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Abstract
We propose a dual-band terahertz metamaterial sensor (MS), which exhibits the low loss and high quality (Q) factor of electromagnetically induced transparency (EIT) effects at the frequencies of 0.89 THz and 1.56 THz simultaneously. The physical natures of EIT effects are analyzed by using numerical simulations and a “two particle” model. Further, THz sensing is performed based on the shifts of two EIT resonances when the analyte is coated at the metamaterial surface. The sensitivities of the sensor are investigated with respect to different thicknesses, cover areas and refractive indexes of the coated analyte film. Results show that the first EIT resonance is suitable for sensing the analyte with the refractive index from 1.5 to 2, while the second EIT resonance is more suitable for sensing the refractive index of the analyte from 1 to 1.5. The sensitivity is 280.8 GHz/RIU, the average Q value is 14.3, and the figure of merit (FOM) value is 4 for the first EIT resonance. Meanwhile, the sensitivity is 201.6 GHz/RIU, the average Q value is 56.9, and the FOM value is 11.5 for the second EIT resonance. Such a metamaterial sensor with high refractive index sensitivity and dual-band would have great potentials for promoting the developments of multi-band/broadband terahertz sensing and detection technology.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial is an unnatural electromagnetic material composed of periodically arranged sub-wavelength metal elements [1,2]. By constructing different metal elements, metamaterial can exhibit many peculiar properties that are not available in nature [3]. Recently, there have been many reports on new electromagnetic (EM) phenomena of metamaterials, such as negative refraction [4], super imaging [5], camouflage [6] and electromagnetically induced transparency (EIT) effect [7]. By employing the resonance characteristics and limited field enhancement effects of metamaterials, researchers have developed many functional devices, such as filters [8], absorbers [9], and polarizers [10]. As one of important categories of functional devices, sensor has become a major research focus in the fields of metamaterials [11,12]. At present, researchers have proposed various optical frequencies, infrared and terahertz for metamaterial sensors (MSs) [13–15], and they have been widely used in biosensing and medical sensing [16–19].
Nowadays, the analog of EIT effect in metamaterial has become increasingly attractive for scholars. Traditional EIT effect is found in the three-level atomic system [20,21]. It refers to the phenomenon that the originally opaque medium produces a narrow-band transparent window through the coupling of energy levels [22]. In the metamaterials, different energy levels can be viewed as bright and dark modes [23]. Due to the strong coupling interference between resonance modes, the resulting EIT effect is sensitive to variation in the external dielectric environment for metamaterial. Even a small crosstalk will cause a large change in the frequency spectrum for metamaterial, which includes the shift of the frequency, the change of the half-width and the like [18]. These variations are attributed to the changes in the external dielectric environments. Compared with traditional biological/medical detections, the metamaterial-based sensor has unique advantages including non-labeling, non-destructive, time-saving and low-cost, so the EIT effect based on metamaterial is particularly suitable for the biomedical and chemical sensing [24].
Very recently, EIT sensors based on metamaterials have been largely reported. For example, W. Pan et al. proposed a sensor based on EIT effect with sensitivity of 96.2 GHz/RIU and figure of merit (FOM) value of 7.8. The sensing performance of EIT sensor was demonstrated by experiments, and the maximum frequency shift of 112.0 GHz was achieved [25]. X. Yan et al. proposed a biosensor based on EIT effect with a sensitivity of 455.7 GHz/RIU. Through experimental research, the results of biosensor and biological method show relatively good consistency, which indicates the great potentials by using sensitive biosensor based on EIT metamaterial for cell measurement [18]. W. J. Cai et al. proposed a sensor using graphene materials, where the EIT effect was realized by couplings of two graphene rings. The sensitivity of EIT resonance reaches 2.26 THz/RIU and the FOM value is 6.21 [23]. F. Y. Li et al. proposed a sensor based on multiple electromagnetically induced reflection (EIR) effects to simulate the concentration sensing of ethanol. The sensitivities of three EIR peaks of sensor are 103.7 GHz/RIU, 107.1 GHz/RIU and 112.05 GHz/RIU, respectively [26]. Although some reported MSs have high sensitivities, FOM values and quality (Q) factors, it still has many problems that need to be improved. For example, firstly, most sensors have only one working frequency band, which brings great limitations to the sensing applications. Secondly, although some dual-band/multi-band sensors have been reported, their operating bands are continuous in the spectrum. Thus, there are fewer biomolecules matching with their working frequency bands. Thirdly, the sensing effects of multiple bands are almost the same in the most reported sensors, which limits the scope of its application.
