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Abstract
In this letter, we have proposed a bi-functional switchable broadband polarization converter based on the hybrid graphene-metal metasurface. Turning the bias voltage to change Fermi level Ef from 0 to 1.0 eV, the metasurface can switch between quarter-wave plate (QWP) and half-wave plate (HWP) in the frequency band 1.38-1.72 THz. Besides, the metasurface simultaneously works as a broadband QWP and HWP in different frequency range when Ef = 1.0 eV. In addition, when Ef is in the range of 0.3 eV-0.6 eV, the metasurface can work as bi-functional broadband QWP in different frequencies as well. The physical mechanism of the bi-functional polarization converter can be explained by the electric field amplitude distributions. What’s more, we find that the metasurface can work well with a tolerance to the incident light polarization angle of about ± 12.5°, which can also change the converted wave from RHCP to LHCP with the incident polarization angle change of 90°. The hybrid metasurface with the advantages of switchable bi-functions, wide operating bandwidth, and ultra-thin thickness, may achieve potential applications in tunable devices for terahertz communications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, with the development of generation and detection technology, terahertz (THz) wave has attracted increasing attentions for its superior features, which leads to the broad application prospect, such as telecommunications, security inspections, and imaging etc [1]. For further implementation of the applications, many efforts have been made to manipulate the THz wave, in which polarization is one of the most significant regulation parameters to develop related devices, such as switches and polarization converters. The traditional way to control the polarization is employing birefringent materials or chiral materials, which are mostly in large volume and limit the integration [2]. Such a defect can be overcome by the metasurface, which is an artificial layered material that can adjust the polarization, amplitude and phase of electromagnetic waves flexibly and effectively in various frequency ranges. Till now, many polarization conversion devices based on metasurface have been proposed, such as linear-to-linear [3–7], linear-to-circular [8,9], and circular-to-circular polarization converters [10], in which the actively tunable THz polarization converters gradually become an important research focus due to the application requirements.
Graphene is one of the most widely used active materials in tunable optical device design, due to its excellent features, such as good optical transparency, adjustable electromagnetic performance [11], and high electron mobility [12,13]. Up to now, pure graphene metasurfaces [14–18], graphene-metal hybrid metasurfaces [19–23] and graphene-dielectric hybrid metasurfaces [24] have been reported to actively control the polarization state. Among these studies, some developments have been made in designing broadband or bi-functional polarization converters, which have become two major trends. Based on these researches, integrating both broadband and bi-function into one metasurface is also important in practical applications.
In this paper, we propose a bi-functional switchable broadband THz polarization converter based on a graphene-metal hybrid metasurface, which is composed of a square ring formed by the gold double split-ring and the complementary graphene double split-ring on the top of a bi-layer dielectric spacer over the fully reflective gold mirror. Adjusting the Fermi level Ef from 0 to 1.0 eV, the hybrid metasurface can work as different wave plates in different bands. At the OFF state, where Ef = 0, the metasurface works as a broadband quarter-wave plate (QWP). At the ON state, where Ef = 1.0 eV, the metasurface works as a broadband QWP at lower frequencies and also a half-wave plate (HWP) at higher frequencies. In the frequency band 1.38-1.72 THz, the metasurface can switch between QWP and HWP by turning the bias voltage. Besides, when Ef is in the range of 0.3 eV-0.6 eV, the metasurface can work as bi-functional broadband QWP as well, simultaneously converting the x-polarized incident wave into the left-hand circular polarization (LHCP) wave at lower frequencies and into the right-hand circular polarization (RHCP) wave at higher frequencies. Our proposed graphene-metal hybrid metasurface can convert the linear-polarized incident wave into different polarization states at different bands by turning the Fermi levels, with the advantages of switchable bi-functions, wide operating bandwidth, and ultra-thin thickness, which may achieve potential applications in tunable devices for THz communications.
2. Structure design
The graphene-metal metasurface is constructed by a square ring consisting of the anisotropic double-split gold ring and the complementary double-split graphene ring, which is on a bi-layer dielectric spacer (SiO2/Neltec NY9208) over the golden mirror, as schematically shown in Fig. 1(a). In simulation, we use the finite-difference time-domain (FDTD) method to calculate the reflections, where periodic boundary conditions are used in both the x and y directions, and perfectly matched layers are applied in the z direction. We set the conductivity of gold as 4.1×107 S/m, the refractive index of SiO2 as n1 = 2, and the refractive index of Neltec NY9208 as n2 = 1.73. As a result, the geometric parameters are optimized as shown in Figs. 1(b) and 1(c).
