The inherent limitations of metal-based metamaterials are the key factors limiting the rapid development of the field of flexible terahertz metamaterials. The advantages of carbon nanotube-based materials and devices in terms of weight, cost, and flexibility of free bending, make them of great use for flexible terahertz metamaterials and devices. Here, a flexible terahertz metamaterial sensor, based on a subwavelength periodic array structure of carbon nanotube thin films, is reported. The proposed flexible metamaterial can achieve the surface plasmon resonance to generate local field enhancement phenomenon, resulting in enhanced resonance transmission peaks. We observed that the resonant frequency and amplitude modulation can be continuously adjusted when the device is subjected to a small external strain. In addition, we found that the terahertz transmission spectrum changes significantly when analytes or dielectric layers, with different refractive indices, thicknesses, or carrying pore defects, are added on the surface of the carbon nanotubes film or below the polyimide substrate of the flexible metamaterials sensor in the bent state. Our results show that these materials and designed device strategies will aid in developing new terahertz functional devices, such as strain sensors, biochemical sensors, curved surface defect detectors, and wearable terahertz imagers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metamaterials are carefully constructed materials, usually consisting of various periodically arranged subwavelength structures, that can manipulate electromagnetic waves in unique ways . They can be used for a wide range of applications, including the formation of superlens , invisibility cloaks , strain sensors , pesticide sensors , etc. Thus, they have received a great deal of attention from the researchers in physics, materials science, optics, and chemistry . In addition, the terahertz (THz) applications have been further expanded by the introduction and continuous development of metamaterials, because conventional and natural materials show negligible response to THz radiation. Conversely, THz time-domain spectroscopy can detect the amplitude and phase of the electric field simultaneously, and can measure the electromagnetic response characteristics of metamaterials comprehensively. Therefore, the development of THz technology and that of metamaterials are symbiotically related.
According to available reports, most of the demonstrated THz metamaterials were prepared on rigid substrates (e.g., silicon, sapphire) [7–16]. However, there is a demand for flexible metamaterials that can be wrapped around objects for developing invisibility devices , attached to curved surfaces as strain sensors , covered by curved surfaces as defect detection sensors, or used as flexible analyte sensors. Advances in polymer technology and laser engraving have made it possible to prepare THz metamaterials on thin substrates that are flexible to accommodate large mechanical deformations . There are some studies on flexible THz metamaterials, which are generally prepared from flexible substrate metals [20–25], such as polydimethylsiloxane (PDMS), polypropylene (PP), polyethylene terephthalate (PET), and polyethylene naphthalate (PEN). In addition to the advantages of flexible substrates (e.g., high transparency, light weight, low cost, and portability), non-planar flexible metamaterials have more potential applications than metamaterials made on rigid substrates . Carbon nanotubes (CNTs) are reported to have a maximum tensile strength close to 200 GPa and a Young's modulus in the range of 500 ∼ 600 GPa, which make them the strongest materials that are available today. CNTs are super flexible and can be bent to large angles without fracture [26–28]. Compared with the subwavelength structure of the metals-based metamaterials, which have the limited tunability of optical constants of metals, the flexible CNT thin films can act as potentials candidates for manufacturing THz metamaterials, thereby expanding the application scopes of flexible THz metamaterials [29,30]. Since their discovery in 1991 by Iijima, CNTs have exhibited outstanding electrical and optical properties, which have inspired their unique applications in optoelectronics and THz science and technology [5,31]. However, the research on flexible CNT-based THz metamaterials is still extremely rare.
In this study, we focused on the emerging flexible THz metamaterials that are based on CNT subwavelength structures. We designed and synthesized a flexible THz metamaterial that can support surface plasmon polaritons and can be used as a sensor, with potential applications in strain detection, detection of surface defects, and analyte detection.
