Tunable Terahertz Metamaterial Using an Electric Split-Ring Resonator with Polarization-Sensitive Characteristic

: We present a tunable terahertz (THz) metamaterial using an electric split-ring resonator (eSRR), which exhibits polarization-sensitive characteristics. The proposed eSRR is composed of double symmetrical semicircles and two central metal bars. By changing the lengths of two metal bars, the electromagnetic responses can be tuned and switched between dual-band and triple-band resonances in transverse magnetic (TM) mode. Furthermore, by moving the bottom metal bar to change the gap between the two metal bars, the ﬁrst resonance is stable at 0.39 THz, and the second resonance is gradually blue-shifted from 0.83 to 1.33 THz. The tuning range is 0.50 THz. This means that the free spectrum ranges (FSR) could be broadened by 0.50 THz. This proposed device exhibits a dual- / triple-band switch, tunable ﬁlter, tunable FSR and polarization-dependent characteristics. It provides an e ﬀ ective approach to perform tunable polarizer, sensor, switch, ﬁlter and other optoelectronics in THz-wave applications.


Introduction
It is generally accepted that the terahertz (THz) range is the frequency range of 0.1-10 THz. In recent years, THz technology has attracted growing attention with the progress of THz sources and instrumentation [1,2]. THz technology has been widely used in many fields, including but not limited to filtration [3], molecule identification [4], imaging [5,6] and environmental monitoring systems [7] because it has many fascinating electromagnetic characteristics, such as being harmless to the human body and having artificial magnetism and high chemical sensitivity [8][9][10][11]. However, the electromagnetic responses of general natural materials to THz waves are always very weak and cannot meet the requirements for real-world applications. Currently, people put much effort into incremental THz-wave efficiency by using metamaterials [12][13][14] to enhance the coupling effect between the THz wave and the metamaterial.
In this study, we propose a tunable THz metamaterial using an eSRR to exhibit polarization-sensitive characteristics. An eSRR is composed of double symmetrical semicircles and two central metal bars on silicon on an insulator (SOI) substrate. By changing the relevant geometrical dimensions of the semicircles and two central metal bars, the resonances of the eSRR device are always stable in transverse electric (TE) mode, and the resonances of TM polarized mode can be tuned with a tuning range of 0.50 THz by moving the bottom metal bar. Moreover, the resonances can be switched between dual-band and triple-band resonances by changing the lengths of two metal bars. Figure 1 shows schematic drawings of the 3D view of the eSRR device and the corresponding geometrical denotations of the unit cell. The eSRR device is composed of double symmetrical semicircles and two central metal bars on the SOI substrate. The thickness of the Au layer is kept constant at 300 nm. The corresponding geometrical denotations of the eSRR unit cell are represented in Figure 1b. They are lengths (L 1 , L 2 ) of the metal bars, the gap (g) between the two metal bars, gaps (g 1 ) between semicircles and bars, and outer and inner radiuses (R, r) of semicircles. The metal line width is kept as a constant at 4 µm. The period of the eSRR is 80 µm × 80 µm. The proposed eSRR device is designed based on finite difference time domain (FDTD) solutions. The periodic boundary conditions are applied along the xand y-axis directions, while the boundary condition of the z-axis direction is a perfectly matched layer (PML). The monitor of resonant frequency is set under the eSRR device to calculate the transmission of the incident THz wave. The resonant frequency (f LC ) can be expressed by [36]:

Materials and Methods
where c 0 is the light velocity in a vacuum, L eq and C eq are the equivalent inductance and capacitance of eSRR, ε c is the relative permittivity of the materials within the eSRR, l is the size of models, w is the metallic line width, and g eq is the equivalent gap width of the eSRR. The resonant frequency of the eSRR can be tuned by changing different parameters. According to Equation (1), the impact of metallic thickness is minor [37][38][39]. Here, the Au layer is designed to be 300 nm in thickness.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 9 filter application. Therefore, the requirement of realizing a tunable THz filter with a large tuning range has become a hot topic of scientific research. In this study, we propose a tunable THz metamaterial using an eSRR to exhibit polarizationsensitive characteristics. An eSRR is composed of double symmetrical semicircles and two central metal bars on silicon on an insulator (SOI) substrate. By changing the relevant geometrical dimensions of the semicircles and two central metal bars, the resonances of the eSRR device are always stable in transverse electric (TE) mode, and the resonances of TM polarized mode can be tuned with a tuning range of 0.50 THz by moving the bottom metal bar. Moreover, the resonances can be switched between dual-band and triple-band resonances by changing the lengths of two metal bars.

