Voltage-tunable dual-layer terahertz metamaterials

This paper presents the design, fabrication, and characterization of a real-time voltage-tunable terahertz metamaterial based on microelectromechanical systems and broadside-coupled split-ring resonators. In our metamaterial, the magnetic and electric interactions between the coupled resonators are modulated by a comb-drive actuator, which provides continuous lateral shifting between the coupled resonators by up to 20 μm. For these strongly coupled split-ring resonators, both a symmetric mode and an anti-symmetric mode are observed. With increasing lateral shift, the electromagnetic interactions between the split-ring resonators weaken, resulting in frequency shifting of the resonant modes. Over the entire lateral shift range, the symmetric mode blueshifts by ~60 GHz, and the anti-symmetric mode redshifts by ~50 GHz. The amplitude of the transmission at 1.03 THz is modulated by 74%; moreover, a 180° phase shift is achieved at 1.08 THz. Our tunable metamaterial device has myriad potential applications, including terahertz spatial light modulation, phase modulation, and chemical sensing. Furthermore, the scheme that we have implemented can be scaled to operate at other frequencies, thereby enabling a wide range of distinct applications.

and supporting beams ( Figure S1d). In order to protect the patterned device layer from damage in the following steps, a 600nm-thick SiO 2 passivation layer is deposited on the front side using PECVD ( Figure S1e). Then, backside alignment and photolithography is performed and the SiN x film is etched with RIE, followed by etching through the Si substrate using DRIE ( Figures S1f and g). The last step ( Figure S1h) is to etch the buried oxide layer and passivation layer with Silox Vapoxy III etchant (Transene, Inc., Danvers, MA, United States) to release the movable structure. The second wafer, which is a single crystal o 1004 silicon wafer, is coated with low-stress SiN x film on both sides. Subsequently, 150-nm-thick gold SRRs are patterned on the top side with lift-off process ( Figure S1i). Then, the silicon wafer is etched through with KOH wet etching from the window opened on the backside SiN x film ( Figure S1j). After the wafer-level fabrication, the two wafers are diced into chips. For clarity and conciseness, we name the chips with comb-drive structures on SOI substrate as Chip 1 and the others as Chip 2. Polyimide bonding pads are patterned on Chip 2 via photolithography of the Figure S1 Fabrication process flow of the tunable metamaterial. 1 photosensitive polyimide (HD8820, HD Microsystems, Parlin, NJ, United States). Finally, we bond a pair of Chips 1 and 2 together with ± 2 μm alignment error using a flip chip bonder (FC150, Suss MicroTec AG, Garching bei München, Germany) under 200 g force and 175°C temperature.

CHARACTERIZATION OF THE METAMATERIAL
The electromagnetic response of the real-time tunable metamaterial is characterized by THz time domain spectroscopy (THz-TDS), as shown in Figure S2. A 1 kHz Ti:sapphire regenerative amplifier laser producing 1.55 eV near-infrared pulse (800 nm, 3 mJ, 35 fs) was utilized. A Teflon plate blocks the residual incident 800 nm optical beam and allows the THz beam to pass. The THz pulses are focused on the sample or the reference with a plane mirror and a parabolic mirror. The electric field of the THz pulses is polarized perpendicular with the gaps of the SRRs. The transmitted THz pulses are collimated and focused in the detection ZnTe crystal with a pair of parabolic mirrors. The 800-nm optical detection pulses are also fed to the ZnTe crystal. The THz field rotates the polarization of the detection pulses due to the Pockels effect. The polarization rotation is proportional to the electric field strength of the THz pulses. Then, the detection pulses are fed to a quarterwave plate, converted to be elliptically polarized, and split into two orthogonal linearly polarized pulses with a Wollaston prism. A pair of balance photodiodes are used to detect the two orthogonal pulses and the differential signal, measured by a lock-in amplifier, is an indicator of the instantaneous THz electric field. The THz electric field is measured in the time domain by controlling the delay time between the THz pulses and the detection pulses with a motorized delay stage. We can obtain the time domain signal of the sample and reference individually. Then, a Fourier transform is performed on the time domain signal to obtain the frequency spectrum of the reference [E r (ω)] and metamaterial samples (E s (ω)). The transmission spectrum of the sample is calculated by T(ω) = E s (ω)/E r (ω). A DC voltage power supply is used to apply voltage to the comb-drive actuator. By sweeping the applied voltage, the spectra of the metamaterial are measured at different lateral shifts.

