MEMS Based Structurally Tunable Metamaterials at Terahertz Frequencies

Transcription

1 DOI /s MEMS Based Structurally Tunable Metamaterials at Terahertz Frequencies Hu Tao & Andrew C. Strikwerda & Kebin Fan & Willie J. Padilla & Xin Zhang & Richard Douglas Averitt Received: 23 January 2010 / Accepted: 20 April 2010 # Springer Science+Business Media, LLC 2010 Abstract We present the design, simulation, fabrication and characterization of structurally tunable metamaterials showing a marked tunability of the electric and magnetic responses at terahertz frequencies. Our results demonstrate that structurally tunable metamaterials offer significant potential to realize novel electromagnetic functionality ranging from dynamical filtering to reconfigurable cloaks or detectors. Furthermore, this approach is not limited to terahertz frequencies and may be readily used over much of the electromagnetic spectrum. Keywords Terahertz. Metamaterial. Bimaterial. Bianisotropic. Tuning 1 Introduction Recently, artificially structured electromagnetic (EM) materials have become an extremely active research area because of the possibility of creating materials which exhibit novel EM responses not available in natural materials, such as negative refractive index, superlensing, cloaking, and more generally, coordinate transformation materials design [1 4]. This has attracted tremendous interest of researchers world-wide including physicists, material scientists and engineers. Such EM composites, often called metamaterials (MMs), are subwavelength composites where the EM response originates from oscillating electrons in highly conducting metals such as gold or copper allowing for a designed specific resonant response of the electrical permittivity (μ) or magnetic permeability (ε), and are scalable to H. Tao : K. Fan : X. Zhang Department of Mechanical Engineering, Boston University, 110 Cummington Street, Boston, MA 02215, USA X. Zhang xinz@bu.edu A. C. Strikwerda : R. D. Averitt (*) Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA raveritt@physics.bu.edu W. J. Padilla Department of Physics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, USA

2 operate at nearly any frequency over the entire EM spectrum. This is especially important for the technologically relevant terahertz frequency regime (1 THz ¼ Hz) which is difficult to be reached due to lack of functional sources and detectors, thus commonly referred to as the THz gap [5 9]. A great deal of MM structures and devices were initially implemented at microwave frequencies partly due to the ease of fabrication and characterization [10 12]. Decent progress has been made towards creating THz MMs using standard photo-lithography and metal deposition technologies [7, 13, 14]. However, the fabrication of sub-wavelength unit cells becomes increasingly challenging in moving from the microwave to higher frequencies, i.e. THz frequencies and optical frequencies. To date, the majority of this work has been on single-layer planar composites patterned on semiconductor substrates such as silicon or gallium arsenide for a designed resonant response of the electrical permittivity or magnetic permeability. It is not only possible to design a MM for a specific EM response, but also to realize further tunability. Tunable MMs with dynamic EM resonant responses through an external stimulus are highly desired, especially in the THz regime. This implies the possibility to real-time manipulate THz radiation, which has enormous applications such as short-range wireless THz communication and ultrafast THz switches/modulators. Recently, researchers have ventured to create tunable THz MMs by modifying the dielectric properties of the substrates or the resonators through optical pumping and electrical modulation [15 19]. It is well known that the overall properties of a material are not only determined by the nature of the constituent atoms but also depend dramatically on the lattice structure. The same rule applies to metamaterials, and even better to some extent. Compared with natural materials where the tunability of their properties through tuning the crystal lattice is somehow limited by the chemical bonding and nature of the atoms themselves, the range of tunability for MMs is much broader as the lattice effects can be made much stronger by an appropriate design. Therefore, structural tunability is a new and straightforward way for real-time control of the EM properties of MMs such as the polarization, directionality, and amplitude. Since 1 THz corresponds to 300μm in wavelength, the geometric dimensions of these sub-wavelength resonators are in the order of tens of microns or even smaller for higher frequencies, where MEMS technologies are proven to show extreme power and flexibility in terms of fabrication. In this paper, we demonstrate structurally reconfigurable THz metamaterials with tunable electrically and magnetically resonant responses through mechanically reorienting the micro-fabricated resonators within their unit cells. This approach can be potentially used for novel MM applications with multi-functionality via tunability and can be readily employed over much of the electromagnetic spectrum. 2 Design and simulation Split ring resonators (SRRs), first theoretically introduced by Pendry in 1999 and experimentally verified by Smith et al. in 2000, are the canonical sub-wavelength particle used in the majority of MMs to date [4, 20]. The SRRs were originally designed and utilized for magnetic responses. As shown in Fig. 1, when a time varying magnetic field polarized normal to the plane of the SRRs, circulating currents will be induced within the ring, resulting in an out of phase or negative magnetic response above the resonant frequency. In principle, SRRs can also be used as electrically resonant particles as they exhibit a strong resonant permittivity at the same frequency as the magnetic resonance by

