Electromechanically Tunable Metasurface Transmission Waveplate at Terahertz Frequencies

Dynamic polarization control of light is essential for numerous applications ranging from enhanced imaging to materials characterization and identification. We present a reconfigurable terahertz metasurface quarter-waveplate consisting of electromechanically actuated micro-cantilever arrays. Our anisotropic metasurface enables tunable polarization conversion cantilever actuation. Specifically, voltage-based actuation provides mode selective control of the resonance frequency, enabling real-time tuning of the polarization state of the transmitted light. The polarization tunable metasurface has been fabricated using surface micromachining and characterized using terahertz time domain spectroscopy. We observe a ~230 GHz cantilever actuated frequency shift of the resonance mode, sufficient to modulate the transmitted wave from pure circular polarization to linear polarization. Our CMOS-compatible tunable quarter-waveplate enriches the library of terahertz optical components, thereby facilitating practical applications of terahertz technologies.


Introduction
Precise control of the polarization state of an electromagnetic wave is of great importance in applications in astrophysics, chemistry, microscopy and advanced optics 1 .
Conventionally, material birefringence is used to construct polarization sensitive optical components such as quarter-wave and half-wave plates 2 . However, the majority of polarization components are limited by the material response and lack of tunability. A notable exception is commercially available photo-elastic modulators that efficiently tune the polarization state using piezoelectric transducers, though they are relatively bulky and working at mid-infrared and shorter wavelength regimes. The development of artificial electromagnetic (EM) materials, including metamaterials and metasurfaces, provides a route to break the limitation of natural materials, enabling versatile and compact control of EM wave propagation from microwave to visible frequencies 4,5 .
With metamaterials or metasurfaces, it is possible to not only obtain the desired permittivity, permeability, and chirality at a chosen frequency, but also tune and reconfigure the effective parameters to construct so-called "metadevices" 29 . Different approaches, including optical excitation 30-33 , electrical gating [34][35][36] , phase change 37,38 , and mechanical actuation [39][40][41][42][43][44][45][46][47][48] have been investigated to modulate the amplitude and phase response of metamaterials. Notable polarization based devices include a switchable 4 quarter-waveplate 49 and tunable optical activity 42 to extend the operating bandwidth and modulate the polarization state. Recently, a metamaterial device consisting of microelectromechanical systems (MEMS) bimorph cantilevers has been demonstrated to control the polarization of terahertz radiation 50 . This device operates in reflection, complementing our transmission-based device as discussed in greater detail below.
In this paper, we employ single-layer micro-cantilevers to construct a terahertz (THz) metasurface with a highly anisotropic response, allowing us to tune the resonance frequency for radiation polarized along one axis (x-axis) without affecting the response along the orthogonal direction (y-axis). The large resonance frequency tuning range (~230 GHz) achieved with electrostatically actuated cantilevers modifies the polarization of the transmitted wave from circular polarization to linear polarization, yielding a reconfigurable quarter-waveplate operating in transmission. Our theoretical analysis based on an equivalent circuit model and finite element simulations unveil the physics of the experimental results. The dimensions of the structure can be adapted to design metasurface devices for other frequency ranges, including microwave and infrared. Our device is fabricated using surface micromachining, which is compatible with CMOS, providing opportunities for reconfigurable and reprogrammable quarter-waveplates and other polarization control devices.

