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Abstract
This paper presents an electrically controllable reflective broadband linear polarization (LP) converter based on liquid crystals (LCs) for cross-polarization conversion (CPC) in the terahertz frequency range. The proposed structure achieves a high polarization conversion ratio (PCR) exceeding 0.9 within the frequency range of 236.8 - 269.6 GHz. A vital feature of this design is the dynamic control of polarization conversion by re-orienting the nematic liquid crystal molecules through voltage bias switching between ‘on’ and ‘off’ states, allowing for precise manipulation of cross-polarized and co-polarized reflected waves. Experimental results validate the simulation outcomes, demonstrating excellent agreement. In contrast to conventional reflective polarization converters with fixed frequency responses, the proposed electrically controllable polarization conversion offers significant potential in imaging and optical communications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves are a range of electromagnetic waves typically spanning from 0.1 to 10 THz. They find extensive applications in diverse fields, including wireless communication, imaging, spectroscopy, and security inspection [1–4]. Developing functional devices such as switches, filters, phase shifters, and polarization converters [5–8] is crucial to advance terahertz technology further. The manipulation of electromagnetic wave polarization holds tremendous significance, as it plays a vital role in various applications like imaging, sensing [9], and wireless communications. Consequently, there is a growing demand for innovative solutions that enable efficient modulation of electromagnetic wave polarization.
Periodically arranged metasurfaces have been extensively studied to manipulate electromagnetic wave polarization, leading to various metasurface-based polarization converters. Mei et al. designed a broadband linear polarization converter using a double U-shaped structure, which exhibited a bandwidth of 7.4 GHz and operated at normal incidence [10]. Yu et al. proposed a transparent broadband reflective metasurface employing four C-shaped structures of different sizes, achieving a polarization conversion rate exceeding 90% [11]. These converters introduced a dynamic element to electromagnetic wave manipulation through flexible structural parameter design. However, due to the fixed operating frequency determined by the geometry, polarization conversion tuning proves challenging for these configurations. To address this limitation, metasurfaces have been combined with materials such as phase change media and graphene [12–14], enabling dynamic tuning of the electromagnetic responses. For instance, Fu et al. proposed a dual-band and dynamically regulated terahertz linear polarization converter based on a graphene metasurface, achieved by adjusting the Fermi energy level and relaxation time of the graphene [15]. Cheng et al. presented a switchable broadband reflective cross-polarization converter utilizing a graphene metasurface, which demonstrated a high polarization conversion ratio of over 80% and a relative bandwidth of 60.16% at a Fermi energy of 0.9 eV [16]. However, the complex fabrication process and poor process stability pose practical challenges to implementing these tunable polarization converters.
Liquid crystals, renowned for their strong optical anisotropy and birefringence, have garnered significant attention in the construction of tunable metasurfaces due to their advantages of cost-effectiveness and simplicity of fabrication [17–19]. Researchers have developed polarization-sensitive devices with tunable conversion rates by exploiting the ability to externally bias and efficiently adjust the effective dielectric constant of LC materials. For example, Yang et al. designed a tunable terahertz polarization converter utilizing liquid crystal, where the polarization rotation angle could be adjusted by varying the bias voltage [20]. Xu et al. introduced a terahertz resonant switch based on the polarization transition induced by a composite subsurface liquid crystal operating at 0.82 THz frequency [21]. Vasić et al. proposed an electrically tunable reflective polarization converter based on liquid crystal permeation, which enables dynamically controllable conversion of linear polarization to cross polarization, right circular polarization, and left circular polarization at the target operating frequency [22]. However, the reported LC-based polarization converters were designed with a subwavelength grating configuration, resulting in a Fabry-Perot-like resonant cavity that limits the operating bandwidth of the devices. Furthermore, these converters primarily focused on transmissive-type polarization conversion, while reflective-type polarization conversion, crucial for polarization tuning, innovative reflective surface design, and antenna applications, was overlooked [23–25].
In this paper, we propose an electrically controllable reflective polarization converter that offers tunable broadband linear polarization conversion. Our design incorporates an LC material sandwiched between a C-shaped metasurface and a metallic plate, allowing dynamic control of cross- or co-polarization conversion by applying different bias voltages. For cross-polarization conversion, the design achieves a PCR exceeding 90% within the frequency range of 236.8-269.6 GHz, with a relative bandwidth of 13%. Additionally, by applying a 20 V voltage on the metallic plate, the cross-polarization conversion vanishes, resulting in a PCR close to 0. The switching between cross-polarization and co-polarization conversion offers promising potential for imaging and sensing applications.
