1. Introduction

Metamaterials are artificially designed functional materials of the array of subwavelength structures, which can be designed for different demands such as wireless communication, digital coding, biosensing, and so on [1–9]. Especially, the change of dielectric constant on the metamaterial surface causes the shift of the transmission spectrum of metamaterial, which is possible to use this phenomenon for biosensing. Metamaterial biosensor has advantages such as label-free, no damage, non-contact, and noninvasive in vitro detection [10–13]. Therefore, in recent years, it has attracted enormous research interest with the development of micro/nanofabrication technology. Especially, Metamaterials have obvious resonance dips or peak in the terahertz (THz) spectra when the structure period of metamaterial in micrometers. THz spectra regime (0.1-10THz) refers to a band missing between the electronic band and the near-infrared band. Meanwhile, the fingerprint vibrational frequency of most of the biological molecules such as protein and deoxyribonucleic acid (DNA) and others bio-samples just lay in the THz regime [11,14–17], which indicates that the sensing detection of some biomolecules or biological tissues could be carried out in the terahertz band. In other words, terahertz technology has broad application space or potential in the field of life science. THz technology also has many advantages such as low photon energy under tens of MeV that does not disturb chemical bonding, sensitive interaction to molecular behaviors such as vibration, and torsion, and sufficiently high signal-to-noise ratio with broadband spectra in a single measurement. Compared with the Raman spectroscopy detection of the intermolecular interaction in proton-bound, terahertz wave spectroscopy is considered as one of the most promising methods to detect biomarkers [18]. Combining the advantages of metamaterial and terahertz wave spectroscopy, many studies have shown widespread applications in biosensors [17,19,20]. For example, in 2017, Manoj et al. presented the dimensional features of the terahertz asymmetric split ring resonator with periodic dimension at a micron-scale [21], which was used to detect different analysts with a sensitivity of 41 GHz/RIU. In addition, the researchers also verified that terahertz metamaterials can be used to detect proteins [7,8,22,23], DeoxyriboNucleic Acid (DNA) [24–28], viruses [13,14,29] and other biological samples as well as physical quantities [30–32] such as film thickness [33]. In THz metamaterial biosensor application, researchers pay more attention to sensitivity and less attention to improve the quality (Q) factor and figure of merit (FOM). For the performance of the biosensor, the Q factor represents the sharpness of the resonance dip or peak, which is of great significance for the THz testing system to identify the offset of the resonance dip or peak. The FOM is a more accurate parameter defined as the ratio between the sensitivity and the full-width-half-maximum (FWHM). FOM usually could describe the performance of biosensor because of a noticeable frequency shift besides resonances with narrow FWHM, which could minimize the overlapping between the detection thresholds [34]. Therefore, to explore the performs of the metamaterial biosensor, Q factor, FOM, and sensitivity are the main parameters to be investigated [1–4,35].

