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Abstract
In this study, we propose a terahertz stretchable metamaterial that can measure uniaxial strain. Gold dolmen resonators formed on a sheet of polydimethylsiloxane (PDMS) is deformed by strain, and its resonance peak exhibits the gradual decrease in reflectance without a frequency shift, which is suitable for imaging applications at a single frequency. The metamaterial was designed by mechanical and electromagnetic simulations and fabricated by microfabrication including a transfer process of gold structures from a glass substrate to a PDMS sheet. By measuring the reflectance and observing the deformation under different strains, the reflectance decrease was obtained at 0.292 THz despite the appearance of wrinkles on gold structures. Linear response and repeatability up to 20% strain were also confirmed. Furthermore, the strain measurement through a sheet of paper was demonstrated, suggesting that our method can be applied even in situations where opaque obstacles in the visible region exist.
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1. Introduction
Stretchable strain sensors play a crucial role in a wide range of fields such as robotics, biomechanics, and biomedical engineering [1–3]. Stretchability that follows the movement of soft robots and the human body far exceeds the scope of conventional strain gauges; for example, to follow the deformation of human skin, it must withstand up to 30% strain [4]. In recent years, with the development of flexible electronics, various strain sensors with high stretchability have been proposed [5]. These sensors use soft conductive materials such as conductive polymers and liquid metals, or have structures designed to exhibit high deformability even in hard materials. However, it is currently difficult to avoid complex wiring for signal acquisition and power supply and device failure due to partial wiring breaks.
While electrical sensors generally have the difficulties of wiring, optical sensors such as imaging sensors can obtain information via light without electrical contacts. For example, a camera can capture the deformation of an object and also measure strain by digital image correlation [6]. Although this method are simple, the strain resolution depends on the spatial resolution of the camera image. Therefore, measurement methods based on optical responses such as changes in reflectance and transmittance, absorption and emission in response to strain are often used [7]. For example, sensors that change color in response to strain have been proposed based on structural coloration [8–16], plasmonics [17–23], and mechanochromism [24–28].These methods using light with high spatial resolution and sensitivity is useful. However, the light is often blocked by obstacles. For example, even if a sensor that changes color according to strain is attached to human skin, it will not be visible when they are wearing clothes. In the visible range, many objects are opaque due to absorption or scattering. Therefore, sensors that use other electromagnetic wave bands are required when the object to be measured is hidden behind obstacles.
In recent years, terahertz waves in the frequency band of 0.1 to 10 THz have attracted attention in terms of their transparency through materials [29]. Terahertz waves are transparent to many dielectric materials except metals and can also be used for imaging applications because they have straight propagation properties similar to light. Although X-rays can also penetrate many materials, including metals, they can cause damage to the human body [30]. On the other hand, there is no such fear with terahertz waves due to their low photon energy. The use of terahertz waves has the potential to open up strain measurement in situations that are impossible with light, and several terahertz strain sensors, particularly those based on metamaterials, have been reported so far [31–33]. Metamaterials are artificial optical materials containing resonators that interact with electromagnetic waves and can be designed with optical properties that do not exist in nature [34–36]. Among them, deformable metamaterials can be used as tunable filters and mechanical sensors [37–49]. Terahertz strain sensors are also one type of deformable metamaterials. Li et al. proposed a sensor that measures biaxial strains from the shift of the resonant frequency caused by gap changes between adjacent gold resonators formed on a stretchable sheet [31]. Biaxial strains were distinguished by the direction of polarization. Khatib et al. also used a similar deformable metamaterial and calculated uniaxial strain from the transmission intensities obtained with two orthogonal polarizations at multiple frequencies [32]. Everitt et al. reported another calculation method based on cross-polarization measurement with an aluminum bowtie-shaped metamaterial [33]. However, these methods require measurements at multiple wavelengths and polarizations to determine strain and are not suitable for real-time measurements. In imaging applications using a camera that cannot capture spectral shifts, it is desirable to obtain intensity contrasts against strain at a single frequency. Therefore, metamaterials that exhibit such properties are required. Furthermore, although the ability to measure biaxial strains with a single metamaterial is attractive, an unusual camera and light source are required to distinguish between two orthogonal polarizations. In the case of obtaining biaxial strains from camera images, it is only necessary to distinguish the positions of uniaxial sensors and arrange two orthogonally.