3 Fig. 1 a A single SRR excited purely by magnetic field normal to SRR plane with electric field parallel to the gap; b as-excited circulating current on resonance; c the same SRR excited purely by in plane electric field perpendicular to the SRR gap with magnetic field lying in plane of the SRR; d equivalent circuit of SRR with the gap as the capacitance and the current path as the inductance. rotating the incident THz radiation 90 with the electric field perpendicular to the gap and the magnetic field lying completely in the SRRs plane. This enables development of electric MMs using the same SRR structures for constructing magnetic MMs [6, 7, 21]. The SRR can be regarded equivalently as an LC resonator, and the resonance frequency of the qffiffiffiffi 1 electric and magnetic SRRs can be calculated by w 0 ¼ LC, where the inductance results from the current path of the SRR and the capacitance is determined by the gap dimensions. For many potential applications, it would be desirable to create metamaterials that exhibit a dynamical and tunable response. For example, the dynamic control of metamaterial properties has been demonstrated at both microwave and terahertz frequencies by modifying the dielectric properties of the SRRs and/or the substrate to modify the inductance and/or capacitance [15, 16, 18]. It is known that the resonant responses of the MMs also depend on the coupling efficiency of the SRRs to EM fields, as shown in Fig. 2. However it is not easy to get full range tuning of the EM coupling for the planar THz SRRs, as in this case the wave has to propagate along the SRR plane to get the full magnetic resonant response, which is difficult Fig. 2 Concepts to tune the magnetic resonance strength (a) and electric resonance strength (b) by rotating the whole sample plane to change the electromagnetic fields coupling efficiency.

4 to be experimentally characterized in the terahertz regime since the incident light is usually limited normal to the SRR plane for measuring the transmisson and reflecivity. So instead of rotating the entire SRR sample plane, we managed to rotate individual meta-atoms to tune the EM fields coupling efficiency while keep the sample plane normal to the incident light. This is accomplished by fabricating planar arrays of SRRs on bimaterial cantilevers gold (Au) and silicon nitride (SiNx) in the present case designed to pop-up out of plane in response to a thermal stimulus, as shown in Fig. 3. For incident EM radiation at the resonant frequency of the SRR, a component of the magnetic field parallel to the z-axis (H z ) will drive the magnetic dipole (m zz ) of the SRR while a component of the electric field along the y-axis (E y ) will drive the electric dipole (p yy ) response. For SRRs, the resonance strength depends sensitively on projection of the components of H along z and, similarly, E along y. This in turn implies that the electromagnetic response is a sensitive function of orientation, which therefore could be controlled by manipulating the orientation of the resonators. Furthermore, though SRRs can be tuned to show either purely negative electric or magnetic response by being exposed to different orientation of incident radiation and polarizations of electric or magnetic fields, the electric and magnetic resonant responses are coupled. This results in a complicated bianisotropic EM behavior, leading to considerable complexity in characterizing the comprehensive EM response of metamaterials [22 25]. SRRs are bianisotropic meaning that E y contributes to m zz and H z contributes to p yy. Two sets of samples with different orientation of the SRRs (e.g. the 90 rotation with respect to the cantilevers) are fabricated and characterized with two orthogonal polarizations of the EM fields, as shown in Fig. 4. Thus it is difficult to understand the full bianisotropic EM responses for previously demonstrated planar THz MMs. However, this could be addressed by our approach by popping up the SRRs out of the plane to get full coupling of both electric and magnetic fields, offering the means to create novel functional responses. This provides the comprehensive EM response of the proposed structurally tunable metamaterials, including: a) pure tunable electrically resonant response; b) pure tunable magnetically resonant response; c) bianisotropic response; d) non-resonant response. To better understand the metamaterial response, numerical simulations were conducted using CST Microwave Studios. Due to the highly non-cartesian orientation of these Fig. 3 a Schematic of structurally tunable THz MMs; b dimensions of a single SRR unit cell: unit cell length (a): 100; width of the supporting silicon frame (b): 12; length of the supporting SiNx plate (c): 80; SRR side length (d): 72; width of the bimaterial leg (e): 4; length of the bimaterial leg (l): 80; SRR line width (w): 8; SRR gap distance (g): 4; All units are in microns.