To obtain a metamaterial biosensor with high sensitivity, optimizing structural parameters of metamaterials was an important aspect. Therefore, many researchers had put a lot of effort into optimizing the structure to get a narrow resonance dip or peak, high Q factor, and narrow FWHM. For example, Rakesh et al. investigated tunable multi-band electromagnetically induced transparency effect (EIT) of the terahertz metamaterial which comprise of inter the cut-wire (CW) and outer asymmetric double c resonators (DCRs) [36]. The performances (Q factor and FWHM) were explored by the distance between DCRs. Riad et al. developed a THz metamaterial biosensor platform based on a highly flexible substrate [32]. Its maximum sensitivity reached 139 GHz/RIU. Moreover, the metamaterial structure based on the flexible substrate has also been reported to detect the cancer biomarkers in the early stage. Besides the metamaterial with only one resonance dips in THz regime, the metamaterials with multi-resonance dips were developed and applied in a biosensor to detect biomarkers, which have merits such as high Q factor, and high sensitivity because those metamaterial biosensors often have self-calibration function. Multi-resonance dips in different resonance modes often had different sensitivity in transmission spectra in one testing. Another method to improve the performance of metamaterial biosensors was to use the asymmetry of the metamaterial structure. Metamaterial with asymmetric structure often shown sharp transmission spectra based on Fano resonance [19,20,37,38]. Meanwhile, a few researchers would analyze the influence of the representative structural parameters of the metamaterials, such as the gap size of split resonance ring (SRR) [39], the gap between the dual SRRs [40]. However, when the amount of sample (DNA [41], microorganisms [42], dangerous molecule [33] was very small, all parameters of the metamaterial had an impact on the biosensing performance. Usually, the various structures (SRR) of metamaterials were designed and fabricated on rigid substrates such as high resistance silicon or quartz, due to the requirements of the early manufacturing process and device performance stability. However, these rigid substrates have serious shortcomings such as the large dielectric coefficient, which prevents the extensive application of THz metamaterial biosensor. With the improvement of fabrication technology, the flexible substrates metamaterials with a low dielectric constant are gradually replacing the hard substrates. Besides the merits such as low dielectric constant, stable performance, and foldability, flexible substrates also have no harm to biological substances [43], which is compatible with some biological substances. Therefore, THz flexible metamaterial biosensors could improve the detection limit, especially, for trace detection of cancer biomarker, which maybe is an important application direction of flexible metamaterial biosensor in the future. This flexible metamaterials biosensor can be used for not only liquid sample detection and rigid surface detection, but also surface sensing detection of curved objects. Its application prospect is getting bigger. To expand the application scope, multiple parameters of its susceptibility were studied theoretically, such as sensitivity, Q factor, FOM, etc.

To overcome the drawbacks of the hard substrate metamaterial biosensor, here, a metal elliptical split-ring resonator array with subwavelength structures based on flexible thin-film (parylene-c) was presented, which was simple structure and cost-effective. We focused on the structural parameters (ring width, the period ratio of the structure, gap width, and axial ratio) of the elliptical split-ring to improve the performances of flexible THz metamaterial biosensor. The finite-difference time-domain method was used to analyze the transmission spectra.

2. Materials and methods

As shown in Fig. 1(a), a flexible metamaterial biosensor was designed in the THz regime. The structure of the proposed metamaterial biosensor was a sandwich structure composed of a dielectric layer, a metallic layer, and a flexible substrate layer. The variable dielectric layer stands for the sample layer and was 5µm in thicknesses. The middle layer was a metallic layer composed of elliptical split-ring as shown in Fig. 1(b). The elliptical split-ring (as shown in Fig. 1(c)) had major axis size a, short-axis size b, ring width e, gap width g, and thickness of gold film 100 nm. The original geometric parameters of metamaterials were set as a = 20µm, b = 14µm, e = 4µm, g = 2µm, c = 30µm, d = 24µm. The parameter design of the metallic layer mainly based on the characteristics of SRR structure and the conditions for meeting the LC resonance to improved sensitivity [44]. The bottom layer was a flexible substrate (parylene-c thin film) that had the same period of the bottom layer and thickness of less than 20µm. The parylene-c thin film had relative permittivity (${\varepsilon _1}$) of 2.75 and loss tangent ($\tan \delta $) of 0.05. Since the elliptical split-ring structure was susceptible to the polarization direction, the x-direction and y-direction were set to the electric field direction and the magnetic field direction, respectively. And the z-direction was the direction in which the incident light travels. In exploring the performances of metamaterials biosensor, the direction of the electric field is interchangeable with the direction of the magnetic field. Finite Difference Time Domain (FDTD) Solutions was used as a software to explore or predict the performances of the flexible metamaterials biosensor. The full-field electromagnetic wave was set as light sources. The metal material is set from the material library of the FDTD software, and the dispersion relation was considered into its material attribute. The periodic boundary conditions were applied along with the x and y directions while the perfectly matched layer (PML) boundary condition was set in the z-axis direction. The plane wave irradiated the structure with the electric field along the x-axis direction. All the simulation work is carried out in the frequency field. The transmission spectra and the electric field and surface current distributions were recorded through different monitors.