In this study, we propose a terahertz stretchable metamaterial that can measure uniaxial strain from the reflection intensity at a single frequency and polarization. As a structure that exhibits intensity changes at a single frequency, we employed a dolmen resonator that also exhibits electromagnetically induced transparency [50–54]. Deformable dolmen resonators are known to exhibit tunable transmittance and reflectance [37,45]. To realize a strain sensor that exhibits the desired characteristics, the dimensions of the dolmen resonator were tuned through mechanical and electromagnetic simulations. Then, reflective strain measurements were demonstrated using the actually fabricated metamaterials.
2. Design and simulation
2.1 Design of unit cells
The proposed metamaterial is a periodic structure and can be defined by its unit cell that is the unit structure of periodic structure. Figure 1 shows the dimensional parameters that define the unit cell. Three gold bars B1, B2, and B3 were placed on a sheet of polydimethylsiloxane (PDMS), a type of silicone rubber. B2 and B3 were perpendicular to B1, forming a dolmen resonator structure. The longitudinal direction of B1 was defined as the y-axis, and those of B2 and B3 were defined as the x-axis. The length and width of B1 were l1 and w1, and those of B2 and B3 were l2 and w2, respectively. The distance between B1 and B2, or B1 and B3, was d1, and that between B2 and B3 was d2. The unit cell was square in its initial state but changed to a rectangle when stretched. The length of the unit cell in the x-axis, which was the stretching direction, was px, and the length in the orthogonal y-axis was py. Assuming that the dimensional changes of the gold bars after stretching were negligible, when px increased by Δpx by stretching, the dimensions including the PDMS, py, d1, and d2, deformed by Δpy, Δd1, and Δd2, respectively. The strain for each dimension was defined as Δpx/px, Δpy/py, Δd1/d1, and Δd2/d2.
2.2 Mechanical simulation
To determine the dimensional change due to stretching, the relationships of the changes in Δpy/py, Δd1/d1, and Δd2/d2 with respect to the change in Δpx/px were investigated. We performed mechanical simulations based on finite element analysis (COMSOL Multiphysics, COMSOL, Inc.). Figure 2 shows the deformation and von Mises stress when a 10% strain was applied in the x-axis direction, as one of the typical simulation results. In the simulations, the stresses σx and σy acting on the x-axis and y-axis sides of the unit cell were evaluated while changing the values of Δpx and Δpy. In the case of x-axis stretching, combinations of Δpx and Δpy were found such that σy was zero. The dimensions were given as px = py = 550 µm, l1 = 380 µm, w1 = 100 µm, l2 = 320 µm, w2 = 80 µm, d1 = 40 µm, and d2 = 120 µm. The Young’s modulus and Poisson’s ratio of gold were 70 GPa and 0.44, and those of PDMS were 750 kPa and 0.49, respectively. The thicknesses of gold and PDMS were 200 nm and 80 µm, respectively.
From the simulation results, we first confirmed that the dimensional changes of the gold bars were less than 1/100 of those of PDMS and could be ignored. Then, the rates of changes in Δpy/py, Δd1/d1, and Δd2/d2 with respect to the change in Δpx/px were calculated, and the following relational expressions were obtained.
The result that the signs of the coefficients in Eqs. (1) and (3) were negative and the sign of Eq. (2) was positive is consistent with the fact that PDMS shrinks in the y-axis direction due to the Poisson effect when stretched in the x-axis direction. Regarding von Mises stress, it was largest near the center of gold bars B2 and B3 as shown in Fig. 1(b). Considering the tensile strength of the 200 nm gold thin film to be 390 MPa [55], the simulation results estimated that the Δpx/px when the gold bars break was 31%. However, it should be noted that these simulations did not consider nonlinearities such as incompressibility of PDMS and buckling of gold bars, so the results for large strains may not be necessarily accurate.