2. Structure and design
In this study, to fully evaluate the feasibility of the proposed structure, we set and simulated a model with a form factor of approximately 22 mm × 5 mm, as shown in Fig. 1(a). In the fabricated CNT films of our previous publications, the CNTs are aligned orderly in the films . THz resonant transmission properties of CNT films strongly depend on the polarization direction of THz waves. The excitation of the spoof surface plasmon resonant mode is observed at the CNT metamaterial when the THz polarization is parallel to the carbon nanotube axis. The spoofed surface plasmon mode resonance disappears when the THz polarization is perpendicular to the carbon nanotube axis. The reason for this phenomenon is the unique electronic property due to the quantum confinement of electrons in CNTs. In the radial direction of CNT, the electrons are limited by the thickness of the graphene sheet monolayer, which leads to the electrons only propagate along the carbon nanotube axis. Thus, the spoof surface plasmon wave can be excited during THz electric field polarization parallel to the direction of CNT alignment. A comprehensive and in-depth analysis of the proposed design is performed by using the finite-difference time-domain (FDTD) solver in the CST Microwave Studio software. The perfectly matching layer boundary conditions are applied along the x- and y- directions, while the open add space boundary conditions are set in the z-direction. The transmission spectra as well as the electric field distribution are recorded by different monitors. These metamaterials are composed of polyimide (PI) and CNT films. The periodic pattern on the flexible CNT film is designed as a groove structure with arc at both ends. PI films are flexible polymers with excellent mechanical durability and high transparency at THz frequency, as shown in Fig. 1(a). The substrate is a PI, with a thickness of W1 = 14 µm and a dielectric constant of 3.5, which shows high transparency in the THz range .
In this paper, the material parameters of CNT films were obtained from the experimental results of our group’s previous publications [5,32]. CNT films are regarded as a kind of macroscopic film material, which is fabricated through drawing from vertically aligned carbon nanotube arrays. The effective conductivity of CNTs is of order of 106 S·m−1 in the frequency range of 0.8–1.0 THz . Thus, the top layer of thickness W2 = 10 µm consists of a thin CNTs etched with groove of arc at both ends arrays, which is modeled as a lossy medium with average conductivity, σ = 1.0 × 106 S·m−1. As for the designed geometric parameters, the length and width of the single groove structure are L1 = 27 µm and L2 = 117 µm, respectively, and the radius of the arc at both ends of the groove is 13.3 µm. The period of the unit structure along the x- and y- directions is Px = 166 µm and Py = 178 µm, as shown in Fig. 1(c).
3. Results and discussions
3.1 Carbon nanotube-based THz flexible metamaterials with strain sensing capabilities
In this part, we studied the THz spectral transmission characteristics of a flexible CNT-based metamaterial under different bending conditions. Figure 2 shows the schematic diagrams of the designed flexible structure bent in different directions. When the arc is upward, the film faces outward (FO), and is subjected to tensile stress or strain. We define this bending mode as the FO bending, as shown in Fig. 2(a). In contrast, when the film is facing inward (FI), it is exposed to compressive stress or strain. This mode is defined as the FI bending, which is illustrated in Fig. 2(b).
The bending strain (deflection) is a function of: (i) the initial length, L = 22.0 mm, of the flexible sample fixed between the two ends of the test fixture and (ii) the change in step size (Δl), after compression by external force. In this study, we set the Δl, to change from 0 to 2.2 mm, corresponding to the relative change in length, i.e., Δl/L×100%, and which can reach upto 10%. Δl1 = 0.2 mm and Δl2 = 0.3 mm are the minimum and maximum bending steps, respectively. These are equivalent to 0.9% and 1.4% strain of the initial sample length, respectively. Usually, the bending process is similar to buckling; thus, a uniform curvature may not be obtained. In this study, we assumed that the buckling beam of the film specimen is continuously bent into a sinusoidal shape, driven by a force . The relationship between the radius of curvature (R) of the cantilever beam and the variation in the Δl is expressed by the following equation :
Therefore, we can calculate the actual radius of the center of the bended specimens proposed by us, with increasing compression length, using Eq. (1). The corresponding results are R = 36.73, 25.97, 21.20, 18.36, 16.42, 14.40, 12.98, 11.91, 11.07, 10.39 mm.
