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"Exclusive-OR"operation with Fano resonant MEMS Metamaterial

In recent years, a range of reconfigurable metamaterials controlled with thermal, electric, magnetic and optical signals have been developed for dynamically manipulating the intensity, phase and wave-front of electromagnetic radiation across the broad electromagnetic spectrum ranging from microwave to optics. Here for the first time, we demonstrate a reconfigurable metasurface performing exclusive OR (XOR) logical operation using two independent control electrical inputs and an optical read-out in the form of far-field Fano intensity states at terahertz wavelengths. At the same time, the near field resonant confinement enables a universal NAND logical operation. Further, by using a single electrical input control and an optical readout, a logical NOT operation is achieved at the far-field intensity states of the Fano resonance. The proposed reconfigurable microcantilever based Fano design that exhibits multiple logical operations can create a versatile platform for realization of programmable and randomly accessible metamaterials with enhanced electro-optical performance, multichannel data processing and encryption techniques for high speed wireless networks which are now being pushed towards terahertz wavelengths.

Recent trend in the metamaterial research is greatly advancing towards realizing functional and reconfigurable metamaterials 1-3 that enable a real-time control over their structural and optical properties, thereby creating exceptional opportunities in the field of active metamaterials and plasmonics. They possess unique advantage in active manipulation of the near fields in all the three spatial directions by exploiting sensitive changes to their micro/nano scale movements, which makes them more resilient and merits their applications as future generation state-of-the-art active photonic devices. The dynamic control over the near-field features has provided a new paradigm of controlling and manipulating the lightmatter interactions, which gives enhanced and tunable nonlinear properties in the metamaterial. Over the years, a range of tunable metamaterials have been demonstrated, where their optical features are actively controlled through their structural reconfiguration using the electrical controls 4-7 , magnetic fields 8,9 , thermal gradients [10][11][12] and optical pulses [13][14][15] .
A class of reconfigurable metamaterials based on micro/nano-electro-mechanical systems (MEMS/NEMS) mainly operating in the terahertz (THz) to near-infrared frequencies have enabled dynamic manipulation of THz properties such as magnetic response 4,10 , transparency 16 , near-perfect absorption 17 and THz anisotropy 5 . However, the ability to flexibly control near-and far-field interactions by establishing independent structural reconfigurations of meta-atoms at the unit cell regime of metamaterial has been challenging.
The future prospects and challenges of functional metamaterials lie in achieving multiple controls within the unit cell of the metamaterial, which could provide a flexible platform for realizing extremely versatile metamaterials manifesting enhanced electro-optical performance 18 . Multiple controls within the unit-cell will enable a precise tailoring of nearfield interactions between the meta-atoms by relatively maneuvering their structural properties, thereby obtaining the optical properties on demand. The nano/micro sized switchable metamaterials 2,7 have given a promising pathway to control near-field coupling between the metamolecules by establishing the independent/multiple controls over the structural reconfiguration of the constituent resonators within the unit cell of the metamaterials. However, such demonstrations have been solely restrained to investigating the system responses in terms of single-input-output (SIO) configurations. In the hindsight of enhancing their multifunctional capabilities in digital [19][20][21] and multiple signal processing applications, one way is to establish multi-valued dependency between the input and output characteristics of the metamaterial. Here, we experimentally realize excitation of sharp Fano resonance in a MEMS reconfigurable metamaterial exhibiting multiple-input-output (MIO) 3 characteristics in its near-and far-field optical properties. By preparing the structural geometry of the MEMS-Fano metamaterial device in various meta-stable states, we realize "exclusive OR" (XOR) and NAND logical operations in the far-field and the near-field optical characteristics, respectively by using two independently controlled electrical inputs and an optical/near field read-out at terahertz wavelengths. XOR is a very important function that is not linearly separable into more basic logical functions, which makes it more resilient and useful in the information and computational technologies as parity generators, one-time pad (OTP) based unbreakable cryptography protocols 22,23 , pseudorandom number generators and digital encoders or decoders in signal processing. It serves as a key component in the central processing unit (CPU), performing full-and half-adder operations in storing and processing the data. On the other hand, the NAND logical operation is a functionally complete set logical operator which can be used to express all the basic set logical operations by defining a network of NAND gates. Further, we show that the SIO configuration of Fano excitation can constitute the NOT logical operation using the single electrical control and optical readout at the far-field intensity state of Fano resonance. The multi-logical operations of the proposed MEMS Fano design together with the volatile and nonvolatile 24,25 regimes of MEMS actuation can enhance the digital functionalities of the metamaterials in realizing optical memory registers to encode, harvest, process and send the information in form of encoded/decoded optical bits across the far-to near-infrared frequencies.

