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Abstract
A tunable metasurface absorber (MA) based on polymer network liquid crystal is introduced in this paper. Despite the well-designed unit cell patterns, the proposed MA can achieve both large frequency tunability and wide-angle stability. Compared with traditional liquid crystal-based metasurfaces, the measured results suggest that the recovery time of the proposed structure was reduced by half. By applying an external voltage on the top electrode of the liquid crystal layer from 0 to a saturation voltage of 10 V, the absorption peak of the MA can be tuned from 112.7 GHz to 102.2 GHz, with a maximum frequency tunability of 9.3%, which is significantly higher than other proposed liquid crystal-based metasurfaces. Moreover, the proposed tunable absorber can maintain absorption greater than 90% with incident angles reaching up to 60° for both transverse electric and transverse magnetic polarizations. This design provides an efficient way for developing low-power consumption terahertz devices with large frequency tunability and wide-angle stability.
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1. Introduction
Terahertz (THz) waves are electromagnetic waves with frequencies in the range of 0.1 to 10 THz. The potential applications of THz waves in imaging, sensing, and spectroscopy have attracted the extensive attention of various researchers [1]. However, most natural materials have low interaction with the THz waves, which has hindered the development of THz technology in the past decades. Metamaterials are artificial materials with unique electromagnetic properties that natural materials do not have. The emergence of metamaterials paves a new way to develop THz devices. The peculiar properties of metamaterials stem from their precise geometry and size, much smaller than the wavelengths at which they act, allowing them to affect waves. As the two dimensional form of the metamaterial, metasurface offers many advantages such as reduced size and light weight, and the metasurface absorbers (MAs) have drawn great attention since the metamaterial-based absorber has been experimentally demonstrated at microwave and THz frequencies [2,3]. In the past two decades, MAs have been developed from a single absorption band to a double absorption band and even multiple absorption bands [4–8] and from a narrow band to a broadband absorption [9–14].
For applications such as THz spectral imaging and detection, finding a way to tune the THz wave dynamically is essential. Hence, it is indispensable for MAs to realize the tunable working frequency within a specific range. Researchers have found that some materials with tunable electromagnetic properties, such as graphene [15] and strontium titanate [16], can be used to achieve frequency tuning. However, the structural fabrication of these materials is still challenging.
Liquid crystal (LC) is one of the candidate materials for constructing tunable metasurfaces. The effective dielectric constant of LC can be continuously adjusted by applying an external bias to orient liquid crystal molecules. Due to the low loss, low profile, and low cost of liquid crystal devices at higher frequencies, their application in tuning the electromagnetic waves has received increased attention [17–27]. However, there are three major flaws in the reported LC-based metasurfaces. First, the frequency tunability of reported LC-based metasurfaces is not large enough due to the patterned design and the relatively small birefringence of LC material [22]. Second, the connecting bias lines in the metallic resonator negatively affect the wide-angle responses of LC-based metasurfaces [25]. Third, the response time of traditional LC-based devices is slow, especially for the recovery of molecules orientation after removing the external bias.
This work proposes a tunable MA based on polymer network liquid crystal (PNLC) at lower THz range. To overcome the aforementioned flaws, following improvements were adopted in the presented design. First, the lab-synthetized LC material with large birefringence was utilized to enhance the frequency tunability. Second, the bias lines were integrated as an essential part of the resonant structure, which minimized the negative effect of introducing bias lines after cell design. Third, as the molecular force in the PNLC is much larger than that in the LC material, one can anticipate a shorter recovery time of the tunable metasurface when the bias voltage is removed. Compared with traditional liquid crystal-based metasurfaces, the measured results suggest that the recovery time of the proposed structure was reduced by half. The proposed structure achieved a maximum frequency tunability of 9.3% with lab-synthetized LC material and proper unit cell design. Moreover, the MA exhibits wide-angle absorption for both transverse electric (TE) and transverse magnetic (TM) polarizations. The experimental results show that the absorptivity is over 90% with an incident angle up to 60°.
2. Structure design
To enhance the response time of the LC-based metasurface, here we introduced the difunctional monomer RM257 into the LC material to form the PNLC. The synthesis of the PNLC can be obtained in the following steps: the mass ratio of 95% LC host (Xi’an Modern Chemistry Research Institute, Xi’an, China) is first mixed with a mass ratio of 5% difunctional monomer RM257 (Jiangsu Hecheng Advanced Materials Co., Ltd., Nanjing, China) and a small amount of photoinitiator Benzoin Methyl Ether (Tokyo Chemical Industry Co., Ltd., Tokyo, Japan). Then, the photopolymerization precursor is filled into the LC cell. After this, a UV curing process for 40 min is performed to induce the crosslinking of the polymer network.
