axis and the polarization direction of the incident waves is along the x axis. There are two kinds of graphene gratings designed: EPG and PGG. The EPG structure is the ordinary grating that has the uniform graphene grid width of W = 12μm and the air gap of g = 8μm, so that its grating constant is 20μm as shown in Fig. 1(a). For the PGG, the 4 gradient increasing grids line as a gradient grid group, which has an initial grid width of W1 = 24μm and a uniform difference of 4μm in the adjacent grids, W2 = 28μm, W3 = 32μm, W4 = 36μm, so the whole width of this gradient grid group is P = 200μm as shown in Fig. 1(b). Several grid groups are periodically arranged to form the graphene PGG. Therefore, this PGG is still a periodic structure, but a series of aperiodic gradient grids formed one large lattice cell. Notice that, both EPG and PGG have the same filling factor fEPG = fPGG = 12/20 in our design for comparison.
Fig. 1 The schematic diagram of the graphene gratings operating as switchable QWP: (a) EPG; (b) PGG, and the parameters are the following: W = 12μm, g = 8μm, P = 200μm, W1 = 24μm, W2 = 28μm, W3 = 32μm, W4 = 36μm, t1 = 10μm, td = 50nm. The structure of the graphene electrodes is also inserted in this figure.
The surface conductivity of a monolayer graphene film can be calculated by the Kube formula, which is described with interband and intraband contributions as [26]
where is the Fermi–Dirac distribution, e is the electron charge, ω is the radian frequency of THz waves, μc is the chemical potential (i.e. Fermi energy EF), Γ = 0.11meV is the scattering rate, kB is the Boltzmann constant, ћ is the reduced Planck's constant, and T = 300K at room temperature in our discussion.In order to achieve a sufficient chemical potential under a low bias voltage, we use a pair of ultrathin and transparent conductive layer (e.g. doped silicon) as negative back electrode in our devices. The monolayer graphene films connect to the positive electrode, and there is a thin dielectric layer between the back electrode and the graphene film as shown in Fig. 1(a). When EF>>kBT, the chemical potential of graphene can be controlled by applying a bias voltage, which can be expressed by [27,28]
where νf = 106m/s is the Fermi velocity, td = 50nm and εd = 3.89 are the thickness and the permittivity of dielectric layer thin dielectric layer between the back electrode and the graphene, ε0 is the permittivity of vacuum, Vg is the bias voltage. According to Eqs. (1) and (2), it is obvious that the surface conductivity depends on μc which can be tuned by bias voltage Vg.The basic working principle of these devices is designed as follows: when there is no biasing (Vg = 0V), the chemical potential of graphene μc = 0eV, the conductivity of graphene is as low as the dielectric material in the THz regime, so such thin dielectric structure will not change the polarization state of the incident wave. In this case, an incident LP mode outputs the same LP mode through the graphene grating, so we call it OFF state. When there is a bias voltage Vg = 43.1V applied leading to μc = 0.5eV, which is calculated by Eq. (2), the conductivity of graphene is as high as the metal-like material in the THz regime by Eq. (1) [29], and this double layers graphene grating shows the strong optical anisotropy in the THz regime not only due to the structural asymmetry but also the effect of localized field enhancement between the double layers of graphene. This large artificial birefringence can be applied as the wave plate. Here, we choose the filling factor f = 12/20, which would lead to the nearly identical transmission amplitudes of the orthogonal polarization components and the phase differences shows a positive linearly increasing dependence on frequency. In this case, this graphene grating can work as a QWP in the certain THz frequency band to convert a LP mode as a LCP or RCP mode, so we call it ON state. Thus, this QWP can be switched between OFF and ON by the electrical biasing.
A single layer graphene grating has a very low phase difference (<<0.5π) due to insufficient thickness, and its co-polarized and cross-polarized amplitude transmissions Txx≠Tyx, so it cannot achieve a THz QWP. Instead, the double layers of graphene grating can achieve a high-performance QWP due to the localized enhancement effect in the spacer layer between the double layers of graphene as a cavity structure. If the thickness of spacer layer is too small, the phase difference between two orthogonal components is small (<0.5π). But if it is too thick, the resonances between the two layers of graphene are located in the operating frequency range of 0.2-2THz, and the transmission will decrease accordingly, so it is also impossible to realize a high-performance QWP. Therefore, the thickness of spacer layer is a critical parameter that is designed optimally as t1 = 10μm in this work.