2.3 Electromagnetic simulation
Next, we performed electromagnetic field simulations based on rigorous coupled-wave analysis (DiffractMOD, Synopsys, Inc.) to determine the changes in reflectance of the metamaterial due to stretching. The values of the dimensions that make up the unit cell were the same as in the mechanical simulation, and the rates of changes were given by Eqs. (1) to (3). The refractive index of PDMS was set to 1.6. The incident polarization was in the y-axis direction in Fig. 1(a). The side where the gold bars were formed receives the incident wave while the opposite side was in contact with an infinitely thick PDMS. Figure 3(a) shows the reflectance spectra calculated while changing the applied strain, that is, Δpx/px. The spectrum has two peaks, P1 and P2, on the low frequency side and high frequency side. When the strain was 0%, P1 was confirmed at 0.275 THz and P2 at 0.306 THz. Note that if the metamaterial is attached to another material other than PDMS, the peak frequency will shift slightly due to the deference in refractive index. As the strain was increased, the P1 peak gradually shifted to lower frequencies. On the other hand, the P2 peak continued to appear at the same frequency, and its reflectance gradually decreased. Additionally, the P2 peak was lost when the strain was higher than 15%. These characteristics of P2 are considered to be suitable for the purpose of observing strain at a single frequency.
Fig. 3. (a) Calculated reflectance spectra under different strains. (b), (c) Calculated z-axis component of the electric field Ez at 0% and 20% strain, respectively.
To clarify the physical background of this reflectance changes at a single frequency, the electromagnetic field distribution was calculated at 0.306 THz. Figures 3(b) and 3(c) show the z-axis component of the electric field Ez at 0% and 20% strain, respectively. When the strain was 0%, electric field enhancement was observed at both longitudinal edges of gold bar B1. On the other hand, when the strain was 20%, electric field enhancement occurred in B2 and B3. In dolmen resonators, this resonant mode is the same as the quadrupole seen in electromagnetically induced transparency [45]. Therefore, the reflectance change at the P2 peak can also be considered as a kind of electromagnetically induced transparency, with the reflective bright mode resonance appearing at 0% strain and the transmissive, that is, non-reflective dark mode resonance appearing at 20% strain.
3. Fabrication
3.1 Fabrication processes
We fabricated the designed metamaterial using microfabrication. Figure 4 shows the fabrication processes. A 20 mm × 20 mm × 0.5 mm glass substrate was used as the initial substrate. First, nickel and gold films of 200 nm each were deposited by sputtering. The nickel layer is an adhesion layer for the gold layer and also serves as a sacrificial layer in the subsequent separation process from the glass substrate. Second, a photoresist (OFPR-800 LB 200cp, Tokyo Ohka Kogyo Co., Ltd.) was spin-coated and baked on a hot plate. The rotation speed and time of spin coating were 3000 rpm and 20 s, respectively. The bake temperature and time were 110 °C and 10 min, respectively. Then, the photoresist was exposed at a dose of 200 mJ/cm2, developed with 2.38% tetramethylammonium hydroxide (TMAH), and rinsed with pure water. Third, the gold layer was etched using a gold etchant (AURUM-302, Kanto Chemical Co., Inc.) using the photoresist pattern as a mask. Afterwards, the resist pattern was removed with acetone and isopropyl alcohol (IPA). Fourth, the entire sample was immersed in (3-mercaptopropyl)trimethoxysilane (MPTMS) solution for 20 minutes and rinsed with ethanol. MPTMS treatment increases the adhesion between gold and PDMS and prevents the gold pattern from peeling off from the PDMS sheet due to mechanical stresses while stretching [56]. The MPTMS solution was obtained by adding 46 µl of MPTMS to 10 ml of ethanol. Fifth, liquid PDMS (KE-106, Shin-Etsu Chemical Co., Ltd.) was spin-coated onto the nickel layer with the gold pattern and cured in an oven. The PDMS base agent and curing agent were mixed at a ratio of 10:1. The rotation speed and time of spin coating were 1000 rpm and 30 s, respectively. The curing temperature and time in the oven were 100 °C and 2 h, respectively. The resulting PDMS film thickness was 80 µm. Finally, the entire sample was immersed in a 35% hydrochloric acid to etch the nickel layer and separate the glass substrate from the PDMS to which the gold pattern was transferred [57]. It is worth mentioning that three sides of the PDMS were cut with a knife so that the nickel layer was exposed to the hydrochloric acid, allowing the PDMS naturally peeled off from the substrate.