Furthermore, to fully understand the characteristics of the designed flexible THz CNT-based metamaterial, we investigated the THz transmission response of the metamaterial during the FO and FI bending, when an extrusion force is applied on the metamaterial. Figure 3(a) and 3(b), depict the resonance peaks of the proposed flexible metamaterial, at two different bending directions, as a function of frequency at different compression lengths. It can be observed that in the horizontal state, which is without strain, i.e., Δl/L×100% = 0%, a resonance window appears in the metamaterial at 1.0072 THz with a transmission amplitude of 0.796. The relationship between the Δl and the magnitudes of the resonance peak and frequency, during the FO bending and FI bending of the designed flexible metamaterial, is plotted in Fig. 3(c) and 3(d), respectively. The small blue ball in the figure indicate the transmission amplitude magnitude, and the small red ball indicate the resonance frequency magnitude. As the compression length changes from 0 to 0.8 mm, step-by-step, the sample Δl/L changes from 0 to 3.6%. The transmitted amplitude for the FO bending increases from 0.796 to 0.863, as shown in Fig. 3(c), and the relative transmission intensity (ΔT/T × 100%) becomes 8.42%. The compression length changes from 0.8 mm to 2.2 mm, which indicates that the sample Δl/L changes from 3.6% to 10% of the transmitted amplitude change, from 0.863 to 0.822. For this case, the relative transmission intensity becomes ΔT/T × 100% = 4.75%. For the aforementioned changes, the resonance frequencies decrease from 1.012 THz to 1.0048 THz and 1.0048 THz to 0.964 THz, respectively, which are equivalent to 0.7% and 4.1% reduction, respectively. In contrast, for a gradual change in the FI bending compression length from 0 to 1.0 mm and from 1.0 mm to 2.2 mm, the transmission amplitude increases from 0.796 to 0.84 and decreases from 0.84 to 0.82, respectively. The corresponding relative transmission intensities change by 5.53% and 2.38%, respectively. In addition, for the resonant frequency shifts downward, from 1.0072 THz to 0.9856 THz and 0.9856 THz to 0.9664 THz, which are equivalent to 2.1% and 1.9% reduction, respectively, as shown in Fig. 3(d). Based on this analysis, we can conclude that the sensitivity of the FO bending to the applied strain is slightly higher than that of the FI bending.
Further, we investigated the variation of the resonance frequency shift and amplitude modulation with relative length in the resonance mode by step-by-step variation of the metamaterial bending degree during FO bending, as shown in Fig. 4. The model that is based on the flexible THz metamaterial strain sensor is illustrated in Fig. 4(a). From Fig. 4(b), it can be seen that the Δf increases approximately linearly as the relative length changes from 0 to 10%. The fitting function is expressed as: Δf = 4.57959 × (Δl/L) - 6.89633. For transmission amplitude modulation, first, we, see an upward trend and then, a downward trend, as shown in Fig. 4(c). As the relative length changes from 0 to 3.6%, the ΔT gradually increases from 0 to 6.9%. Contrarily, as the relative length changes from 3.6% to 10%, the ΔT gradually decreases from 6.9% to 2.7%. Thus, we use a linear fitting function to fit these two parts of the curve separately. When the relative length change is less than 3.6%, the fitting function is expressed by: ΔT = 1.85319 × (Δl/L) - 0.34057. When the relative length change is greater than 3.6%, the corresponding fitting function is expressed as: ΔT = 8.47605 - 0.55805 × (Δl/L). The fitting coefficients that are obtained from the linear fitting results are used to evaluate the sensitivity of the sensor. The linear resonance frequency sensitivity is 4.58 GHz/%. In addition, when the relative change in metamaterials length, after bending, is less than 3.6%, the amplitude modulation sensitivity is 1.85 and it is 0.56, when the change is greater than 3.6%.