Materials and Methods
The working principle of the tunable metasurface is shown in Fig. 1. The unit-cell is a suspended cantilever, of which the free-end overlaps with an underlying capacitive pad. For x-polarized normal incidence light (θ = 0 o in Fig. 1a), the unit-cell can be considered as a second order LC resonator (as shown in Fig. 1b), in which the inductance is associated with the cantilever and the capacitance is formed by the cantilever tip and underlying pad. The array of unit-cells is patterned on a slightly doped silicon wafer that is coated with an insulating silicon nitride thin film. A voltage across the cantilevers and 5 the substrate induces an electrostatic force to pull the cantilevers downward. The change in capacitance modifies the resonant response. Conversely, for the y-polarized incident wave (θ = 90 o in Fig. 1a), only the wires connecting adjacent cantilevers (which can be modeled as an inductor, as shown in Fig. 1c) need to be considered. The overall transmission response of the metasurface, which is represented by the Jones vector and transmission matrix T, can be written as 1 (1) where and are the x-and y-polarized components of the incident wave, respectively; and denote the transmitted electric field along x-and y-axis, respectively. For the transmission matrix of the cantilever metasurface, the off-diagonal elements are negligible due to weak cross-polarization coupling. The diagonal element complex transmission coefficients txx and tyy, can be modeled by the following equations according to transmission line theory 51 : where Zxx and Zyy are effective impedances for the x-and y-polarization directions, respectively, Z0 is the impedance of free space, and D represents the transmission loss at the substrate/air interface. According to the equivalent circuit model shown in Fig. 1b and 1c, we can express these impedances as Zxx = R1+iL1+1/(iC1) and Zyy = R2+iL2.
Simply speaking, cantilever actuation modifies the impedance Zxx by changing the capacitance C1 without affecting Zyy, leading to modulation of the transmission 6 characteristics for x-polarized incidence. As such, the anisotropy of the cantilever array and associated response enables control of the polarization state of the transmitted wave as discussed below.
The designed structure was fabricated using surface micromachining on a slightly doped silicon substrate. The fabrication process flow is shown in Fig. S1. The fabricated tunable metasurface and the mechanical response are shown in Fig. 2. A DC voltage was applied to the cantilever and the substrate through the bonding wires (Fig. 2a). The area of the cantilever array is 88 mm 2 . The rectangular hole in the beam is designed for ease of releasing and the dimple in the free-end of the beam enhances the capacitance change and prevents adhesion between the cantilever beam and the underlying capacitive pad (Fig. 2b). The cantilevers bend upwards due to residual stress after releasing. When a voltage is applied, the electrostatic force between the cantilever and the substrate pulls the cantilevers downwards. The beam curvature as a function of applied DC voltage has been characterized using a laser interferometer (ZYGO), as shown in Fig. 2c. Initially, the height of the tip, i.e. the distance between the bottom of the dimple and the top of the capacitive pad, is ~0.9 µm, as shown in Fig. 2d  shown in Fig. 2c, was applied. The tip height of the cantilever was adjusted to match the measured results for different applied voltages.

Results and Discussion
The transmission spectra of the metasurface for different applied voltages has been characterized using terahertz time domain spectroscopy (THz-TDS), as described above.
To verify the metasurface anisotropy, the transmission for x-and y-polarized terahertz pulses (Figs. 3a-3d) were measured by rotating the sample 90º about the incident axis.
At zero voltage, a strong resonance is observed for x-polarization at 1.04 THz with a transmission amplitude of 0.03, while there is no obvious resonance observed for ypolarization. Numerical simulations were performed using CST Microwave Studio (details in the Materials and Methods section) to study the metasurface EM response.
The simulations show good agreement with experimental results of the transmitted 9 amplitude and phase. For x-polarization at 1.04 THz, currents are excited in the copper cantilever structure, corresponding to the LC resonance mode as illustrated in Figs. 3e and 3f. The electric field (Fig. 3f) is concentrated in the gap between the cantilever tip and the underlying capacitive pad, consistent with the tip-pad structure being the dominant contributor to the overall capacitance. However, the fringe field along the cantilever beam indicates that the contribution to the capacitance between the beam and silicon substrate cannot be ignored. For y-polarized THz pulses, current in the connection wires (Fig. 3g) are present, equivalent to an inductor as illustrated in Fig. 1c with, as expected, no electric resonance (Fig. 3h). Quantitatively, the equivalent circuit model [Eqs. (2) and (3) THz pulses demonstrates that the metasurface operates as a THz modulator [44][45][46]51 .
In contrast, for y-polarized (tyy) THz pulses, the transmission amplitude and phase are unchanged upon deflection of the cantilevers (and therefore the applied voltage) as shown by red curves in Figs. 3a-3d. In short, the results in Fig. 3 demonstrate the anisotropic tunability of the cantilever metasurface, which enables creating a tunable quarter-waveplate as we now discuss.
Based on the Jones vector and measured transmission spectra (txx and tyy), we can calculate the Stokes parameters 1 , including S0, S1, S2, and S3, which fully describe the polarization state of a transmitted wave for an arbitrary incident polarization, as detailed in the Materials and Methods section.
We consider a normally incident wave with a polarization angle ( in Fig. 1a) (Fig. S6).
From Fig. 5c, we can observe that our device exhibits a fair amount of insertion loss due mainly to reflection at the air/metasurface interface and limited polarization conversion efficiency. In theory, the maximum transmitted intensity is 50% for a single layer metamaterial waveplate 21 , while our tunable metasurface exhibits a transmittance of ~20% for circular polarization (e.g. VDC = 0V, 0.81 THz) and ~10% for linear polarization (e.g. VDC = 40V, 0.81 THz). Even though the transmitted intensity is not ideal, our device achieves a significant and functional tunability of the polarization state.
Moreover, the insertion loss can be decreased by adjusting the geometry of the quarterwaveplate to improve the conversion efficiency and eliminate reflective losses.
Specifically, optimizing the anisotropy of the metasurface will increase the polarization conversion efficiency 19 , and adding a metasurface anti-reflection layer will eliminate the reflection loss 21 . In short, a high-efficiency waveplate with a large tunable response is expected by further optimizing the metasurface.
The tunability of the polarization state exists not only for an incident polarization angle of 34º, but also for arbitrary polarization angles. The calculated CPRs from the measured Stokes parameters for different incident polarization angles () from 0º to 180º show the polarization state of transmitted waves, presented in Figs. 5e-5g. When VDC = 0, right-hand circular polarized transmission can be achieved for incident waves with polarization angles from 0º to 57º, while left-hand circular polarization is achievable for polarization angles from 123º to 180º over this frequency range (0.4 -1.0 THz). As the applied voltage increases, it seems that the overall spectra of CPR shift to lower frequencies, demonstrating the tunable polarization state of transmitted waves for arbitrarily polarized incidence.
Compared with the MEMS-cantilever based tunable polarization control recently demonstrated 50 , the design and performance of our device is different in several respects. First, our device is designed to operate in transmission whereas in Ref. [50] the device operated in reflection mode. In Ref. [50] actuation of bimorph cantilevers is  [44][45][46]52 . In particular, cantilevers provide a route to control the response of each unit-cell individually with well-designed routing strategies, similar to deformable mirrors 53 . For example, we can combine microcantilever actuators with gradient metasurface structures that are designed for beam steering or focusing 54 to enable real-time tunable devices by controlling the phase discontinuities at the unit-cell level 46,50,52 , as well as other applications, such as digital coding metasurfaces [55][56][57][58] . This paper presents a micro-cantilever based reconfigurable quarterwaveplate to manipulate the polarization of THz radiations dynamically, facilitating the development and applications of THz technologies.