Figure 1 shows the geometry of the proposed absorber. The top and bottom substrates of the structure are made of quartz glass, while the inner sides of the two substrates are plated with a layer of copper. The copper on the upper substrate is etched to form a pattern layer, and the copper layer on the lower substrate serves as a reflector. The PNLC, which acts as the medium with a tunable dielectric constant, is placed in the spacing of two substrates. Since an external electric field can control the orientation of the PNLC molecules, by applying a bias voltage on the patterned and reflection copper layer, one can change the relative permittivity of the PNLC. As a result, the electromagnetic response of the PNLC-based metasurface can be electrically adjusted. To maximize the tunable range of the absorber, a skinny layer of polyimide (Pi) was coated on the surface of the pattern and reflection copper layer, and the liquid crystal molecules were aligned in parallel by rubbing. In such a case, the liquid crystal molecules parallel the patterned layer without bias voltage (ε⊥). By increasing the bias voltage, the liquid crystal molecules will gradually become perpendicular to the patterned layer and finally reach a saturated state (ε||).
Fig. 1. Schematic diagram of the (a) unit cell structure and (b) copper patterned layer. Sketch of the orientation of LC molecules under the electrode patch at (c) unbiased and (d) fully biased states.
The geometric dimensions of the unit cell structure shown in Fig. 1 are as follows: a = 800 µm, b = 750 µm, c = 50 µm, r = 240 µm, w = 50 µm, w1 = 70 µm. The thickness of the upper and lower quartz substrate is 500 µm, while the PNLC layer thickness is 45µm. The relative dielectric constant and loss tangent of the quartz glass substrates are 3.78 and 0.02, respectively.
The absorptivity can be defined as $A = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$, where ${S_{11}}$ is the reflection coefficients and ${S_{21}}$ is the transmission coefficients of the structure. In the simulation, the existence of the reflective plate layer makes the transmission coefficient ${S_{21}}$ almost zero. Therefore, the absorption rate can be expressed by the following formula: $A = 1 - {|{{S_{11}}} |^2}$. The simulation results were obtained using a finite-element method. In the simulations, unit cell boundary conditions were applied in the x and y directions, and the Floquet port condition was employed in the z-direction.
3. Numerical simulation results
The LC material is treated as a homogenous isotropic material in the simulation, hence the effective index of the LC material can be described as [28]
where no and ne represent the ordinary and extraordinary indices, while φ is the director angle of the LC molecule. As a nonmagnetic material, the permittivity of the LC material can be obtained byThe measured ε⊥ and ε|| of the LC material are 2.41 and 3.6 within the frequency range of 90 to 140 GHz, respectively, while the loss tangent of the LC material is 0.02. From Eq. (2), one can infer that with the orientation angle of the LC molecule shifts towards the z-axis, the LC permittivity increases and finally becomes equal to ε||.
The simulated absorption spectra of the proposed structure for the LC director angle φ of 0°, 30°, 45°, 60°, and 90°, which correspond to the LC permittivity of 2.41, 2.63, 2.89, 3.20, and 3.6, are illustrated in Fig. 2. With the orientation angle of the LC molecule rotated from 0° to 90°, the peak absorption frequency decreases from 113.1 to 100.8 GHz, with a frequency tunability (fmod=Δf/fmax) of 10.9%. Moreover, the THz waves can be effectively absorbed during the whole frequency tuning range, as the simulated absorptivity maintains almost unity in the operation band.
To investigate the resonance mechanism of the structure, the surface current distributions on the patterned layer and the ground plate of the metamaterial absorber at the absorption peak frequency of 113.1GHz were simulated. As shown in Fig. 3(a), the surface current on the resonator is strongly concentrated on the top and bottom bar parallel to the incident wave's electric field. Hence, the excited electric dipole resonances are responsible for electromagnetic wave absorption. Meanwhile, the current flow in the opposite direction on the ground plate leads to magnetic resonances (Fig. 3(b)), enhancing the resonance intensity.
