Three-Dimensionally Coupled THz Octagrams as Isotropic

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Three-Dimensionally Coupled THz Octagrams as Isotropic Metamaterials Kriti Agarwal, Chao Liu, Daeha Joung, Hyeong-Ryeol Park, Jeeyoon Jeong, Dai-Sik Kim, and Jeong-Hyun Cho ACS Photonics, Just Accepted Manuscript • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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Type: Article Three-Dimensionally Coupled THz Octagrams as Isotropic Metamaterials Kriti Agarwal+, Chao Liu+, Daeha Joung+, Hyeong-Ryeol Park#, Jeeyoon Jeong⁋, Dai-Sik Kim⁋, and Jeong-Hyun Cho+* + Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA # Department of Physics, Chung-Buk National University, Cheongju 28644, South Korea ⁋ Department of Physics and Astronomy and Center for Atom Scale Electromagnetism, Seoul National University, Seoul 08826, South Korea *E-mail: [email protected] Keywords: split-ring resonators, optical sensors, isotropic metamaterials, self-assembly, octagram SRRs Abstract: Split-ring resonator (SRR) based metamaterials have been studied for the development of highly sensitive, small-sized, low-power chemical and biomolecular sensors. However, the anisotropic behavior arising from their two-dimensional (2D) structure presents substantial challenges leading to ambiguity in their transmission spectra. In this paper, we present the design of a three-dimensional (3D) isotropic octagram split-ring resonator (OSRR) demonstrating a three-dimensionally coupled resonance behavior that overcomes the anisotropic response of conventional 2D SRRs, leading to a strong, distortion-free, and polarization invariant transmission response. The OSRR undergoes 3D coupling through the splits at the corners of the 3D structure (cube) which remains invariant under any polarization along the coordinate axes. The strong coupling between resonant segments provides the OSRR with 25 times higher sensitivity than the corresponding 2D structure, allowing the resonant frequency to be reliably monitored for small changes in concentration of a targeted substance. The isotropic frequency response of the 3D OSRR, without ambiguity in the amplitude caused by the polarization

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dependence, also allows monitoring the amplitude for minute changes in concentration which are too small to cause any shift in resonant frequency. Thus, the detection range for the presented 3D OSRR stretches from large to minute variations of targeted substance.


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Terahertz (THz) spectroscopy has emerged as an attractive avenue for label-free, fast, and versatile detection of chemical and biological substances.1-3 Recent development of high power and long propagation length THz sources has promoted its use in free-space spectroscopy, microstrip line, and metallic mesh methods for the analysis of biomaterials.4-8 Sensors based on the the free-space spectroscopy, in principal, measure changes in dielectric constant due to the binding of the molecules. However, this method requires large quantities of the sample materials to achieve a reliable response.9 As a solution to minimize sample quantities required for detection, microstrip line-based sensors inducing enhanced electric field have been developed; however, the strong electric field confinement exists only between the substrate and the strip line, decaying severely in the air region above the strip line.10, 11 This decay limits the sensitivity of the structure since the high field confinement area is inaccessible to the targeted molecules. On the other hand, another class of sensors i.e. metallic mesh based structures, benefit from strong localization of the electromagnetic field at the openings of the mesh and operate by sensing changes in the refractive index near the surface of the metal-air interface.12 However, the frequency response for these structures resembles that of a high-pass filter (no narrow peak exists) with a very low signal transduced at low concentrations of the target molecules.13 Thus, for higher sensitivity detections of small target molecules, it is necessary to leverage structures that induce a strong coupling between the incident electromagnetic wave and the metallic resonant structure to deliver sharp edges in the transmission response and create an area of high field confinement for detection of the targeted material.14 Split-ring resonator (SRR) based metamaterial structures have been extensively studied because of the relatively sharp edges in their frequency response as well as their ability to manipulate electromagnetic waves and produce strong confinement of the magnetic (H) field


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within the arms of the resonator and the electric (E) field confinement within the split. The split contributes capacitance to the resonant frequency which is directly proportional to the relative permittivity. The confinement of the E field within the capacitance controlling split makes it a hotspot that has higher sensitivity than the surrounding areas where the electric field is much weaker. Hence, when a SRR is exposed to a biomolecule, a large shift in resonant frequency is seen as a function of the relative permittivity of the external molecule near the split.15 The dependence of the resonant frequency on the aforementioned parameters has allowed SRRs to be used in a wide range of sensors to detect micro-organisms,16-18 strain,19 dielectric constants,20 and displacement21 without the effects of ambient temperature and pressure. Especially, THz SRRbased biosensors offer an attractive avenue for the development of small scale, label-free detectors capable of being introduced orally or intravenously due to their microscale dimensions, which are comparable to that of most micro-organisms, and the non-ionizing nature of THz radiation.22, 23

Figure 1. Transmission characteristics of a 2D C-shaped split-ring resonators with length (L) = 36 µm, width (w) = 4 µm, and gap (g) = 4 µm, showing the angular dependence of incident THz light, such that the 1st mode decreases and 2nd mode increases as the incident angle (θ) increases from 0 to 90°.