5 Fig. 4 Schematic of the experimental setup for structurally tunable THz metamaterials: a pure tunable electrically resonant response; b pure tunable magnetically resonant response; c bianisotroic response; d nonresonant response. structures, the simulations were performed using the tetrahedral mesh and unit cell boundary conditions using the frequency solver. The value of the conductivity used for gold with conductivity of S/cm and the SiNx was modeled using a constant permittivity of 7. The structure was modeled as depicted in Figs. 5a and 7a, where the two bi-metallic cantilevers are taken to be a constant length, and then curved at a constant bending angle to achieve the desired angle of deflection for the planar MM structure suspended between them. First, we consider the results of case #1 with the pure tunable electrically resonant responses, as shown in Fig. 5. When the SRRs lie in plane, the incident polarization is such that only the electric field (E) drives the electric response of the SRRs. For this case, with the SRRs in plane, the electric field E drives the electric dipole resonance leading to a strong decrease in the transmission at 0.5 THz (black line). As cantilever bending reorients the SRRs out of the plane of the substrate, the projection of E along y deceases leading to a gradual decrease in the resonance strength, as shown in Fig. 5c. For any orientation of the SRRs, no component of H along the x-direction ever pierces the plane of the SRR and thus no magnetic resonance or bianisotropic response is possible. Figure 5d shows the real part of the electric permittivity (ε real ) extracted from the full-wave simulations for the structure at various degrees. A reasonable Lorentzian-like response is obtained highlighting the electric nature of the resonance. Therefore, the resonant response is purely electric. Then we consider the results of case #2 with the pure tunable magnetic resonant response, as shown in Fig. 6. The polarization is rotated by 90 degrees in comparison to Fig. 5a. When the SRRs lie in plane, the incident polarization is such that neither the electric field (E) nor the magnetic field (H) drives the magnetic or electric response of the SRRs. Thus, the transmission (black line) as a function of frequency is featureless. However, as the cantilever legs bend upward, the SRRs gradually bend out of plane. As this occurs, a component of H drives the magnetic dipole resulting in the appearance of a weak resonant feature at 0.5 THz (red line). With increasing bending of the cantilever legs and commensurate reorientation of the SRRs, the magnetic resonance strength increases which, in turn, leads to a strong decrease in transmission, as shown in Fig. 6c. Eventually, the resonant response should be maximized as the cantilever bending angle saturates at 90. As no component of E projects along the x-direction for any orientation of the SRRs, there is no bianistropic response.

6 Fig. 5 Simulation of pure tunable electrically resonant responses of the structurally tunable THz metamaterials: a schematic of the unit cell; b schematic of polarization of the incident radiation; c transmission spectrum as a function of frequency; 4) extracted effective permittivity (ε) as a function of frequency. Thus, the decrease in transmission results from a magnetic resonance that is driven entirely by the incident magnetic field. Figure 6d shows the real part of the magnetic permeability (μ real ) extracted from the full-wave simulations for the structure at various degrees. A reasonable Lorentzian-like response is obtained highlighting the magnetic nature of the resonance, showing that the resonant response is purely magnetic. Next we consider the results of case #3 with the SRRs rotated by 90 degrees with respect to the cantilever legs while keep the same polarizations of the EM fields as case #2, resulting in the bianisotropic response, as shown in Fig. 7. For any angle of the SRR with respect to the plane of the substrate, the electric dipole resonance will be driven. Upon increasing the out-of-plane angle, the magnetic resonance will also be driven as H couples to the magnetic dipole along z. Nevertheless, as the simulation results reveal, there is no substantial change in the resonance transmission, though slight shifts of the resonance have been observed. This constant transmission as a function of angle results from the bianisotropy of the SRRs which now plays an important role and will be discussed in more details in the Characterization and Discussion Section. Finally, for case #4 with the polarization of the EM field rotated by 90 degrees while keeping the same orientation of the SRRs as in case #3, the resonant electric or magnetic dipolar response is not coupled to for any angle of the SRRs as they bend out of plane, as shown in Fig. 8. However, as the SRRs reorient out of the plane of the substrate there is a broadband increase in the transmission. This response results from the fact that there are