The strain (ɛ) at the top of the flexible metamaterial during bending can be expressed as:
We obtained the relationship between the Δf and ΔT as a function of the applied bending strain, as shown in Fig. 4(d) and 4(e). This relationship follows an exponential evolution, which is described by: Δf = 1.612 × exp(ɛ/0.318) - 5.079, ΔT1 = 0.350 × exp(ɛ/0.216) - 0.342, and ΔT2=10.85834 - 7.13876×ɛ. Here, we use an exponential fitting function, denoted by ΔT1, when the relative change in the bending length is less than 3.6% and a linear fitting function, denoted by ΔT2, when the relative change in the bending length is greater than 3.6%.
From the aforementioned analysis, we can conclude that the frequency and intensity of the resonance of the metamaterial is modulated by the variation in the degree of bending. Compared to the previous reported results [4,19,34], in this study, we observed that transmitted amplitudes from both the bending modes exhibit an initial rise followed by a falling trend. For FO bending, as the bending degree changes, the transmission amplitude first rises to a maximum value of 0.863, followed by a decline to a value of 0.822, with the inflection point occurring at 1.0048 THz and a corresponding transmission amplitude of 0.863. The sensitivity of the strain sensor is compared with the previous reports in Table 1. Compared with the previously proposed metal-based flexible THz metamaterial devices [34,35], our proposed devices have acceptable sensitivity as refractive index sensor. In addition, it has the advantages of simple structure, low cost, easy preparation.
3.2 Application of carbon nanotube-based flexible THz metamaterial as a trace liquid analyte sensor
The resonance characteristics of an analyte change when it is covered with a metamaterial; this principle is used to detect the analyte . To extend the applications of the proposed device in the field of biosensors, the proposed design is investigated as a refractive index sensor in this study. For this configuration, the sample Δl/L × 100% change of the flexible device is 4.5%. To investigate the feasibility of detecting analytes by using the proposed flexible devices, our study is divided into two parts, as shown in Fig. 5(a) and 5(b). In the first part, we filled the groove structure of the flexible film with only the analyte, as shown in Fig. 5(a). In the second part, the surface of the flexible CNT film is covered with a fixed amount of analyte, when the groove structure of the flexible film is filled, as shown in Fig. 5(b). t1 = t2 = 10 µm represent the thicknesses of the analyte added to the etched groove structure on the film (first part) and covering the film surface (second part), respectively. The transmittance is calculated as a function of the resonance frequency for the different analyte refractive indices (n). Here, we consider the analyte layer as a lossless analyte with different refractive indices, given by n = 1.33, 1.38, 1.43, 1.48, 1.53, and 1.58.
The simulation results are shown in Fig. 5(c) and 5(d). It is clearly observed that the resonant frequency undergoes a significant redshift as the refractive index of the analyte layer increases from 1.33 (water) to 1.58, in intervals of 0.05. The inset in Fig. 5(c) shows that as the n of the analyte changes from 1.33 to 1.58, the resonant frequency of the sensor decreases by 41 GHz, from 0.947 THz to 0.906 THz, and the amplitude decreases from 0.813 to 0.786. Notably, after the flexible film surface is covered with a t2 = 10 µm thick analyte layer, the resonant frequency and transmission amplitude of the sensor decrease from 0.911 THz to 0.851 THz and 0.804 to 0.765, respectively, with changes in the refractive index of the analyte. It can be seen that the resonance frequency and transmission amplitude shifts increase linearly with the increasing refractive index of the analyte. To show the linear performance of the sensor at a particular refractive index, the simulated data is fitted with a linear function, as shown in Fig. 5(e) and 5(f). For the filled groove structure of the flexible film case, the fitting functions are expressed as: Δf = 167.314×Δn - 223.442 (GHz) with an R2 value of 0.9967, and ΔT = 11.24467×Δn - 14.71058 (%) with an R2 value of 0.9547. For the analyte covered film surface, the fitting function is expressed as: Δf = 229.714×Δn - 303.234 (GHz) with an R2 value of 0.0.9891 and ΔT = 15.916×Δn - 21.179 (%) with an R2 value of 0.99897. The average sensitivity of the proposed THz metamaterial sensor is 167.314 GHz/RIU and 11.24467%/RIU for the filled groove structure of the flexible film case and 229.714 GHz/RIU and 15.916%/RIU the analyte covered film surface case, in the range of n = 1.33∼1.58. The sensitivity of the liquid analyte sensor is compared with the previous reports in Table 1. The THz metamaterial device based on flexible CNT films proposed in our work can also be used as a liquid analyte sensor. The refractive index sensitivity is 229.7GHz/RIU. Therefore, compared with the previously proposed metal-based flexible THz metamaterial devices [36,37], our proposed devices have acceptable sensitivity as refractive index sensor. In addition, it has the advantages of simple structure, low cost, and easy preparation.