Fabrication process
We developed a surface micromachining process to fabricate the tunable metasurface waveplate. First, 400-nm-thick silicon nitride films were coated on both sides of the substrate using low-pressure chemical vapor deposition (LPCVD). Then, photolithography was performed on the top side of the wafer followed by reactive ion etching (RIE) to open windows for ground electrodes. Subsequently, a layer of aluminum was patterned as ground pads using a lift-off process with annealing in H2/N2 mixing gas at 400 ºC for 30 minutes to obtain ohmic contact between the metal and silicon. Next, ground pads and interconnect wires were patterned by subsequent processes including photolithography, e-beam evaporation of 10-nm chromium and 150-nm gold layers and lift-off. Afterwards, a 400-nm-thick polyimide film was spin-coated on the wafer and cured in N2 ambient at 275 ºC for 1 hour as the sacrificial layer. The cured polyimide film was etched through at the anchors with a titanium layer as the mask and partially etched at the cantilever tips for the formation of dimples. Then, 1-µm copper cantilever structures with 10-nm chromium adhesive films were patterned using the lift-off process.
Finally, the sacrificial polyimide layer was completely removed by employing O2 plasma etching.

Terahertz time domain spectroscopy based on photo-conductive antennas
The fabricated samples were characterized using the terahertz time domain spectroscopy (THz-TDS) based on photo-conductive antennas, as shown in Fig. S2a.

Equivalent circuit model of the tunable metasurface
The transmission coefficient of the metasurface can be intuitively explained using the equivalent circuit model. As shown in Figs. 1b and 1c, the response to x polarized light is equivalent to a RLC resonator while the response to y polarized light is equivalent to a RL circuit. According to transmission line (T.L.) theory, the transmission coefficients for x and y polarized incidence, denoted by txx and tyy, respectively, can be calculated by Eqs.

Tunable polarization state revealed by Stokes parameters
Stokes parameters of the transmitted waves can be derived using the equations in the Methods section of the main text. The full set of stokes parameters, including S0, S1, S2, and S3, can be plotted in a Poincare plot to visualize the polarization state of a wave. Fig.   S5a is the Stokes parameters for 34° incident polarization angle, calculated from experimental transmission coefficients and plotted on a normalized Poincare sphere.
Each point on the curves corresponds to the Stokes parameters of a specific frequency and each curve corresponds to one specific applied voltage. In the Poincare sphere, the point intersects with the z-axis (i.e., S1 = 0, S2 = 0, and S3 = 1) corresponds to pure circular polarization while the intersection with the x-y plane (i.e. S1 0, S2 0, and S3 = 0) corresponds to linear polarization. All other points represent elliptical polarization 33 states. We can read the orientation angle ( ) and ellipticity angle ( ), which are depicted in Fig. S5b, directly from the plot. In Fig. S5a, the Stokes parameters at 0.81 THz are highlighted by the solid dots for different applied voltages. When VDC = 0 V, it is close to (0, 0, -1), manifesting circular polarization. When VDC = 40 V, the Stokes parameters locate at (-0.99, 0.13, 0), meaning linear polarization. The polarization states are plotted in Fig. S5c for each voltage. We can capture more information from the full set of Stokes parameters using Poincare sphere.