Materials and Methods
where c0 is the light velocity in a vacuum, Leq and Ceq are the equivalent inductance and capacitance of eSRR, εc is the relative permittivity of the materials within the eSRR, l is the size of models, w is the metallic line width, and geq is the equivalent gap width of the eSRR. The resonant frequency of the eSRR can be tuned by changing different parameters. According to Equation (1), the impact of metallic thickness is minor [37][38][39]. Here, the Au layer is designed to be 300 nm in thickness.

Results and Discussion
In our design, the TE electric field is perpendicular to the g1 parameter, and the transverse magnetic (TM) electric field is perpendicular to the g parameter. To clarify the electromagnetic responses of the eSRR device, we first simulate the transmission spectra of only two metal bars or

Results and Discussion
In our design, the TE electric field is perpendicular to the g 1 parameter, and the transverse magnetic (TM) electric field is perpendicular to the g parameter. To clarify the electromagnetic responses of the eSRR device, we first simulate the transmission spectra of only two metal bars or two semicircles to figure out the source of the individual resonance. Figure 2a,b show the transmission spectra of metal bars with different L 1 values in TE and TM modes, respectively. By increasing the L 1 value of the bottom metal bar from 12 µm to 24 µm under the condition of L 2 = 12 µm, there is no resonance in TE mode and the electromagnetic responses can be switched between dual-band and triple-band resonances in TM mode, as shown in Figure 2a,b, respectively. By increasing the gap between two semicircle-shaped metamaterials (g 0 ) from 6 to 10 µm under the condition of R = 20 µm, there are two stable resonances in TE mode and one stable resonance in TM mode, as shown in Figure 2c,d, respectively. Therefore, we investigate the electromagnetic responses of the eSRR device with different L 1 values by keeping the parameters of g 1 = 6 µm, L 2 = 12 µm, and R = 20 µm, as shown in Figure 3. In TE mode, there are two stable resonances (ω 1 , ω 2 ) at 0.69 and 1.21 THz, as shown in Figure 3a. Meanwhile, by increasing L 1 values, the electromagnetic responses can be tuned and switched between dual-band (L 1 = L 2 ) and triple-band (L 1 L 2 ) resonances in TM mode, as shown in Figure 3b. The first (ω 1 ) and second (ω 2 ) resonances are both stable at 0.39 and 1.34 THz, while the third (ω 3 ) resonance is gradually red-shifted from 1.71 to 0.83 THz by increasing the L 1 value from 8 to 24 µm. The tendencies of resonances and L 1 values of the eSRR device are summarized in Figure 3c. The corresponding electric (E) and magnetic (H) field distributions with L 1 = 24 µm are illustrated in Figure 4. In TE mode, the E-and H-field energies are distributed around the semicircles at 0.69 (ω 1 ) and 1.21 THz (ω 2 ). In the TM mode, the E-and H-field energies are distributed around the semicircles at 0.39 THz (ω 1 ). Such a result shows that the first resonance of the eSRR comes from the semicircle structures. The E-field energy is distributed on the upper and lower parts of the upper metal bar, and the H-field energy is distributed in the center of the upper metal bar monitored at 1.34 THz (ω 2 ). This means that the second resonance of the eSRR is caused by the upper bar. When f = 0.83 THz (ω 3 ), the E-field energy is distributed on the upper and lower parts of the lower metal bar, and the H-field energy is distributed in the center of the lower metal bar, which indicates that the third resonance of the eSRR is generated by the lower bar. Therefore, when the length of the lower bar changes (different L 1 values), the electromagnetic responses of the eSRR can be tuned and switched between the dual-band and triple-band resonances in TM mode.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 9 two semicircles to figure out the source of the individual resonance. Figures 2a and 2b show the transmission spectra of metal bars with different L1 values in TE and TM modes, respectively. By increasing the L1 value of the bottom metal bar from 12 μm to 24 μm under the condition of L2 = 12 μm, there is no resonance in TE mode and the electromagnetic responses can be switched between dual-band and triple-band resonances in TM mode, as shown in Figure 2a,b, respectively. By increasing the gap between two semicircle-shaped metamaterials (g0) from 6 to 10 μm under the condition of R = 20 μm, there are two stable resonances in TE mode and one stable resonance in TM mode, as shown in Figure 2c,d, respectively. Therefore, we investigate the electromagnetic responses of the eSRR device with different L1 values by keeping the parameters of g1 = 6 μm, L2 = 12 μm, and R = 20 μm, as shown in Figure 3.    When two metal bars are equal at a certain length (i.e., L = L1 = L2 by keeping R = 20 μm and g1 = 6 μm), the corresponding electromagnetic responses of the eSRR device are shown in Figure 5. There are two stable resonances (ω1, ω2) at 0.69 and 1.21 THz in TE mode, as shown in Figure 5a. In TM mode, the first resonance (ω1) is very stable at 0.39 THz, while the second resonance (ω2) is gradually red-shifted from 1.71 to 0.82 THz by increasing the L value from 8 to 24 μm, as shown in Figure 5b. The tuning range of the second resonance and the free spectrum range (FSR) is 0.89 THz. This characteristic is very suitable for THz filter and sensor applications. The tendency of resonances and L values of the eSRR device are summarized in Figure 5c. Figure 6 represents the corresponding E-and H-field distributions with L = 12 μm. It is worth mentioning that the E-field energy is distributed on the upper and lower parts of the two metal bars and the H-field energy is distributed in the center of the two metal bars monitored at 1.33 THz in TM mode, which is obviously different from the case where the lengths of two metal bars are not equal (L1 ≠ L2).  