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Abstract
A terahertz phase shifter based on liquid-crystal-integrated metasurface is proposed, which contains a three-slotted array structure and comb grating. The orientation of the liquid crystal molecules can be completely controlled by the direction of the electric field. From the acquired experimental results, it was demonstrated that the phase shift exceeds 300° in the range of 378.6 - 390.8 GHz, whereas the maximum phase shift reaches 374.1° at 383.1 GHz. The molecular reorientation transient process induced by the external electric field in the liquid crystal was measured and analyzed. Based on the molecular reorientation mechanism, which can be divided into three processes, a rapid modulation mechanism was demonstrated. From the performance of the proposed device, an actively controllable phase delay and reflectance with a cycle switching time of approximately 0.3 s was achieved, which is remarkably faster than the usual cycle time that exceeds 8 s. Our work provides useful ideas for improving the response speed of LC-based terahertz devices, which is considered of great significance for several applications, in terms of terahertz reconfigurable devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous development of the terahertz (THz) technology in recent years, a wide range of applications in communications [1,2], imaging [3,4], nondestructive testing [5,6], and biomedicine [7,8] has emerged. Moreover, metasurfaces provide effective methods for manipulating THz waves, such as phase modulation [9,10], amplitude modulation [11,12], polarization conversion [13,14], and orbital angular momentum generation [15,16]. As far as terahertz wave manipulation is concerned, especially beamforming and beam steering have attracted a wide attention [17,18]. For THz beamforming, the manipulation of the phase profile of THz waves is quite important. Therefore, based on the implementation of tunable or programmable metasurface-based materials, the phase modulation technique is particularly critical and its development has been greatly promoted [19–21].
Among the various material configurations, the nematic liquid crystal (NLC) has been widely investigated due to its continuously adjustable dielectric properties, low drive voltage requirements, small insertion losses and relatively reduced cost, etc. Hence, many LC-based terahertz wave manipulation techniques, and especially phase modulation techniques, have been reported in the literature [22,23]. At present, the continuous phase modulation ability of LC-based devices has been proved experimentally [24,25]. However, the response times are typically extremely slow, while they are often difficult to be acquired. The underlying origin of this effect is the free relaxation time, which is consumed by the molecular reorientation transient process, and largely hinders the speed of the THz LC-based device. Therefore, for the rapid and continuous manipulation of terahertz, the shortening of the relaxation time of liquid crystals is undoubtedly a significant and crucial task [26,27]. Nevertheless, very few reports in the literature have specifically focused on the operation speed of LC-based devices due to the manifestation of the slow molecular reorientation process in the thick LC cell.
In this work, fully electrically methods were used to directly control an LC for the rapid and continuous realization of terahertz wave manipulation. The proposed device was designed by employing a metasurface structure consisting of an array of slotted structures. More specifically, the comb grating was used as a bias loading electrode and the liquid crystal was used as a tunable medium. The electric field can be generated in the LC layer in either the transverse or the longitudinal direction by applying positive or negative voltages adjacent to the grating electrodes. The phase of the reflective electromagnetic wave can be dynamically manipulated at voltage less than 12 V. The molecular reorientation transient process induced by the external electric field in the NLC was measured and thoroughly analyzed. Furthermore, a rapid two-state modulated process was demonstrated. Our work provides useful insights and design principles for various applications, in terms of development of the next-generation terahertz reconfigurable device.