The effect of analyte thickness on the sensitivity of the sensor is also studied for a fixed refractive index via simulations. In this case, the flexible sensor is coated with an analyte layer having a refractive index of 1.35. Since the surface of the metamaterial is etched with a periodically arranged array of groove with circular arcs at both ends, the added analyte should first enter the groove structure and eventually form a stack on the film surface as the thickness of the injected analyte layer is increased step-by-step, as shown in Fig. 6(a). Figure 6(b) shows the frequency-dependent transmission of the reported flexible metamaterial sensor at different analyte thicknesses (n = 1.35 is constant), with the thickness gradient set to 4 µm. As indicated in the inset in Fig. 6(b), the resonant frequency decreases from 0.988 THz to 0.9112 THz and the transmission amplitude decreases from 0.855 to 0.799, as the analyte layer thickness increases from 0 to 18 µm. Figure 6(c) shows the resonant frequency and transmission amplitude shifts as functions of the analyte layer thickness. Here, we define the sensitivity (S) as the change in resonance frequency divided by the change in the analyte layer thickness, i.e., S = Δf /Δt. Further, the expected value of sensitivity is determined by linear fitting, as shown in Fig. 6(c). The fitting functions are expressed as: Δf = 4.45714 × Δt - 2.74286 (GHz) with an R2 value of 0.9947. The above results show that the sensitivity of the metamaterial sensor is 4.45714 GHz/µm when the thickness is increased from 0 to 18 µm. Figure 6(d) shows the variation of the resonance peaks with frequency at different analyte layer thicknesses; these curves are divided into three groups according to the refractive indices of the different analytes. Here, we fix the analyte refractive index at 1.33, 1.4, and 1.6, respectively, and vary the thickness from 0 to 20 µm, at an interval of 10 µm. These results show that an analyte, with a higher refractive index, produces more pronounced shifts in the resonant frequency as the analyte thickness is varied.
3.3 Carbon nanotube-based flexible THz metamaterial for ultrathin dielectric thickness sensing
The transmission spectral characteristics of the flexible device with the addition of different thicknesses of dielectric layers at the bottom were analyzed, as shown in Fig. 7(a). The feasibility of using the flexible CNT-based metamaterial sensors in thickness measurement of thin samples is also evaluated. As described in the previous section, the flexible device is in a bent state and the sample Δl/L change is 4.5%. In this study, the permittivity of the dielectric layer material is 2.9.