3.2 Fabrication results
To observe the deformation of the fabricated sample, it was fixed with tape on a frame that could move in one direction. Then, strain was applied by moving the frame. Note that only tensile strain can be applied; compressive strain cannot be applied because the entire PDMS sheet will bend. Figures 5(a) and 5(b) show the samples at 0% and 14.7% strain, respectively. The number of unit cells was 22 × 22, resulting in a metamaterial formed in a 12.1 mm square in the initial state. Figures 5(c) and 5(d) show microscopic images of a unit cell at 0% and 14.7% strain, respectively. In addition, Table 1 summarizes the designed and measured dimensions of the unit cell. The sample was successfully fabricated with fabrication errors of 3 µm or less in the initial state. From the results at 14.7% strain, the change rates in Δpy/py, Δd1/d1, and Δd2/d2 with respect to Δpx/px were obtained to be −0.37, 5.76, and −0.61, respectively. Compared with the coefficients in Eqs. (1) to (3), the measured values also have the same signs. However, there was a large difference in Δd2/d2, which was more than twice the value in Eq. (3). One reason for this is that buckling occurred in the gold bar B1 as seen in Fig. 5(d), and the stress distribution changed. As a result, while l1, the longitudinal length of B1, was assumed to remain unchanged in the simulation, it actually became shorter due to the formation of a wrinkled structure.
Fig. 5. (a), (b) Photographs of the fabricated metamaterial at 0% and 14.7% strain, respectively. (c), (d) Microscopic images of a unit cell at 0% and 14.7% strain, respectively.
Table 1. Designed and measured dimensions of a unit cell
To investigate the details of the wrinkle structure, as seen on gold bar B1 in Fig. 5(d), the surface profile was measured using a laser confocal microscope. Figure 6 show the microscopic image of wrinkle and its surface profile. A total of 11 peaks were observed, including a small peak at −57 µm position. The average depth and interpeak distance were 2.7 µm and 19.8 µm, respectively. It is worth mentioning that although there were some differences in shape, a similar wrinkle structure was observed in all gold bars, which may affect the optical properties of the metamaterial as a whole.
4. Results and discussion
4.1 Reflectance measurement
The reflectance of the fabricated metamaterial was measured using a terahertz wave emitting and receiving device (TeraScan 1550, TOPTICA Photonics AG). Figure 7(a) shows the experimental setup. The emitter and receiver were attached to a reflective optical system with an internal structure as shown in Fig. 7(b), where off-axis parabolic mirrors (OAPMs) were placed so that the metamaterial to be measured was located at their focal points. The metamaterial was fixed on a movable frame and can be stretched by moving the handle. A gold mirror was used as a reference for reflectance calculations.
Fig. 7. (a) Photograph of the reflectance measurement setup. (b) Schematic diagram of the reflective optical system.
Figure 8(a) shows the reflectance spectra measured under different strains. The frequency step was 5.7 GHz. A peak corresponding to P2 in Fig. 3(a) was confirmed at 0.292 THz. Similar to the simulation, as the strain was increased, the reflectance tended to decrease. On the other hand, although the P1 peak was initially observed at 0.269 THz, the obvious shift with strain seen in the simulation was not observed in the experiment. We believe that the difference between the simulated and actual spectra is mainly due to an unexpected change in the shape of the metamaterial, that is, the wrinkles on gold bars.
Fig. 8. (a) Measured reflectance spectra under different strains. (b) Reflectance at 0.292 THz for various strains repeatedly applied.
Figure 8(b) shows the measurement results of the reflectance at a single frequency of 0.292 THz for various strains repeatedly applied. The reflectance showed a decreasing trend up to approximately 30% strain, and after that it remained at the same value. A coefficient of determination of 0.82 was obtained using linear regression in the strain range from 0% to 20%. On the fitting line, the reflectance at 0% strain is 66.6%, showing a decrease of 1.78 for every 1% strain. By using this relationship, it is possible to estimate strain Δpx/px from reflectance R as shown below.
Surprisingly, this sample was able to be repeatedly measured at strains up to 44.7%, which exceeds the 31% breaking strain of the gold bars predicted by simulation. Reasons for this may include differences in actual dimensions and nonlinearities which were not taken into account in the simulation.
Figure 9 shows the reflectance spectra measured after repeated application of 20% strain and return to 0% strain. Measurements were taken after every 5 stretches. Even after 30 stretches, the spectrum maintains almost the same shape, indicating repeatability at strains up to 20%.
4.2 Demonstration of strain measurement
Next, we measured the temporal change in reflection intensity of the fabricated metamaterial and demonstrated strain measurement. The advantage of using terahertz waves is expected to be the ability to measure strain through opaque materials in the visible range. Therefore, we placed a sheet of paper with a density of 72 g/m2 (Clean Paper Blue, AS ONE Corporation) between the reflective optical system and the metamaterial and attempted to measure strain in a state that the metamaterial was hidden behind the paper. Figure 10(a) shows the experimental setup with paper in place. In the measurement, the handle of movable frame was moved repeatedly so that the strain was approximately 0%, 10% and 20%. The paper was not placed during the first strain, but was placed before the second strain and removed after the third strain. The thickness of the paper measured with a micrometer was approximately 90 µm.