2. Design and the mechanism
The unit cell structure of the proposed polarization converter is depicted in Fig. 1. Two separate quartz substrates, with the identical thickness of 200 µm, host the C-shaped metasurface and the copper layer etched on their respective bottom and top surfaces. The LC material is sealed within the resulting cavity, which possesses a thickness of 300 µm. Consequently, the C-shaped metasurface and the copper layer function as electrodes, allowing control over the orientation of the LC molecules via external voltage. The structural dimensions of the proposed design are as follows: h = 300 µm, D1 = 400 µm, D2 = 360 µm, D3 = 100 µm. In addition, the thickness of the copper ground is set to 0.5 µm. To establish the initial orientation of the LC molecules without biasing, a thin polyimide (Pi) layer with a thickness of approximately 0.2 µm is spin-coated onto the quartz substrates, enabling control over the LC molecule alignment based on the friction direction of the Pi layer. For instance, as shown in Fig. 1(c), the orientation of nematic LC molecules can be represented by the Euler angles θ and φ denoting the angles between the long axis of the LC molecule and the x-y and x-z planes, respectively. In this case, the friction direction of the Pi layer was set at θ = 0° and φ = 45°, ensuring that the long axis of the LC molecule remained parallel to the friction direction of the Pi orientation layer in the absence of external bias.
Fig. 1. (a) Schematic diagram of the unit cell structure. (b) The layout of the C-shaped resonator. (c) Definition of the optical axis and Euler angles of the liquid crystal molecule.
The finite element method (FEM) was used to perform the numerical investigation of the proposed polarization converter. In the simulations, the dielectric constant and loss tangent of the quartz substrates were set to 3.78 and 0.002, respectively. The ultrathin thickness of the Pi layer rendered its contribution negligible in the analysis. Moreover, the nematic LC mixture filled in the cavity had normal permittivity ε⊥=2.61 and extraordinary permittivity ε‖=3.6 in the frequency band 220-290 GHz. The LC material is considered a homogeneous medium with a dielectric tensor ε given as follows [26].
Here, $\Delta \mathrm{\varepsilon } = {\mathrm{\varepsilon }_\textrm{||}} - {\mathrm{\varepsilon }_ \bot }.$ θ and φ are the Euler angles illustrated in Fig. 1(c).
The proposed structure is designed to have a y-polarized THz wave incident with the electric field vector parallel to the y-axis. The asymmetry of the C-shaped metasurface leads to both co-polarized and cross-polarized components in the reflected THz wave. Therefore, the PCR is employed to assess the conversion efficiency of the converter, defined as the ratio of the reflected cross-polarization component to the total reflection. The PCR can be written as follows [27].
Here, rxy and ryy are the reflections associated with the y-to-x and y-to-y polarization conversions, respectively.
Figure 2(a) shows the simulated co-polarization and cross-polarization reflection coefficients (ryy and rxy) of the LC molecules with Euler angles θ = 0° and φ = 45°, which correspond to the state without external biasing (planar alignment). As shown in Fig. 2(a), the cross-polarization component rxy is greater than -2 dB, and the co-polarization component ryy is below -12 dB in the 237.54-269.98 GHz frequency range. Therefore, the proposed structure effectively achieves linear polarization conversion. However, when a saturation bias voltage of 20 V was applied to the bottom electrode, the orientation of the long axis of the LC molecule rotated perpendicular to the metallic ground due to the induced vertical electrostatic field. In this situation, the Euler angles of the LC molecules are θ = 90° and φ = 45° (vertical alignment). The simulated ryy and rxy of the LC molecules with θ = 90° are shown in Fig. 2(b). One can observe that the cross-polarization reflection coefficient is significantly lower than -45 dB, indicating a significantly smaller reflection compared to the co-polarization component. The calculated PCR results for LC molecules with planar and vertical alignment are illustrated in Fig. 2(c). In the ‘off’ state without external bias voltage (planar alignment), it is evident that the proposed structure achieves a PCR value exceeding 0.9 over a broadband frequency range of 236.8 - 269.6 GHz, with a relative bandwidth of 13%. However, the linear cross-polarization conversion effect disappears when the converter operates in the ‘on’ state with a saturated bias voltage (vertical alignment) and the PCR value approaches 0. Hence, the polarization conversion effect can be easily controlled by simply switching the biasing states of the proposed LC-based converter.