It can be clearly seen from Fig. 7(a) that the resonant frequency of the flexible metamaterial sensor undergoes redshift with increasing dielectric thickness. In general, an increase in the thickness of the dielectric layer leads to a greater absorption loss, which weakens the resonance; therefore, the intensity of the resonance decreases with the increasing thickness. In Fig. 7(b), the relationship between the frequency shift and the different thicknesses of the dielectric layer is shown. We define the frequency shift as: Δf = ft - ft=0, where ft is the resonance frequency when the thickness of the dielectric layer is t, and ft=0 is the resonance frequency when no dielectric layer is added. Notably, the resonance frequency no longer shifts when the thickness increases to around 31 µm, indicating that the increase in thickness no longer affects the resonant frequency. We fitted the simulated data with an exponential function, expressed as: Δf = 141.58×exp(–t/11.16) + 110.53, wherein the total frequency shift saturates at 894 GHz. evaluate the feasibility of using the flexible sensor in measuring ultrathin dielectric thicknesses, we analyzed the frequency-dependence of the device sensitivity on the thickness of the dielectric layer via linear fitting. Here, we consider only the case wherein the dielectric layer thickness is less than 10 µm, as shown in Fig. 7(c). The fitting functions are expressed as: Δf = 5.3673×t - 0.8727 (GHz) with an R2 value of 0.9968, and the resulting largest sensitivity is 5.3673 GHz/µm. Similarly, the frequency sensitivity when the thickness of the dielectric layer reaches detection saturation is also indicated in the inset of Fig. 7(c). It implies that when the thickness of the analyte layer is increased to 31 µm, it no longer affects the resonance and the device sensitivity is reduced to almost zero.
To understand the physical characteristics of the resonant frequency of the proposed thickness sensor at different analyte thicknesses (e.g., 0 µm, 4 µm, 8 µm, 12 µm, 31 µm), the analyte refractive index is fixed at 1.6. We examined the electric field distribution of the proposed sensor, which is calculated by the FDTD method, as shown in Fig. 8. The electric field distribution in the x-y plane of the flexible metamaterial is shown in Fig. 8(a). It is clear that a strong electromagnetic resonance is generated in the gap. The distribution of different thicknesses of the dielectric layers in the x-z plane is shown in Fig. 8(b) and 8(f). When no dielectric layer is added below the substrate, i.e., t = 0, the enhanced electromagnetic intensity becomes concentrated at the interface between the substrate and air, and the resulting enhanced resonant field distribution, along the z-direction, can be seen in Fig. 8(b). Therefore, the resonance of the device gets affected by the addition of the dielectric layer under the substrate, resulting in a change in resonant frequency with changing film thickness. As previously described, this resonance field distribution decays exponentially, rather than linearly, along the z-direction. When the thickness of the dielectric layer reaches 31 µm, the resonant electric field becomes confined primarily in the analyte layer, as shown in Fig. 8(f). Further variations in the dielectric layer thickness produce no effect on the resonant frequency, which is consistent with the results shown in Fig. 7(b).
3.4 Carbon nanotube-based flexible THz metamaterial for dielectric defect detection
In this section, we discuss the application of the proposed flexible CNT metamaterial in detecting defects in open-hole dielectrics via spectral sensing. As shown in the schematic diagram in Fig. 9 (a), the CNT film, PI substrate, and dielectric layer with hole defects form a sandwich structure, where the bottom layer has a dielectric constant of 3.5 and thickness of 20 µm. The proposed flexible metamaterial is in the bending state and the sample Δl/L variation is 4.5%.