Fig. 10. (a) Photograph of the experimental setup for strain measurements through paper. (b) Temporal changes in strain estimated from the reflectance of metamaterial.
Figure 10(b) shows the temporal change in strain estimated from the reflectance according to Eq. (4). The estimated value was around 0% for 7 s before applying the first strain. Strains of 10% and 20% were applied sequentially, and the estimated values changed accordingly. However, there was an error between the estimated and applied values. In this experiment, the strain was applied by moving the handle while checking with a ruler, so it may had been different from the true strain. When the strain was returned to 0% at 30 s, the estimated value also returned to zero. When paper was placed at 48 s, the estimated value increased despite no strain being applied. It is assumed that the absorption and reflection loss by the paper reduced the received intensity and caused the estimation error. Nevertheless, the estimation results generally followed the subsequent 10% and 20% strains, and finally returned to 0% after the paper was removed at 132 s, which is consistent with the repeatability confirmed in Fig. 9.
4.3 Discussion
From the above results, a metamaterial that can measure uniaxial strain from the reflected intensity at a single frequency has been achieved. It also exhibits a linear reflectance change up to at least 20% strain and has a repeatability of returning to its original spectrum even after the strain is removed. Compared to previous terahertz strain sensors, our metamaterial provides a high contrast of reflection intensity versus strain at a single frequency, making it suitable for real-time measurements using imaging sensors. The principle behind this phenomenon is the resonance mode change on the dolmen resonator as shown in Figs. 3(b) and 3(c).
One of the interesting findings of this study was that resonance peaks were still observed even in the presence of wrinkles on gold bars. The fact that surface roughness of a few µm has almost no effect on the reflectance of gold film in terahertz waves, especially in the subterahertz range below 1 THz, suggests that the effect of the wrinkles with the surface profile observed in Fig. 6 could be ignored [58]. However, since there were some differences in the spectral shapes between simulation and measurement, such as the absence of a peak shift in P1, the relationship between wrinkles and the optical response of terahertz stretchable metamaterials needs to be further explored.
One of the limitations of our method is the error between the estimated value and the true value as seen in Fig. 10(b). In particular, it is necessary to distinguish between the decrease in reflectance when the paper is placed and that due to strain. As proposed in previous research [32], a correction can be made from the measurement results in two frequencies with different sensitivities to strain. In our metamaterial, the reflectance for the two peaks, P1 and P2, can be used. Alternatively, in the case of imaging, it may be possible to detect the decrease in brightness of the entire image due to the insertion of obstacles.
Three cases are assumed regarding changes in reflection intensity due to the presence of obstacles. Figure 11 shows a conceptual diagram of each case. First, as shown in Fig. 11(a), if the distance between the obstacle and the metamaterial, d, is sufficiently larger than the coherence length of the incident wave, Δz, multiple reflections between the obstacle and the sample can be ignored. When the incident and reflected waves pass through the obstacle, their intensities decrease by the amount of transmission loss. In this case, the received intensity, I, is the incident intensity, I0, multiplied by the reflectance of metamaterial, R, and the square of transmittance of obstacle, T2; that is, I = RT2I0. Here, it is assumed that the reflectance of the obstacle is negligibly small or that the reflected wave at the obstacle does not reach the receiver due to the arrangement of the optical system. The received intensities corresponding to the two reflection peaks, P1 and P2, are I1 = R1T2I0 and I2 = R2T2I0, respectively, assuming that there is no difference in T at each frequency. Here, R1 and R2 are the reflectance at P1 and P2, respectively. If R1 does not depend on strain while R2 depends on strain, the normalized intensity at P2 by P1, I2/I1 = R2/R1, depends only on R2, which is proportional to strain, regardless of the presence or absence of obstacles. Therefore, the influence of obstacles can be corrected by normalization using two frequencies.
Fig. 11. Conceptual diagrams of three cases with obstacles. (a) Case where the distance between the obstacle and the metamaterial is sufficiently larger than the coherence length of the incident wave. (b) Case where the distance is equivalent to or smaller than the coherence length. (c) Case where the distance is equivalent to or smaller than the decay length of the near field on the gold bars.