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However, the polarization dependence of the SRR transmission response poses a major drawback. For example, when the H field is polarized perpendicular to the split containing arm of the resonator, the structure is in 1st mode (magnetic resonance). However, when the E field is polarized perpendicular to the split containing arm of the resonator, the structure is in 2nd mode (electric resonance). As the SRR is rotated from 0° to 90°, the 1st mode reduces and the 2nd mode increases (Figure 1), the reverse phenomenon takes places on rotating from 90° to 180°. The maximum 1st mode transmission amplitude (Tθ) achieved at θ = 0° decreases as a function of the rotation angle such that transmission, T(θ), at any angle (θ) is given by T(θ)=1-(1-Tθ) * |cos2θ|.24 This presents an ambiguity in the transmission spectrum, such that variation due to the presence of external molecules cannot be discerned from the rotation of structures (SRRs). Thus, limiting their application as sensors when the orientation of the resonator is difficult to control such as invivo detection processes. In this paper, we present the design and fabrication of an isotropic (orientation invariant transmission response) three-dimensional (3D) octagram-based split-ring resonator (OSRR), the eight-pointed 3D octagram ensures uniform coupling of each resonator segment in all directions for any x, y, and z orientation, thus overcoming the anisotropic polarization dependent transmission response of the 2D C-shaped SRR structure. As a proof of concept, simulation and measurement data have been presented that support the perfect isotropic nature of the 3D resonator. Moreover, the sensitivity of the 3D OSRR in comparison to the 2D coupled net is presented where the 3D uniform coupling between the metallic resonant segments enhances the sensitivity of the SRR structures. Due to the perfectly isotropic behavior and high sensitivity, the innovative three-dimensionally coupled OSRR can be used for fast, non-contact, non-labeled


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detection of chemical and/or biological molecules without the ambiguity produced by the anisotropy of the conventional SRR structures.

■ ANALYSIS From Figure 1, it can be deduced that a unit cell of SRR structures consisting of resonators oriented such that the unit cell simultaneously undergoes electric and magnetic resonance might demonstrate an overall polarization invariant response due to superimposition of the two resonant modes. This can be accomplished by a unit cell with four resonators (Figure 2a) where two of them (SRR1 and SRR3) have magnetic field perpendicular to the gap (1st mode), while the other two (SRR2 and SRR4) have electric field perpendicular to the gap (2nd mode). Using ANSYS Electromagnetics Suite (version 16.0.0), the structure for a unit cell consisting of four resonators with length (L) = 36 µm, and split gap (g) = 4 µm was simulated. In such a configuration, during rotations of the structure about the z-axis (similar to Figure 1) the decrease in 1st mode resonance of SRR1 will be compensated by a proportional increase in 1st mode for SRR2 and vice-versa for 2nd mode as well. SRR3 and SRR4 ensure that the resonators within the unit cell couple equally in all directions. While this configuration corrects for z-axis rotations, other issues arise when angles between the incident wave and SRR surface are changed in x-, y-, and z-axes simultaneously (when 3D rotations of the SRR substrate are applied); the 1st mode resonance shows a large change in the resonant frequency, as well as the transmission amplitude (Figure 2b). For the 2D SRR structure the highest change in amplitude occurs when the incident electric field lies perpendicular to the plane of SRRs (and the wave vector is parallel to the SRR plane) producing no resonances in the structure. Therefore, the 2D SRR structures even with varying orientations within a unit cell cannot provide a three-dimensionally isotropic


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transmission response (an isotropic transmission response being where rotation about any axes should not change the amplitude and/or resonant frequency). In order to resolve the 3D anisotropy, the SRR structure needs to be designed such that resonance can be excited in the structure for all directions of the incident E field.

Figure 2. Illustration and the simulated transmission response of the 2D and 3D coupled SRRs that can be subjected to 3D rotations consisting of, (a, b) A 2D array of SRRs with L = 36 µm, w = 4 µm, and g = 4 µm, demonstrating simultaneous 1st and 2nd modes and an anisotropic response for 3D rotations. (c, d) 3D cube that is structurally invariant for 90° rotations with L = 36 µm, w = 4 µm, and g = 4 µm with high variation in frequency response for other rotation angles due to coupled superimposed resonances. (e, f) Symmetric two-dimensionally coupled resonators with the unit cell consisting of a 3×3 array of X shaped


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symmetric resonators of length 250 µm and width 20 µm showing the highly distorted coupled frequency response because of non-uniform coupling. The red, blue, and green arrows denote the direction of polarization of the incident wave. The black arrows illustrate the direction of 3D rotation of the SRR structure. The rotation angles were chosen to encompass a wide range of angles as well as the angles with the highest degree of asymmetry (45°).