When two metal bars are equal at a certain length (i.e., L = L1 = L2 by keeping R = 20 μm and g1 = 6 μm), the corresponding electromagnetic responses of the eSRR device are shown in Figure 5. There are two stable resonances (ω1, ω2) at 0.69 and 1.21 THz in TE mode, as shown in Figure 5a. In TM mode, the first resonance (ω1) is very stable at 0.39 THz, while the second resonance (ω2) is gradually red-shifted from 1.71 to 0.82 THz by increasing the L value from 8 to 24 μm, as shown in Figure 5b. The tuning range of the second resonance and the free spectrum range (FSR) is 0.89 THz. This characteristic is very suitable for THz filter and sensor applications. The tendency of resonances and L values of the eSRR device are summarized in Figure 5c. Figure 6 represents the corresponding E-and H-field distributions with L = 12 μm. It is worth mentioning that the E-field energy is distributed on the upper and lower parts of the two metal bars and the H-field energy is distributed in the center of the two metal bars monitored at 1.33 THz in TM mode, which is obviously different from the case where the lengths of two metal bars are not equal (L1 ≠ L2). When two metal bars are equal at a certain length (i.e., L = L 1 = L 2 by keeping R = 20 µm and g 1 = 6 µm), the corresponding electromagnetic responses of the eSRR device are shown in Figure 5. There are two stable resonances (ω 1 , ω 2 ) at 0.69 and 1.21 THz in TE mode, as shown in Figure 5a. In TM mode, the first resonance (ω 1 ) is very stable at 0.39 THz, while the second resonance (ω 2 ) is gradually red-shifted from 1.71 to 0.82 THz by increasing the L value from 8 to 24 µm, as shown in Figure 5b. The tuning range of the second resonance and the free spectrum range (FSR) is 0.89 THz. This characteristic is very suitable for THz filter and sensor applications. The tendency of resonances and L values of the eSRR device are summarized in Figure 5c. Figure 6 represents the corresponding Eand H-field distributions with L = 12 µm. It is worth mentioning that the E-field energy is distributed on the upper and lower parts of the two metal bars and the H-field energy is distributed in the center Appl. Sci. 2020, 10, 4660 5 of 9 of the two metal bars monitored at 1.33 THz in TM mode, which is obviously different from the case where the lengths of two metal bars are not equal (L 1 L 2 ).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 9  The lower metal bar is connected to the suspending microelectromechanical systems (MEMS) comb driver moving along the y-axis direction to change the gap between two metal bars (i.e., g value) and determine tunability and applicability. The transmission spectra of the eSRR with different g values are shown in Figure 7. There are two stable resonances in TE mode, as shown in Figure 7a. In TM mode, the first resonance (ω1) is very stable at 0.39 THz and the second resonance (ω2) is gradually blue-shifted from 0.83 to 1.33 THz by increasing the g value from 0 to 12 μm, as shown in Figure 7b. The tuning range is 0.50 THz. That means that FSR can be broadened by 0.50 THz. Therefore, the eSRR could be controlled to broaden the tuning of FSR by increasing the g value and narrowed by increasing the L value, which can be used in a tunable bandwidth filter. The tendencies of resonances and g values of the eSRR device are summarized in Figure 7c. In order to further understand the physical mechanism of electromagnetic responses of the eSRR, the corresponding E-and H-field distributions of the eSRR with g = 6 μm are plotted in Figure 8. The E-field energy is distributed on the upper and lower parts of the two metal bars, and the H-field energy is distributed in the center of the two metal bars monitored at 1.30 THz in TM mode. Therefore, by moving the lower metal bar to a different position, the  The lower metal bar is connected to the suspending microelectromechanical systems (MEMS) comb driver moving along the y-axis direction to change the gap between two metal bars (i.e., g value) and determine tunability and applicability. The transmission spectra of the eSRR with different g values are shown in Figure 7. There are two stable resonances in TE mode, as shown in Figure 7a. In TM mode, the first resonance (ω1) is very stable at 0.39 THz and the second resonance (ω2) is gradually blue-shifted from 0.83 to 1.33 THz by increasing the g value from 0 to 12 μm, as shown in Figure 7b. The tuning range is 0.50 THz. That means that FSR can be broadened by 0.50 THz. Therefore, the eSRR could be controlled to broaden the tuning of FSR by increasing the g value and narrowed by increasing the L value, which can be used in a tunable bandwidth filter. The tendencies of resonances and g values of the eSRR device are summarized in Figure 7c. In order to further understand the physical mechanism of electromagnetic responses of the eSRR, the corresponding E-and H-field distributions of the eSRR with g = 6 μm are plotted in Figure 8. The E-field energy is distributed on the upper and lower parts of the two metal bars, and the H-field energy is distributed in the center of the two metal bars monitored at 1.30 THz in TM mode. Therefore, by moving the lower metal bar to a different position, the The lower metal bar is connected to the suspending microelectromechanical systems (MEMS) comb driver moving along the y-axis direction to change the gap between two metal bars (i.e., g value) and determine tunability and applicability. The transmission spectra of the eSRR with different g values are shown in Figure 7. There are two stable resonances in TE mode, as shown in Figure 7a. In TM mode, the first resonance (ω 1 ) is very stable at 0.39 THz and the second resonance (ω 2 ) is gradually blue-shifted from 0.83 to 1.33 THz by increasing the g value from 0 to 12 µm, as shown in Figure 7b. The tuning range is 0.50 THz. That means that FSR can be broadened by 0.50 THz. Therefore, the eSRR could be controlled to broaden the tuning of FSR by increasing the g value and narrowed by increasing the L value, which can be used in a tunable bandwidth filter. The tendencies of resonances and g values of the eSRR device are summarized in Figure 7c. In order to further understand the physical mechanism of electromagnetic responses of the eSRR, the corresponding E-and H-field distributions of the eSRR with g = 6 µm are plotted in Figure 8. The E-field energy is distributed on the upper and lower parts of the two metal bars, and the H-field energy is distributed in the center of the two metal bars monitored at 1.30 THz in TM mode. Therefore, by moving the lower metal bar to a different position, the eSRR device exhibits different optical characteristics. This design provides an effective approach to realize the tunable THz filter, polarizer and sensor applications.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 9 eSRR device exhibits different optical characteristics. This design provides an effective approach to realize the tunable THz filter, polarizer and sensor applications.

