Tunable multi-resonance of terahertz metamaterial using split-disk resonators

We present three tunable multi-resonance of terahertz (THz) metamaterials. They are composed of single-, dual-, and triple-split-disk resonators (SDRs) on Si substrates, which are denoted as SDR-1, SDR-2, and SDR-3, respectively. They exhibit extraordinary electromagnetic characteristics. SDR-1 exhibits polarization-dependence owing to the asymmetrical SDR structure. To increase the flexibility and applicability of SDR configuration, SDR-2 and SDR-3 are presented to modify the distances between the SDR layers. By moving the top SDR layer of SDR-2, a controllable resonance with a 0.32 THz shifting and tunable free spectrum range (FSR) of 0.15 THz at transverse magnetic mode is achieved, while an electromagnetically induced transparency-like effect appears at the transverse electric mode. The spectral bandwidth of SDR-3 can be tuned to 0.10 THz, and the resonant intensity becomes controllable by moving the middle SDR layer of SDR-3. Furthermore, by moving the top SDR layer of SDR-3, the tuning ranges of resonance, FSR, and bandwidth of SDR-3 are 0.23 THz, 0.20 THz, and 0.08 THz, respectively. Such designs of SDR configurations provide a high-efficient THz resonator in the THz-wave applications such as filters, switches, polarizers, sensors, imaging, and so on.


I. INTRODUCTION
Terahertz (THz) wave is the electromagnetic spectrum between the microwave and infrared wavelength range. It is a hot technique topic and is hopefully to be widely employed in various applications including but not limited to semi-conductor lasers, imaging, detectors, sensors, and radars. [1][2][3][4][5][6][7][8][9] The major drawback of the THz wave is the lack of high-efficient interaction coupling with the device because the THz wave has high transmission in common plastics, insulation materials, woods, and rubbers, and high reflection for metals. 10 These traditional materials cannot be interacted well with the THz wave, which will impede the practical applications of the THz wave technique.
In this study, we present a high-efficient design of tunable THz metamaterial with multi-bandwidth by using multiple split-disk resonators (SDRs). The proposed tunable SDRs are, respectively, composed of single-, dual-, and triple-SDR layers on Si substrates. To investigate the electromagnetic responses of tunable SDRs, threedimensional finite difference time-domain (FDTD) solutions are employed to simulate the optical properties of SDRs in the full-field plane electromagnetic wave. The propagation direction of the incident light is set to be perpendicular to the x-y plane in the numerical simulations, and periodic boundary conditions are adopted along the xand y-axis, while perfectly matched layer boundaries are assumed along the z-direction. The spectrum monitor is set on the bottom side of the proposed device to calculate the transmission spectra. Three SDR devices exhibit the characteristics of polarization-dependence, tunable resonance, tunable bandwidth, and large controllable free spectrum range (FSR).  field, and wave vector, respectively. The configurations of SDRs are composed of single-, dual-, and triple-SDR layers to form the SDR-1, SDR-2, and SDR-3, respectively. The SDRs are tailored Au layers on Si substrates. The permittivities of Au and Si materials are simulated as constant in this study. They are 10 4 for the Au layer and 10 for the Si substrate. The materials and thicknesses of SDR layers are tailored to be Au thin films in 300 nm thickness. The geometrical parameters of SDRs are illustrated in Fig. 1(b), where D, W, and Ls are the disk diameter (D = 60 μm), split width (W = 4 μm), and split length (Ls = 30 μm) of the SDR structure, respectively. The periods of SDRs are kept constant as 80 μm × 100 μm. Figures 1(c) and 1(d) show the cross-sectional views of SDR-2 and SDR-3 along the red dashed-squares in Fig. 1(a), respectively. There is a height (h 1 ) between bottom and top SDRs for SDR-2, while there are heights from bottom to middle SDRs (h 1 ) and from bottom to top SDRs (h 2 ) for SDR-3. By changing these h 1 and h 2 values, the resonances of SDR-2 and SDR-3 could be tuned owing to the guide-mode theory to generate the multi-resonances. According to the Drude-Lorentz model, 1,2 the resonant frequency is a function of the refraction index of electromagnetic radiation. This resonant frequency of an external frequency-dependent perturbation can be expressed as 51

