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Electromechanically tunable metasurface transmission waveplate at terahertz frequencies

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Abstract

Dynamic polarization control of light is essential for numerous applications ranging from enhanced imaging to material characterization and identification. We present a reconfigurable terahertz metasurface quarter-wave plate consisting of electromechanically actuated microcantilever arrays. Our anisotropic metasurface enables tunable polarization conversion through 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 230GHz 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-wave plate enriches the library of terahertz optical components, thereby facilitating practical applications of terahertz technologies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. 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. Notable exceptions are commercially available photo-elastic modulators that efficiently tune the polarization state using piezoelectric transducers [3] and liquid crystal retarders that stem from the voltage controllable birefringence [4], 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 [5,6]. Design-based control of the effective permittivity and permeability achieved with metamaterials has led to the realization of negative refractive index [7] and controllable chirality [8,9] and enabled, as examples, superlensing [10], perfect absorption [11], and transformation optics for advanced wave manipulation [1214]. Based on the generalized laws of refraction and reflection [15], planar metasurfaces can control the phase front of the outgoing wave for beam focusing [16] and steering [17], among others [1820]. In particular, anisotropic metamaterials and metasurfaces support polarization conversion [2125] and optical activity [2629].

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” [30]. Different approaches, including optical excitation [3134], electrical gating [3537], phase change [38,39,40], and mechanical actuation [4150] have been investigated to modulate the amplitude and phase response of metamaterials. Notable polarization-based devices include switchable quarter-wave plates [40,51] and tunable optical activity [44] 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 [52]. This device operates in reflection, complementing our transmission-based device as discussed in greater detail below.

In this paper, we employ single-layer microcantilevers 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 (230GHz) achieved with electrostatically actuated cantilevers modifies the polarization of the transmitted wave from circular polarization to linear polarization, yielding a reconfigurable quarter-wave plate operating in transmission. Our theoretical analysis based on an equivalent circuit model and finite element simulations unveil the physics of the experimental results. Comparing with the tunable reflective metasurface wave plate [52], our device exhibits similar efficiency and has the potential to be more easily integrated with existing optical systems, facilitating the development of advanced THz optical systems. Furthermore, 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-wave plates and other polarization-control devices.

2. 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° in Fig. 1(a)], the unit-cell can be considered as a second-order inductive-capacitive (LC) resonator [as shown in Fig. 1(b)], 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 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° in Fig. 1(a)], only the wires connecting adjacent cantilevers [which can be modeled as an inductor, as shown in Fig. 1(c)] 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]

[ExtEyt]=T[ExiEyi]=[txxtxytyxtyy][ExiEyi],
where Exi and Eyi are the x- and y-polarized components of the incident wave, respectively; Ext and Eyt denote the transmitted electric field along x and y axes, 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 [53]:
txx=2ZxxZxx+Z0D,
tyy=2ZyyZyy+Z0D,
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 including the reflection loss at the substrate/air interface and absorptive loss in the substrate. According to the equivalent circuit model shown in Figs. 1(b) and 1(c), we can express these impedances as Zxx=R1+iωL1+1/(iωC1) and Zyy=R2+iωL2. Simply speaking, cantilever actuation modifies the impedance Zxx by changing the capacitance C1 without affecting Zyy, leading to modulation of the transmission 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.

 figure: Fig. 1.

Fig. 1. (a) Schematic of the tunable cantilever metasurface array. Inset: close-up view of the metamaterial. Each unit-cell consists of a cantilever, capacitive pad, and interconnect wire. The electromagnetic wave is normally incident with a given polarization angle θ. (b), (c) Equivalent circuit models for the x(θ=0°) and y(θ=90°) polarizations, respectively.