Fig. 3. Simulated surface current distribution on (a) the patterned layer and (b) the ground plate at the resonant frequency of 113.1 GHz
Moreover, the impedance matching theory was utilized to check the electromagnetic response of the proposed MA at peak absorption frequencies. The normalized input impedance can be described as:
The normalized input impedance of the proposed MA at two extreme tuning frequencies, e.g., 100.8 and 113.1 GHz, was calculated, and the results are shown in Figs. 4(a) and (b). It can be seen that the input impedance is approximately matched with the free space impedance at the two frequencies, where the real and the imaginary parts of the normalized input impedance are near unity and zero. Hence, the proposed MA exhibits strong electromagnetic wave absorption within its frequency tuning ranges.
Fig. 4. The normalized input impedance of the MA for an (a) unbiased state and (b) full biased state.
The arrangement of the bias lines is essential in the design of LC-based tunable metasurface because it significantly influences the structure's performance, especially at wide angles. The electromagnetic resonances are determined by the split ring and its connected bars for the proposed resonator. To reduce the impact of the bias lines, the connected square rings were utilized in this absorber. Figure 5(a) shows the absorption spectra of the proposed structure with/without the bias lines. One can observe that the bias lines (square ring) have a negligible effect on the absorption spectrum of the absorber for the unbiased and complete biased status. It can be further convinced by the electric field distributions for the two topologies shown in Figs. 5(b) and (c), where the resonance mode matches each other well. Moreover, the top electrode's area was enlarged by including the bias structure, providing a better capability in re-orientating LC molecules.
Fig. 5. (a) Simulated absorption spectra of two different topologies under unbiased and full biased states. Simulated electric field distributions for the topology (a) with and (b) without the bias structure.
The absorption dependence on the structure geometries is further analyzed. Figure 6(a) shows the effect of the split ring radius r on the absorption spectrum. As r increases, the resonance frequency of the absorber moves toward higher frequencies. It is because with the increase of r, the length of the vertical bars connected with the ring decreases. Since the resonance mode analysis shown in Fig. 3 shows that the absorption originated from the dipole resonances, the shorter dipole leads to a higher resonance frequency.
Fig. 6. Absorption spectrum dependence on (a) the split ring radius r, (b) the split ring width c, (c) the gap width w1, and (d) the vertical bar width w.
Moreover, as shown in Fig. 6(b), when the split ring width c increases, the peak absorption frequency undergoes an apparent redshift. There are two reasons for this phenomenon: first, the increasing c leads to a longer electric length of the dipole. Second, the larger c also enhances the equivalent capacitance between adjacent split rings, hence the resonance frequency shifts to lower frequencies. On the contrary, with the increase of the gap width w1 of the split ring, the peak absorption frequency shifts to a higher region (Fig. 6(c)), as both the electric length of the dipole and the equivalent capacitance decrease. Finally, the influence of the vertical bar width w on the absorption spectrum is shown in Fig. 6(d). As shown in Fig. 6(d), by increasing w, the resonance frequency shows a blueshift. It is known that a greater width leads to a smaller equivalent inductance, thus a higher resonance frequency.
For metasurface absorbers, the absorption characteristics at wide angles are essential for their applications. The absorption spectrum of the proposed structure at different incident angles for both TE and TM polarizations is simulated. Figure 7(a) shows the absorption spectrum for TE polarization under oblique incidences. The peak absorptivity and the absorption frequency nearly maintain the same trend for incidence angles from 0 to 60°. For TM polarization, as can be seen from Fig. 7(b), the resonance frequency of the absorber shows a small redshift with the increase of angle θ. However, the absorptivity remains above 90% when incident angle θ reaches up to 60°, and the MA exhibits wide-angle stability. It is observed that a small absorption peak appears when incident angle is larger than 30°, the reason is attributed to the high order dipole resonances.
Fig. 7. Simulated absorption spectrum at different incidence angles for (a) TE and (b) TM polarizations.
4. Fabrication and experimental results
As shown in Fig. 8(a), to verify the absorber's performance, we fabricated a PNLC-based MA with a size of 4 × 4 cm and a structure of 50 × 50 cells, and the measurement setup is shown in Fig. 8(b). The measured results for the absorption spectrum of the sample with different bias voltages are shown in Fig. 9. The re-orientation of the LC molecules is more difficult when approaching a fully rotated status. Hence the tuning ability of the device becomes weaker with the continuous increase of the bias voltage. Moreover, as the bias voltage increases from 0 to saturation (10 V), the peak absorption frequency of the sample is tuned from 112.7 to 102.2 GHz, with a measured maximum frequency tunability of 9.3%. The measured tunability is smaller than that of the simulation (10.9%), one major reason is that for saturation voltage, the LC molecules lying beyond the patterned electrode cannot be fully reoriented, as the effective permittivity ε|| would getting smaller.
