Electromechanically Rotatable Cross-Shaped Mid-IR Metamaterial

: We present an electromechanically rotatable infrared (IR) cross-shaped metamaterial (CSM) in the mid-IR wavelength range. The CSM conﬁguration is composed of double gold layers with cross-shaped nanostructures. To investigate the fano-resonance within CSM nanostructures, the aspect ratios and length ratios of CSM are compared and discussed. The electromagnetic responses exhibit the characteristics of large tuning range, tunable broad and narrow bandwidths. By properly tailoring the aspect ratio of CSM, the resonance can be tuned with bidirectional tuning in the range of 650 nm. CSM with di ﬀ erent length ratios exhibit narrowband resonances around the wavelength of 4.6 µ m and broadband resonances in the wavelength range of 5.0 µ m to 6.5 µ m. These characteristics of CSM with di ﬀ erent aspect ratios and length ratios could be potentially used in IR narrowband and broadband ﬁlter. To further increase the ﬂexibility of proposed electromechanically rotatable CSM, an actively tunable narrowband and broadband ﬁlter in the mid-IR wavelength range is performed. This study provides a unique approach to realizing an IR ﬁlter, with high ﬂexibility. bidirectional the variation of r value shows that the transmission bandwidths could be modiﬁed to be narrow around the wavelength of 4.6 µ m and broad in the wavelength range of 5.0 µ m to 6.5 µ m. These characterizations of CSM with di ﬀ erent t and r values could be potentially used in high-e ﬃ ciency mid-IR narrowband and broadband ﬁlter. Furthermore, we propose an active tuning mechanism using a poly-Si MEMS-based electrothermal actuator to increase the ﬂexibility of CSM. This approach exhibits that the bandwidth of CSM could be tuned by rotating the top cross-shaped metamaterial.

To meet the requirements of certain functions in the real-world applications, the active tunability is attractive to make metamaterials possess high flexibility and applicability. Therefore, the suitable tuning methods of metamaterials are required to improve the metamaterial performances and tunabilities of optical characteristics, which has long been a research topic of interest for scientists. There have been reported many literatures to demonstrate tunable metamaterials by using thermal annealing, ferroelectric materials, semiconductor materials or diodes, laser pumping, liquid crystal, electrostatic force, and microelectromechanical systems (MEMS) technology [17][18][19][20][21][22][23]. Among these tuning approaches, MEMS technology is an alternative method to directly change the geometrical structures of metamaterials. It involves semiconductor, electronic engineering, mechanical engineering, medicine, physics, information engineering and other disciplines and technologies [24][25][26][27][28]. It is an independent intelligent system. There have been many MEMS-based tunable metamaterials reported, including MEMS-based resonant cloaking metamaterial [29], active phase transition metamaterial [30], tunable ultrathin metamaterial [31], CMOS-MEMS broadband metamaterial [32], electromagnetically induced metamaterial [33], MEMS-modulated metamaterial [34], and so on. However, these approaches cannot be controlled, and manipulated the unit cell by unit cell. Therefore, these proposed MEMS-based approaches are limited in certain applications and have less tuning range, which will confine their flexibility and applicability in real-world applications.
To overcome the above-mentioned confinements, we propose a tunable cross-shaped metamaterial (CSM) using MEMS technology. CSM is composed of top and bottom tailored Au layers, which can be realized by using MEMS technology to derive an electrothermal actuation force to perform the cross-shaped nanostructures rotated at an angle and then tune the resonant frequency. It can be electromechanically rotated CSM unit cell individually. By changing these geometrical configurations, CSM shows different electromagnetic characteristics and flexible tunability. The corresponding fano-resonances within CSM nanostructures are investigated to figure out the suitable design. Figure 1a shows the schematic drawing of MEMS-based CSM and the corresponding CSM unit cell. It is composed of double tailored Au layers with a gap between them. The top Au layer is connected to a poly-Si electro-thermal actuator, which can be rotated by driving different voltages to exhibit high flexibility. The geometrical parameters are metallic lengths along x-and y-axis directions, which are denoted as L 1 and L 2 , respectively. The metallic width (W) of CSM is varied simultaneously when discussing the electromagnetic characteristics in this study. The metallic thicknesses of two Au layers are kept as constant as 200 nm. The gap is also kept as constant as 100 nm. The reconfiguration of CSM is proposed to compare and discuss different aspect ratios (t = W/L), length ratios (r = L 1 /L 2 ), and rotation angles of the top metamaterial layer. The fabrication process of MEMS-based CSM device is illustrated in Figure 1b. First, an Au thin-film with 200 nm in thickness was deposited by using lift-off process, as shown in Figure 1b-i. Second, SiO 2 and poly-Si thin-films with 500 nm and 40 nm in thicknesses, respectively, were deposited by using the plasma enhanced chemical vapor deposition (PECVD) process, as shown in Figure 1b-ii. Third, poly-Si thin-film was patterned by using the reactive ion etching (RIE) process, as shown in Figure 1b-iii. Fourth, an Au thin-film was deposited by using the lift-off process, as shown in Figure 1b-iv. Finally, the nanostructures were released by using vapor HF, as shown in Figure 1b-v. In the future, we will design and demonstrate CSM device by using MEMS technology and following up this fabrication process. Such CSM device possesses flexibility and applicability which could be used in widespread applications with active tunability, such as switch, filter, absorber, sensor, and so on.