Design and Fabrication
To precisely elucidate the operation of XOR and NAND functionalities possessing MIO features in the metamaterial, we fabricated a micro-electro-mechanical systems (MEMS) based metamaterial design consisting of two split ring resonators (SRR-1 and SRR-2) that are independently actuated by applying the voltages V 1 and V 2 , respectively (shown in Fig. 1(a)). The device is fabricated using the photolithography technique, where periodic array of SRRs made of deformable bimorph structures consisting of 900 nm thick aluminum (Al) on top of 50 nm aluminum oxide (Al 2 O 3 ) layer are patterned on a lightly doped silicon (Si) substrate (refer to Methods Section for the device fabrication details and characterization, and the Supplementary Information Fig. S1 -S4). Due to the residual stress in the bimorph layers, the cantilevers are bent up, thereby increasing their released heights (h). Scanning electron microscope image of the fabricated MEMS Fano-metamaterial is shown in Fig. 1(a) in the colored scale that illustrates the maximum asymmetric state of the device with SRR-1 snapped down on the substrate using voltage V 1 = 30 V and SRR-2 retained in the released state of the bimorph cantilevers with V 2 = 0 V. The out-of-plane reconfiguration of the released cantilevers is achieved through electrostatic actuation, by applying voltage across the Al layer and silicon substrate. Metal lines connecting the SRR-1 and SRR-2 cantilevers are electrically isolated from each other and this allows for the independent reconfiguration of h 1 and h 2 through application of voltage V 1 and V 2 , respectively. The selective reconfiguration at the sub-unit cell level provides the flexibility to introduce dynamically tunable structural asymmetry along the z-axis, defined by an effective asymmetry parameter, , where (h 1 , h 2 ) and s are the released heights and length of the cantilever arms of SRR-1 and SRR-2, respectively. Fig. 1 voltage is applied across the resonators i.e. V 1,2 = 0 (see, Fig. 1(b)), the arms of the two SRRs are symmetrically inclined at same heights h ( = 0) along the z-direction that results in the excitation of strong dipole type of resonance at 0.78 THz for the incident THz radiation polarized in the E y direction. When voltage (V 1 ) is applied across the Al lines of the released cantilevers (say, SRR-1) and Si substrate, the SRR-1 cantilevers gradually deflect towards the fixed substrate due to the attractive electrostatic force. This deformation in the height of the SRR-1 cantilevers creates a structural asymmetry () along the z-axis of the sample. As a result, near field coupling between the asymmetric structures exhibits Fano-type of interference effects that excites a sharp trapped mode (Fano-type) resonance 26,27 feature (at 0.6 THz) within a broad dipolar resonance. Upon continuously increasing V 1 across the SRR-1, strength of Fano resonance grows and reaches its maximum amplitude for V 1 = 30V (where V 2 = 0V), as shown in Fig. 2(a). Subsequently, when the voltage V 2 is applied across SRR-2, its cantilever arms are gradually pulled towards the substrate, as a result the asymmetry in the structure progressively decreases. Due to the decreasing asymmetry, the Fano resonance starts to weaken and shows a monotonic decrease with increasing V 2 and completely diminishes as V 2 finally reaches 30 V, as shown in Fig. 2 respectively. Although this scenario showing the distinctive pathways resembles the hysteresis behavior as observed in many natural phase change materials (VO 2 and Ferrites), but indeed it is a two output states for two input controls (V 1 and V 2 ) to form a closed loop in |T|. This behavior in the optical response of the system constitutes multiple-input-output (MIO) configuration in the intensity state of the Fano resonance. In the numerical simulations, the sequential control of the two voltage inputs (V 1 and V 2 ) is expressed as one control parameter in terms of asymmetry () of the structure, which is a critical parameter for the excitation of Fano resonances. In Fig. 3(b), the transmission intensity (|T|) of Fano resonance is plotted for the increasing and decreasing scenario of structural asymmetry parameter (), where the SRR-1 and SRR-2 are actuated sequentially (as shown in the insets of Fig. 3(b)). The output intensity response in the far field displays two distinct values for the same asymmetry parameter () depending on the increasing or decreasing asymmetry sequence in the system, mimicking a hysteretic type of closed loop.