7 Fig. 6 Simulation of pure tunable magnetically resonant responses of the structurally tunable THz metamaterials: a schematic of the unit cell; b schematic of polarization of the incident radiation; c transmission spectrum as a function of frequency; 4) extracted effective permeability (μ) as a function of frequency. higher frequency electric dipole resonances associated with the cantilever legs and in-phase currents driven in the SRRs. As the cantilever legs and SRRs reorient out of the plane defined by the substrate, the E field component projected along the dipoles decreases leading to an increased transmission that approaches 90%. In the following sections, the detailed fabrication and characterization will be described. 3 Fabrication The structurally tunable terahertz metamaterials were fabricated using a surface microfabrication process followed by a KOH wet etching process, as shown in Fig. 9. Au and SiNx were chosen for the huge difference between their thermal expansion coefficients ( K 1 for SiNx vs K 1 for Au at room temperature) for facilitating the further curvature modification for reorienting the SRRs out of plane. The process started with a 4 P type <100> 500 μm thick silicon wafer with low pressure chemical vapor deposition (LPCVD) coated 400 nm thick SiNx films on both sides. The SiNx film on the front side serves as the supporting plate for SRRs and the bottom layer of bimaterial legs, and the SiNx film on the back side serves as the etching windows for structure release at the last step. The SRRs and the top layer of bimaterial legs were patterned using standard photolithography methods. A layer of 200-nm-thick Au/Cr film was e-beam evaporated

8 Fig. 7 Simulation of the bianisotropic responses of the structurally tunable THz metamaterials: a schematic of the unit cell; b schematic of polarization of the incident radiation; c transmission spectrum as a function of frequency. Fig. 8 Simulation of the non-resonant responses of the structurally tunable THz metamaterials: a schematic of the unit cell; b schematic of polarization of the incident radiation; c transmission spectrum as a function of frequency.

9 Fig. 9 a Fabrication process flow; b & c Optical microscopy photographs of a portion of as-fabricated structurally tunable metamaterials. followed by rinsing in acetone for several minutes. The next step was to pattern the photoresist mask and it was followed by the removal of unwanted SiNx layer employing reactive ion etching (RIE) technique. Finally, the back side SiNx etching window was patterned by RIE with photoresist as dry etching mask, and the Si substrate beneath the pop up metamaterial elements was etched in KOH solution. This results in an array of freestanding SRRs which are connected to the supporting substrate by the cantilever legs. The periodicity of the array is 100 μm, with the overall dimensions of the SRR 72 μm 72 μm and the overall dimensions of the array are 1 cm 1 cm. The as-fabricated pop up structures were nearly flat with the bending angle under 5 degrees. Rapid thermal annealing (RTA) was used to set the orientation of the SRRs at a specific angle with respect to the substrate, as shown in Fig. 10. For the ease of fabrication and characterization of this first generation reconfigurable metamaterial we have chosen a thermal tuning approach. However, we note that other MEMSbased approaches such as electrostatic, thermal resistance heating and/or piezoelectric actuation would enable similar reconfigurability albeit with a slight increase in complexity. 4 Characterization and discussion To characterize the electromagnetic response as a function of orientation, terahertz timedomain spectroscopy (THz-TDS) was employed. The THz electric field was coherently measured after transmission through the metamaterial sample and a suitable reference, which in this case is air (i.e. the sample is simply removed). Fourier transformation of the time-domain waveforms then provided the frequency dependent THz electric field amplitude and phase. Dividing the sample spectrum by the reference we obtain the normalized field transmission t(5) and phase Φ(5) of the metamaterial sample [26, 27]. All