2. Structure design and principle
A schematic diagram of the proposed device is illustrated in Fig. 1(a). The phase shifter is composed of seven layers. From top to bottom, the following layers were used: quartz substrate, an array of three-slotted resonant structures, Polyimide (PI), LC, PI, grating electrodes, and a quartz substrate. The upper and lower quartz substrates were set in parallel to support the resonant structure and the grating electrodes, respectively. The LC was filled with C-09-2 which was formulated by isothiocyanatotolane liquid crystal components and acted as tunable material. Its thickness was controlled by the incorporated polystyrene microspheres with a diameter of 45 µm. The slotted resonant structure is complementary to the dipole structure and has a similar terahertz response with a larger metal coverage area and more uniform electric field distribution [28]. Multi-resonant elements based on slotted structures are used to increase the phase shift and bandwidth of the phase shifter, and the optimal values are determined by a numerical optimization process [29]. The employed resonant structure consists of three slotted structures of different lengths and widths arranged in parallel. The interval between the edge of slot 1 and slot 2 is 15 µm, while the interval between the edge of slot 2 and slot 3 is 26 µm. As can be ascertained from Fig. 1(a), each unit of the grating electrode contains five grid lines, which are divided into two groups of intersecting distribution. More explicitly, one group contains only three grating lines, which is named positive voltage grating and the other group has two gratings and is named negative voltage grating. The two sets of gratings can be fed separately and reflect electromagnetic waves with polarization directions parallel to the comb gratings. The grating structure has been designed for better reflection performance in operating frequency. Furthermore, the employment of such a grating distribution can avoid electric field interference between adjacent units. The specific structure dimensions of the fabricated structure are shown in Table 1.
Table 1. Dimensions of the unit structure.
Figure 1(b) shows the metallographic microscope photos of the three-slotted resonant structure and grating, respectively. The dielectric constant and loss angle tangent of the quartz substrate with a thickness of 300 µm were ɛr = 3.75 and tanδ = 0.002, respectively. The parameters of the LC were ɛ⊥ = 2.47, tanσ⊥ = 0.02, ɛ// = 3.25, and tanσ// = 0.02. The triple-slotted array and the grating structure of Cu were deposited on a 2 × 2 cm quartz substrate, respectively. The actual size of the sample was about 2 × 2.5 cm2.
Within the NLC, the orientation of the rod-shaped molecules, which includes a polar group that produces a dipole moment, can be changed by the application of an external electric field. Thus, the dielectric constant is ${\varepsilon _{eff}} = n_o^2n_e^2/(n_o^2co{s^2}\theta + n_e^2si{n^2}\theta )$, where θ is the angle between the electric field vector and the NLC director [30]. For the proposed phase shifter, the three-slotted array acts as both a resonant structure and a ground electrode. Similarly, the grating structure plays the role of both a reflective surface and a feed electrode. In the unbiased state, the LC molecules are initially distributed parallel to the quartz substrate due to the alignment of the PI film. More specifically, the direction of the long axis of the LC molecules is perpendicular to the comb grating, whereas the dielectric constant of the LC is defined as ɛ⊥. By applying a bias voltage between the triple-slotted metal structure and the metal grating, the LC molecules are reoriented. As the bias voltage is increased to the saturation level, LC molecules are reoriented along the electric field direction, and the effective dielectric constant of the LC layer reaches the maximum value of ɛ//. During this period, the dielectric constant of LC can be adjusted within the range of Δɛ = ɛ// - ɛ⊥. After that, the bias voltage is removed and the LC molecule will slowly return to its initial state. However, the natural recovery of LCs is usually slower and the free relaxation time consumed is longer. Therefore, the two sets of gratings were fed separately here. More specifically, appropriate positive and negative voltages were applied to the positive and negative gratings, respectively, while the bias voltage was removed. In this way, a transverse electric field was generated between the adjacent gate lines in the LC layer, thus accelerating the molecular reorientation of the LC.