3D SRRs with various configurations that contain SRRs oriented along all three axes (x, y, and z) have been investigated for providing isotropy under 3D rotations.25,26 One technique for achieving this is to pattern 2D SRRs on the faces of cubic structures (Figure 2c).27 However, using this approach, the resonators and the splits continue to be two-dimensional; this induces non-uniform coupling between the resonators on different faces, resulting in multiple resonance behaviors (Figure 2d). In each SRR, the resonant arms containing the split couple strongly to their neighbors owing to the electric field confined within the split. For the cube shown in Figure 2c, at the initial position and for rotations about any axes (θx, θy or θz), a total of two resonators always have the split perpendicular to the direction of the E and H vectors, or the wave vector (k) and hence could keep the overall superimposed transmission response invariant for some specific rotation angles. For instance, at θy = 45°, the structure shows a large shift in 1st mode resonant frequency as well as the transmission amplitude (Figure 2d). This large difference in amplitude between θy = 0° and 45° can be attributed to the change in the resonance of the SRR1 resonator. At the initial position (θy = 0°), SRR1 has the E field perpendicular to the split of the SRR and the incident light parallel to the plane of the resonator, giving it a weaker 2nd mode resonance than if the light was incident perpendicular to the plane of the resonator. SRR2, and SRR3 have 1st mode resonance at the initial position; however, since SRR3 has the E field perpendicular to the plane of the resonator and the incident light parallel to the SRR plane it does not produce any significant resonance. On rotating the cube (θy = 45°), the incident light is not completely parallel to SRR1 any longer; thus, it undergoes a stronger 2nd mode resonance causing an increase in the transmission amplitude. Similarly, SRR3 also undergoes a stronger 1st mode


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resonance at θy = 45° than at the initial position. For the standalone case a proportional decrease in the 1st mode resonance of SRR2 should have been seen thereby keeping the total transmission response constant. However, due to the presence of four SRRs with strong E field within their split at the 1st mode resonance in close proximity to each other, there exists a strong coupling between them resulting in an anisotropic resonance behavior (Figure 2d). The above anisotropy in the transmission response indicates the need for symmetric resonators that minimize the switching between the 1st and 2nd modes of the 2D C-shaped SRRs and compensate for the non-uniform coupling to their neighbors. To realize a symmetric array of resonators, an X-shaped configuration on a planar substrate can be considered. Due to the shape dispersing in multiple directions, the resonator at the center of the unit cell couples equally in all directions in the XY plane (Figure 2e). However, the resonator at the edges can only couple to half as many resonators since the resonators at the edges have lesser neighbors than the resonators at the center. This produces multiple transmission drops (Figure 2f) corresponding to the resonance of each SRR within the unit cell. The first drop corresponds to the resonance of the SRR at the center of the unit cell as seen by the strong surface current for the center SRR at 0.25 THz (lowest resonant frequency due to highest coupling) (Figure S1 in Supporting Information). The peaks at higher frequency correspond to the edge and corner SRRs, giving them a higher surface current at a frequency of 0.64 THz. When the 2D non-uniformly coupled unit cell is rotated along any direction, the transmission response is rendered incomprehensible due to the multiple resonances. Similar results are obtained for the 2D unit cell consisting of nine partially symmetric C-shaped SRRs (Figure S2 in Supporting Information). Therefore, to achieve perfect isotropy, the multiple peaks caused by non-uniform coupling need to be eliminated, and the anisotropy due to the switching between 1st and 2nd mode


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should be minimized. The 2D structure should be redesigned such that each resonator couples to an equal number of neighboring resonators and at each angle of rotation the modes in the resonator should remain exactly same. This can be achieved by folding the 2D unit cell into a 3D cube consisting of six faces with resonators on each face, where the resonant segments are forced to couple to their neighbor through the split created at the corner of the cube (Figure 3a), thus forming a fully symmetric eight pointed 3D star (octagram). Furthermore, if we consider the resonator on the top face of the cube in Figure 3a, the split at the corner of the X-shaped segments couple it equally in all directions to the resonators on the side walls of the cube which in turn couple to the resonator on the bottom face. The splits at the corner, which have a high E field

Figure 3. (a)Isotropic Frequency Surface composed of a 3D Au OSRR on a SU-8 cube of length (a) = 500 µm, resonator length (L) = 674 µm, width (w) = 20 µm, and split gap (g) = 16.55 µm, (b) The single isotropic transmission peak at 0.13 THz for the 500 µm cube which is invariant for any rotations of any angle about x, y, and z axis, unlike the distorted anisotropic 2D response. (c) Uniform current distribution of the 3D coupled resonator on the faces of the cube of length 500 µm at 0.13 THz with the arrows


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showing the direction of the surface current. (d) Graph of maximum change in transmission seen between the initial (0°) position and the angles in part (b) as a function of the split gap length in the OSRR, showing the decrease in isotropy of the structure when gap length (g) between the individual X-shaped resonant segments defined on each face is increased from 1.5 µm to 36.5 µm.

confinement at resonance induce a strong uniform coupling between the segments on each face of a cube effectively creating a 3D octagram based split-ring resonator (OSRR). Since the split is three-dimensional, it is equally affected by the E, H and k vectors for all orientations of the cube. Thus, the 3D split gives an isotropic transmission response to the OSRR defined on a 500 µm sized cubic structure with a single resonant drop at 0.13 THz and with a constanttransmission amplitude, which is invariant under 3D rotations (Figure 3b). The 3D nature of the resonator is further evidenced by the strong surface current on all the faces of the cube (Figure 3c, and movie file M1 in Supporting Information). In the absence of 3D coupling, when the electric field is polarized perpendicular to the surface of the resonator, no resonance is observed and the surface current is ~0 (Figure S3e, f in Supporting Information). However, the 3D coupled system acts as a single resonant structure. For the 3D OSRR each resonant segment induces resonance in its neighbor, creating a surface current on entire 3D resonator surfaces. When the 3D gap, g, between the X-shaped resonant pairs shown in Figure 3a changes, the coupling between them also varies. When the split gap is small (1.5-16 µm), the entire cube acts as a single 3D resonator due to the strong coupling between the resonators defined on each face of the cube, and the response is isotropic with welldefined resonance drops (Figure 3d). However, as the gap increases (g ≥ 21 µm), the coupling between resonant pairs decreases, causing them to act as six independent resonators giving an anisotropic response with a large change in transmission amplitude at resonance between different orientations. Addition of a 2D gap to the individual resonators of the 3D OSRR also