NOT logical operation:
The proposed design provides a flexibility of tuning the asymmetry of the structure to show either anisotropic or isotropic coupling between the adjacent metaatoms just by adequately coding the input electrical signaling sequence. Fig. 4(a) represents the experimentally measured variation in the intensity of the Fano resonance with respect to the voltage V 2 applied on SRR-2, by keeping SRR-1 in contact with the substrate with V 1 = 30 V (decreasing pathway of the asymmetry). For the voltage V 2 = 0 (V 1 = 30 V), the Fano resonance possesses the maximum intensity (T) value and by increasing voltage (V 2 ), T gradually decreases and finally becomes zero at V 2 = 30 V, as the symmetry is restored in the system. In the initial structural state of the device, where the SRR-1 is put in contact with the substrate and the SRR-2 is kept in the released state (V 2 = '0') shows the asymmetric structural configuration of the device that results in the excitation of the Fano resonance in 8 the far-field intensity state (F = 1). As the voltage V 2 = 30 V (i.e. V 2 = '1') is applied, the microcantilever arms of SRR-2 resonator comes in contact with the substrate thereby restoring the structural symmetry of the device that annihilates the Fano resonance feature in the structure (i.e. F = 0). This correlation between the input voltage states of SRR-2 and the optical readout in the form of Fano resonance far-field intensity state manifests the logical NOT operation, as shown by the truth table presented in inset Fig. 4(a). Further, numerically calculated T values plotted in Fig. 4(b) shows isotropic variation with respect to decreasing and increasing pathways of the asymmetry (), where by keeping the SRR-1 in contact with the substrate, the released height of SRR-2 is decreased and increased respectively, as shown in the inset of Fig. 4(b). This configuration of Fano tuning signifies the single input-output (SIO) characteristics in the MEMS Fano-metamaterial, which is due to the isotropic nature of coupling between the resonators during the increasing and decreasing pathways of asymmetry.

NAND logical operation:
In addition to the XOR and NOT logical operations using the farfield characteristics, the near-field characteristics reveals the universal NAND logical operation in the form of confined electric fields measured at the tip of the microcantilever resonators in their ON and OFF states. Numerically calculated electric field strengths are plotted in Fig. 5(a), where the absolute E-field for structural configurations (i), (ii) and (iii) shows enhanced field strengths compared to structural configuration (iv), where both microcantilevers are prepared in ON states. The absolute strengths of the confined electric fields are plotted in Fig. 5(b) that highlights the distinctive variation for the increasing and decreasing pathways of the asymmetry. For the symmetric state with both the microcantilevers prepared in the OFF states (i), the electric field confinement is nearly an order of magnitude greater than the symmetric configuration with both the microcantilevers are prepared in the ON state (iv). Whereas, for the two asymmetric configurations of the microcantilevers (ii and iii), the field confinement in the structure shows similar strengths to the symmetrically prepared OFF state (i) of the structure. Higher strength of the electric field confinement is labeled as the binary '1', whereas lower electric field strength is represented by binary '0', as shown in Fig. 5(b). Therefore, the change in the confined electric field strength measured at the tip of the microcantilevers in their various metastable structural configurations (i -iv) constitutes a logical NAND function as described by the truth table given in Fig. 5(c). The NAND operation signifies that near field output state of the device is true (logical '1') when either one or both the input structural states of the device are false (logical '0'), otherwise it results in the false output state (logical '0'). The NAND logical operation is significant owing to its unique feature of functional completeness (universal gate), as any boolean function can be implemented by using the combination of several NAND gates.