SIMPLIFIED LUMPED MODEL OF THE BC-SRRS
The BC-SRRs can be simplified as two RLC resonators with mutual inductance L 12 (neglecting the mutual capacitance for simplification) as shown in Figure S3a   Kirchhoff's voltage law 1 , the current in each SRR can be solved using the following coupled equations: where C i , R i , and L i are the lumped capacitance, resistance and inductance of the i th SRR, I 1 and I 2 are the current in SRR1 and SRR2, g 1 and g 2 are the capacitive gap in SRR1 and SRR2, and L 12 is the mutual inductance between the SRRs. The transfer function of the system can be determined by solving the equations 1 C 1 s I 1 ðsÞ þ R 1 I 1 ðsÞ þ L 1 sI 1 ðsÞ -L 12 I 2 ðsÞ ¼ E y ðsÞg 1 1 C 2 s I 2 ðsÞ þ R 2 I 2 ðsÞ þ L 2 sI 2 ðsÞ -L 12 I 1 ðsÞ ¼ E y ðsÞg 2 The values of C i , R i , and L i can be extracted from the numerical simulation with CST Microwave Studio and are listed in Table S1. We can calculate I 1 (s)/E y (s) and I 2 (s)/E y (s) with these parameters. According to Ref. 1, the total electric dipole density in the BC-SRRs unit-cell is given by where V is the volume of each unit-cell calculated by V = P 2 (d+t), in which P is the periodicity of the SRRs, d is the vertical distance between the SRRs, and t is the thickness of the silicon frame in SRR1. In the frequency domain, we can get The frequency response of electric dipole density (P y ) is plotted in Figure S3b. We assume that the mutual inductance is 14 pH for the aligned case. There are two peak values in amplitude spectrum of P y , corresponding to the resonant frequencies of the BC-SRRs. The peak values in the electric dipole density correspond to the transmission minima of the BC-SRRs (black curve in Figure 4a). With increasing lateral shift, the mutual inductance becomes smaller. The first mode shifts to higher frequency and the second Figure S4 The simulated tunable transmission response of the BC-SRRs with different resonance frequency mismatch (f diff ) with 20 μm lateral shift.

Table S1
The parameters used in the lumped model Parameters Value 3 0 L 2 (pH) 47 g 1 (μm) 14 g 2 (μm) 2 mode shifts to the lower frequency. At the same time, the peak value of the electric dipole density at the first mode increases, resulting in a decreased transmission at the resonant frequency. However, the electric dipole density at the second mode almost keeps constant. The change of electric dipole density is one reason of the change in the transmission response. Even though we only take the inductive coupling into account (e.g we neglect capacitive coupling and other effects, such as bianisotropy of the BC-SRRs), this simple model can be used to understand the basic response of the coupled SRRs and provide insight into the experimentally observed transmission changes.

THE EFFECT OF RESONANT FREQUENCY MISMATCH
In this paper, a pair of resonance frequency matched SRRs are used in the metamaterial unit-cells. To investigate the effect of frequency mismatch on the tunable response of the metamaterials, the gap of SRR2 (g 2 ) is changed to introduce resonance frequency mismatch (f diff ) between SRR1 and SRR2 in the simulations using CST Microwave Studio. The tunable transmission of the BC-SRRs with different resonance mismatch for 20 μm lateral shift are plotted in Figure S4. The tuned parameters, i.e. resonance frequency shift of Modes 1 and 2 and the modulation depth at 1.03 THz, are listed in Table S2 for a 20 μm lateral shift.
From the results, we can conclude that the BC-SRRs with matched resonance frequency have the greatest tunability and largest modulation depth at 1.03 THz.

THE EFFECT OF PERIODICITY
The numerically simulated transmission spectra of the BC-SRRs with different periodicities are shown in Figures S5. When the BC-SRRs are aligned (Δ = 0 μm), the resonance dip of each mode becomes sharper with an increase of the periodicity, indicating an increased quality factor. Resonant frequency tuning of the BC-SRRs is not strongly affected by the periodicity for a constant lateral displacement (i.e. by comparing Figure S5a and b). However, if a larger lateral displacement can be realized by the actuator, larger tuning may be achieved. For our current case, P is 58 μm and L is 40 μm, we cannot misalign the array of SRRs completely because the movable SRRs overlap with the adjacent SRRs when the lateral shift is larger than P/2. As a result, we cannot fully decouple the BC-SRRs. If P is 80 μm and L is 40 μm and we can achieve 40 μm lateral displacement, and there will be no overlapped areas between the BC-SRRs leading to minimum coupling. Currently, due to the limitation in the lateral shift (maximum is~25 μm), the periodicity has little effect on the tunability. However, we can control the quality factor with the periodicity.