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affects the isotropy of the structure. When a 2D gap of length, g2D, in the middle of the resonators is added to the 3D OSRR (Figure S4a in Supporting Information), the isotropic response of the symmetric OSRR reverts to that of the non-uniformly coupled 2D resonators, resulting in an anisotropic resonance behavior (Figure S4b-d in Supporting Information) similar to the resonators shown in Figure 2c, e. Thus, a 3D OSRR with a corner split that is equally mediated by the incident light, as well as the magnetic and the electric field polarization creates a perfectly isotropic and well-defined transmission response (Figure 3b) that overcomes the disadvantages of planar 2D SRRs which contain multiple resonant peaks that are highly polarization dependent.

■ FABRICATION

Figure 4. Illustration and optical images of the fabrication process for the 3D self-assembled microstructures. (a) Deposition of Cr/Cu sacrificial layer by e-beam evaporation on a Si substrate followed by electroplating of 300nm thick Au OSRR (b) SU-8 spin coating and patterning by photolithography for the formation of panels with dimensions 500×500×10 µm. (c) SPR 220 spin coating and patterning by photolithography for 21 µm thickness hinges. (d) Self-assembled 500 µm 3D cube with isotropic Au OSRR of segment lengths 675 µm, width 20 µm, and split gap ~16 µm, patterned on SU-8 panels and folded using SPR 220 hinges.

500 µm sized cubes with symmetric X-shaped resonator segments were fabricated using a self-assembly process28-33 to experimentally demonstrate the use of the 3D OSRR design as


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isotropic octgrams (Figure 4). The OSRRs were patterned on a cubic surface with transparent SU-8 2010 (MicroChem) panels and SPR 220 -7.0 (MEGAPOSIT) hinges. A 10 nm chromium (Cr) adhesion layer followed by a 300 nm thick copper (Cu) layer was deposited using electron beam evaporation on a silicon (Si) wafer. The Cu layer acts as a sacrificial layer, as well as seed layer for a subsequent electroplating process used for depositing 300 nm thick Au OSRR. Following the electroplating of the Au OSRR (Figure 4a), ~10 µm thick SU-8 polymer panels were spin coated and patterned via conventional photolithography process (Figure 4b). Lastly, ~21 µm thick polymer hinges of SPR 220-7.0 positive photoresist were patterned between the panels (Figure 4c). It should be noted that polymer based materials should be used for hinges and panels since the presence of any other metallic components except the Au SRRs can lead to a distorted response with multiple anisotropic resonant peaks.32,

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The Au SRRs are the only

metallic resonant structures present and the remainder of the polymer based cube and hinges are transparent to the THz waves. The 2D structure before folding, consists of six SU-8 panels with X-shaped symmetric Au resonators and SPR 220 hinges on top of the panels (Figure 4c). The 2D stucture was submerged in APS Copper etchant 100 (Transene) for 3 hours to etch the Cu sacrificial layer and release the structure from the substrate. The released 2D structures were transferred to water and placed on a hot plate for the self-assembly process. When heat energy is applied to the 2D structure, the SPR 220 hinges melt and reflow generating a surface tension force to fold the structure (Figure S5g in Supporting Information). After locking of the hinges is achieved at a folding angle of 90°, the heat source is removed. On cooling to room temperature, the SPR 220 hinges resolidify and secure the 3D cubic structure (Figure 4d). Following the reflow of the SPR 220 polymer hinge, the 2D net (Figure 4c) folds into the 3D cubic structure, with each face containing the symmmetric resonant segments that together form the 3D OSRR


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with split gap length for patterning chosen to be 2 µm, and thickness ~300 nm, present on the outside of a cube with SU-8 panels (Figure 4d). Further details of the fabrication procedure can be found in the experimental section. ■ RESULTS The cubic structure fabricated by the self-assembly process was characterized using THz time-domain spectroscopy (TDS) (0.1 THz to 1.0 THz).34-36 For measurement, the cube was attached to a piece of Scotch double sided tape that is transparent to the incident THz light. The tape with the adhered cube was fixed onto an aperture with a diameter of 3 mm. The aperture was attached to a rotational mount (Figure 5a) and THz pulse generated from a commercial GaAs emitter which passed through the cube and aperture was received by the detector. The cutoff frequency for the 3.0 mm aperture was found to be ~0.1 THz. The normalized transmission response was found by dividing the signal received from the OSRR cube with that of a blank cube without OSRR patterns (Figure 5b). The normalized response exceeded 1.0 for the nonresonant frequencies due to the errors introduced in the manual positioning of the 500 µm cubes at the center of the large aperture with a diameter of 3 mm (6 times larger) required by the diffraction-limited THz TDS measurement system. If the position of the two cubes had an offset among their position on the aperture at the center of rotation, then the Gaussian-like THz power received at certain rotation angles in the presence of the OSRR structure maybe greater than that received with the blank cube; resulting in a normalized transmission response that is greater than 1.0. The final value of the resonant frequency and transmission for the OSRR was found by averaging the measured resonance at twelve different random positions of the cube except the two (maximum and minimum) positions resulting in the largest deviation. The first mode resonance was measured using the 3 mm aperture and was found to have an average resonant