II. MATERIALS AND METHODS
where f is the frequency, f p is the plasma frequency, f LC is the resonant frequency, and F is a dimensionless quantity, as the subscripts e and m refer to electric and magnetic response, respectively. Here, Leq and Ceq are the equivalent capacitance and inductance in the SDR configuration. f LC is derived to be a function of geometrical parameters. In the designs of SDR-2 and SDR-3, Cs and C h are two types of capacitances formed within the gaps of SDRs and vertical spaces between two SDRs, which can be represented as 51 where ε0 is the free space permittivity, εc is the relative permittivity of the materials within the gap, t is the thickness of the SDR layer, and S is the area along the x-y plane of the tailored Au thin film of the SDR structure. i is one or two, the capacitance between the bottom and second SDRs or the top and middle SDRs. Therefore, the resonant frequency can be tuned by changing the distances between two SDR layers, i.e., h 1 and h 2 values along the z-axis direction. on the contour of split. It means that the resonance of SDR-1 at the TE mode is generated by LC resonance. At TM mode, there is single-resonance at 0.52 THz, as shown in Fig. 2(a), which is generated by one inductive element (the frames or the loops) within SDR-1 as the E-and H-field distributions shown in Figs. 2(d) and 2(e), respectively. The monitors of field distributions are installed at 0.52 THz at TM mode. The E-field distributions are focused on the contour of disk rather than constraining in the split of SDR-1. It indicates the resonance of SDR-1 at TM mode generated by dipole resonance. As the above-mentioned results, SDR-1 exhibits polarization-dependent characteristics. Figures 3(a) and 3(b) show the transmission spectra of SDR-2 with different h 1 values changing from 6 μm to 1 μm at TM and TE modes, respectively. The electromagnetic responses of SDR-2 are distinctly different at TM and TE modes due to the asymmetrical SDR-2 structure. In Fig. 3(a) Fig. 5(a). By changing the h 1 value from 5 μm to 1 μm, the first resonance is red shifted from 0.54 THz to 0.41 THz with a tuning range of 0.13 THz. The corresponding bandwidth of the first resonance becomes narrower from 0.12 THz to 0.02 THz.

