1. Introduction

There has been a significant development in terahertz wave generation and detection technology in the last two decades [1,2]. Hence, terahertz waves can be more widely used for communication, imaging, and material detection [3,4]. Today, the application of the terahertz band is of great scientific importance and practical value. For further research and applications, it is also necessary to design functional devices to manipulate terahertz waves [5,6]. Recently, many devices for manipulating the phase, amplitude, and polarization angle of THz waves have been reported [7–9]. The active control of devices is generally achieved by tunable materials such as graphene, pin diodes, and liquid crystal (LC) [10–12]. The coding metasurface was first proposed by prof. Cui to manipulate the propagation of microwave frequency range from 7.5 GHz to 15 GHz in 2014 [13]. It is easier to be designed and fabricated to provide a higher degree of freedom for manipulating electromagnetic waves. Nowadays, the coding metasurfaces have been extended to terahertz region due to its own advantages [14–17]. Coding metasurface enables many complex functions, such as dynamic target tracking and beamforming [18–20]. Jin et al. developed a self-adaptive metasurface with THz wave detection and modulation capabilities and achieved deflection of terahertz beams within an angular range of 42.8° [21]. However, it requires complex adjustments and rapid modulation speed. LCs have received much attention because of their stability, low insertion losses, continuously adjustable dielectric properties, and flexible means of modulation [22–24].

There are numerous ways to control LC, such as electric fields, magnetic fields, and polyimide (Pi) alignment layers [25–28]. Moreover, LCs respond in a wide range from the millimeter wave band to the terahertz band and are widely used in terahertz beam steering [29–32]. For instance, Fu et al. implemented terahertz beam manipulation in different encoding states using LC-based programmable metasurface [33]. The relative dielectric constant of LC can be continuously adjusted in a particular range depending on the amplitude of the control force [34,35]. However, the long response time of LC in the modulation process has always been a problem. Especially when the thickness of the LC layer increases, the time required for reorientation also increases. This phenomenon is evident in the microwave and terahertz bands when the thickness of LC reaches the micron level [36]. The response time of LC at electric field is related to the thickness of LC layer, viscoelastic coefficient, and electric field amplitude. It can be accelerated by reducing the thickness of LC layer and increasing the control voltage. A large drive voltage is required to have a fast response of the LC molecules, which is not conducive to the integration of the device and the design of the control circuit. Ideally, the LCs must continuously be subjected to a strong driving force during the modulation process. However, it depends on the structure of the device and the characteristics of the LCs.

On the one hand, the response speed of the LC can be improved by adding polymers [37]. On the other hand, LC can be modulated by novel structures to reduce response time [38]. Using a continuous voltage amplitude to drive the phase shifter is challenging to ensure the stability and speed of the control, especially in the case of a relatively small driving voltage but a thick LC layer, which requires a long time to wait for the LC to stabilize. Although different voltages can continuously modulate the LC, it leads to different modulation speeds and higher power supply requirements.

This paper presents an LC phase shifter based on digital coding metasurfaces. Unlike the previously reported phase shifters that modulate the phase with the amplitude of voltage, the proposed structure achieves gradient phase control by switchable coding patterns of the voltage applied to the gratings. The voltage can be applied between the gratings and the resonant structure to form a vertical electric field or between two gratings to form a horizontal electric field. The structure of gratings providers more flexibility to the control of the LC. The states of the phase shifter in four coding states were measured experimentally. The phases of the reflected wave differ in each of the four coding states. Due to coding, this discrete variation in the phase of the reflected wave occurs over the entire frequency range of the resonance. The experimental results show that the maximum phase shift is greater than 180° in the 117.1–125.9 GHz range. The modulation speed is approximately doubled compared to the state without electric field confinement.

2. Design and simulation

The schematic diagram of the designed reflective phase shifter based on the digital coding metasurfaces is illustrated in Fig. 1(a). The structure has three main parts: resonant structures, LC layer, and gratings. The metallic resonant structure and grating are built on quartz substrates. There is a LC layer between the metallic resonant structure and the gratings. The period length of the metallic structure unit was p1 = 840 μm. The length and width of the split ring were both p2 = 630 μm. The widths of the right and left arms were w1 = 184 μm, and w2 = 89 μm. The width of the slit was w3 = 40 μm. The width of the feed line connecting the resonant structure was w4 = 30 µm. The grating width was lx = 30 µm, and the grating spacing was ly = 75 µm. The thickness of the quartz substrate hq = 1000 μm, dielectric constant ε_q= 3.78, and loss tangent tanδ_q= 0.002. The thicknesses of the metal unit and grating were hc = hg = 0.5 μm. The material of the metal unit is copper, whose conductivity was s = 5.8 × 10⁷ S/m. The thickness of the LC layer was hl = 40 μm. The LC mixture (C-09-2) was filled in the LC layer, in which the dielectric constant in the z-direction ranges from ε_min= 2.52 to ε_max = 3.61 and loss tangent tanδ_c = 0.02 in the 90 GHz - 140 GHz band [39]. Due to the anisotropy of LC molecules, the relative dielectric constant in the z-direction changes from ε_min to ε_max as the orientation of LC molecules changes from the x-axis to the z-axis. By applying voltages to the gratings and resonant structure, the LCs can be reoriented in the direction of the electric field, which changes the dielectric constant in the z-direction and the phase of the reflected wave. The incident wave changes its phase after being reflected by the device at different electric field distributions.