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frequency of 0.19 THz and transmission of 0.698 (Figure 5b). The simulated transmission spectrum (Figure S6 in Supporting Information), with the same dimensions as the measured cube, demonstrates a resonant frequency of 0.18 THz. The higher transmission in the simulated spectrum as compared to the measured response is primarily caused by the smaller size of the port used for simplifying the time for simulation; this leads to 51% of the surface area of the port to be covered by the cubic OSRR in contrast to the measurement setup where only 3.5% of the area of the aperture was covered by the cube. The 5% change in resonant frequency could be attributed to the insufficient spectral and error resolution used for simulation due to computational limitations as well as the SU-8 baking temperatures.37 Despite the discrepancy between the simulated and measured response, it should be noted that this effect is experienced uniformly for all orientations of the OSRR. Thus, the measured resonant frequencies at the 1st mode remain nearly constant at 0.19 THz within the minimum spectral resolution, which experimentally confirms the isotropic response of the 3D OSRR in the frequency domain. The maximum change in the 1st mode resonant frequency for the various values of θx, θy, θz from 0° to 360° (12 different orientations) was found to be ±0.0045 THz (2.3%) whereas the corresponding maximum variation in transmission was ±0.055 (8.4%). Thus, the first mode resonant frequency and transmission amplitude were measured to be almost constant similar to the simulated transmission response (Figure 3b) with a single peak that remains invariant in amplitude and frequency for different orientations of the cube. This demonstrates the isotropic transmission response of the 3D OSRR due to the uniform coupling between the resonators through the 3D gaps. The 2.3% change in resonant frequency and the 8.4% change in amplitude as opposed to the perfectly isotropic response of the simulated OSRR could be attributed to variation in thickness of the materials and the small ripples in Au OSRR due to the weaker


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adhesion of Au to SU-8, as well as the non-uniform boundary spacing applied by the circular aperture to the cube. The higher order modes (occuring between 0.3-0.5 THz) could not be observed with an aperture diameter of 3.0 mm since only 33% of the area of the aperture is covered by cube, generating a large amount of noise to view the weaker higher order modes; however, different aperture shapes and size can be fabricated that allow optimal measurement of the isotropic response of higher order modes. Furthermore, the measured OSRR contains segments of width ~20 µm allowing the OSRR to cover only 10% of the area of each surface of the cube. Thus, the width of the Au layer can be increased along with a closer area matching between the cube and aperture in order to decrease the incident photons arriving at the detector without interacting with the OSRR to enhance the transmission amplitude. Detailed information about the characterization/measurement procedure can be found in the experimental section. In order to achieve a measured response similar to the simulated perfectly isotropic response, a TDS system that applies uniform boundary spacing needs to be developed as well as the adhesion of metal OSRR pattern to the polymer panels needs to be improved. As an example, the measured transmission spectra for the 2nd mode resonance with an aperture of diameter 1 mm (Figure S7 in Supporting Information) contains negligible error in the normalized transmission response from position mismatch resulting in a trasmission below 1.0 for the entire frequency range and an isotropic resonance peak at 0.38 THz.


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Figure 5. Schematic of the THz time domain spectroscopy (TDS) setup showing the GaAs THz emitter and the ZnTe detector. The incident wave is perpendicular to the top face of the cube which is attached to the circular aperture with a Scotch double sided tape. (b) Transmission characteristic of the 500 µm 3D OSRR measured by THz TDS measured while rotating the aperture and cube along the angle θz using circular apertures of diameter 3 mm for measuring the 1st resonance peak where each color represents the measured response at a different random position. The isotropic resonant frequency was measured to be 0.18 THz for 1st mode.

To characterize sensitivity of 3D OSRR, simulations of the 3D octagram (Figure 3a) and the planar 2D net of symmetric SRRs (Figure 2e) were carried out for varying permittivity of the medium surrounding the cube. Due to the inability to control the orientation of the small anisotropic 2D resonators on the thin (~10 µm thickness) SU-8 panels, it is challenging to apply the same conditions to 3D and 2D structures for appropriate comparisons, thus, simulations rather than TDS measurements were carried out for varying permittivity. Moreover, since the aperture size is fixed, the difference in surface area of the aperture covered by the 2D and 3D can lead to a discrepancy in the results. When exposed to a biomolecule, the resonant frequency, fr =1/(LC)0.5 (where L is the inductance due to the gold resonant structure and C is the capacitance of the 2D/3D splits) changes proportionally to the relative permittivity (ϵr) of the biomolecule being detected. Changes in the exposed biomolecule, whether through changes in chemical composition or through concentration increases also directly correspond to a modification in the permittivity; thus, to evaluate the 3D OSRR for biomolecule monitoring and sensing, the freespace permittivity was increased from 1 to 6 and the corresponding resonant frequency shift in 1st mode resonance per unit volume of the biomolecule was simulated. For a 2D array of SRRs defined on a planar substrate with small volumes of a target molecule, only one of the resonator may demonstrate a change in resonance; thus, unable to change the overall transmission response. However, for the 3D OSRR the metal patterns on each face of the cube are strongly coupled to the neighboring faces (as evidenced by the surface current on the cube, even on the