III. RESULTS AND DISCUSSIONS
On the contrary, the bandwidth of the second resonance becomes broader from 0.02 THz to 0.12 THz. The corresponding E-field distributions are shown in Fig. 6(a). The E-field energy is constrained in the split region, and the coupling intensity between the top and middle SDR layers is weaker. The H-field energy is strongly coupled in the space between the top and middle SDR layers and gradually weakened by decreasing the h 1 value, as shown in Fig. 6(b). Furthermore, there is a Fano resonance at 1.27 THz at TM mode. This Fano resonance is red shifted from 1.27 THz to 1.10 THz by changing the h 1 value from 5 μm to 1 μm. The corresponding resonant intensity is gradually decreased and then vanishes under the condition of h 1 = 1 μm because the fields coupling between the top and middle SDR layers become weaker with the decrease in the h 1 value. At TE mode, five resonances are red shifted from 0.27 THz to 0.22 THz, 0.48 THz to 0.41 THz, 0.57 THz to 0.48 THz, 0.70 THz to 0.64 THz, and 0.76 THz to 0.66 THz, respectively, by changing h 1 values, as shown in Fig. 5(b). The second resonance is the Fano resonance generated from the stronger capacitance coupling within the SDRs. It is enhanced by the change from h 1 = 5 μm to h 1 = 1 μm due to the inference coming from the bottom SDR layer, and its bandwidth becomes The corresponding E-and H-field distributions are shown in Figs. 6(c) and 6(d), respectively. The coupling intensity of the E-field energy is gradually enhanced when two SDR layers are closer. Meanwhile, the H-field energy is confined within the split region of the top SDR layer and then gradually gets transferred to the bottom SDR layer caused from the coupling efficiency, which is enhanced between the middle and bottom SDR layers by decreasing the h 1 value. Figures 7(a) and 7(b) show the transmission spectra of SDR-3 by changing the h 2 value at TM and TE modes, respectively, and keeping the h 1 value constant as 1 μm. In Fig. 7(a), the first and third resonances of SDR-3 are almost kept constant around 0.40 THz and 1.10 THz by changing the h 2 value from 6 μm to 3 μm at TM mode. The variations are within 0.01 THz. Apparently, the second resonance is red shifted from 0.74 THz to 0.50 THz by changing the h 2 value from 6 μm to 2 μm. The tuning range of resonance is 0.23 THz. The corresponding bandwidth becomes narrower from 0.13 THz to 0.05 THz with a tuning range of 0.08 THz. Furthermore, the FSR between the first and second resonances can be tuned from 0.32 THz to 0.12 THz with a range of 0.2 THz. The E-field distributions are concentrated around the contour of SDRs, as shown in Fig. 8(a). The H-field distributions are confined between the top and middle SDR layers, as shown in Fig. 8(b). The third resonance is Fano resonance, which becomes gradually weaker by decreasing the h 2 value. At TE mode, there are four resonances at 0.22 THz, 0.39 THz, 0.48 THz, and 0.61 THz. The first and third resonances are almost kept constant with a little variation of 0.02 THz. The second resonance is red shifted from 0.39 THz to 0.28 THz by changing the h 2 value from 6 μm to 2 μm. The tuning range of resonance is 0.11 THz. Furthermore, the FSR between the first and second resonances can be tuned from 0.17 THz to 0.07 THz with a tuning range of 0.10 THz, while the FSR between the second and third resonances can be inversely broadened from 0.09 THz to 0.18 THz with a tuning range of 0.09 THz by changing the h 2 value from 6 μm to 2 μm. Owing to the change of interaction between SDR layers, the corresponding E-and H-field distributions of the second resonance are presented in Figs. 8(c) and 8(d), respectively. The E-field energy is distributed in the space between the top and middle SDR layers. On the contrary, the H-field energy is confined in the split region. The fourth resonance is red shifted from 0.61 THz (h 2 = 6 μm) to 0.55 THz (h 2 = 2 μm) with a tuning range of 0.06 THz. The FSR between the third and fourth resonances is narrowed from 0.13 THz to 0.09 THz with a tuning range of 0.04 THz. These results indicate that the SDR-3 device is multi-functional, which can be used in the tunable filter, tunable FSR, and tunable optoelectronic THz-wave applications.

IV. CONCLUSIONS
In conclusion, we present a high-efficient design of tunable THz metamaterial to tune the resonance, FSR, and bandwidth by using SDR layers. These results show that these are single-, dual-, and triple-resonances depending on polarization and the specific design of SDRs at TM mode. By changing the h 1 value of SDR-2, the tuning ranges of resonance and FSR are 0.32 THz and 0.15 THz at TM mode, respectively. At TE mode, the resonance could abruptly generate or vanish by moving the SDR layer, which provides a potential application in the future THz switches. For SDR-3, moving the top SDR layer or the middle SDR layer leads to different results. By fixing the top SDR layer and moving the middle one, the resonant bandwidth could be tuned in the range of 0.10 THz and the resonance is gradually enhanced or weakened at TE and TM modes, respectively. Moreover, by fixing the middle SDR layer and moving the top one, the resonant bandwidth could be controlled with a range of 0.08 THz and the tuning range of FSR is up to 0.20 THz at TM mode, while two FSRs can be tuned in the ranges of 0.10 THz and 0.09 THz at TE mode. These characteristics indicate the SDR designs potentially to be realized as a tunable filter by using the MEMS technique to modify the electromagnetic response of SDR with reconfigurable geometrical dimensions. Moreover, the proposed device can be a polarization switch by manipulating the geometrical dimensions of SDR and changing the incident angle of light. Such an SDR design provides a high-efficient resonator in THz-wave applications, which opens up an avenue for the real-world applications in THz filters, THz polarizers, THz switches, THz sensors, THz imaging, and so on.