 

Fig. 1. Schematic diagram of the flexible metamaterial structure. (a) Metamaterial biosensor and transmission spectrum testing method; (b) The cross-section of flexible THz metamaterial biosensor; (c) The unit cell of the 2D split elliptic resonance ring.

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At 0-3 THz range, the real part and imaginary part of the metal refractive index change is not too big, which causes the dispersion absorption of Au thin film is very small, comparing with moisture absorption in THz regime. Therefore, dispersion absorption of Au thin film did not be discussed. In fact, the dielectric constant or refractive index of Au material changes slightly with wavelength or frequency, that is to say, in the simulation, its dispersion relation has been taken into account. It is just the final result of the simulation output. Meanwhile, parylene-c thin film is a kind of polymer material, and its dielectric constant is much smaller than that of high-resistivity silicon. The polymer thin film used as a substrate less than 20µm, which can overcome the reflection interference brought by the thick substrate. The transmittance of parylene-c thin film is greater than 98%. Therefore, losses of parylene-c thin films are negligible.

The simulation results have shown that there was a single resonance dip in the THz regime. Since the resonance dip shape of the LC resonance mode could be regulated by the changes of parameters of metamaterial structure, the LC resonance could produce field enhancement at the resonance frequency. With the refractive index of the dielectric layer increasing, the resonance dip had a frequency-shift [45]. Therefore, to explore the performances of flexible THz biosensor changing with the variable dielectric layer (tested sample), the different surface dielectric constants (ε=1, 1.74, 1.796, 1.85, 1.904, and 1.96) was set in FDTD software. Different permittivity (or refractive index) was used in the simulation calculation, which was mainly used to simulate the permittivity (or refractive index) of biological elements in the microenvironment. In general, the refractive index of liquid biological samples is between 1.33 and 1.6 or the dielectric constant is between 1.7689 and 2.56. In the simulation, the changing trend was mainly studied. Therefore, dielectric constant 1.796, 1.85, 1.904 and 1.96 were mainly used. The goal was to explore the change rule and then discuss the sensing performance. As shown in Fig. 2(a), the position of the resonance dip changed with different dielectric constants, which illustrated that the frequency-shift increase with the differences of dielectric constant increasing. The simulated and measured transmission spectra of the flexible elliptical split-ring metamaterial were presented by the black and the red lines, respectively, in Fig. 2(b), where resonance dip frequency difference was less than 4 GHz. Therefore, the results illustrated measured transmission spectra matched well with that of simulation results at ε=1 (Fig. 2(b)), which illustrates that the simulation model was correct. Therefore, these simulation models were used in other cases such as ε=1.796, 1.85, 1.904, and 1.96. The feasibility of using elliptic split-ring resonance metamaterial as a biosensor was verified by simulation and measurement. Fig. 2(c) shown the fabricated prototype of flexible elliptic split-ring resonance metamaterial and Fig. 2(d) shown the microscopic image of the fabricated results (arrays and single metamaterial structures). The simulation results show that the sensitivity, Q-factor, and FOM reached 243 GHz/RIU, 14.2@ε=1, and 3.3, respectively.

 

Fig. 2. The frequency-shift varies with different permittivity. (a) Simulated transmission spectra of the metamaterial surface permittivity versus frequency. (b) Simulated (black line) and measured (red line) transmission spectra of the metamaterial. (c) Fabricated flexible metamaterial on wafer-scale (d) Microscopic image of the fabricated metamaterials (arrays and single metamaterial structures)