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faces with E field perpendicular in Figure 3c), changes in permittivity surrounding the tips of any resonator cause a domino reaction, providing the isotropic 3D coupled OSRR with a much higher sensitivity than the corresponding 2D coupled SRR. This results in a large shift in resonant frequency which is 10-25 times higher at small permittivity changes (∆ϵr = 6) for the 3D OSRR as compared to the 2D planar SRR (Figure 6a). Thus, the 3D coupling induces a shift in resonant frequency (δfr) upon exposure to target molecules that is much higher than the corresponding shift for 2D planar sensors. For lower variations in permittivity (from 1 to 4) the 3D OSRR always demonstrated a shift that was around 25 times higher than the 2D structure, and about 10 times higher for relative permittivity between 4-6 (Figure 6a). For most biological samples and chemicals, the change in permittivity is much smaller (maximum ∆ϵr ~ 0.35) than the large shift in permittivity (∆ϵr = 6) described in Figure 6a. Thus, to monitor small molecular changes, the detection ability of the 3D OSRR structure needs to be assessed for smaller variations in permittivity (maximum ∆ϵr ~ 0.35). One such example is the monitoring of rising levels of glucose in the blood. Diabetes affects about 9.3% of the population;38 however, the cumbersome process of repeated extraction of blood for monitoring the fluctuating glucose levels has prompted detailed study into and establishment of refractive index models in GHz-THz range for glucose in blood with rising concentration of glucose allowing development of optical sensors.39-42 Hence, glucose was chosen as an example to assess the performance of the OSRR due to the widely established relationship between refractive index and concentration of glucose in blood.


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Figure 6. (a) Graph showing the shift in resonance per unit volume (δfr) of targeted molecules (as a function of the permittivity due to the molecules) for the 3D coupled OSRR when compared to the 2D coupled symmetric X-shaped SRR showing the higher sensitivity obtained using the 3D structure. (b) Change in transmission response of the cube due to rising glucose level evaluated at different levels corresponding to normal fasting, after eating, and critical; demonstrating the advantage of the isotropic OSRR through measurement of amplitude for small changes in permittivity (inset, showing the resonant frequency and transmission amplitude for the permittivity corresponding to each glucose level).

Three critical levels can be identified for glucose level within the human body, firstly, the baseline level before eating (fasting); secondly, the level after eating that most humans temporarily undergo; thirdly, the critical level which can result in adverse consequences if not treated immediately. The corresponding maximum change in relative permittivity for the three levels between 7 mmol/L and 20 mmol/L is only 0.35 (Figure S7 in Supporting Information). For the fasting condition with a glucose level of 7 mmol/L and ϵr = 2.1025, the resonant frequency of a 3D OSRR was 0.105 THz (Figure 6b, black line). When the glucose level rises after eating to 10-11 mmol/L, relative permittivity increases to ϵr = 2.28 (Figure S7 in Supporting Information), resulting in the resonant frequency shift to fr = 0.100 THz and the frequency change is ∆fr = 0.005 THz for 11 mmol/L (Figure 6b, green line). However, as seen in the inset of Figure 6b (red line), for changes between 7-10 mmol/L and more importantly for a higher critical glucose level between 11-20 mmol/L representing relative permittivity range 2.1-2.45, the resonant frequency


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appears to remain a constant. The actual change in resonant frequency between the concentrations of 7 mmol/L and 10 mmol/L is only 0.002 THz (from 0.103 THz to 0.105 THz, as shown in Figure S8a in Supporting Information when simulated with a resolution of 0.001 THz). However, the spectral resolution for most THz TDS systems is limited to 0.0005 THz, hence, making the resonant frequency appear to be constant (Figure S8b in Supporting Information). It should be noted that this observation indicates that the resonant frequency cannot be the only source used for the measurement of the glucose level. However, the 3D OSRR offers the capability to monitor the increase in glucose level not only by monitoring the resonant frequency change but also by measuring the change in the transmission amplitude at the unchanged resonant frequency. When the permittivity changes from 2.1025 to 2.2350 the transmission amplitude also appears to change by ~6.6 dB between 7 mmol/L and 10 mmol/L (Figure 6b, inset black line). This large change in amplitude is caused by the small shift (0.002 THz) in the position of the peak maximum, which subsequently modifies the amplitude at the previous resonant frequency (~5.9 dB change, Figure S8c in Supporting Information). A similar phenomenon occurs when the concentration increases from 11 mmol/L to 20 mmol/L. In contrast, under similar conditions the 2D array would not be able to transduce any reliable signal since the amplitude change could also be attributed to change in orientation of the structure. However, the isotropic nature of the 3D OSRR means that for large changes in permittivity the resonant frequency can be monitored for the detection of the molecules; but even for smaller changes in permittivity which cannot cause a shift in resonant frequency, the amplitude can also be monitored since there are no other parameters except substances around resonators that can cause it to change. Thus, the 3D OSRR with a polarization invariant isotropic transmission has a large detection range including large changes in the composition of the substance (permittivity)


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producing a change in resonant frequency and smaller changes in the targeted substance causing a change in transmission.