Discussion
The flexibility to operate the device with the MIO and the SIO characteristics using the two independent input controls provides the useful feature of realizing multiple logical operations in its near-field and the far-field optical characteristics. The observed MIO optical characteristics in the proposed MEMS Fano-metamaterial exploits the nonlinear spatial distribution of near-fields extended along the z-axis of the sample. Independent and sequential actuation of SRR-1 and SRR-2 cantilevers mediates the anisotropic Fano coupling between the resonators that show contrasting coupling strengths depending on whether the adjacent fixed resonator cantilever is closer or farther away from the surface of the substrate.
Continuous and sequential actuation of the adjacent resonators plays a critical role in the observed anisotropic excitation of Fano resonances that illustrates the MIO states for a given V 1 and V 2 (or ). As seen from inset of Fig. 3(b), during the increasing  configuration, as the fixed resonator cantilever (SRR-2) is positioned away from the substrate, hence the resonator arm is in the vicinity of a weak spatial field distribution. Therefore, it requires larger structural asymmetries (higher excitation threshold) to excite the Fano resonance.
While decreasing the asymmetry, the SRR-1 positioned on the substrate is likely to possess greater influence on the near field coupling occurring in the asymmetric structure that results in stronger excitation of Fano features at smaller asymmetries (lower excitation threshold).
In summary, we demonstrate excitation of sharp Fano resonances in a MEMS based metamaterial using two independent voltage controls that constitutes a digital XOR, NOT and NAND logical gates in its far-and near-field optical properties in the terahertz wavelengths. The reported multi-functionalities of the proposed MEMS Fano-metamaterial are largely suitable for real world applications such as active sensors possessing tunable mode volumes, tunable nonlinear devices and modulators. Alongside, the MIO characteristics of the MEMS Fano-metamaterial could potentially provide a flexible platform for developing the next generation randomly accessible, digital and programmable metamaterials for precise tailoring of optical properties and multichannel data processing across the wide band of electromagnetic spectrum.

Sample Fabrication:
The MEMS Fano-metamaterial was fabricated using a complementary metal-oxidesemiconductor (CMOS) compatible process as described below. First, the lightly doped 8 inch silicon substrate of 725 µm thickness was cleaned and a 100 nm thick sacrificial SiO 2 layer was deposited using low pressure chemical vapor deposition (LPCVD) process. Following this conventional photolithography process was used to pattern the anchor region. With the designed pattern, the parts of sacrificial SiO 2 for anchor regions were dry etched using reactive ion etching process. After this, a 50 nm thick Al 2 O 3 layer was deposited using the ALD process, followed by the sputter deposition of 900 nm thick Al. Note that the bimorph layers (Al/Al 2 O 3 ) were in physical contact with Si substrate at the anchor region, and in the remaining part of the wafer, it was on top of sacrificial SiO 2 layer. Then, the second photolithography step was carried out for defining the cantilevers and metal lines of metamaterial patterns. Following this, both Al and Al 2 O 3 layers were dry etched to form the designed metamaterial. Finally, vapor hydrofluoric was acid (VHF) was used to isotropically etch the SiO 2 sacrificial layer underneath the bimorph structures, thereby suspending it over the Si substrate with an air gap between them. At the anchor region, since the bimorphs were in physical contact with Si substrate; the VHF release process was not time controlled, and this ensured higher yield of the devices. Due to the residual stress in the bimorph cantilevers, the released cantilevers were bent up, thereby increasing the initial tip displacement.

Electromechanical Characterization of the MEMS device:
The deflection/actuation profiles of released microcantilevers were measured using Lyncee Tec. reflection digital holographic microscope (R-DHM). The released chips are wire bonded to a printed circuit board (PCB). Separate voltage supplies (V 1 and V 2 ) are used for the actuation of SRR 1 and SRR 2 microcantilevers, respectively. Silicon (Si) substrate was chose as the ground potential, and the microcantilevers were positively biased. When voltage is applied across the released cantilevers and Si substrate, the attractive electrostatic force deforms the suspended cantilevers towards the fixed Si substrate. This mechanical deformation of cantilevers induces a restoring force that opposes the electrostatic force causing the deflection at the first place. Hence, the final position of the cantilever at a given voltage is determined by the equilibrium position, where the electrostatic force and restoring force balances each other. As the applied voltage increases, the electrostatic force increases much higher than the restoring force and at a critical value known as the Pull in voltage (> 25 V), the electrostatic force will be higher than the restoring force, thereby bringing the microcantilevers to be in physical contact with Si substrate (shown in inset of Fig.   2(a)).The pull-in can be clearly observed through the optical microscope fitted on the R-DHM. The Al 2 O 3 layer beneath the Al layer, will ensure that there is no current flowing from Al layer to Si substrate, when pull in occurs. This is crucial because if the current flows through the Al/Si junction, then the temperature will rise up locally thereby melting the Al tips with the Si substrate, and will cause a permanent damage to the device.