Fig. 1. (a) The schematic diagram of the polarization converter. (b) The top view and (c) the side view of the unit cell, in which the geometric parameters are p = 82 µm, w = 5 µm, g = 26 µm, l = 46 µm, s = 10 µm, h = 0.28 µm, h1 = 0.8 µm, and h2 = 33 µm.
The optical conductivity of graphene, including in-band and inter-band contributions, can be derived from Kubo's formula below [25],
The feasible manufacturing processes are as follows. Firstly, the thick Au layer can be deposited on the back side of the Neltec NY9208 substrate by electron beam evaporation. Then an ultrathin and transparent conductive layer serving as the bottom gate [28] and the silica layer can be successively deposited onto the front side of Neltec NY9208. Here, the Neltec NY9208 is an ideal material to act as the spacer in our design due to its low absorption and high transparency in terahertz frequency, while the silica layer acts as an adhesive layer making the graphene easy to be transferred. Then, the graphene layer grown by CVD can be transferred onto the silica layer, which can be etched by oxygen plasma to obtain the designed pattern. Next, the complementary metal structures can be achieved by standard lithography. Finally, a thin transparent ion-gel layer can be spin-coated onto the structures, contacting to the Au electrode serving as the top gate. As a result, external voltage can be applied by connecting the bottom gate and the top gate to tune the Ef of graphene. Setting ε0 and ε1 to represent the permittivity of vacuum and silica, respectively, the Ef can be tuned by the external voltage Vex following the expression of $ E_f\approx \hbar v_f\sqrt {\pi \varepsilon _0\varepsilon _1V_{{\rm ex}}/eh_1} $ [29], which then modulates the surface conductivity σg to affect the optical response of the metasurface.
3. Numerical results and discussions
In this paper, we take the x-polarized incident light for analyzation. The reflected wave is expressed as Er = Exrex + Eyrey = |rxx|exp(iΦxx)Exiex + |ryx|exp(iΦyx)Eyiey, where |rxx| and |ryx| are the reflection coefficients related to x-to-x and x-to-y polarization conversion, respectively, and Φxx and Φyx are the corresponding phases. The Stoke parameters [30,31] were introduced to describe polarization conversion as follows,
When ΔΦ = Φxx - Φyx = 2nπ ± π (n is an integer), the x-polarized incident light can be reflected to y-polarized light. The polarization conversion rate (PCR) to describe its conversion efficiency can be defined as PCR = |ryx|2 / I [32]. In this way, PCR = 0 means no linear polarization conversion, and PCR = 1 is related to complete linear polarization conversion.
Firstly, we calculate the reflection of the complete metal square ring without graphene, and the simulations results of the |rxx| and |ryx| are shown by the dotted lines in Fig. 2(a). It is obvious that there is no polarization conversion, corresponding with the dotted lines indicating χ = 0 in Fig. 2(b). Replacing the diagonal parts of the gold ring as graphene double split-ring, as shown in Fig. 1(a), the symmetry is broken to result in the polarization conversion. Adjusting the external voltage to 0 V, Ef = 0, this state is labelled as OFF and the simulation results are shown by the solid lines in Figs. 2(a) and 2(b). We can see that the reflection coefficients |rxx| and |ryx| are approximately equal to each other, accompanied by the phase difference close to -π/2. Besides, the normalized ellipticity χ is almost -1 in the frequency range of 1.12-1.72 THz. Therefore, the hybrid metasurface can convert the x-polarized incident wave into the RHCP reflected wave at the OFF state, working as a broadband QWP. Turning the voltage to 4.5 V to increase the Ef to 1 eV, the state is labelled as ON. As shown in Fig. 2(c), the reflection coefficient |ryx| is much larger than |rxx| in 1.38-1.85 THz, with the phase difference close to -π or 0. In the meanwhile, the PCR larger than 0.9, as displayed in Fig. 2(d). Thus, the metasurface efficiently converts the x-polarized incident wave into y-polarized reflected wave at the ON state, working as a broadband HWP. As a result, controlling the Ef to switch between ON and OFF states, the graphene-metal hybrid metasurface can work as a switchable broadband wave plate, efficiently converting between QWP and HWP in the frequency range of 1.38-1.72 THz.