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To understand the evolution of the LC resonance in the elliptical split-ring structure, the induced electric field and surface current were explored. The induced electric field profile of the resonance of elliptic split-ring at the resonance frequency (f = 1.014 THz @ ε=1) shown in Fig. 3(a), which illustrated that the place of electric field enhancement was at the gap of the elliptic split-ring. To further explore the change of electron in the metal under resonance state, we explored the distribution of surface current as shown in Fig. 3(b). The surface current formed a loop along the elliptic split-ring, oscillated back and forth, and produced a strong magnetic response. It resonated with the incident magnetic field in the z-axis direction, making the incident energy gradually consumed in the elliptic split-ring. The typical characteristic of LC resonance was that the surface current flowed in one direction along with the metal structure, which illustrated that the excitation mode of metamaterial was LC resonance. The “hot spot” happened at the gap as shown in Fig. 3(a). Therefore, the influence on sensitivity was mainly the changes in the dielectric constant of the tested samples at the gap.

 

Fig. 3. Schematic diagram of surface electric field and surface current at the resonance frequency. (a) Electric field distribution; (b) Surface current distribution.

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To understand comprehensively the resonance frequency-shift of the LC resonance effect, the contours of the resonance frequency shift for the various parameters of permittivity (ε) and ring width (e) presented in Fig. 4. The x-axis represented as the resonance frequency. The y-axis represented as parameters (ε and e). The strength of the signal was indicated through the color bar. The resonance frequency increased with the ring width increasing when ring width ranged from 2µm to 6µm and other geometric parameters remain unchanged (a = 20µm, b = 14µm, g = 2µm, c = 30µm, d = 24µm) as shown in Fig. 4(b). The transmittance at resonance frequency gradually decreased with ring width increasing. However, the resonance frequency decreased with the permittivity increasing as shown in Fig. 4(a), where the transmittance at resonance frequency also gradually decreased with permittivity increasing. Besides permittivity, to develop a flexible metamaterial biosensor with high performances (sensitivity, FOM, and FWHM), the geometric structure parameters of metamaterial biosensor also should be explored detailly.

 

Fig. 4. Contours of simulated transmission spectra for different permittivity and ring widths. The color bar shows the magnitude of transmission intensity. (a) The transmission intensity changes with permittivity at the different resonance frequency; (b) The transmission intensity changes with ring width at the different resonance frequency.

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To analyze the resonant frequency of the metamaterial changes with the surface dielectric constant (tested sample). The electromagnetic dynamics theory was applied. According to the knowledge of two curl equations related E(r) to H(r), the electric field condition could be expressed as [46]

3. Results and discussion

3.1 Working principle based on LC resonance

When THz wave was perpendicular to the metamaterial surface and the electric field direction was parallel to the gap, the simulation results of the transmission spectra shown that a resonance frequency occurred at 1.014 THz @ ε=1 as shown in Fig. 2. At this frequency point, the exciting internal charge moved along the edge of the ring by the electric field effect and generated a ring current. Therefore, the elliptic split-ring resonance could be equivalent to a magnetic dipole perpendicular to the surface of the metamaterial. Meanwhile, the induced current made these charges gather at the gap of the elliptic split-ring resonance and produced an electric field, which was equivalent to an electric dipole. Therefore, the elliptic split-ring resonance would form the LC resonance perpendicular to the alternating magnetic field. The phenomenon of magnetic resonance driven by the electric field was called the electric field excited coupled magnetic resonance, which was called electric magnetic resonance. The mode of excitation was directly excited by the electromagnetic wave.

Then the resonance frequency of elliptic split-ring resonance was given as the following equation:

3.2 Q factor and FOM calculation for designed biosensor

Usually, the sensing performance of the sensor was mainly characterized by sensitivity, Q factor, and FOM. Q factor represents the sharpness of resonance dip, which affects the identification of frequency shift. Theoretical analysis shows that the higher Q factor means better sensing performance. The Q-factor plays a decisive role in the performances of the biosensor. Here, Q-factor could be calculated as the following formula (5) [47].