We simulate the transmission signals by using Lumerical FDTD Solution based on the finite difference time domain method. In our simulation, periodic boundary conditions are applied in the x and y directions representing a unit cell, and an open boundary condition is set in the z direction. The plane wave is normally incident into the structure along the z axis, and the polarization direction of the incident waves was along the x axis. All the material and geometric parameters in the simulation modeling are used the data mentioned above. The co-polarized and cross-polarized amplitude transmission Txx and Tyx are obtained by Txx = Exx/Eair and Tyx = Eyx/Eair, and the phase difference between two orthogonally polarized components is defined as φ = φyx-φxx = arg(Tyx)-arg(Txx). To determine the polarization state of THz wave, we introduce the Stokes parameters as follows [30]:
The performance of the QWP is indicated by the relative electric field S0, polarization azimuth angle α and normalized ellipticity χ, which are defined as α = 0.5arctan(S2/S1) and χ = S3/S0, where χ = 0, 1 or −1 indicating a perfect LP, LCP or RCP wave, respectively, and they can be obtained by using these four parameters. The results shown in Fig. 2 are the transmissions and polarization azimuth angles of the graphene gratings without biasing (μc = 0eV), which indicates that the graphene grating is switched in the OFF state in the frequency range of >0.9THz for the EPG and >0.7THz for the PGG. According to Eq. (1), the surface conductivity of graphene is the function of frequency, and the lower the frequency, the larger the surface conductivity is. This means that the graphene film still presents the weak metal-like property in the frequency range of 0-0.9THz for the EPG or 0-0.7THz for the PGG even at 𝜇c = 0eV, so a poor polarization conversion will occur in this case, and some intensity of cross-polarized component can be detected. This structure indicates a low frequency cut-off characteristic.
Fig. 2 Co-polarized and cross-polarized amplitude transmissions, polarization azimuth angles, and the corresponding ellipticities of the graphene gratings in the OFF state: (a) EPG; (b) PGG.
When the graphene grating is biased (μc = 0.5eV), χ>0.95 and Txx≈Tyx in the range of 1.2-1.55THz for the EPG and 0.8-1.18THz for the PGG, as shown in Figs. 3(a) and 3(b), respectively, so they are switched to the ON state of the QWP. In the operating bandwidth of these QWPs marked by yellow region (where χ>0.95 and Txx≈Tyx conditions can be satisfied) in Fig. 3, these switchable QWPs can convert a LP to a near-perfect LCP or RCP. In this case, the conversion efficiency is meaningful, which can be expressed by η = (|Exx| + |Eyx|)/|E0|, where |Exx| and |Eyx| are the amplitude for the co-polarized and cross-polarized components at the central operating frequency, and |E0| = 1 is the total amplitude of incident wave. For example, the amplitude for the co-polarized and cross-polarized components are |Exx| = 0.422 and |Eyx| = 0.437 respectively as shown in Fig. 3(a), so η = 0.859 for the EPG, while |Exx| = 0.406 and |Eyx| = 0.403 as shown in Fig. 3(b), so η = 0.809 for the PGG.
Fig. 3 Co-polarized and cross-polarized amplitude transmissions, phase differences between orthogonal components, and the corresponding ellipticities of the graphene gratings in the ON state: (a) EPG; (b) PGG.
Although the operating bandwidth of PGG is only a little larger than that of EPG (380GHz v.s. 350GHz), it is worth noting that the PGG graphene grating has a larger phase difference compared to that of the EPG at the same frequency with the same filling factor, so it reaches π/2 phase difference in a lower frequency range, of which central frequency is 1THz v.s. 1.4THz. Therefore, it is more meaningful to define “effective operating bandwidth” expressed by Δω/ω0, where Δω and ω0 are the bandwidth and the central frequency, respectively. The effective operating bandwidth of EPG is 0.25. The central frequency of the PGG moves down to 1.0THz and its effective bandwidth increases to 0.38, which is 1.52 times to the EPG, so the effective operating bandwidth of PGG is significantly improved compared with that of EPG.