In this context, a dual-band terahertz EIT MS at the operating frequencies of 0.89 THz and 1.56 THz has been numerically realized based on EIT effects. MS consists of a metal bar, two fork-like structures (FSs), and a split ring (SR). Resonance couplings among different resonators induce the dual-band EIT effects. The nature of the EIT effect analog in proposed metamaterial is investigated by using numerical simulations and a “two particle” model [27,28]. One of the most important features of this sensor is that two transparent windows have different advantages for sensing analyte with different refractive indexes. To be specific, the first transparent window is suitable for sensing the analyte with the refractive index of 1.5 to 2, such as MS2 virus (1.97), PRD1 virus (1.87) [29], polymethyl methacrylate (1.6) [30], etc. The second transparent window is used for sensing the analyte with the refractive index of 1 to 1.5, such as the molds (1.11–1.36) [31]. Moreover, the sensing performance of the second EIT window outperforms that of the first EIT window. This EIT metamaterial sensor can sense for dual-band THz waves, which may greatly promote the progresses of THz-related practical applications, such as multi-band/broadband THz medical or biological detections.
2. Design and simulation analysis of the EIT sensor
The geometry of MS with dual-band EIT effects is schematically illustrated in Fig. 1(a) and Fig. 1(b). Metamaterial unit is composed of a metal bar, two FSs, and a SR. These substructures can couple with incident electromagnetic waves and produce strong resonances. Moreover, resonant couplings among them will induce dual-band EIT effects, as will be shown below. Three substructures are made of gold with a thickness of 0.5 µm. These gold patterns are placed on quartz substrate with a permittivity of 3.75 [32], the loss tangent of 0.0004 and the thickness of 15 µm [33,34]. Geometric parameters of MS in Fig. 1(b) are optimized, as specifically shown in Table 1. These parameters are optimized by using CST Microwave Studio simulation software. In our simulations, the frequency domain solver and period boundary condition are used. In order to verify the validity of proposed MS, transmission responses of MS under x-polarized incident waves are investigated, seen from Fig. 1(c). It is found that there are two EIT windows appearing in transmission spectrum. The first EIT window with transmittance 0.83 centers at 0.89 THz and the center frequency of the second transparent window with transmittance 0.88 is at 1.56 THz. Therefore, two low-loss transparent windows are realized.
Fig. 1. Geometric configuration of MS unit cell. (a) Structural configuration, (b) Top view of structure, (c) Transmission spectrum of sensor.
Table 1. Geometric parameters of unit structure (µm)
To understand the underlying physical nature for dual-band EIT effects, the transmission spectra of different substructures are investigated. Take the first transparent window as an example, the metal bar and SR as a subunit (See Fig. 2(a)) can couple strongly with incident EM waves and yields a strong resonance centered at 0.78 THz with the low Q factor of 2.7, as shown in Fig. 2(b). Here, the Q is defined as $Q = {f_0}/FWHM$. The f0 represents the center resonance frequency, and FWHM represents the resonance linewidth at half-maximum [35]. While the single FRs (See Fig. 2(c)) produces a resonance at 0.94 THz with the Q of 24.6, as shown in Fig. 2(d). Resonance frequencies of these two substructures are very close, but their Q factors are significantly different. As a consequence, the substructure with the lower Q value in Fig. 2(a) serves as a bright element, while the substructure with a relatively high Q value in Fig. 2(c) is considered as a dark element. When the above two substructures are put together, due to destructive interference of scattering fields between them, a transparent window appears at 0.89 THz with two transmission valleys centered at 0.84 THz and 0.99 THz. This kind of transparent window induced by couplings between bright and dark modes is generally regarded as the EIT effect.