Materials and Methods
The optical properties of the proposed CSM device are simulated through Lumerical Solution's finite difference time domain (FDTD)-based simulations (LUMERICAL version: 8.12.631). The propagation direction of incident light is set to be perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are also adopted in the x-and y-axis directions, and perfectly matched layer (PML) boundaries conditions are assumed in the z-axis direction. The reflection (R) and transmission (T) of lights are calculated by two monitors set on both sides of the device. In these configurations, Si material serves as the substrate with the tailored Au layer atop. The permittivity values of Au and Si materials in the mid-IR wavelength range are calculated according to the Drude-Lorentz model [35,36].

Results and Discussions
The transmission and reflection spectra of CSM with different t (W/L) values in mid-IR wavelength range under the condition of L = L1 = L2 = 2000 nm are shown in Figure 2a Figure 3(a), the resonant peak is blue-shifted 50 nm from the wavelength of 4.70 μm (r = 0.2) to 4.65 μm (r = 1.0) and the resonant dip is blue-shifted 30 nm from the wavelength of 5.58 μm (r = 0.2) to 5.55 μm (r = 1.0). By increasing the metallic width to 400 nm (W = 400 nm), the resonant peak is blue-shifted 100 nm from the wavelength of 4.66 μm (r = 0.2) to 4.56 μm (r = 1.0), and the resonant dip is blue-shifted 140 nm from the wavelength of 5.52 μm (r = 0.2) to 5.38 μm (r = 1.0), as shown in Figure 3(b). When W = 800 nm, the first resonance is red-shifted 330 nm from the wavelength of 4.82 μm (r = 0.4) to 5.15 μm (r = 1.0), and the second resonance is red-shifted 340 nm from the wavelength of 6.08 μm (r = 0.4) to 5.38 μm (r = 0.6), as shown in Figure 3c. In the case of W = 1200, the full width at half maximum (FWHM) of resonance can be tuned from 180 nm to 520 nm, by changing r = 0.6 to r = 1.0 in 0.1 steps, as shown in Figure 3d.