The simulation results are displayed in Fig. 9(b)–9(e). First, we consider the effect of different sizes of the dielectric layer defect holes on the transmission spectrum of the flexible metamaterial. Here, the defect holes are assumed to be square-shaped with length l, as shown in Fig. 9(a). When l is varied from 0 (no hole) to 100 µm, in intervals of 20 µm, the frequency change is nearly absent, whereas the transmission amplitude drops significantly. Notably, the positions of the defect holes in the dielectric layer are randomly distributed, and their number is 10, which better fits the actual situation. Figure 9(b) shows the sensitivity of the designed metamaterial as a function of the variations in the defect sizes of the analyte layer for a fixed defect location. It can be seen that the relative ΔT increases from 0% to 6% with the period of the defective hole in the analyzed layer, whose thickness varies from 0 µm to 100 µm. The sensitivity of the device is evaluated with a linear fitting function, as indicated by the red line in Fig. 9(c). The fitting function is expressed as: ΔT = 61.45594×l - 0.47106 with an R2 value of 0.98505. From this linear fit, we obtain a sensitivity of 61.46%/mm. Figure 9(d) shows the transmission through the metamaterial sensor as a function of the frequency, with changes the location of the defects in the analyzed layer. The defects are assumed to be arranged vertically, inclined, horizontally, and randomly on the analyzed layer. In this case, we have also set the number of defects to 10. As shown in the inset of Fig. 9(d), the locations of the defects were changed to a vertical distribution along the direction of the magnetic field (H) of the coordinate y-axis, an tilted distribution along the direction of 45 degree with the x-axis, horizontal distribution along the direction of the electric field (E) of the coordinate x-axis, and finally a random arrangement. From Fig. 9 (d), it can be seen that the random distribution exhibits the maximum variation range. The results show that the amplitude shows a clear trend of reduction. Among the arrangements, the random distribution exhibits the maximum variation. Finally, we also studied the effect of the variation of number of defect holes in the analyzed layer on the transmission spectrum of the metamaterial sensor. Here, the defective holes are arranged horizontally, with a period of l = 80 µm. The corresponding simulation results are shown in Fig. 9(e). In the inset of Fig. 9(e), we can visualize that there is a significant decrease in the transmission amplitude of the metamaterial sensor as the number of defective holes in the dielectric layer gradually increases from 0 (no defects) to 10.
To explain the underlying resonance mechanism, we simulated the electric field distribution at the resonant frequency, f0, after adding the dielectric analyte to the substrate of the flexible metamaterial, as shown in Fig. 10(a)–10(f). The electric field distributions at the resonant phases 0° and 130° in the absence of defective medium are shown in Fig. 10(a) and 10(b), respectively. We observe that the presence of 4 and 6 defective holes in the analyzed dielectric layer trigger a resonant phase difference in the metamaterial device, as shown in Fig. 10(c) and 10(e). There are two defective holes in the defective medium. The electric field at the resonant frequency is most densely concentrated at the defective holes when the phase is zero, whereas the distribution is nearly zero when the phase is 130°, as indicated in Fig. 10(c) and 10(d), respectively. The same phenomenon is observed when there are 6 defective holes in the analyzed defective layer, as shown in Fig. 10(e) and 10(f), and they are different from the situation when there are no defects in the analyzed layer in Fig. 10(a) and (b). Therefore, at the resonance frequency, a larger number of defective holes cause a phase difference in a larger region. This may explain the increase in the number of defective holes in the dielectric layer, with minor defects, leading to a decrease in the resonance amplitude of the flexible CNT metamaterials.
In summary, we propose and theoretically demonstrate an optically transparent and flexible material operating at THz frequency, which consists of a flexible CNT film etched with a groove structure with circular arcs at both ends, on a PI substrate. By numerical analysis, we conclude that the plasma mode of the flexible CNT, on the proposed metasurface, has many potential applications in sensing, specifically, such as strain sensing under bending conditions; analyte sensing with different refractive indices, thicknesses, and addition of analyte to the metamaterial surface; thickness sensing with different thicknesses of analyte layers deposited under the flexible substrate; and defect detection with pore defects in the analyzed layers. The sensitivity of strain sensing is 4.58 GHz/%. A resonant frequency shift of about 4.3% can be obtained when the strain is ɛ = 1.08×10−3. In addition, as an analyte thickness sensor, the device has a maximum frequency sensitivity of 5.3673 GHz/µm with a correlation coefficient of 0.9968. It is confirmed that these materials and devices can be used to develop new and advanced THz functional devices.
National Natural Science Foundation of China (61975163, 11704310); Natural Science Foundation of Shaanxi Province (2020JZ-48); Open Project of Key Laboratory of Engineering Dielectrics and Its Applications, Ministry of Education (KEY1805); Youth Innovation Team of Shaanxi Universities.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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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