10 Fig. 10 Scanning electron microscopy (SEM) photographs of one portion of as-fabricated structurally tunable metamaterials after release and rapid thermal annealing (RTA) processes at increasing temperatures with a step of 50 C for 10 min. measurements were performed at normal incidence. To characterize changes in transmission associated with reorientation of the SRRs within the unit cells, a procedure was employed to lock in the orientation. As described in the previous section, RTA is a good option which sets the orientation of the SRRs at a specific angle with respect to the substrate at a specific temperature. Following each THz-TDS measurement, RTA at a higher temperature would lead to a further increase in the bending. In particular, RTA from 350 C to 550 C was performed in steps of 50 C. In this way, it was possible to measure response over a large angular range from 0 to nearly 90 degrees (i.e. the SRRs in-plane the plane of the substrate to nearly perpendicular). Figure 11 displays the experimental results, which are in good agreement with the simulation results. The experimental resonance is somewhat weaker and broader in comparison to the simulation results, which likely arises from effective inhomogeneous broadening due to fabrication tolerances and slight variability in the cantilever leg bending angles across the 1 cm 2 structure. As these results reveal, the reorientation of the SRRs leads to dramatic changes in the electromagnetic response. As the SRRs increasingly bend out of the plane of the substrate, de-activation of the electric resonance results in a 50% increase in the transmission for case #1, as shown in Fig. 11a. Activation of the magnetic resonance results in a 30% decrease in the transmission for case #2, as shown in Fig. 11b. For the largest simulated angle of 80 degrees, the resonance has vanished. For the largest experimental bending a resonance is still present clearly indicating that such an 80 bending angle has not been experimentally achieved. This is also consistent with the SEM measurements, as the cantilever bending angle saturates at 500 C for the present case. The thermal-mechanical response of the cantilevers could be improved by optimizing the geometries of the bimaterial legs. In addition, in the simulations, at 60 degrees there is a clear resonance shift (and to a lesser extent at other frequencies) which is not experimentally observed because of the aforementioned inhomogeneous broadening. Figure 11c displays the experimentally measured data for case #3 where the electric resonance is driven for all angles of the SRRs, while the magnetic coupling increases as the SRRs pop-up out of plane. There is no substantial change in the transmission as a function of the angle of the SRRs, which is consist to the simulations of the bianisotropic EM responses. In particular, no change in the resonant response is expected as a function of orientation if, approximately, the magnetic polarizability (α m ) times the electric polarizability (α m ) is equal to minus the square of the magnetoelectric polarizability (α em ). Such an equality holds for SRRs whereby, as a function of orientation, any decrease in the total

11 Fig. 11 THz-TDS measured transmission spectra for the responses of the structurally tunable metamaterials as a function of frequencies: a magnetic response; b electric response; c bianisotropic response; and d non-resonant response. electric dipole response (driven by E and H) is compensated by an increase in the total magnetic dipole response. To understand this somewhat counterintuitive result, we refer to Fig. 12 which shows a SRR with the axes labeled and two specific field configurations. Figure 12b shows the field orientation at normal incident with the SRRs in the plane of the substrate while Fig. 12c shows, for simplicity, the case where the angle of incidence in 90 degrees and the SRRs is remains in the plane of the substrate (this is analogous to the case where the field remains fixed and the SRRs are at 90 degrees with respect to the substrate). For propagation along the z direction as shown in Fig. 12b, the dispersion relation is [23, 28, 29]: k 2 z ¼ w2 m 0 " yy ð1þ For propagation along the x direction as shown in Fig. 12c, the dispersion relation is: kx 2 ¼ w2 m zz " yy m 0 " 0 k 2 yz ð2þ In these equations, the ε yy is the electrical permittivity along y with the E oriented along y, μ zz is the magnetic permittivity along z with H along z, and κ yz results from magnetoelectric coupling and embodies the bianisotropy. Independence of the transmission on the orientation of the SRR or, in the present discussion, on the angle of incidence will