Results and Discussions
The transmission and reflection spectra of CSM with different t (W/L) values in mid-IR wavelength range under the condition of L = L 1 = L 2 = 2000 nm are shown in Figure 2a   To further investigate the tunability of an electromechanically rotatable CSM device, it is designed to rotate an angle between double tailored Au layers by using MEMS-based electrothermal actuator. Figure 4a shows the layout of a CSM unit cell. The lengths of hot arm (Lh), cold arm (Lc), flexure (Lf) and connecting rod (L3) are 4800 nm, 4000 nm, 800 nm and 1400 nm, respectively. The widths of hot arm, flexure, and connecting rod are 50 nm, while the width of cold arm (wc) is 500 nm. The total thickness (h) of electrothermal actuator is 40 nm. Herein, the reconfiguration of electromechanically rotatable CSM is proposed, to compare and discuss different rotation angles of top metamaterial layer, by driving different voltages on electrothermal actuator. The displacement is generated through the asymmetric heating of hot and cold arms. By driving a voltage on CSM device,  To further investigate the tunability of an electromechanically rotatable CSM device, it is designed to rotate an angle between double tailored Au layers by using MEMS-based electrothermal actuator. Figure 4a shows the layout of a CSM unit cell. The lengths of hot arm (Lh), cold arm (Lc), flexure (Lf) and connecting rod (L3) are 4800 nm, 4000 nm, 800 nm and 1400 nm, respectively. The widths of hot arm, flexure, and connecting rod are 50 nm, while the width of cold arm (wc) is 500 nm. The total thickness (h) of electrothermal actuator is 40 nm. Herein, the reconfiguration of electromechanically rotatable CSM is proposed, to compare and discuss different rotation angles of top metamaterial layer, by driving different voltages on electrothermal actuator. The displacement is generated through the asymmetric heating of hot and cold arms. By driving a voltage on CSM device, To further investigate the tunability of an electromechanically rotatable CSM device, it is designed to rotate an angle between double tailored Au layers by using MEMS-based electrothermal actuator. Figure 4a shows the layout of a CSM unit cell. The lengths of hot arm (L h ), cold arm (L c ), flexure (L f ) and connecting rod (L 3 ) are 4800 nm, 4000 nm, 800 nm and 1400 nm, respectively. The widths of hot arm, flexure, and connecting rod are 50 nm, while the width of cold arm (w c ) is 500 nm. The total thickness (h) of electrothermal actuator is 40 nm. Herein, the reconfiguration of electromechanically rotatable CSM is proposed, to compare and discuss different rotation angles of top metamaterial layer, by driving different voltages on electrothermal actuator. The displacement is generated through the asymmetric heating of hot and cold arms. By driving a voltage on CSM device, the higher current density in narrower hot arm will expand more than that of the wider cold arm. The arms are jointed at the free end, where the driving force of actuator moves the CSM laterally in an arcing motion towards the cold arm side [37]. According to the equation of the U-shaped electrothermal actuator, the deflection in the free end of actuator is linear to the driving voltage [37]. The relationship of driving voltages and displacements of electromechanically rotatable CSM device are summarized in Figure 4b. The maximum driving voltage is 20 volts, to actuate the CSM unit cell rotated to 45 • . The surface thermal flows of electrothermal actuator at the driving voltages of 12 volts, 14 volts, 16 volts, and 20 volts are simulated using COMSOL software, which are plotted in Figure 5a-d, respectively. Here, we choose the condition of CSM with W = 800 nm, as an example to demonstrate that the electromechanically rotatable CSM can be realized by using a MEMS-based electrothermal actuator. Figure 6a,b show the transmission and reflection spectra of electromechanically rotatable CSM device with different rotation angles, respectively. By changing the rotation angle as 0 • , 15 • , 30 • , and 45 • , the resonances of transmission spectra can be tuned to the FWHM values of the CSM device, i.e., spectrum bandwidth as 300 nm, 650 nm, 1040 nm, and 1200 nm, respectively, as shown in Figure 6a, while the narrowband resonance of reflection spectra is blue-shifted 200 nm from the wavelength of 4.37 µm to 4.17 µm, as shown in Figure 6b. It is clearly observed that the proposed electromechanically rotatable CSM device exhibits the tunable abilities of broad and narrow bandwidth for the transmission and reflection spectra, respectively. Such tuning approach provides a suitable design for a tunable mid-IR filter application with high flexibility.
Crystals 2020, 10, x FOR PEER REVIEW 5 of 8 arms are jointed at the free end, where the driving force of actuator moves the CSM laterally in an arcing motion towards the cold arm side [37]. According to the equation of the U-shaped electrothermal actuator, the deflection in the free end of actuator is linear to the driving voltage [37]. The relationship of driving voltages and displacements of electromechanically rotatable CSM device are summarized in Figure 4b. The maximum driving voltage is 20 volts, to actuate the CSM unit cell rotated to 45°. The surface thermal flows of electrothermal actuator at the driving voltages of 12 volts, 14 volts, 16 volts, and 20 volts are simulated using COMSOL software, which are plotted in Figure  5a-d, respectively. Here, we choose the condition of CSM with W = 800 nm, as an example to demonstrate that the electromechanically rotatable CSM can be realized by using a MEMS-based electrothermal actuator. Figure 6a,b show the transmission and reflection spectra of electromechanically rotatable CSM device with different rotation angles, respectively. By changing the rotation angle as 0°, 15°, 30°, and 45°, the resonances of transmission spectra can be tuned to the FWHM values of the CSM device, i.e. spectrum bandwidth as 300 nm, 650 nm, 1040 nm, and 1200 nm, respectively, as shown in Figure 6a, while the narrowband resonance of reflection spectra is blueshifted 200 nm from the wavelength of 4.37 μm to 4.17 μm, as shown in Figure 6b. It is clearly observed that the proposed electromechanically rotatable CSM device exhibits the tunable abilities of broad and narrow bandwidth for the transmission and reflection spectra, respectively. Such tuning approach provides a suitable design for a tunable mid-IR filter application with high flexibility.