3.3 Impact of physical parameters on the performances

3.3.1 Gap width affects the performances of the flexible metamaterial biosensor

Through the above analysis, the sensing area of the metamaterial mainly located in the gap. The change of gap-related geometric parameters would affect the transmission spectrum and sensing performance. To obtain better sensing performances, the gap width change on how to affect the sensing performance was investigated. To explore the variation trend of transmission spectrum, the gap width was divided into 10 intervals from 1 to 3µm and other geometric parameters keep unchanged (a = 20µm, b = 14µm, e = 4µm, c = 30µm, d = 24µm). The resonance frequency (@ε=1) changed from 0.9906 THz to1.079 THz with gap width increasing as shown in Fig. 5(a). Meanwhile, the depth of the resonance dips increased from −8.2572 dB to −9.65826 dB with the gap width increasing. The change of Q-factor went down and then went up as shown in Fig. 5(b). Especially, the Q-factor reached the minimum value (Q = 12.91) at g = 1.75µm. When the gap width was more than 1.75µm, the Q-factor increased quickly with the gap width increasing. The change of FOM also went down and then went up as shown in Fig. 5(c). The value of FOM was between 2.9 (g = 2µm) and 3.8 (g = 3µm). The sensitivity fluctuated with gap width increasing as shown in Fig. 5(d). Especially, the sensitivity decreased quickly as gap width increasing from 1.2µm to 2µm. The sensitivity reached a maximum of 247 GHz/RIU at gap width equal to 1.2µm. To explain the influence of the width of the gap on the performance of the metamaterial biosensor, three representative electric field distribution (gap width = 3µm, 1.75µm, 1µm) were selected to plot the change of the surface electric field streamline at the resonance frequency as shown in Fig. 6. The results illustrated that the surface electric field line became denser with the gap width decreasing, which proved that the intensity of the resonance dips became stronger and caused the coupling of the metal edge on both sides of the elliptic split-ring. When the gap width was 1.75µm, the coupling at the gap increased mostly, which led to FWHM widening, Q-factor reduced to the minimum. When the gap width was greater than or less than 1.75µm, the electric field streamlines at gap width decreased. The Q-factor increased.

 

Fig. 5. Simulated transmission spectra of the variations of metamaterial gap width versus frequency. (a) Changing of the different transmitted spectra with the gap width; (b) Q-factor changing with the gap width; (c) FOM changing with gap width; (d) Sensitivity changing with the gap width.

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Fig. 6. Streamlines of the simulated surface electric field for different gap widths. (a) Streamlines for gap width g = 1µm at the resonance frequency at 0.99THz; (b) Streamlines for gap width g = 1.75µm at the resonance frequency at 1.028THz; (c) Streamlines for gap width g = 3µm at the resonance frequency at 1.078THz.

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3.3.2 Influence of changing elliptic length-short axis ratio on the performances of the flexible metamaterial biosensor

Keeping the other geometric parameters unchanged (b = 14µm, e = 4µm, g = 2µm, c = 30µm, d = 24µm) and only changing the elliptic length-short axis ratio (a/b) from 1 to 2, the resonance frequency changes from 0.715 THz to1.164 THz as shown in Fig. 7(a). FWHM decreased with a/b value increasing from 1 to 2. Q-factor reached the largest value (Q = 15.4) when the elliptic length-short axis ratio (a/b) was 1.12 as shown in Fig. 7(b). The sensitivity reached the maximum 290 GHz/RIU (Fig. 7(c)) when the length-short axis ratio (a/b) was 1. Besides, FOM reached a maximum value of 4.1 as shown in Fig. 7(d). According to formula (7), FOM was related to sensitivity and FWHM. FOM had the same changing trend as the sensitivity. However, as shown in Figs. 7(b) and (d), the Q-factor and FOM reached the maxima value when the length-short axis ratio (a/b) was equal to 1.12, which indicated that the elliptic split-ring resonance had a better performance than that of the circular structure (a/b = 1). Besides, when a/b was equal to 1.12, the sensing area increased, structural unit coupling and sensing performance became stronger. When the elliptic length-short axis ratio (a/b) increased, the inductance L increased. There are two states in the resonance of metamaterials. In the first state, the elliptical edge symmetric about the x-axis will produce resonance. When the spacing between each elliptic split-ring approaches the width of the gap, the intensity of resonance peak will be enhanced and the resonance peak linewidth will be reduced. In the second state, the area of metal increases with the increase of the ratio, which leads to the decrease of surface current, the decrease of resonance intensity and the increase of resonance peak width. Therefore, when the ratio is greater than 1.12, the influence of the first state on the transmission spectrum is greater than that of the second state, therefore, the full-width-half-maximum of the resonance peak decreases with the ratio increasing. Then, Q-factor and FOM increased. When the ratio is less than 1.12, the influence of the second state on the transmission spectra is greater than that of the first state, which results in the decrease of Q-factor and FOM value with the ratio increasing. Therefore, the surface electric field reaches maximum at the gap and at resonance frequency. As a result, sensitivity decreased. When the elliptic length-short axis was 1.12, the coupling at the gap increased quickly, which led to FWHM narrowing, Q-factor, and FOM increasing.