Fig. 2. (a) The reflection coefficients, phase difference and (b) the ellipticity χ as a function of frequency, where the dotted lines show the results of a complete metal square ring, and the solid lines show the results of the graphene-metal hybrid ring with Ef = 0. (c) The reflection coefficients, phase difference and (d) the PCR as a function of frequency when Ef = 1.0 eV.
Besides, we also turn the Ef to research the properties of the hybrid metasurface between the OFF and ON states, and the corresponding ellipticities are displayed in Fig. 3(a). To have a clear observation, we enlarge the shadow sections for χ > 0.9 and χ < -0.9 and show them in Fig. 3(b). When the Ef increases from 0 to 0.6 eV, the metasurface acts as a broadband QWP for the frequencies varying between 1.15 THz and 1.75 THz, converting the x-polarized incident wave into the RHCP reflected wave. As the Ef increasing, the working bandwidth of the QWP gradually decreases from about 0.6 THz to 0.1 THz, accompanied by the blue-shift of the minimum frequency, as shown in Fig. 3(c). When the Ef increases from 0.3 eV to 1.0 eV, the metasurface acts as a broadband QWP, converting the x-polarized incident wave into the LHCP reflected wave for the frequencies varying between 0.75 THz and 1.3 THz. In the meanwhile, the working bandwidth of the QWP has a slightly decrease, accompanied by the blue-shift of the working band, as shown in Fig. 3(d). As a result, when Ef is in the range of 0.3 eV-0.6 eV, the metasurface can work as bi-functional broadband QWP, simultaneously converting the x-polarized incident wave into the LHCP wave at lower frequencies and into the RHCP wave at higher frequencies. On the other hand, at the ON state where Ef = 1.0 eV, the metasurface works as a bi-functional broadband wave plate as well, it is a QWP converting the x-polarized incident wave into the LHCP wave at lower frequencies and also a HWP converting the x-polarized incident wave into the y-polarized wave at higher frequencies. Therefore, the metasurface works as a bi-functional broadband wave plate can convert the linear-polarized incident wave into different polarization states at different bands for different Fermi levels.
Fig. 3. (a) Ellipticities χ related to different Ef, and (b) show the enlarged shadow sections. (c) The minimum frequency fmin, maximum frequency fmax and bandwidth fΔ for (c) χ < -0.9 and (d) χ > 0.9.
In order to further understand the physical mechanism of the polarization converter in this paper, we calculate the electric field amplitude distributions at 1.6 THz for both the OFF and ON states, and display them in Fig. 4. At the OFF state, the graphene behaves like a dielectric material. As shown in Fig. 4(a), the electric field is mainly localized on the golden parts, with the 2-fold rotational symmetry. Consequently, the metasurface acts as a QWP, related to the results in Fig. 2(b). At the ON state, the graphene behaves like a metallic material. As displayed in Fig. 4(b), the electric responses are concentrated at the corners of both the graphene and golden structures, with a mirror symmetry in the diagonal direction. As a result, the metasurface acts as a HWP, corresponding with the phenomenon in Fig. 2(d). Therefore, the symmetry related to the electric field response varies as tuning the Ef, leading to different polarization conversion in the hybrid metasurface.
Fig. 4. The electric field amplitude distributions at 1.6 THz for (a) the OFF state and (b) the ON state.
In simulation, we find that the geometric parameters of the metasurface play an important role in affecting the ellipticity, especially the length of the graphene and the thickness of the Neltec NY9208 layer. Setting the Ef = 0.1 eV, we define the duty cycle as α = g / (l + g), and change the lengths g and l of the graphene and the meal while keeping the (l + g) fixed. As shown in Fig. 5(a), when α = 0.5, that is l = g, the ellipticity χ is basically around -0.9. Therefore, the graphene should be shorter than the metal, keeping α < 0.5, to maintain the ellipticity. After parameter optimization, the best value of α to balance the ellipticity and the bandwidth is about 0.36. As the conductivity of the graphene is different from that of the metal, the duty cycle influences the symmetry of structure, which then affects the symmetry of field. Therefore, changing the duty cycle of the structure leads to the variation of the ellipticity. The ellipticities as a function of the thickness h2 are shown in Fig. 5(b), where an optimal polarization conversion performance is obtained when h2 = 33 µm. In this case, the spacer thickness affects the optical path difference between the waves reflected from the top and bottom metal layers, resulting in a certain phase difference which affects the ellipticity. Therefore, it is necessary to optimize the spacer thickness to achieve the desired ellipticity.