Conclusion
In conclusion, a reshaping MEMS-based electromechanically rotatable CSM is presented, which is composed of double Au metamaterial layers. By tailoring the geometrical parameters of CSM, the corresponding electromagnetic behavior exhibits tunable bandwidth, large tuning range of resonance, and tunable narrowband resonance characteristics. The variation of t value shows that the resonance could be modified with red-shift of 400 nm and blue-shift of 650 nm to form the bidirectional tuning. Meanwhile, the variation of r value shows that the transmission bandwidths could be modified to be narrow around the wavelength of 4.6 μm and broad in the wavelength range of 5.0 μm to 6.5 μm. These characterizations of CSM with different t and r values could be potentially used in high-efficiency mid-IR narrowband and broadband filter. Furthermore, we propose an active tuning mechanism using a poly-Si MEMS-based electrothermal actuator to increase the flexibility of CSM. This approach exhibits that the bandwidth of CSM could be tuned by rotating the top crossshaped metamaterial. By rotating at an angle from 0° to 45° in 15° steps, the electromagnetic

Conclusion
In conclusion, a reshaping MEMS-based electromechanically rotatable CSM is presented, which is composed of double Au metamaterial layers. By tailoring the geometrical parameters of CSM, the corresponding electromagnetic behavior exhibits tunable bandwidth, large tuning range of resonance, and tunable narrowband resonance characteristics. The variation of t value shows that the resonance could be modified with red-shift of 400 nm and blue-shift of 650 nm to form the bidirectional tuning. Meanwhile, the variation of r value shows that the transmission bandwidths could be modified to be narrow around the wavelength of 4.6 μm and broad in the wavelength range of 5.0 μm to 6.5 μm. These characterizations of CSM with different t and r values could be potentially used in high-efficiency mid-IR narrowband and broadband filter. Furthermore, we propose an active tuning mechanism using a poly-Si MEMS-based electrothermal actuator to increase the flexibility of CSM. This approach exhibits that the bandwidth of CSM could be tuned by rotating the top crossshaped metamaterial. By rotating at an angle from 0° to 45° in 15° steps, the electromagnetic

Conclusions
In conclusion, a reshaping MEMS-based electromechanically rotatable CSM is presented, which is composed of double Au metamaterial layers. By tailoring the geometrical parameters of CSM, the corresponding electromagnetic behavior exhibits tunable bandwidth, large tuning range of resonance, and tunable narrowband resonance characteristics. The variation of t value shows that the resonance could be modified with red-shift of 400 nm and blue-shift of 650 nm to form the bidirectional tuning. Meanwhile, the variation of r value shows that the transmission bandwidths could be modified to be narrow around the wavelength of 4.6 µm and broad in the wavelength range of 5.0 µm to 6.5 µm. These characterizations of CSM with different t and r values could be potentially used in high-efficiency mid-IR narrowband and broadband filter. Furthermore, we propose an active tuning mechanism using a poly-Si MEMS-based electrothermal actuator to increase the flexibility of CSM. This approach exhibits that the bandwidth of CSM could be tuned by rotating the top cross-shaped metamaterial.
By rotating at an angle from 0 • to 45 • in 15 • steps, the electromagnetic bandwidth can be tuned from 300 nm to 1200 nm. It is enhanced 4-fold. These results open an avenue for filter, absorber, detector, sensor, and switch applications with high-flexibility in mid-IR wavelength range.