 

Fig. 7. The effect of elliptic length-short axis ratio (a/b) changes on sensing performances. (a) Transmitted spectrum changing of different with the ratio a/b; (b) Q-factor changing with the ratio a/b; (c) Sensitivity changing with the ratio a/b; (d) FOM changing with the ratio a/b.

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3.3.3 Influence of period ratio and ring width on the performances of the flexible metamaterial biosensor

To get the optimal sensing performances, the characteristics affected by the period ratio (c/d) of flexible metamaterials was explored in detailly. In the first case, keeping the other geometric parameters constant (a = 20µm, b = 14µm, e = 4µm, g = 2µm, d = 24µm) and only changing the period ratio (c/d) from 1 to 2, FOM, sensitivity, and Q-factor changed with the period ratio (c/d) shown in Figs. 8(a), (c), and (e). And the resonance frequency point and transmission spectra changes as shown in Fig. 8(g). Meanwhile, FOM (Fig. 8(a)), and sensitivity (Fig. 8(c)) had the same trend. The sensitivity varies from 217 GHz/RIU to 247 GHz/RIU. FOM varies from 4.03 to 4.58. According to the formula (7), FWHM had less influence on FOM. Changing the period ratio (c/d), the Q-factor increased with the increased from 16.47 to 17.80 of period ratio (c/d) as shown in Fig. 8(e). The change of the ring width also influences the performances of the flexible metamaterial biosensors, therefore, the detailed analysis of how to affect FOM, sensitivity, and Q-factor should be carried out in detailly. In the second case, keeping the other geometric parameters constant (a = 20µm, b = 14µm, g = 2µm, c = 30µm, d = 24µm) and only changing the ring width from 2µm to 6µm, the resonance frequency changes as shown in Figs. 8(b), (d) and (f). FOM, sensitivity, and Q-factor are shown as a function of ring width. The FOM and sensitivity had the same trend when ring width changes. FWHM had less influence on FOM and it had a maximum value (FOM = 4.2, S = 340 GHz/RIU) at ring width is 3µm as Figs. 8(b) and (d). Changing the ring width, the Q-factor had a maximum value (Q = 14.2) at ring width 4.5µm as shown in Fig. 8(f).

 

Fig. 8. The period ratio (c/d) and ring width (e) affect the performances of flexible metamaterial biosensor. (a)-(b) FOM changing with the period ratio (c/d) and ring width (e); (c)-(d) Sensitivity changing with the period ratio (c/d) and ring width (e); (e)-(f) Q-factor changing with the period ratio (c/d) and ring width(e); (g)-(h) Changing of the different transmitted spectrum with the period ratio (c/d) and ring width (e).