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The designed structure was fabricated using surface micromachining on a slightly doped silicon substrate and the process is detailed in Supplement 1. The doping in the substrate presents a trade-off; it is necessary in order to apply a driving voltage to actuate the cantilevers, but it also attenuates the THz transmission somewhat. 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. 2(a)]. The area of the cantilever array is 8×8mm2. 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. 2(b)]. 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. 2(c). Initially, the height of the tip, i.e., the distance between the bottom of the dimple and the top of the capacitive pad, is 0.9μm, as shown in Fig. 2(d). With increasing voltage, the beam was pulled downward by the electrostatic force between the cantilever and the substrate. The pull-in voltage, at which the cantilever snaps down to the capacitive pad, is approximately 38 V.

 figure: Fig. 2.

Fig. 2. (a) Photograph of an integrated metasurface chip and (b) scanning electron microscope (SEM) image of the metasurface. (c) Deflection profile of the cantilever curvature at different voltages. (d) The measured tip height versus applied DC voltage, with a pull-in voltage of 38V.

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The tunable transmission of the metasurface was measured using THz time domain spectroscopy (THz-TDS), as detailed in Supplement 1. An 800-nm Ti:Sapphire laser with a 25-fs pulse duration and a 80-MHz repetition rate was employed to excite a biased photoconductive antenna to generate THz pulses. THz pulses were focused on the metasurface, and transmitted pulses were sampled by another photoconductive antenna to measure the time-resolved transmission signal, which was Fourier transformed to the frequency domain [Esample(ω)]. The spectrum of the incident pulse, denoted by Eref(ω), was measured using air as the reference. The transmission spectrum of the metasurface can be calculated by t(ω)=Esample(ω)/Eref(ω). Since the response of the metasurface was anisotropic, we measured the transmission spectra for two orthogonal polarization states, i.e., txx and tyy, by rotating the sample by 90°. A DC voltage source was applied to actuate the cantilevers, and the transmission coefficients (txx and tyy) were measured for a given voltage. Time domain signals were windowed to remove etalon artifacts as described in Supplement 1.

From the measured transmission coefficients, the x- and y-polarized components of the transmitted waves can be calculated with the Jones matrix [Eq. (1)]. Linearly polarized normal incidence radiation is described by Ei(ω)=(Exix+Eyiy)ei(ωz/c+ωt), in which x and y denote the unit vector along x- and y- axes, respectively, ω is the angular frequency, c is the speed of light, and z is the position. Given a polarization angle θ [as shown in Fig. 1(a)], we can obtain Exi=|Ei(ω)|cosθ and Eyi=|Ei(ω)|sinθ. The x and y components of the transmitted wave are Ext=txxExi and Eyt=tyyEyi, for which txx and tyy are the transmission coefficients for x and y polarization, respectively. The polarization information of the transmitted wave can be represented by the Stokes parameters [S0,S1,S2,S3], in which S0=|Ext|2+|Eyt|2, S1=|Ext|2|Eyt|2, S2=2Re(ExtEyt*), and S3=2Im(ExtEyt*) [1]. Among the parameters, S0(=I) is the total intensity of the wave, S1(=Ipcos(2ψ)cos(2χ)) is the component of horizontally or vertically linear polarization, S2(=Ipsin(2ψ)cos(2χ)) is the component of 45° or 45° linear polarization, and S3(=Ipsin(2χ)) is the component of circular polarization, p is the degree of polarization, ψ is the orientation angle, and χ is the elliptical angle, as shown in Fig. S6b in Supplement 1. The circular polarization ratio (CPR=S3/S0) and axial ratio (AR=tan(χ)) can be employed to describe the polarization state of a wave.

A 3D model of the metasurface was created in CST Microwave Studio. In the model, a unit-cell cantilever with corresponding capacitive pad on the silicon substrate was included, and periodic boundary conditions were employed. The silicon substrate was treated as a lossy dielectric material with a permittivity of 11.86 and a conductivity of 0.1 S/cm, silicon nitride was considered as a dielectric material with permittivity of 7.0, gold is metallic with conductivity of 4.6×105S/cm, and copper is metallic with conductivity of 5.8×105S/cm. Since the silicon wafer we used is slightly doped with a nominal conductivity of 0.1 S/cm, the transmission is attenuated by 40% when the THz pulses propagate through the substrate according to our simulation, which is validated by transmission coefficient in the experimental results shown below. The geometric parameters in the simulations are consistent with those of the fabricated sample. The frequency solver was utilized to simulate the transmission coefficients for both polarizations. For the initial case (VDC=0), the measured curvature of the cantilever, as shown in Fig. 2(c), was applied. The tip height of the cantilever was adjusted to match the measured results for different applied voltages.