Fig. 5. (a) The duty cycle α-dependent ellipticity χ and (b) the h2-dependent ellipticity χ when Ef = 0.1 eV.
As the polarization conversion comes from the anisotropy of the hybrid metasurface, which is related to the polarization of the incident light, we vary the polarization angle to explore the response of the metasurface by setting Ef as 0.1 eV. As shown in Fig. 6(a), we use the u-v axis to describe the incident wave, which has a rotation angle φ respect to the x-y axis describing the metasurface. In this case, the ellpiticity χuv under the polarization angle φ is defined as χuv = 2|ruu||rvu|sinΔΦ’ / (|ruu|2 + |rvu|2), where ΔΦ’ = Φuu - Φvu. Taken the frequency of 1.5 THz as an example, it is clear that the χuv gradually turns from -1 to + 1 when the polarization angle increases from 0 to 90°, with the converted wave changing from RHCP to LHCP. The variation of the χuv related to φ has a periodic change at 180°, resulted from the central symmetry of the hybrid metasurface. Moreover, when the incident polarization angle changes from 0 to 12.5°, |χuv| remains larger than 0.9, which means that the metasurface still works as a RHCP when the incident light is polarized in the range of ± 12.5° respect to the x-axis. Similarly, it works well as a LHCP when the incident light is polarized in the range of ± 12.5° respect to the y-axis, where |χuv| is larger than 0.9. In practical application, the polarization tolerance of the incident light is about 25° for both the RHCP and LHCP. Figure 6(b) shows the ellpiticity χuv as a function of the polarization angle in the working band of 1.15-1.75 THz, which indicates that the broadband property of the metasurface is maintained at all the polarization angles. As described in Figs. 6(c) and 6(d), the variation of the |ruu| is almost symmetric to that of the |rvu| with regard to 45° as the polarization angle changing, leading to the transition of the reflected wave from RHCP to LHCP.
Fig. 6. (a) Polar plot of the ellipticity χuv at 1.5 THz. The two-dimensional map of the (b) χuv, (c) |ruu| and (d) |rvu| as a function of the frequency and the polarization angle.
Finally, we compare our work with other recent polarization converters, as shown in Table 1. Although the ultra-broadband or broadband polarization converters have been realized in Refs. [8], [14] and [20], they can only realize a single function. Although Ref. [24] can achieve bi-function and active control, the relative bandwidths are narrower than our design. Therefore, the hybrid metasurface we designed is an actively tunable bi-function polarization converter with relative broad band working in the terahertz band.
Table 1. The comparison between references and our work.
4. Summary
In summary, we have proposed a tunable bi-functional broadband polarization converter based on the hybrid graphene-metal metasurface. Turning the bias voltage to change the OFF/ON state, the metasurface can switch between QWP and HWP in the frequency band 1.38-1.72 THz. Besides, the metasurface simultaneously works as a broadband QWP and HWP in different frequency range at the ON state. In addition, when Ef is in the range of 0.3 eV-0.6 eV, the metasurface can work as bi-functional broadband QWP in different frequencies as well. Analyzing the electric field amplitude distributions, we have explained the physical mechanism of the bi-functional polarization converter. What’s more, we find that the metasurface can work well with a tolerance to the incident light polarization angle of about ± 12.5°, which can also change the converted wave from RHCP to LHCP with the incident polarization angle change of 90°. Compared with the conventional polarization converter, the proposed metasurface shows more advantages, such as switchable bi-functions, wide operating bandwidth, and ultra-thin thickness, which has good prospect in implementing THz devices.
Funding
National Natural Science Foundation of China (11804178, 11274188); Natural Science Foundation of Shandong Province (ZR2018BA027); National Laboratory of Solid State Microstructures, Nanjing University (M31003).
Disclosures
The authors declare no conflicts of interest.
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