 

Fig. 1. (a) Schematic diagram of the tunable phase shifter. Illustrations of (b) resonant structures and (c) gratings. The incident and reflected waves are both y-polarized.

Download Full Size | PDF

The six gratings in the middle of the unit cell are vertical electric field gratings. The direction of the electric field generated between these gratings and the resonant structures is parallel to the z-axis. Two gratings on both sides are set up as horizontal electric field gratings. The direction of the electric field generated between these two gratings is parallel to the x-axis. A voltage Vth1 was applied between the vertical electric field gratings and the resonant structure in the operating state. Another voltage, Vth2, was applied between the horizontal gratings, as shown in Fig. 2(a). Different electric field distributions can be obtained by programming the switching states of the voltages on the structure. Theoretically, if the electric field is strong enough, the LC molecules will reorient along the electric field direction. In this case, the different operating states of the device can be obtained by programming. Two different voltages, Vth1 and Vth2, are used because the LC requires different drive voltages for different thicknesses at the x-axis and z-axis. Here, the first place of the code is the state of the resonant structure, followed by the states of the eight gratings of the metasurface unit cell. The closed state of the switch is defined as ‘1’ and the open state as ‘0’. Figure 2(b) shows the electric field distribution of the LC layer in four coding states, ‘a’: 101110000, ‘b’: 100001110, ‘c’: 101111110, and ‘d’: 010000001. The variation of the switching state achieves different electric field distributions in the LC layer. The LC molecules are reoriented along the direction of the electric field, which achieves different states of the reflective wave phase. Theoretically, more complex encodings can be implemented for gratings, but here only these four encoding states are studied to simplify the experiments and simulations process.

 

Fig. 2. (a) Control circuit of phase shifter unit with nine programmable switches. (b) Electric field distribution of the LC layer in the four code states, ‘a’: 101110000, ‘b’: 100001110, ‘c’: 101111110, and ‘d’: 010000001.

Download Full Size | PDF

The electric field states in the x-y plane in the LC layer at coding states of ‘c’ and ‘d’ were further simulated, as shown in Fig. 3(a) and (b). It can be seen that the electric field is concentrated between the resonant structure and the grating. The LC is divided into tunable and non-tunable regions according to Fig. 2(b), Fig. 3(a), and Fig. 3(b). The tunable part can be divided into six parts according to the distribution of the six vertical electric field gratings, as shown in Fig. 3(c). Dashed lines and serial numbers mark tunable parts. The state of LC molecule deflections in these regions can be manipulated by switching the voltage on the corresponding grating.

 

Fig. 3. The electric field distribution in the x-y plane in the LC layer at (a) ‘101111110’ and (b) ‘010000001’ states. (c) Six tunable regions of the LC layer.

Download Full Size | PDF

The reflection spectrum of the phase shifter was calculated by the numerical finite-difference time-domain (FDTD) method. The polarization direction of the incident wave is parallel to the y-axis and grating. In the simulation, periodic boundary conditions are applied in the x-axis and y-axis directions. When the coding states change from ‘c’ to ‘d’, the dielectric constant of the LC in the tunable region changes from 2.52 to 3.61, the phase curves of the reflected waves at different encoding states were also calculated, as shown in Fig. 4(a), where the maximum phase shift is 245° at 122.3 GHz. The phase of the reflected wave varies by 0°, 93°, 181° and 245° for coding states of ‘a’, ‘b,’ ‘c,’ and ‘d’, respectively. The resonant frequency shifts from 125.4 GHz to 114.2 GHz. Moreover, the amplitude rises from -8.5 dB to -5.5 dB, as shown in Fig. 4(b). The LC-metasurface-based phase shifter has a certain loss in the operating condition. This is caused by the ohmic loss in resonance process and loss tangent of the LC. The loss can be reduced by low loss tangent LC materials and optimizing resonant structures with higher reflectivity.

 

Fig. 4. (a) The phase and (b) amplitude curves of the phase shifter at different coding states from the simulation.

Download Full Size | PDF

3. Experiments and results

A 20 × 20 array of metasurfaces was fabricated on quartz substrates by photolithography and wet etching. The metal structures and gratings are aligned under the microscope, and the spacing between the arrays and gratings is controlled with the help of 40 µm polystyrene microspheres. The filled LCs are sealed by epoxy resin. The fabricated samples are shown in Fig. 5(a).