3. RESULTS AND DISCUSSION

The transmission spectra of the metasurface for different applied voltages has been characterized using THz-TDS, as described above. To verify the metasurface anisotropy, the transmission for x- and y-polarized terahertz pulses [Figs. 3(a)3(d)] were measured by rotating the sample 90° 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 y polarization. Numerical simulations were performed to study the metasurface EM response. The simulations show good agreement with experimental results of the transmitted 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. 3(e) and 3(f). The electric field [Fig. 3(f)] 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, currents in the connection wires [Fig. 3(g)] are present, equivalent to an inductor as illustrated in Fig. 1(c) with, as expected, no electric resonance [Fig. 3(h)]. Quantitatively, the equivalent circuit model [Eqs. (2) and (3)] is validated by fitting the experimental and simulation results with proper parameters, including R1, L1, C1, R2, L2, and D, in the circuit model, as described in Supplement 1.

 figure: Fig. 3.

Fig. 3. (a)–(d) Amplitude (left) and phase (right) of the transmission coefficients for x (txx, blue lines) and y (tyy, red lines) polarization at different voltages. The solid lines are experimental results, while the dashed lines are from the simulation. (e), (f) On resonance simulated current and electric field distribution, respectively, for x polarization, and (g) and (h) are for the y polarization [note: (e)–(h) are for 0 V].

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With an applied voltage, the cantilevers are pulled downward, and the resonance frequency of the metasurface redshifts for the x-polarized THz pulses due to the increased capacitance, as shown in Fig. 4(a). The maximum resonance frequency shift is 230GHz, at 40 V DC bias. The frequency shift as a function of the applied voltage saturates for voltages >40V since the cantilevers are pulled down to the capacitive pads, preventing further deformation of the beam. The amplitude of txx is strongly modified at certain frequencies. For example, at 0.81 THz and 1.04 THz absolute modulation of the transmission amplitudes of 34% and 26% are achieved, respectively, as shown in Fig. 4(b). The resonance fully recovers to the original zero voltage state when the voltage is turned off. The cantilever-pad spacing was modified in the numerical simulations to match experimental results, indicating that the tunable transmission coefficient originates from deformation of the cantilever. The tunability for x-polarized THz pulses demonstrates that the metasurface operates as a THz modulator.

 figure: Fig. 4.

Fig. 4. (a) Resonance frequency of x-polarization transmission coefficient shifts to lower frequency (redshifts) as the applied voltage increases, showing a 230-GHz tuning range of the resonance frequency. (b) Transmission amplitude for different voltages from 0 to 40 V at 1.04 THz (blue) and 0.81 THz (red), demonstrating the amplitude modulation capability of the metasurface.