Conclusions
In conclusion, a tunable THz metamaterial using eSRR is presented to demonstrate the electromagnetic responses could be tuned by changing geometrical parameters. By changing the length of the lower metal bar, the electromagnetic responses can be tuned and switched between dual-band and triple-band resonances. The tuning ranges of the FSR can be broadened by 0.50 THz Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 9 eSRR device exhibits different optical characteristics. This design provides an effective approach to realize the tunable THz filter, polarizer and sensor applications.

Conclusions
In conclusion, a tunable THz metamaterial using eSRR is presented to demonstrate the electromagnetic responses could be tuned by changing geometrical parameters. By changing the length of the lower metal bar, the electromagnetic responses can be tuned and switched between dual-band and triple-band resonances. The tuning ranges of the FSR can be broadened by 0.50 THz

Conclusions
In conclusion, a tunable THz metamaterial using eSRR is presented to demonstrate the electromagnetic responses could be tuned by changing geometrical parameters. By changing the length of the lower metal bar, the electromagnetic responses can be tuned and switched between dual-band and triple-band resonances. The tuning ranges of the FSR can be broadened by 0.50 THz and narrowed by 0.89 THz by changing g and L values, respectively. The eSRR device exhibits tunable and switchable polarization-sensitive characteristics. The gap between semicircles and central metal bars would not influence the electromagnetic response of the eSRR, which indicates that the eSRR device has high stability to allow manufacturing tolerance. These results pave the way for the use of eSRR devices in tunable filters, switches, detectors, sensors and other THz optoelectronics applications.