Second, as shown in Fig. 11(b), when the distance, d, becomes less than the coherence length, Δz, interference due to multiple reflections between the obstacle and the metamaterial must be considered. In fact, the coherence length of uni-traveling-carrier photodiodes (UTC-PDs), the terahertz emitter used for our experiments, can reach several meters [59]. Therefore, we believe that this is the case for the experiment performed in Fig. 10(a). To further explore this case, we performed additional simulations that included a sheet of paper as an obstacle. The thickness and refractive index of paper was assumed to be 90 µm and 1.5, respectively [60]. Note that although it appears to be oblique incidence in Fig. 11(b), the direction of incidence was perpendicular to the metamaterial and paper. Figure 12(a) shows the reflectance spectra of metamaterial when d changes from 400 µm to 500 µm. Considering that the distance between the metamaterial and the end face of the reflective optical system was approximately 1 mm, this value of d seems to be consistent with the actual experimental value. The frequencies of P1 and P2 almost unchanged compared to the case without paper. However, even when the strain was zero, the reflectance at P2 changed with d while that at P1 almost unchanged. This result suggests that normalization by P1 as in the first case cannot correct the intensity change at P2. Figure 12(b) shows the reflectance changes with strain at the frequency of P2 of 0.306 THz. Although the initial value at zero strain is different, the reflectance decreases with strain at approximately the same rate as in the case without paper. This response is consistent with the fact observed in Fig. 10(b) that even though the initial value changed upon insertion of paper, the estimated strain followed the applied strain.
Fig. 12. (a) Calculated reflectance spectra of metamaterial when the distance between the paper and the metamaterial, d, changes from 400 µm to 500 µm. (b) Reflectance changes with strain at the frequency of the reflection peak P2 of 0.306 THz for each d.
Finally, as shown in Fig. 11(c), when the distance, d, reaches a value equivalent to or smaller than the decay length of the near field on the gold bars, l, the refractive index of the obstacle influences the properties of the metamaterial itself. Figure 13 shows the reflectance spectra when d changed from 0 µm to 50 µm, assuming that the obstacle is paper as in the second case. As d decreased, both P1 and P2 peaks shifted to lower frequencies. In this case, the frequency of P2 depends on the position of the paper. Therefore, it is impossible to estimate strain at the same frequency as when there is no paper.
Fig. 13. Calculated reflectance spectra when the distance between the paper and the metamaterial, d, changed from 0 µm to 50 µm.
From the above considerations, correction by normalization using two wavelengths is possible only when the distance between the obstacle and the metamaterial is sufficiently large compared to the coherence length of the incident wave. When the distance becomes shorter than the coherence length, the initial value of the estimated strain changes, although the change rate of reflectance with strain remains approximately constant. If an obstacle gets close enough to touch the near field of the gold bar, it is difficult to estimate strain at the same wavelength. These points represent current limitations of our method and will need to be addressed in the future.
To realize future strain measurement systems, subterahertz optical systems developed for other applications may be applicable. Since the subterahertz waves has high permeability through clothing, it is expected to be applied to body scanners [61]. In addition, its control technologies have been actively developed for the next-generation mobile communication system [62–64]. Our stretchable metamaterial also functions in the subterahertz range and is expected to be used in a wide range of fields where strain measurement is required.
5. Conclusion
We proposed a terahertz stretchable metamaterial that exhibits a change in reflection intensity at a single frequency in response to uniaxial strain. The deformation due to strain of the unit cell containing dolmen resonators was investigated by mechanical simulations, and the accompanying change in reflectance spectrum was calculated by electromagnetic simulations. A metamaterial with gold resonators on PDMS was fabricated by microfabrication. Then, its deformation due to strain, including wrinkles, was evaluated. The desired peak appeared at 0.292 THz through reflectance measurements. Linear regression confirmed that the reflectance decreased by 1.78% for 1% strain. Furthermore, it was confirmed that the original spectrum could be obtained even after 30 repetitions of 20% strain. To demonstrate strain measurement through opaque materials in the visible range, we performed reflectance measurements through paper and obtained estimated values that follow changes in strain over time.
Funding
Japan Society for the Promotion of Science (JP22K14211).
Acknowledgments
Part of this work was performed in the Micro/Nano-Machining Research and Education Center, Tohoku University.
Disclosures
The authors have no conflicts to disclose.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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