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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. 3(a)3(d). In short, the results in Fig. 3 demonstrate the anisotropic tunability of the cantilever metasurface, which enables creating a tunable quarter-wave plate 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 [θin Fig. 1(a)] of 34°. The full set of Stokes parameters can be presented by the Poincare plot (Fig. S6 in Supplement 1). For clarity, we use some key parameters derived from Stokes parameters, including the total intensity (I), axial ratio (AR), and circular polarization ratio (CPR), to describe the characteristics of the transmitted wave. I is defined as the ratio of the transmitted intensity to the incident intensity, AR is the ratio of the minor to major axes of the transmitted polarization ellipse, and CPR is the ratio of the intensity of the circularly polarized wave to the overall transmitted intensity [22]. Ideally, |AR| and |CPR| are 1 for a pure circularly polarized wave, while they are 0 for a pure linearly polarized wave. Of note, the sign of CPR represents the handedness of the circularly polarized wave: a positive sign corresponds to left-hand polarization, while a negative sign to a right-hand polarization when the wave is propagating away from the observer. Experimentally measured ARs and CPRs, as shown in Figs. 5(a) and 5(b), reveal voltage control of the polarization state through cantilever deflection. When VDC is 0 V, AR and CPR of the transmitted wave are close to 0 at the frequency of 1.05 THz, indicative of a linearly polarized wave. At 0.81 THz, AR0.91 and CPR1, indicating a right-hand circularly polarized wave. In the frequency span from 0.792 to 0.842 THz, AR is higher than 0.85 and CPR smaller than 0.99, yielding a circular polarization bandwidth of 50GHz. The intensity is frequency-dependent, as shown in Fig. 5(c), and obtains minimum values at the resonance frequencies at which the x-polarized wave is filtered out in the transmission. Qualitatively, the polarization state of the transmission can be explained by the transmission spectra shown in Fig. 3(a). At 1.05 THz, |txx| and |tyy| are 0.04 and 0.57, respectively, with a 2° phase difference, which indicates a linear polarization. On the other hand, |txx| and |tyy| are 0.34 and 0.52, respectively, with an 85° phase difference at 0.81 THz, corresponding to a transmitted beam with nearly circular polarization.

 figure: Fig. 5.

Fig. 5. (a)–(c): (a) Experimental axial ratio, (b) circular polarization ratio, and (c) intensity spectra for various applied voltages describing the polarization state of the transmitted waves, for θ=34°. (d) Top row is the electric field of the transmitted wave at 0.81 THz for different voltages, demonstrating the capability of tuning the polarization state; the bottom is the AR and CPR at different voltages for θ=34°. (e)–(g) CPR spectra of transmitted waves for incident waves with different incident polarization angles (from 0° to 180°) at applied voltage of (e) 0 V, (f) 25 V, and (g) 40 V, respectively. The dark lines indicate the frequency closest to pure circular polarization for each incident polarization angle. AR, axial ratio; CPR, circular polarization ratio.

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Due to the resonance frequency shift of txx induced by cantilever actuation, the AR and CPR spectra exhibit a significant shift to lower frequencies. The frequencies for pure circular and linear polarized radiation redshift gradually as VDC increases as illustrated in Figs. 5(a) and 5(b). The shifting of AR and CPR leads to modulation of the polarization state over the whole frequency range. In particular, AR is tuned from 0.91 to 0.01 and CPR from 1 to 0 at 0.81 THz as VDC increases from 0 to 40 V, showing that the polarization is switched from circular to linear state, as shown in Fig. 5(d). Top column in Fig. 5(d) demonstrates polarization states at different voltages using the electric field components along the x and y axes. When VDC is 0 V, the transmission is circular. As VDC increased to 25 V, the transmission is elliptical polarized with orientation angle of 93°, and AR of 0.3 corresponding to ellipticity angle of 32°. At VDC=40V (exceeding the pull-in voltage), the linear polarized wave is transmitted from the metasurface with orientation angle of 86°. The amplitude of the transmitted waves is almost constant along the major axis.

The tunable response of the metasurface quarter-wave plate is dependent on the incident angle. According to the simulation, the polarization state of the transmission wave shows only minor changes when the incident angle is within 30°. For larger angles of incidence, the polarization state drifts significantly. Nevertheless, the modulation of the polarization states always exists, as detailed in Supplement 1.