Fig. 2. Simulated results for the proposed structure under normal incidence. (a) Reflection coefficients rxy and ryy with planar alignment of LC directors. (b) Reflection coefficients rxy and ryy with vertical alignment of LC directors. (c) PCR for different alignments.
The operating principle of the proposed polarization converter is further investigated using the coordinate system shown in Fig. 3(a). As mentioned previously, in the absence of external bias, the long axis of the LC molecule aligns parallel to the friction direction of the Pi alignment layers, as depicted in Fig. 3(b). The incident and reflected THz waves, denoted as Ei and Er, can be decomposed into two components along the u and v directions, respectively, as expressed by Eqs. (3) and (4) below [28].
Fig. 3. (a) The coordinate system illustrating the LC molecules with planar alignment. (b) Schematic diagram depicting the orientation of LC molecules with planar alignment. (c) Magnitude, and (d) phase of the reflections for u and v polarizations.
In Eq. (4), ru and rv denote the reflection coefficients of the THz wave in the u and v directions, respectively. Meanwhile, the following equation can further represent the reflected THz wave Er [29].
Here, ruu and rvv denote the co-reflection coefficients with respect to the u and v axes, while φuu and φvv denote the corresponding phases with respect to the u and v axes. Similarly, ruv and rvu are the cross-reflection coefficients with corresponding phases of φuv and φvu with respect to the u and v axes.
The simulated amplitudes and phases of the reflected waves under the ‘off’ state are shown in Fig. 3(c) and (d). According to Fig. 3(c), the amplitudes of the co-polarized reflection coefficients ruu and rvv remain greater than 0.7. However, the cross-polarized reflection coefficients ruv and rvu are almost zero in the respective operating band. Moreover, as shown in Fig. 3(d), the angular phase difference $\Delta \mathrm{\varphi } = {\mathrm{\varphi }_{\textrm{uu}}} - {\mathrm{\varphi }_{\textrm{vv}}}$, a crucial indicator of cross-polarization conversion, is close to ±180° with a frequency range of 236.8-269.6 GHz. It means effective linear cross-polarization conversion has been achieved in the broadband frequency band. It should be noted that there is an amplitude loss of 2.9 dB, which is attributed to the relatively high dielectric loss (0.02) of the LC mixture.
Next, we investigated the electromagnetic responses of the proposed converter in the ‘on’ state with the Euler angle of LC molecules set at θ = 90°. As depicted in Fig. 4(c), the amplitudes of the co-polarized reflection coefficients ruu and rvv are identical throughout the entire frequency range. Furthermore, the angular phase difference Δφ shown in Fig. 4(d) approaches zero within the operational frequency band, indicating the disappearance of the cross-polarization conversion effect and the dominance of the co-polarized reflection component in the power reflection. The controllable polarization conversion mechanism stems from the birefringence effect of the LC material. Due to the slower propagation of the THz wave with a wave vector parallel to the long axis of the LC molecule compared to those parallel to the short axis, an accumulated phase difference arises in the reflected wave under the ‘on’ and ‘off’ states. However, in the proposed structure, the phase difference introduced by the asymmetric metasurface is counteracted by the phase change induced by the rotation of the optical axis of the LCs. As a result, co-polarized reflection can be achieved with an asymmetric structure.
Fig. 4. (a) The coordinate system illustrating the LC molecules with vertical alignment. (b) Schematic diagram depicting the orientation of LC molecules with vertical alignment. (c) Magnitude, and (d) phase of the reflections for u and v polarizations.
The surface current distributions at corresponding resonant frequencies shown in Fig. 5 provides an insight into the mechanism of the polarization conversion effect of the proposed structure. As shown in Fig. 5(a), when LC directors with planar alignment at 243.94 GHz, the surface current on the top metasurface flow from bottom-right of the top patch to top-left of the bottom patch. Similarly, Fig. 5(b) indicates that at 262.42 GHz, intensive current flow towards lower right direction can be observed obviously. The excited current with oblique flow direction is responsible for cross-polarization conversion. Furthermore, Figs. 5(c) and (d) depict the surface current distributions on the metasurface at 243.94 and 262.42 GHz for LC directors with vertical alignment, respectively. For both cases, the surface current flow from top to bottom along y direction, hence cross-polarization components cannot be converted and only co-polarization waves were included in the reflective power. Simulations of LC directors for different bias voltages are performed with the help of electrostatic field distributions [30]. As shown in Figs. 6(a)-(d), with the increase of bias voltage, the LC molecules gradually stand up and finally with orientation along the z direction (vertical alignment).