 

Fig. 5. (a) Image of the sample. (b) A metallographic microscope was used to take microscopic images.

Download Full Size | PDF

The electrodes are designed to be connected to the grating and the resonant array. The different phase states are achieved by switching the voltage on the electrodes during operation. Figure 5(b) shows a microscopic image of the sample taken by a metallographic microscope. The reflection spectrum of the sample in the range of 112-128 GHz was measured with a vector network analyzer (AgilentN5224A) and VNA extension modules (N5262AW08). The measurement setup is shown in Fig. 6, where two waveguide antennas are placed in parallel to measure the reflection spectrum of the sample. The dual-port measurement can compensate for environmental errors and get better test accuracy. The whole experiment was conducted at constant temperature and humidity. The sample was placed in the far-field position of the waveguide antenna. Electromagnetic waves absorbing material was placed around the sample to reduce the effect of surrounding reflections. The reserved feeder line is connected to the dual output DC voltage source.

 

Fig. 6. Environment for sample measurement. The bias voltage is applied through the electrodes connected to the grating and the resonant structure.

Download Full Size | PDF

In this experiment, Vth1 = 5 v and Vth2 = 45 v. Figures 7(a) and (b) show the amplitude and phase of the reflected wave from the test at different coding states. Compared to the simulated data, the maximum phase shift point has moved from 123.3 to 120 GHz, and the maximum phase shift has been reduced from 245° to 233°. The phase shift varies by 0°, 102°, 166° and 233° in coding states ‘a’, ‘b,’ ‘c,’ and ‘d’, respectively. The resonant frequency changes from 114.2 GHz and 125.4 GHz to 114.5 GHz and 126.0 GHz in coding states ‘c’ and ‘d’, respectively. Minor errors may come from inhomogeneities in the controlling electric field and dimensional variations in the fabrication process. The experimental results demonstrate the feasibility of modulating the LC layer by gratings in the subregion. Depending on the needs of practical applications, more complex encoding can also be performed in this way.

 

Fig. 7. Measured (a) amplitude and (b) phase curves of the phase shifter.

Download Full Size | PDF

Fully electrical methods were used to directly control the LC for the rapid and continuous realization of terahertz wave manipulation [38]. The dielectric constant of the LC in all tunable regions changes from ε_max to ε_min. Generally, the slowest change in the LC layer is in the process of transforming from one extreme value to another. It is when the coding states of the phase shifter change from ‘c’ to ‘d’. For the convenience of observation, only the phase variations at 120 GHz were recorded, as shown in Fig. 8. At Vth2 = 45 v; it takes only 2.18 s to reach a phase shift of 233°. However, it takes 4.14 s to reach a phase shift of 233° at Vth2 = 0 v. Compared with the free relaxation of LC molecules at Vth2 = 0 v, the electric field can significantly improve the speed of LC recovery and have more substantial stability at Vth2 = 45 v. The phase shift is slightly less than the natural relaxation at Vth2 = 45 v because the electric field between the gratings is not perfectly horizontal. Moreover, part of the LC molecules is in a non-horizontal state, as shown in Fig. 2(b) in coding state ‘d’. A comparison of the proposed structure and some recently reported LC phase shifters is summarized in Table 1.

 

Fig. 8. The phase shift changes from the ‘101111110’ state to the ‘010000001’ state at different values of Vth2.

Download Full Size | PDF

Table 1. A comparison of the proposed structure and some recently reported LC phase shifters.

View Table

4. Conclusions

This paper presents a novel method of driving a reflective LC phase shifter by digital coding metasurfaces. The proposed structure changes the encoding state by switching the voltage on each grating to obtain the phase of the phase shifter with one-to-one encoding. Also, because the voltage on each grating can be switched, it gives greater flexibility in regulating the electric field. The electric field can be applied between the gratings or between the gratings and the resonant structure. In the experiment, four states of the phase shifter were obtained by encoding. The phase of the reflected wave varies by 0°, 102°, 166°, and 233° at 120 GHz. Ideally, the proposed structure could obtain more coding sequences via eight controllable gratings. The phase of the reflected wave changes with different coding sequences. It has the potential to achieve terahertz beam manipulation based on multi-bit coding metasurfaces. Since a voltage can be applied between the gratings, the phase shifter can quickly switch between the two extreme states. The results obtained from the experiment showed that the response speed at the encoded state is doubled compared to the case without electric field constraint, and the response time was reduced from 4.14 s to 2.18 s. The proposed switchable encoded grating provides a new idea for next-generation LC terahertz devices by switching the voltage on each grating to create a different driving electric field. This method can be further applied to other devices containing reflective or transmissive gratings to drive LC molecules.