From Fig. 5(c), 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 wave plate [23], 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 quarter-wave plate to improve the conversion efficiency and eliminate reflective losses. Specifically, optimizing the anisotropy of the metasurface will increase the polarization conversion efficiency [21], and adding a metasurface anti-reflection layer will eliminate the reflection loss [23]. For our current metasurface quarter-wave plate, the substrate may lead to multiple reflections, thus resulting in iterative phase retardation for the x- and y-polarization incidence. The addition of anti-reflection coating at the backside of the substrate, which can be realized by multi-layer metallic metamaterial structures [54] or patterning the substrate with artificial dielectric structures [55], can eliminate the multiple reflections to improve the performance of the metasurface. Alternatively, thinning the substrate down to less than 10 μm may minimize the substrate effect, improving the transmission efficiency by at least 2 times and making the device more suitable for practical applications [50]. In short, a high-efficiency wave plate with a large tunable response can be expected by further optimizing the metasurface.

The tunability of the polarization state exists not only for an incident polarization angle of 34°, but also for arbitrary polarization angles. The calculated CPRs from the measured Stokes parameters for different incident polarization angles (θ) from 0° to 180° show the polarization state of transmitted waves, presented in Figs. 5(e)5(g). When VDC=0, right-hand circular polarized transmission can be achieved for incident waves with polarization angles from 0° to 57°, while left-hand circular polarization is achievable for polarization angles from 123° to 180° 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.

Examples of tunable polarization at other frequencies are presented in Fig. 6, showing the tunable polarization states of transmitted waves for different incident angles at different frequencies that correspond to the most nearly circular polarized transmission. For example, the transmitted wave is right-hand circularly polarized for incident polarization angle of 26° at 0.88 THz when the applied voltage is 0 V. An increase in the voltage (from 0 V to 25 V) gradually tunes the polarization state to an elliptical polarization. When the applied voltage is 40 V, the transmitted wave is left-hand elliptically polarized. It is similar for other incident polarization angles.

 figure: Fig. 6.

Fig. 6. Polarization states for different incident polarization angles θ (and frequencies) and applied voltages.

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Compared with the MEMS-cantilever-based tunable polarization control recently demonstrated [52], the design and performance of our device is different in several respects. First, our device is designed to operate in transmission whereas in Ref. [52] the device operated in reflection mode. In Ref. [52] actuation of bimorph cantilevers is used to engineer the losses, leading to significant modulation of the resonance frequency amplitude in addition to a frequency shift. It exhibits large tuning range of the phase response and polarization conversion among right-handed circular polarization, linear polarization, and left-handed circular polarization. This requires accurate voltage control for polarization conversion. For our device, copper cantilevers modulate the effective capacitance in the equivalent resistive LC (RLC) circuit model of the metasurface, which shifts the resonance frequency without a large effect on the resonant transmission amplitude. While our metasurface can operate at intermediate voltages, it can easily switch between quarter-wave plate and half-wave plate by simply increasing the voltage from 0 to 40 V (pull-in) voltage. In addition, the fabrication the metamaterial in Ref. [52] requires multiple steps of atomic layer deposition of aluminum oxide, which enables better insulation. In contrast, the fabrication process of our device is less involved and with better yield. The amplitude ratio between transmission and incident wave of our present device is approximately 0.3, similar to the efficiency of the reflective counterpart whose amplitude ratio between reflection and incidence is between 0.2 and 0.4 [52], even though our device has a fairly large insertion loss, which can be reduced with additional engineering. Moreover, for many applications at THz frequencies, transmission-based operation may be preferred over reflection. That is, upon adding a polarization conversion device to an existing THz system, reflective devices may introduce alignment difficulties, while transmissive devices may be directly inserted, requiring less effort to align or adjust. In short, the two devices are complementary and provide new insights into MEMS-based polarization control of THz radiation. Comparing to the tunable wave plates based on phase-change metasurface [40,51], our MEMS tuning mechanism can tune the transmission from circular polarization to linear polarization, providing higher degree of tunability of the polarization state.