The response time at different electric field distributions was also observed. For an LC-based device and under single elastic constant and small-angle approximations, the dynamic response of the LC director reorientation can be described by the free relaxation time τoff and rise time τrise of a homogeneous alignment cell, which can be expressed as follows [23]:
3. Experimental results and analysis
The reflection phase and amplitude of the phase shifter were measured by using the free space method in a continuous wave system [25]. The signal generator and vector network analyzer were controlled simultaneously by Labview software, and the corresponding system time was recorded while changing the voltage and storing the data. The specific experiments are divided into three groups, namely (I), (II) and (III), whereas the feeding schematic and the corresponding electrostatic field distribution are shown in Fig. 2(a). During the initial state, a +12 V bias was applied to both sets of gratings. Next, the amplitude variation of the reflected wave of the device was recorded after removing the bias voltage on both grating sets simultaneously. From the experiments in the group (I), the natural recovery process of LC after removing the voltage was recorded. This result was used as a reference to compare with the next two sets of experiments.
Fig. 2. (a) Feeding schematic and corresponding electrostatic field distribution. (b) Comparison of the reorientation time of the LC molecules in different states.
In group (II) of experiments, the appropriate positive and negative voltages were applied to each of the two grating groups. Similarly, the amplitude variation process of the reflected wave was also recorded. The voltage applied to the two sets of gratings was determined by the designed grating structure. There are more positive voltage gratings than negative voltage gratings in each comb-grating unit. In order to reduce the longitudinal regulation effect of the grating on the LC above it, and ensure the lateral regulation effect between the gratings, a bias of +2 V was applied to the positive voltage grating and −5 V to the negative voltage grating. In Fig. 2(b), the time required for the shift of the resonant frequency by the same frequency interval during the LC molecular reorientation transient process was compared. From the extracted outcomes, it was observed that in the group (I) of experiments, 1225.3 ms were required to shift the resonant frequency from the value of 382.5 GHz to 398.3 GHz (Stage I in Fig. 2(b)). However, in the group (II) of experiments, 844.7 ms were required to move the same frequency interval, which was 1/3 shorter in time. On this basis, the voltage difference over the adjacent gratings continued to increase appropriately. In the third set of experiments (III), after removing the bias voltage, a +5 V voltage was applied to the positive voltage grating and a −5 V voltage was applied to the negative voltage grating. The amplitude variation of the reflected wave was also recorded. It is noteworthy that the resonant frequency was shifted from 382.5 GHz to 398.3 GHz in only 421.8 ms. Compared with group (I), the time was shortened by 2/3, but the whole reorientation time was still greater than 8 s. To avoid test errors, the reorientation times were tested multiple times for each state and averaged. The reorientation time of each stage is shown in Table 2.
Table 2. Averaged reorientation time of LC in different states.
As is shown in Fig. 2(b), the monitored reorientation process of the LC molecules can be divided into three stages, and the corresponding time are defined as te, tc, tf, respectively. During this process, the molecular rotation can be simplified by considering the action of several factors, such as the electric field moment, the elastic force, the viscous moment, the anchoring strength and the terahertz field moment. In the first stage, the electric field moment is regarded as the main acting moment. The reorientation time (te) of the LC molecules is decreased and the main factor in the first stage obviously is the externally applied voltage. In the second stage, all torques act together, and the reorientation time (tc) of both groups (II) and(III) is slightly shortened due to the applied bias voltage. In the third stage, as the LC molecules under the bias state are almost parallel to the electric field, the electric field force on the molecules is very weak. At this time, the other weak torques act on the LC molecules together as the main torque sources, and the molecular reorientation time (tf) is almost equal regardless of the applied different voltages. From the experimental results, it can be seen that by applying appropriate positive and negative voltages to the two sets of adjacent gratings, the LC recovery can be significantly accelerated and the LC reorientation time at stage I is shortened.