The reason for this is resulting from the gradient grids of the PGG. The propagation constant difference between the two orthogonally polarized components of the PGG can be expressed as follows:
where Δkg is the difference of propagation constant between the two orthogonally polarized components from the spatial asymmetry of the wire grating, which is determined by the filling factor of grating structure; and Δkɑ is the additional wave vector introduced by the spatial dispersion of the gradient structure perpendicular to the wire direction, which is determined by the spatial distribution of subwavelength structure. Because the EPG and PGG have the same filling factor in our design, so they have the same Δkg, but the EPG has no Δkɑ since it is a complete periodic structure. On account of this, the PGG graphene grating has a larger, which means a larger phase difference than that of the EPG at the same frequency range. Therefore, it reaches π/2 phase delay at the lower frequency range, and accordingly, the operating frequency of QWP moves to a lower frequency range.Moreover, by rotating the orientation of graphene grating 90° along the center of the structure, the device can change the polarization state from LP to RCP in the same frequency range. However, both graphene gratings are switched ON with a narrow bandwidth of less than 0.4THz. In the next section, to obtain a broadband tunable QWP, we introduce LCs into the graphene grating.
3. Broadband tunable QWP based on graphene grating with LCs
The schematic diagrams of the broadband tunable QWP based on the graphene grating with LCs (EPGLC and PGGLC) are illustrated in Fig. 4. A t2 = 250μm thick LCs layer is filled between the double layers of graphene grating and the silica substrate. The LCs used in this work is NJU-LDn-4 because of its large dielectric anisotropy with no = 1.5 and ne = 1.8 in the wide frequency range from 0.4 to 1.6THz at room temperature [31]. The direction of the external electric field is along the y axis. When no voltage is applied, the LC molecules are arranged in the direction of x axis and the angle between the director angle of LCs and x axis defines as θ = 0°, anchored by a thin alignment layer. The director angle θ is an average angle of LC molecules over the whole LC layer. When the voltage is applied on the electrodes of LCs layer, the LC molecules will be rotated to tend the direction of the electric field. Wang et al. experimentally demonstrated the external voltage of 50V can make the LC molecules of NJU-LDn-4 rotate from 0 to 90° with the two electrodes’ interval d = 0.25mm [32]. Therefore, the interval between the two electrodes in our simulation is also designed to 0.25mm, so the required maximum external voltage is 50V. Since the relationship between the bias voltage and director angle are nonlinear, in order to analyze conveniently, we use the changes of director angle to describe the dynamic optical response of LCs in the following simulation and discussion. The LCs is modeled as a uniaxial model, and its refractive index is given by the tensor as follows [33]
The phase difference between two orthogonally polarized components can be calculated bywhere c is the speed of light in vacuum, f is the frequency, t2 is the thickness of LCs, neffx and neffy are the refractive indices of the x components and y components, which are the function of θ by Eq. (5), and φ0 is the phase difference between the two orthogonally polarized components of output THz waves through double layers of graphene grating. When the different bias voltage is applied, the birefringence of LCs and the phase differences of the whole device will be changed with the dynamic change of the director angle.Fig. 4 Schematic diagram of the broadband tunable QWP based on graphene grating with LCs: (a) EPGLC; (b) PGGLC, and the thickness of LCs layer is t2 = 250μm.