4. CONCLUSIONS

We have demonstrated a cantilever-array-based metasurface to control the characteristics of transmitted THz fields, including amplitude, phase, and polarization. The metasurface is designed with an anisotropic response where electromechanical actuation of the cantilevers shifted the resonance frequency for x polarization by 230GHz with an applied voltage of 40 V without affecting the y polarization. We are able to tune the polarization of transmitted light from circular to linear at 0.81 THz. The significant modulation of the polarization can be achieved at other frequencies by modifying the geometrical parameters of the metasurface. The ability of microelectromechanical cantilever actuators is not limited to polarization control (as demonstrated above), and they can be integrated with other metasurface and metamaterial configurations for different functions [4648,56]. In particular, cantilevers provide a route to control the response of each unit-cell individually with well-designed routing strategies, similar to deformable mirrors [57]. For example, we can combine microcantilever actuators with gradient metasurface structures that are designed for beam steering or focusing [58] to enable real-time tunable devices by controlling the phase discontinuities at the unit-cell level [48,52,56], as well as other applications, such as digital coding metasurfaces [5962]. This paper presents a microcantilever-based reconfigurable quarter-wave plate to manipulate the polarization of THz radiations dynamically, facilitating the development and applications of THz technologies.

Funding

National Science Foundation (NSF) (ECCS-1309835); Army Research Office (ARO) (W911NF-16-1-0361).

Acknowledgment

We thank Boston University Photonics Center for technical support.

 

See Supplement 1 for supporting content.

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Supplementary Material (1)

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Supplement 1       The document provides supplemental information to “Electromechanically Tunable Metasurface Transmission Waveplate at Terahertz Frequencies”?.

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic of the tunable cantilever metasurface array. Inset: close-up view of the metamaterial. Each unit-cell consists of a cantilever, capacitive pad, and interconnect wire. The electromagnetic wave is normally incident with a given polarization angle θ. (b), (c) Equivalent circuit models for the x(θ=0°) and y(θ=90°) polarizations, respectively.
Fig. 2.
Fig. 2. (a) Photograph of an integrated metasurface chip and (b) scanning electron microscope (SEM) image of the metasurface. (c) Deflection profile of the cantilever curvature at different voltages. (d) The measured tip height versus applied DC voltage, with a pull-in voltage of 38V.
Fig. 3.
Fig. 3. (a)–(d) Amplitude (left) and phase (right) of the transmission coefficients for x (txx, blue lines) and y (tyy, red lines) polarization at different voltages. The solid lines are experimental results, while the dashed lines are from the simulation. (e), (f) On resonance simulated current and electric field distribution, respectively, for x polarization, and (g) and (h) are for the y polarization [note: (e)–(h) are for 0 V].
Fig. 4.
Fig. 4. (a) Resonance frequency of x-polarization transmission coefficient shifts to lower frequency (redshifts) as the applied voltage increases, showing a 230-GHz tuning range of the resonance frequency. (b) Transmission amplitude for different voltages from 0 to 40 V at 1.04 THz (blue) and 0.81 THz (red), demonstrating the amplitude modulation capability of the metasurface.
Fig. 5.
Fig. 5. (a)–(c): (a) Experimental axial ratio, (b) circular polarization ratio, and (c) intensity spectra for various applied voltages describing the polarization state of the transmitted waves, for θ=34°. (d) Top row is the electric field of the transmitted wave at 0.81 THz for different voltages, demonstrating the capability of tuning the polarization state; the bottom is the AR and CPR at different voltages for θ=34°. (e)–(g) CPR spectra of transmitted waves for incident waves with different incident polarization angles (from 0° to 180°) at applied voltage of (e) 0 V, (f) 25 V, and (g) 40 V, respectively. The dark lines indicate the frequency closest to pure circular polarization for each incident polarization angle. AR, axial ratio; CPR, circular polarization ratio.
Fig. 6.
Fig. 6. Polarization states for different incident polarization angles θ (and frequencies) and applied voltages.

Equations (3)

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[ExtEyt]=T[ExiEyi]=[txxtxytyxtyy][ExiEyi],
txx=2ZxxZxx+Z0D,
tyy=2ZyyZyy+Z0D,
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