Fig. 5. Surface current distributions on the metasurface at (a) 243.94 and (b) 262.42 GHz for LC directors with planar alignment. Surface current distributions on the metasurface at (c) 243.94 and (d) 262.42 GHz for LC directors with vertical alignment.
Fig. 6. (a) The cross-section selection and the simulated potential differences and LC molecules represented by white bars with different bias voltages of (b) 5 V, (c) 10 V, (d) 15 V and (e) 20 V.
As the polarization conversion is dependent on the geometrical parameters, the effect of different structural dimensions on PCR is investigated and the results are shown in Fig. 7. In the simulation, only one parameter was changed, while the others were keep constant. The influence of outer diameter D1 on PCR is illustrated in Fig. 7(a), as the operation bandwidth is very sensitive to D1. With the increase of D1 from 380 to 400 µm, the bandwidth can be broadened significantly. Figure 7(b) shows the dependence of PCR on different inner diameter D2. It can be seen that with the decrease of D2, the resonance peak split into two frequencies, which broaden the operation bandwidth of PCR conversion. However, the separate resonance peaks degrade the conversion rate as PCR greater than 0.9 could no longer been maintained. The effect of width D3 on PCR is shown in Fig. 7(c), and it can be seen that the change in the value of D3 has almost no impact on the conversion rate. Moreover, the influence of different LC layer thickness h on the PCR is shown in Fig. 7(d). With the increase of LC thickness, the operating frequency redshifts while the conversion bandwidth almost remains the same, and it is possible to tune the operating frequencies of the proposed structure by adjusting the thickness of LC layer. The equivalent circuit model (ECM) shown in Fig. 7(e) helps the explanation of polarization conversion behavior with the variation of structural parameters. According to the equivalent circuit theory, the metasurface can be considered as a series-connected RLC resonant circuit, and either the change of structural dimension or dielectric property of the substrate will affect the response characteristics to the incident electromagnetic waves. Taking the liquid crystal thickness h as an example, a larger h reflects an increase in the distance between the two capacitor plates, and the equivalent capacitance C of the ECM, which is proportional to this distance, also shows an increase. As a result, the resonance frequency derived from the ECM redshifts with the increase of liquid crystal thickness h. Finally, as illustrated in Fig. 7(f), the calculated results of PCR at different incident angles are exhibited to further investigate the angular stability of the design. Despite a small attenuation at the lower frequencies, the PCR remains essentially stable with the incident angle varies from 0° to 15°. With the incident angle increase to 30°, the operation frequency band shows a blue-shift while the bandwidth remains almost the same. Further increase of incident angle leads to a narrower bandwidth but still meets the metric of broadband. Hence, the proposed design is capable of wide angle stability.
Fig. 7. Effect of changes in structural parameters (a) D1, (b) D2, (c) D3, and (d) h on polarization conversion rate PCR. (e) Equivalent circuit model of the structure. (f) Dependence of the incidence angles on PCR.
3. Fabrication and experimental results
As depicted in Fig. 8(a), a prototype of 90 × 90 unit cells was fabricated, totaling 4 × 4 cm2 area. The metallographic microscope photograph displaying the pattern is presented in Fig. 8(b). According to the optimized design, the structural parameters of the C-shaped metasurface are D1 = 400, D2 = 360, and D3 = 100 µm, and the fabrication tolerance is less than ± 2µm. 300 µm diameter polystyrene microspheres were placed between the two quartz substrates to create the LC cavity. The nematic LC material (HFUT-HB01) was subsequently introduced into the cavity using a siphon and sealed with epoxy resin. The experimental setup, shown in Fig. 8(c), employed two THz horn antennas connected to a vector network analyzer (VNA) (Agilent N5224A) via a VNA extender (N5262AW08) to measure the response spectra of the prototype. The cross-reflection coefficient within the 220-290 GHz range was measured by aligning the antennas perpendicular to the polarization direction. In contrast, the co-reflection coefficient was obtained by aligning the antennas parallel to the polarization direction. Due to the size of the extender, the transmitting and receiving antennas cannot be placed perpendicular to the prototype, and the incident angle of the terahertz wave is about 8° in the test. However, as indicated in Fig. 7(f), the PCR of the structure is almost constant when incident angle is smaller than 15°. The experiment was conducted at room temperature of 25°C.