Figure 5 shows the phase difference of the graphene grating with LCs oriented different director angles at different frequencies in the ON state. The phase difference is increased as the director angle of LCs or frequency increase. By adjusting appropriate director angles of LCs corresponding to the different frequency points, the phase difference φ can be equal to 0.5π or 1.5π a wide frequency range, which labeled by the red solid lines and the blue dashed lines in Figs. 5(a) and 5(b). Therefore, the graphene grating with LCs can work as a QWP of which central frequency can be broadly tuned by applying different biasing on the electrodes of LCs to make the director angles of LCs rotate from 0° to 90°. Taking into account the switching characteristics of the graphene grating mentioned in the previous section, there is a lower limit of the operating frequency range of these two QWPs, which is 0.9THz for the EPGLC and 0.7THz for the PGGLC. When the f>1.6THz, Txx≠Tyx, so it cannot obtain the circularly polarized wave but the elliptically polarized wave, and the upper limit of the operating frequency range of these QWPs is 1.6THz. Therefore, the operating frequency range of the QWP is 0.9-1.6THz with its bandwidth of 0.7THz for the EPGLC, while the operating frequency range of the PPGLC is 0.7-1.6THz with its bandwidth of 0.9THz, which is greater than the former. To compare the performance of these two wideband QWPs better, we put their work curves into the same figure, as shown in Fig. 5(c). In addition, when these two QWPs work at the same frequency point, and under the same conditions, the required director angle of LCs in the PPGLC is smaller than that in the EPGLC, which means that the tuning voltage of the device for twisting the LC molecules of the PPGLC is also lower than the EPGLC. Moreover, the PPGLC can also reach 1.5π phase delay in the range of 1.45-1.6THz by applying different biasing on the electrodes of LCs to make the director angles of LCs rotate from 69° to 90°, of which a LP wave is converted to a RCP wave. In summary, the QWP based on the PPGLC not only broadens the operating bandwidth, but also reduces the tuning voltage of the device for twisting the LC molecules, thus improving the device’s operating performance.
Fig. 5 Phase difference of the graphene grating with LCs oriented different director angles at different frequencies in the ON state: (a) EPGLC; (b) PGGLC. The red solid lines and blue dashed lines indicate the phase difference is just equal to 0.5π and 1.5π. (c) Comparison of operating curves of these two QWPs.
To further study the performance of polarization conversion, we simulate the transmission, phase difference and ellipticity of these two QWPs in the ON state at 0.9THz and 1.6THz, respectively, as shown in Fig. 6. For the EPGLC, the two orthogonally polarized components are 0.487 and 0.488, the conversion efficiency η = 0.975, and the ellipticity χ equals nearly to 1 when the operating frequency f = 0.9THz as shown in Fig. 6(a), which indicates that the LP is converted to the LCP, at this point, the required director angle of LCs is 58°. when the operating frequency f = 1.6THz, the required director angle of LCs is 43°, Exx = 0.424 and Eyx = 0.487, η = 0.911, and the LP is converted to LCP with χ≈1, as shown in Fig. 6(b). However, for the QWP based on the PGGLC, the required director angle of LCs θ equals to 51°, which is smaller than the EPGLC, and Exx = 0.398, Eyx = 0.454, η = 0.852, and the LP is converted to LCP with χ≈1 at the same operating frequency 0.9THz, as shown in Fig. 6(c). Similarly, when the operating frequency f = 1.6THz, θ = 29°<43°, Exx = 0.4 and Eyx = 0.362, η = 0.762, and the LP is converted to LCP with χ≈1, as shown in Fig. 6(d). Moreover, it also can be seen as a QWP with a RCP with χ≈-1 in the frequency range of 1.45-1.6THz, we simulate the transmissions, phase differences and ellipticities of these two QWPs in the ON state at 1.45THz and 1.6THz, as shown in Figs. 7(a) and 7(b), respectively. When the operating frequency f = 1.45THz and 1.6THz, the required director angles of LCs are 90° and 69°, respectively.
Fig. 6 Transmissions, phase differences and the corresponding ellipticities of these two QWPs in the ON state at different operating frequencies: (a) EPGLC, f = 0.9THz; (b) EPGLC, f = 1.6THz; (c) PGGLC, f = 0.7THz; (d) PGGLC, f = 1.6THz.
Fig. 7 Transmissions, phase differences and the corresponding ellipticities of the broadband tunable QWP based on the PGGLC structure in the ON state at different operating frequencies: (a) f = 1.45THz; (b) f = 1.6THz.