The absorption spectra of the fabricated sample under oblique incidences for both TE and TM polarizations are further investigated, and the results are shown in Fig. 10. For TE polarization, when the incident angle increases from 0 to 60°, the test results suggest that the proposed structure shows good wide-angle stability, as shown in Fig. 10(a). Moreover, for TM polarization, Fig. 10(b) shows that although the absorptivity decreases with the increase of incident angle, the measured absorption is still higher than 90% when the angle reaches up to 60°. Hence, the proposed absorber exhibits a solid capacity to absorb THz waves at wide angles. Table 1 compares the proposed MA with a few reported LC-based tunable absorbers. The proposed structure shows stronger THz wave absorption at wide angles for both TE and TM polarized incidences. Moreover, the frequency tunability for the proposed structure is significantly larger than those for the reported MAs, with a relatively small saturation bias voltage.
Fig. 10. Measured absorption for oblique incidences with different incident angles for (a) TE polarization and (b) TM polarization.
Table 1. Comparison of the absorption performance between the proposed MA with recently reported LC-based absorbers.
It is known that the response time of LC-based metasurface is determined by the rotation speed of LC molecules, which is independent of the testing frequencies. Hence, we set up the measuring platform shown in Fig. 11(a). According to the electro-optic effect of liquid crystal material, the re-orientation of LC molecules leads to the rotation of the optical axis, so the reflection intensity changes correspondingly. By measuring the intensity of the reflected light during power-on and power-off status, the response time of the proposed sample can be calculated. Here, we focus on the recovery time, defined as the time taken by the relative light intensity to increase from 10% to 90% when the power is off, as it contributes most of the response time of LC-based devices. The measured response time of the proposed PNLC-based MA is shown in Fig. 11(b). As shown in Fig. 11(b), the recovery time of the PNLC-based MA is 2346.2 ms. However, compared to the traditional LC-based metamaterial with identical structure and LC material, the recovery time is 4574.8 ms, approximately twice that of the PNLC-based absorber shown in Fig. 11(c), which can be attributed to the larger splay elasticity of the polymer network. It should be clarified that the time for the UV curing process is 40 min. Although a longer curing time can further reduce the recovery time of a PNLC-based device, the saturation bias voltage will increase significantly. There is a tradeoff between response time and power consumption of the tunable metamaterial, and we prefer a lower saturation bias voltage of 10 V in this research. It should further be noted that the relative long recovery time (2346.2 ms) of the PNLC-based absorber is mainly determined by the large LC thickness (45 µm). By extending the design to higher THz frequencies, the response time of the device can be reduced in merit of smaller LC thickness. Furthermore, we must emphasize that by replacing the LC material with dual-frequency liquid crystal (DFLC), one can obtain significantly faster response time [29–31]. However, the small birefringence of DFLC sacrifices the frequency tunability of the metamaterial, as PNLC was utilized to enhance the response time in the proposed study.
Fig. 11. (a) Measurement platform and the tested response time of the (b) PNLC-based and (c) traditional LC-based metamaterial absorber.
5. Conclusion
This paper proposed a tunable metasurface absorber based on polymer network liquid crystal in lower THz region. The measured response time of the structure was found to be nearly half of the traditional liquid crystal-based metasurface with identical structural geometry. Moreover, the measured results show that the tuning frequency of the proposed absorber can be adjusted from 112.65 to 102.15 GHz with a maximum tunability of 9.3%, which is significantly larger than that of the reported liquid crystal-based metasurfaces. Moreover, the structure also exhibits wide-angle stability, which breaks through the bottleneck of the design of LC-based metasurfaces. For instance, the absorptivity remains above 90% with the incident angle of 60° for both TE and TM polarizations, while the resonance frequency remains stable at the oblique incidences. Moreover, one can easily extend the design to higher THz region. The proposed strategy will most probably find potential applications in tunable terahertz devices with the demand for large frequency tunability and wide-angle stability.
Funding
National Natural Science Foundation of China (61871171, 62001150); Aeronautical Science Foundation of China (2020Z0560P4001); Fundamental Research Funds for the Central Universities (JD2020JGPY0012).
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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