Because the τoff is proportional to the square of the LC cell gap, the response time of the LC-based THz devices is very slow (in minutes order of magnitude). Therefore, the response speed of the device can be further improved by using electrically control to induce orientation of the molecules and avoid the free relaxation time τoff. Under this perspective, in our device, molecules can be fully controlled by the enforcement of an electric field from the two grating groups. To improve the response times, the time of electrically LC-induced molecular reorientation in the designed LC phase shifter was also explored. The overdrive and undershoot method can be used to accelerate the response time. Hence, the voltage difference between the adjacent gratings continued to be increased, and more specifically, the values of +8 V for the positive voltage gratings and −8 V for negative voltage gratings were enforced. The respective LC reorientation process is shown in Fig. 3(a). The extracted time parameters by averaging for three experiments were te = 44.8 ms, tc = 1320.8 ms, tf = 1731.5 ms. In this case, there is no τoff process. By the fully electrically control technique, a rapid phase control over 300° in the range of 378.6 - 390.8 GHz (orange highlighted area) was attained, whereas the maximum phase shift reaches 374.1° at the frequency value of 383.1 GHz, as is shown in Fig. 3(b). In addition, the modulation depth is about 97.7% at 405.5 GHz.
Fig. 3. (a) Reorientation process of the LC under fully electrically controlled with overdrive biased voltage. (b) Amplitude and phase change relative to the applied bias voltage.
If both tc and tf are greater than te, rapid modulation can be achieved by applying less than 1/te Hz AC voltage. In the experiment, the variation of the reflected spectrum of the device was examined by loading a bias voltage with a frequency variation of 0 - 20 Hz. From the collected data, it was found that the device can switch between these two states in a stable periodic manner by applying square wave voltages of 3 Hz. Figure 4 depicts the observed resonant frequency relative to the biased voltage. In the “on” state, positive and negative voltages of +12 V and −12 V were applied, respectively. Because of the existence of a weak transverse electric field, more time is required for the stabilization of the resonant frequency points, and the system sampling time is limited by the response time of the vector network analyzer (VNA), which was about 48 ms. Therefore, a deviation of 0.4 GHz exists at the high-frequency point (orange highlighted area in Fig. 4). As can be observed from Fig. 4, the simplest model to consider is the switching period was about 333 ms.
Fig. 4. Resonant frequency in switching from the +12 V and +12 V to +12 V and −12 V bias voltage state with 3 Hz.
The proposed device can produce greater than 90° phase change at 382.4 GHz and 386.8 GHz, as shown in Figs. 5(b) and 5(c). It provides a potential application of programmable metasurface beam control technology based on “0” and “1” coding [19]. As is shown in Fig. 5(a), the amplitude difference between the two states was greater than 10.4 dB at 387 GHz. Limited by the processing time of the VNA, the on-off curve cannot be accurately obtained. Nevertheless, in this work, a THz LC phase shifter or switch with a response time order of magnitudes faster than the previously reported LC-based devices [23] was demonstrated, with a larger phase shift and lower operating voltage [31]. Furthermore, by designing the molecular structure with a lower te value, the switch-off time can be significantly improved. In this structure, the LC layer can also be replaced by dual-frequency LCs and large birefringent LCs, which can further improve the speed of device or phase shift range.
Fig. 5. Distribution of the (a) amplitude, (b) phase change and (c) phase shift curve relative to the biased voltage of 3 Hz.
4. Conclusions
In summary, a tunable terahertz device consisting of a slotted metasurface-LC-grating structure was proposed. Compared with the traditional metasurface material configurations, a more flexible electrically driven method was realized. The electrically controlled reorientation time of the LC was thoroughly investigated, and fully electrically controlled phase modulation of over 300° was achieved. The developed THz LC phase shifter can be switched rapidly between two states by using a 3 Hz rectangular voltage. A controllable phase shift of 90° at 382.4 GHz and 386.8 GHz and amplitude variation of 10.4 dB at 387 GHz was also realized, respectively, by using a 12 V bias to switch between the “on” and “off” states. Fruitful insights for tuning the switching mechanism for the development of the next-generation LC-based THz devices are provided. Our work paves the way for the fabrication of THz-based devices for various applications including THz metasurfaces, switches, tunable filters, beam control, and so on.
Funding
Natural Science Foundation of Anhui Province (2208085MF160); National Natural Science Foundation of China (62001150); 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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