■ CONCLUSIONS In conclusion, using the self-assembly technique we have developed a cubic 3D octagram based SRR with a perfectly isotropic transmission response that is invariant under rotations about any axes. The split present at the corners of the cube provides a 3D coupling to the SRR structure which is equally affected by all three vectors (k, E, and H) for every possible orientation of the cube. The simulated and measured transmission spectra demonstrate the highly isotropic first mode resonant frequency of the 3D OSRR. The higher order modes demonstrating a 12.5% anisotropy because of a higher interference generated by the aperture were ignored due to their weak amplitude in the measured spectra. The uniformly coupled nature of the 3D OSRR demonstrates a sensitivity (shift in resonant frequency) that is 10-25 times higher than the corresponding 2D structure. The 3D OSRR demonstrates a two-fold advantage for detection of targeted molecules due to the higher sensitivity as compared to the 2D coupled SRR, as well as through amplitude monitoring to identify permittivity changes that are too low to cause a change in resonant frequency. Further research into the design of low noise and high sensitivity detectors can lead to the creation of small scale in-vivo sensors that can be intravenously inserted for noninvasive detection of various diseases.

■ METHODS Terahertz time-domain spectroscopy:


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THz time-domain spectroscopy (TDS) was performed over a frequency spectrum of 0.1– 1.0 THz on the 500 µm sized cubes attached on a circular aperture with a diameter of 3 mm. To generate the THz pulse, a 130-fs Ti:sapphire laser was used to illuminate a GaAs emitter with a pulse train with a center wavelength of 780 nm and 80 MHz repetition rate. The p-polarized THz pulses were normally incident on the surface of the 3D OSRR, and the cubes were rotated from 0-360° along the propagation axis of the incident wave to verify its polarization-independent property. The transmission spectra of both the cube with the 3D OSRR and the reference cube without the metallic patterns were measured using the electro-optic sampling method with a (110)-oriented ZnTe crystal. After taking the Fourier transform of the transmitted time-domain signals, the amplitude of the transmission spectra in the frequency domain was normalized by the reference signal. Thus, the normalized transmission was calculated by dividing the measured response of the cube containing the OSRR 3D pattern with that of the blank SU-8 reference cube. Minor differences in the position of the reference cube and the cube with SRRs cause the transmission response to be >1.0 at a few frequencies. A 10% error may be expected due to the mismatch in position between the reference un-patterned cube and the cubic sensor caused by manually placing the cubes on the aperture.

Finite element modeling of the transmission response: The simulation of the transmission response of the SRRs was performed using Ansys Electromagnetic Suites 16.0.0 with a distributive solve over an MPI cluster. The software uses an FEM technique where the 3D structure is divided into tetrahedral elements that are refined over several recursive calculations to produce a fine mesh. Solutions to the Maxwell’s equations are found producing an S-matrix where the S21 parameter provides the transmission characteristics.


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The 2D/3D C-shaped Au resonators (Figure 1, 2) with the specified length (36 µm), width (4 µm), thickness (300 nm) and gap (4 µm) were simulated on SU-8 substrate/panels. The structure was then encapsulated by a vacuum box, and excitation ports were applied to the top and bottom of the vacuum box. The SU-8 permanent photoresist was modeled using the commercial parameters provided by MicroChem Corp with relative permittivity = 4.1, dielectric loss tangent = 0.015, mass density = 1187 kg/m3, and resistivity 2.8×1016 Ωcm. The electrical conductivity of Au was taken to be 4.1×107 S/m. The 2D unit cell consisting of an array of symmetric resonators was created with nine Xshaped resonators each of length (L) = 674 µm, width (W) = 20 µm, and split gap (g) = 16 µm. The 3D star-shaped SRR on a 500 µm sized SU-8 cube was simulated using the material properties described above. The SPR-220 hinge being a polymer, acts to slightly shift the resonant frequency but this was ignored during the simulation due to computational limitations. The vacuum boxes for the 2D and 3D unit cell were chosen to be large enough, such that distance of the structure from the edge of the vacuum box during rotation did not impact the isotropy of the structures. A frequency sweep from 0.02-2.0 THz in steps of 0.01 THz was run for a mesh refined over 20 adaptive passes with an error tolerance of 0.02 for the S-parameter. The resulting S21 parameter in decibels (dB) was plotted against the frequency to determine the transmission behavior of the structures. The animation of the surface current was used to evaluate the mode of each resonant pair. Given the symmetry in the shape of the structures, 45° rotation angles (θy=45°and θz=45°) were simulated specifically due to the highest expected anisotropy. The other rotation angles (θx=222°, θy=111°, θz=11° and θx=315°, θy=230°, θz=155°) were chosen at random to cover a wide range of angles so that the isotropic transmission capabilities could be fully demonstrated.