Fig. 8. (a) Fabricated prototype and (b) metallographic microscope image of the sample. (c) Measurement setup for the experimental testing.
It is worthy to note that, as shown in Fig. 8(b), to serve the metasurface as top electrode in practice, the adjacent C-shaped patterns in the fabrication are horizontally connected with an extra contact area, which is different from the design with tangent C-shaped patterns. In order to investigate the contact effect on polarization conversion, we compared the PCR for C-shaped patterns with tangency point and extra contact area, and the results are presented in Fig. 9. As shown in Fig. 9, the contact effect has almost no influence on the PCR. Figure 10(a) presents the measured cross-polarized and co-polarized reflection coefficients of the prototype in the “off” state without external biasing. As depicted in Fig. 10(a), the measured cross-polarized reflection coefficient is approximately -2.5 dB within the operating frequency range, slightly lower than the simulated result of about -2 dB. This deviation can be attributed to the reduced effectiveness of pre-orienting LC molecules using the Pi alignment layer when dealing with thicker LC layers. While we have successfully demonstrated orienting the LC molecules with a metasurface featuring a total LC thickness of 100 µm [31], the orientation becomes less optimal as the LC layer thickness increases to 300 µm. Consequently, the cross-polarized reflection coefficient, which relies on the orientation of LC molecules, decreases compared to the ideal conditions assumed in the simulations.
Fig. 10. Measured reflection coefficients rxy and ryy with a bias voltage of (a) 0 V (‘off’ state) and (b) 20 V (‘on’ state). (c) Measured PCR for different operation states.
Furthermore, Fig. 10(b) displays the measured cross-polarization and co-polarization reflection spectra in the “on” state with a bias voltage of 20 V. A comparison with the measured results for the “off” state shown in Fig. 10(a) reveals that the co-polarized coefficient dominates the reflected power across the entire frequency range, indicating the achievement of co-polarization conversion through the application of external bias voltages. Figure 10(c) presents the calculated PCR for both “off” and “on” states based on the measured results. It is evident from the figure that in the “off” state, the measured PCR exceeds 0.9 within the frequency range of 237.6-269.5 GHz, with a relative bandwidth of 12.6%. This experimental demonstration verifies the broadband linear cross-polarization conversion effect of the prototype. Conversely, in the “on” state with a bias voltage of 20 V, the measured PCR approaches 0, as co-polarization reflection occurs instead of cross-polarization.
Table 1 compares the features between the proposed design and some previously reported reflective polarization converters based on metasurfaces. Notably, the designed structure enables dynamic control of the reflection type, switching between cross-polarization and co-polarization conversion. Additionally, the proposed LC-based structure surpasses previous tunable converters based on graphene or VO2 in terms of cost and processing difficulty, thanks to the maturity in LC processing and assembling. It solidifies the potential of the proposed design for practical applications.
Table 1. Comparison of performance: proposed design vs. reported reflective-type polarization converters
4. Conclusion
In conclusion, we have proposed an electrically controllable metasurface based on LCs for broadband cross-polarization conversion at terahertz frequencies. Our numerical results demonstrate that the design achieves efficient cross-polarization conversion with a PCR exceeding 0.9 in the 236.8 - 269.6 GHz frequency range without needing external biasing. By applying external bias voltages, we have successfully demonstrated the dynamic control of the polarization conversion, achieving co-polarization reflection with a bias voltage of 20 V. The ability to manipulate the polarization state of the proposed structure makes it highly promising for imaging and sensing applications. Furthermore, the matured LC processing and assembling techniques contribute to the advantages of the LC-based metasurface in terms of cost and processing difficulty, establishing a solid foundation for practical applications.
Funding
National Natural Science Foundation of China (62001150); Aeronautical Science Foundation of China (2020Z0560P4001); Fundamental Research Funds for the Central Universities (JZ2022HGTB0270).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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