Therefore, combining the switching characteristics of graphene with the tuning characteristics of LCs, two broadband controllable THz QWPs based on the graphene grating with LCs can be obtained in the frequency range of 0.9-1.6THz for the EPGLC and 0.7-1.6THz for the PGGLC, which has two basic functions: one is switched between LP-to-LP mode in the OFF state and LP-to-LCP (or -RCP) mode in the ON state by applying biasing on the graphene grating or not; the other is tuned the central operating frequency in a wide frequency range to realize a tunable LP-to-LCP (or -RCP) conversion by applying the different biasing on the LCs’ electrodes when the device is in the ON state.
4. Conclusion
In conclusion, we designed two kinds of QWPs based on the double layer graphene gratings: EPG and PGG. The results show that the double layer graphene gratings can achieve a switchable QWP to switch between the LP-to-LP mode in the OFF state and LP-to-LCP (or RCP) mode in the ON state with over 0.35THz bandwidth by applying biasing on the graphene grating or not. Moreover, this QWP based on the graphene PGG structure can significantly enhance the phase difference between two orthogonally polarized components compared to that of EPG structure because of the additional phase distribution of the gradient structures. Furthermore, by incorporating LCs into the graphene grating to form a tunable QWP, of which operating frequency can be continuously tuned by electrically controlling the molecular director of the liquid crystals in a wide frequency range of 0.7-1.6THz for the PGGLC, which is wider than the EPGLC. Under the same conditions, the required director angle of LCs for the PPGLC is smaller than the EPGLC when they work at the same frequency, which indicate that the PGGLC can significantly reduce the tuning voltage of the device for twisting the LC molecules, and the device’s operating performance is improved. Therefore, the large bandwidth, lower tuning voltage and switching characteristics of the device will be of great significance for potential THz polarization and phase control applications.
Funding
National Natural Science Foundation of China (NSFC) (61505088, 61671491); Young Elite Scientists Sponsorship Program by Tianjin (TJSQNTJ-2017-12); National Basic Research Program of China (Program 973) (2014CB339800); State’s Key Project of Research and Development Plan (Grant No. 2016YFC0101002).
References and links
1. K. H. Jin, Y. G. Kim, S. H. Cho, J. C. Ye, and D. S. Yee, “High-speed terahertz reflection three-dimensional imaging for nondestructive evaluation,” Opt. Express 20(23), 25432–25440 (2012). [CrossRef] [PubMed]
2. W. L. Lu and A. Argyros, “Terahertz spectroscopy and imaging with flexible tube-lattice fiber probe,” J. Lightwave Technol. 32(23), 4019–4025 (2014).
3. F. Fan, X. Zhang, S. Li, D. Deng, N. Wang, H. Zhang, and S. Chang, “Terahertz transmission and sensing properties of microstructured PMMA tube waveguide,” Opt. Express 23(21), 27204–27212 (2015). [CrossRef] [PubMed]
4. H. Shams, M. J. Fice, K. Balakier, C. C. Renaud, F. van Dijk, and A. J. Seeds, “Photonic generation for multichannel THz wireless communication,” Opt. Express 22(19), 23465–23472 (2014). [CrossRef] [PubMed]
5. G. C. Wang, J. N. Zhang, B. Zhang, T. He, Y. N. He, and J. L. Shen, “Photo-excited terahertz switch based on composite metamaterial structure,” Opt. Commun. 374, 64–68 (2016). [CrossRef]
6. J. Yang, C. Gong, L. Sun, P. Chen, L. Lin, and W. Liu, “Tunable reflecting terahertz filter based on chirped metamaterial structure,” Sci. Rep. 6(1), 38732 (2016). [CrossRef] [PubMed]
7. L. Q. Cong, N. N. Xu, W. L. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3(9), 1176–1183 (2015). [CrossRef]
8. Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Realizing broadband and invertible linear-to-circular polarization converter with ultrathin single-layer metasurface,” Sci. Rep. 5(1), 18106 (2016). [CrossRef] [PubMed]
9. F. Fan, S. T. Xu, X. H. Wang, and S. J. Chang, “Terahertz polarization converter and one-way transmission based on double-layer magneto-plasmonics of magnetized InSb,” Opt. Express 24(23), 26431–26443 (2016). [CrossRef] [PubMed]
10. K. Altmann, M. Reuter, K. Garbat, M. Koch, R. Dabrowski, and I. Dierking, “Polymer stabilized liquid crystal phase shifter for terahertz waves,” Opt. Express 21(10), 12395–12400 (2013). [CrossRef] [PubMed]
11. Y.-Y. Ji, F. Fan, M. Chen, L. Yang, and S.-J. Chang, “Terahertz artificial birefringence and tunable phase shifter based on dielectric metasurface with compound lattice,” Opt. Express 25(10), 11405–11413 (2017). [CrossRef] [PubMed]
12. L. Wang, S. Ge, W. Hu, M. Nakajima, and Y. Lu, “Tunable reflective liquid crystal terahertz waveplates,” Opt. Mater. Express 7(6), 2023–2029 (2017). [CrossRef]
13. 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] [PubMed]
14. K. Wiesauer and C. Jordens, “Recent advances in birefringence studies at THz frequencies,” J. Infrared Millim. Tech. 34(11), 663–681 (2013). [CrossRef]
15. A. K. Kaveev, G. I. Kropotov, E. V. Tsygankova, I. A. Tzibizov, S. D. Ganichev, S. N. Danilov, P. Olbrich, C. Zoth, E. G. Kaveeva, A. I. Zhdanov, A. A. Ivanov, R. Z. Deyanov, and B. Redlich, “Terahertz polarization conversion with quartz waveplate sets,” Appl. Opt. 52(4), B60–B69 (2013). [CrossRef] [PubMed]
16. J. B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31(2), 265–267 (2006). [CrossRef] [PubMed]
17. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef] [PubMed]
18. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014). [CrossRef] [PubMed]
19. L. Q. Cong, N. N. Xu, J. Q. Gu, R. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014). [CrossRef]
20. 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] [PubMed]
21. Z. J. Wang, H. Jia, K. Yao, W. S. Cai, H. S. Chen, and Y. M. Liu, “Circular dichroism metamirrors with near-perfect extinction,” ACS Photonics 3(11), 2096–2101 (2016). [CrossRef]
22. X. Y. Yu, X. Gao, W. Qiao, L. L. Wen, and W. L. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016). [CrossRef]
23. M. Chen, W. Sun, J. J. Cai, L. Z. Chang, and X. F. Xiao, “Frequency-tunable mid-infrared cross polarization converters based on graphene metasurface,” Plasmonics 12(3), 699–705 (2017). [CrossRef]
24. Z. Liu and B. Bai, “Ultra-thin and high-efficiency graphene metasurface for tunable terahertz wave manipulation,” Opt. Express 25(8), 8584–8592 (2017). [CrossRef] [PubMed]
25. H. Park, E. P. J. Parrott, F. Fan, M. Lim, H. Han, V. G. Chigrinov, and E. Pickwell-MacPherson, “Evaluating liquid crystal properties for use in terahertz devices,” Opt. Express 20(11), 11899–11905 (2012). [CrossRef] [PubMed]
26. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
27. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
28. Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014). [CrossRef] [PubMed]
29. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]
30. D. Goldstein and D. H. Goldstein, “The Stokes Polarization Parameters,” in Polarized Light, Revised and Expanded (Marcel Dekker Inc., 2003), pp. 49–81.
31. L. Wang, X. W. Lin, X. Liang, J. B. Wu, W. Hu, Z. G. Zheng, B. B. Jin, Y. Q. Qin, and Y. Q. Lu, “Large birefringence liquid crystal material in terahertz range,” Opt. Mater. Express 2(10), 1314–1319 (2012). [CrossRef]
32. L. Wang, X. W. Lin, W. Hu, G. H. Shao, P. Chen, L. J. Liang, B. B. Jin, P. H. Wu, H. Qian, Y. N. Lu, X. Liang, Z. G. Zheng, and Y. Q. Lu, “Broadband tunable liquid crystal terahertz waveplates driven with porous graphene electrodes,” Light Sci. Appl. 4(2), e253 (2015). [CrossRef]
33. I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]