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To assess the performance of the OSRR as a sensor, the cubes containing the OSRR structure were encapsulated in a box with the wave ports applied to the top and bottom surfaces. The material properties of the box (relative permittivity, and mass density) were changed to mimic blood samples with increasing concentration of glucose. A discrete frequency sweep was carried out in steps of 0.005 THz to find the transmission response at different glucose concentrations.

Fabrication process for the 3D SRR: A sacrificial layer consisting of an adhesion layer of 10 nm thick chromium (Cr) followed by 100 nm thick copper (Cu) was deposited on a commercial silicon wafer using electron-beam (E-Beam) evaporation (Figure S5a in Supporting Information). The SRRs were patterned on the Cu sacrificial layer by spinning S1813 positive photoresist (MICROPOSIT) at 2000 rpm (for thickness of ~1.8µm), followed by a soft-bake at 115°C for 1 min. The photoresist was patterned using conventional photolithography process with a glass-mounted mask (designed in Autodesk AutoCAD) and UV-exposed in a mask aligner followed by developing in MF-319 developer (MICROPOSIT) for 90 sec with agitation. The 300 nm thick gold (Au) SRRs were deposited via electroplating process in Tecnhi Gold 25 ES solution (Technic) for 20 min. (Figure S5b in Supporting Information). After removing S1813 with acetone, SU-8 2010 (MicroChem) panels were spin coated at 4000 rpm (~10µm thickness), followed by soft-baking at 95°C for 2 min 30 s. The sample was then UV-exposed in a mask aligner followed by post-baking at 95°C for 3 min 30 s. Subsequently, SU-8 was developed in SU-8 developer (MicroChem) for 2 min 30 sec and then hard-baked at 200°C for 15 min to further cure the photoresist in order for it to survive high temperature exposure during the folding, and anneal the cracks on the surface of the


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photoresist (Figure S5c in Supporting Information). SPR 220-7.0 positive photoresist (MEGAPOSIT) was spin coated on the sample at 1000 rpm twice, to yield a thickness of ~21 µm for the hinges. The sample was left undisturbed for 3min to even out the photoresist on top of the sample, followed by three baking steps at 60 °C for 30 sec, 115 °C for 90 sec and 60 °C for 30 sec. SPR 220 was left undisturbed for 3 hr and then UV-exposed in a mask aligner for 120 sec and developed in AZ developer for 120 s (Figure S5d in Supporting Information). The 2D structure was thus defined with six SU-8 panels, Au patterns on the face of each panel and SPR 220 hinges between and around panels. The sample was then dipped in APS Copper etchant 100 (Transene) to etch the Cu sacrificial layer and release the 2D nets from the substrate (Figure S5e in Supporting Information). The 2D structure was then transferred from Cu etchant to DI water using droppers. For self-assembly, water with 2D structures was placed on a hot plate and the temperature was gradually increased from 100°C to 250°C until the water boiled. The SPR 220 hinges reflowed under high temperature and generated a surface tension force between the panels to fold the structure. Upon cooling, SPR 220 hinges resolidified and secured the 3D cubic structure (Figure S5f-h in Supporting Information). Using the self-assembly technique, cubic sensors of length, 500 µm were fabricated to have the size close to the aperture in order to minimize the noise during THz-TDS measurements.

■ ASSOCIATED CONTENT Supporting Information Available: The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.XXXXXXX. Transmission characteristic and simulated current distribution for the 2D array of SRRs, effect of the addition of a 2D gap to the 3D OSRR, detailed fabrication process for the 3D


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OSRR, simulated frequency response of the fabricated structure, relative permittivity corresponding to the increase in glucose concentration in blood, detailed simulation of change in transmission spectrum between 7 mmol/L and 10 mmol/L concentrations, video file for the surface current distribution of the OSRR.

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions K. A. and J. H. C. created the design and performed the analysis and simulation of the 3D structure. K. A., C. L., D. J., and J. H. C fabricated the 3D cube through self-assembly. H. R. P., J. J., and D. S. K. performed the THz TDS measurement of the OSRR. The manuscript was prepared by K. A. and J. H. C. Notes The authors declare no competing financial interest.

■ ACKNOWLEDGEMENTS This research was supported by National Science Foundation under Grant No. CMMI1454293 and a start-up fund at the University of Minnesota, Twin Cities. The authors also acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing computing resources that contributed to the simulation results reported within this paper. A portion of this work was also carried out in the Minnesota Nano Center, which receives partial support from the NSF through the NNCI program.


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For Table of Contents Use Only A three-dimensional octagram split-ring resonator (OSRR) fabricated by origami-based selfassembly is introduced that produces an isotropic, polarization invariant transmission spectrum. The isotropic response with a 25 times higher sensitivity that the 2D anisotropic structures, achieved through 3D coupling in the microscale OSRR can be used for the realization of ultrasensitive devices capable of remotely monitoring even minute changes in targeted substances.

Kriti Agarwal, Chao Liu, Daeha Joung, Hyeong-Ryeol Park, Jeeyoon Jeong, Dai-Sik Kim, and Jeong-Hyun Cho*

Three-Dimensionally Coupled THz Octagrams as Isotropic Metamaterials

ToC figure


Three-Dimensionally Coupled THz Octagrams as Isotropic

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