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3.3.4 Influence of polarization direction on the performances of the flexible metamaterial biosensor

To have a better insight into the biosensor performances, the influence of polarization direction on the performances of flexible metamaterials biosensor was also explored. Because the elliptical split-ring structure was not completely symmetrical, the influence of the incident electromagnetic wave was greater than other parameters. Fixing the initial geometric parameters (a = 20µm, b = 14µm, e = 4µm, g = 2µm, c = 30µm, d = 24µm) and keeping them constant except polarization direction, the 10 results were simulated by increasing the polarization angle from 0 to 90 degrees. The intensity of resonance dip changes from −9 dB to −1 dB as shown in Fig. 9(a). The sensitivity was large in the direction of a large polarization angle, however, the weak resonance dip intensity (Fig. 9(b)). According to Fig. 9(c), the change of polarization had little effect on FOM. The different polarization angles had different transmission resonance frequencies as Fig. 9(d). The change of polarization direction leads to the change of FWHM and the intensity of the transmission spectrum. Therefore, Q-factor changed with polarization direction as shown in Fig. 9(d). those results illustrated that resonance dip intensity weakens with the increase of polarization angle. The structure had a small change in Q-factor in the range from 0° to 30°of polarization angle. When it was greater than 30°, the Q-factor became smaller until it disappeared. The different polarization directions would affect the LC resonance by altering the interaction between the gold gap and free spaces. The opposite side of the gap was similar to the two poles of the parallel plate capacitor. When the E between the vertical and parallel plates was applied, the LC resonance intensity is the strongest. When the polarization angle gradually tended to be parallel, the LC resonance intensity gradually decreased until it disappeared. In the experimental verification process, to control the polarization direction, we made a mold for fixing the metamaterial device and controlled the polarization angle by rotating the abrasive tool.

 

Fig. 9. The effect of polarization Angle changes on sensor performance. (a) Changing of the different transmitted spectrum with the polarization Angle; (b) Sensitivity changing with the polarization angle; (c) FOM changing with polarization angle; (d) Q-factor changing with the polarization angle.

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Finally, the effects of the physical parameters were presented in Table 1. And the values in the table correspond to Figs. 5, 7, 8, and 9, respectively. The results have shown that the gap width had a great influence on the Q-factor, which provided an optimization direction for the structural design of metamaterial biosensor. Meanwhile, the influence of the performance of other physical parameters was analyzed and summarized. Seen from the Table 1, the parameters of the optimal structural configuration should be set as optimal value in Table 1. However, there are a number of factors that affect the sensing performance. In Table 1, only the structural parameters are given, however, the samples and application methods are not given. Therefore, the optimal structure parameters should be treated differently.

Table 1. Summary of optimal structure parameter, FOM_Max, Sensitivity_Max and Q_Max.

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To study the correlation theory of flexible substrate metamaterial sensors. The sensitivity, Q, and FOM are discussed from the aspects of SRR structure parameters and permittivity of the tested samples. A majority of metamaterial sensor in the high resistance silicon substrate, the flexible metamaterials has some research. It is usually confined to discuss the transmission spectrum of the refractive index change or the change of the reflection spectrum, and the corresponding sensitivity is calculated. However, the work to discuss the Q, FOM are very few, therefore, it is difficult to form a comparison between the results of our research and that of other work. The most typical study on the properties of metamaterials with elliptic structures is a metamaterial based on graphene materials [2]. Its Q value and FOM are far less than that of a flexible THz metamaterial biosensor designed in this paper.

4. Conclusions

A metal elliptical split-ring resonator array with a subwavelength structure based on flexible thin-film (parylene-c) was proposed. The effects of changing physical parameters on sensitivity, Q-factor, FOM, and FWHM were explored in detailly in the Terahertz regime. The results illustrated that the metamaterial exhibits obvious LC resonance transmission spectrum and sharp transmission dip. The change of gap had a great influence on the performance of the flexible metamaterial biosensor. Especially, the elliptical flexible metamaterial was very sensitive to the polarization direction. The sensitivity of the split-ring resonator array biosensor could reach 243 GHz / RIU near 1.014 THz. Q-factor was 14.2. FOM was 3.3. Therefore, this kind of flexible metamaterial sensor was more suitable for polarization direction sensing, in particular, the detection of certain biological samples sensitive to the direction of polarization.