12 Fig. 12 Schematic for effective isotropic response from bianisotropy of the SRR. result if k x = k z. Equating (1) and (2) and rewriting in terms of the associated susceptibilities (χ e,yy, electric susceptibility; χ m,zz, magnetic susceptibility) yields: # m;zz 1 þ # e;yy ¼ k 2 yz ð3þ Finally, in the limit where # e;yy >> 1 and in the limit where the susceptibilities are written in terms of the polarizabilities of the individual elements (i.e. coupling between unit cell is neglected) our analysis suggests an independence on the orientation if the following expression holds: a m a e ¼ a 2 em ð4þ This equation just states that the magnetic susceptibility times the electric susceptibility is equal to minus the square of the magnetoelectric susceptibility. This is known to hold explicitly for split ring resonators and hence the independent of the orientation of the SRRs that we experimentally observe in Fig. 11c is expected and is a consequence of the bianisotropy. As shown in Fig. 11d, there is no clear resonant response, but there is a change in the transmission as a function of the cantilever bending. This results from two higher frequency dipole resonances. These resonances arise from the vertical bars of the SRR structure and the bending cantilever arms. These resonances can both be seen clearly in Fig. 13 which shows the experimental data on the left and corresponding simulations on the right over a broader frequency range which includes these dipolar resonances. The lower and higher Fig. 13 Simulation and experiment results of the high frequency behavior of the non-resonant responses from measurement (left) and simulation (right). The lower frequency resonance is a result of the vertical bars of the SRR structure, where as the higher resonance is a result of the cantilever arms.

13 Fig. 14 Simulation results of the high frequency behavior of the non-resonant responses showing that a the lower frequency resonance is a result of the vertical bars of the SRR structure and b the higher resonance is a result of the cantilever arms. frequency resonances from the figure are due to the SRR side bars and the cantilever bimaterial legs, respectively. As the bending angle increases, the SRR dipole response weakens due and eventually disappears as the projection of the electric field along the dipole decreases, as shown in Fig. 14a. This is in contrast to the dipolar response of the cantilever legs which is present at every angle, as shown in Fig. 14b. These different responses are a result of the physical orientation of the dipoles. The SRR bars, which are perfectly straight, rotate relative to the electric field, decreasing their coupling as the bending angle increases. The cantilever arms, however, have a fixed base which is always parallel to the electric field. Even at high bending angles, these cantilevers will have a component parallel to the incident electric field, even though a significant portion of the bar has bent out of plane. The other orientations not explicitly mentioned here have similar high frequency behavior, which can be readily, and intuitively, determined by inspecting the SRR and cantilever orientations in the unit cell with respect to the electric field orientation and then applying the arguments described here. It is worth mentioning that, in the present demonstration of structurally tunable metamaterials, each of the SRRs was designed to reorient in an identical fashion in response to an external stimulus. More complex materials could be designed where a fraction of the unit cells remain stationary, as shown in Fig. 15, or different unit cells move in orthogonal directions, as shown in Fig Conclusion In this paper, we present a novel approach to dynamically control the electromagnetic responses of metamaterials realized by mechanically tuning the meta-lattice structure. Our experimental and simulation results reveal that it is possible to create structurally tunable metamaterials where reorientation of the SRRs within the unit cell leads to a tunable electromagnetic response that is dominantly electric or magnetic in nature. Bianisotropic behaviors of SRRs are also discussed for better understanding the functional mechanism of SRR based metamaterials. For these initial proof-of-principle measurements, RTA was used to lock the SRRs into a set orientation which facilitated the electromagnetic characterization

14 Fig. 15 a Schematic of a metamaterial structure which could potentially realized by the similar design presented in this paper with potentially simultaneous electric and magnetic resonance responses, (Inset) the SEM photograph of the MM structure; b the element for magnetic response; c the element for electric response. using THz-TDS. However, it will be possible to actively reorient the SRRs using welldeveloped micro/nano actuation techniques which include thermal resistive, piezoelectric, and electrostatic actuation [30 32]. The structural reconfiguration time can be on the order of milliseconds given the mechanical and thermal response times of the cantilevers. In addition, the cantilever mechanical resonance frequency is several khz which will not substantively interfere with many potential applications which includes reconfigurable filters, negative index surfaces, thermal cantilever-based detection, or fine tuning of the electric or magnetic response for optimizing perfect absorbers or transformation optics derived metamaterials such as cloaks or concentrators. Furthermore, more complex materials could be designed where a fraction of the unit cells remain stationary or different unit cells move in orthogonal directions. The approach of tuning the meta-lattice Fig. 16 a Optical microscopy photograph of a metamaterial structure with different unit cells moving in orthogonal directions, (Inset) Zoom in picture; b SEM photograph of the same sample after selectively rotating different elements out of the plane by RTA.

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