Fig. 2. (a) Schematic diagram and (b) transmission spectrum of the bright element for the first EIT effect; (c) Schematic diagram and (d) transmission spectrum of the dark element for the first EIT effect. These bright and dark elements contribute to form the first EIT window. (e) Schematic diagram and (f) transmission spectrum of the bright element for the second EIT effect; (g) Schematic diagram and (h) transmission spectrum of the dark element for the second EIT effect. These bright and dark elements contribute to form the second EIT window.
On the other hand, for the second transparent window, both resonant structures can directly couple with incident waves and show strong resonances. To be specific, the metal bar and two FSs as a subunit yields a resonance centered at 1.62 THz with Q value of 51.4 (See Figs. 2(e)-(f)). While the independent SR shows the stronger resonance at 1.55 THz with Q factor of 100.7 (See Figs. 2(g)-(h)). As a result, the subunit composed of the metal bar and two FSs is designated as the bright element while the SR is considered as the dark element. When these resonant elements are put together, an additional transparent window occurs at 1.56 THz, and thus two independent EIT effects are achieved.
In order to understand the generation mechanism of the first EIT window, the surface currents at the resonant frequencies of EIT window are simulated, and results are shown in Fig. 3. As shown in Fig. 3(a), at the frequency of 0.84 THz, the counterclockwise quasi-annular currents distribute in two FSs, which results in their weak couplings to free space. Meanwhile, the current flow direction on the metal bar and SR is same, leading to large radiation losses and low transmission [18]. At the peak frequency 0.89 THz of EIT, the counterclockwise annular currents concentrate in dark elements of two FSs. The current flow direction on the left-right two arms of FSs is opposite and their scattering fields are offset in free spaces, and thus the residual currents mainly focus on the upper arm of FSs. Moreover, the current flow direction on the metal bar and SR is the opposite as that of the upper arm of two FSs, resulting in their weak couplings to the free spaces and thus enhancing transmission [25], as displayed in Fig. 3(b). At the second resonance dip that locates at 0.99 THz, it is seen that the currents redistribute in the resonant elements, as shown in Fig. 3(c). Such variation indicates that the destructive interference weakens, and hence the radiative losses are enhanced and the transmission reduces again [18].
Fig. 3. Surface current distributions at (a) 0.84 THz, (b) 0.89 THz, and (c) 0.99 THz, (d) 1.53 THz, (e) 1.56 THz, and (f) 1.59 THz.
The generation mechanism of the second transparent window is similar to that of the first EIT window, and it can be still demonstrated by surface current distributions as illustrated in Figs. 3(d)-(f). Figures 3(d)-(f) displays the current distributions of metamaterial at frequencies of 1.53 THz, 1.56 THz, and 1.59 THz. At 1.53 THz, the current is mainly concentrated in two resonant substructures and the current flow directions on their main arms are same, similar to the dipole resonances that lead to low transmission [25]. At 1.59 THz, the currents on main arms of two resonant substructures show the anti-parallel distribution, standing for the inductive capacitive (LC) resonance in nature [25]. At 1.56 THz, owing to the destructive interferences of scattering fields between two substructures, currents mostly gather in the dark SR element. In this case, the dipole resonance almost disappears, the scattering loss is minimized, and a transparent window is induced [18].
3. “Two particle” model
In the research fields of EIT metamaterials, the “two particles” model is a classic model to describe the EIT effect [27,28]. This model can quantitatively analyze the EIT effect in metamaterial. Therefore, the “two particle” model is also used in our scheme to quantitatively describe the EIT effect. The bright and dark resonators in our structure are simulated as two particles respectively, which satisfy the following coupling equation [28]:
In the above formula, x1 and γ1 represent the amplitude and losses of the bright element, respectively; x2 and γ2 represent the amplitude and losses of the dark element, respectively; δ is the detuning between the resonant frequencies of bright and dark elements; k is the coupling coefficient indicating the coupling degree between the bright mode with dark mode; q is the coupling strength between the bright mode and the incident field.
Carrying out algebraic operation on formula (1), the transmission of the incident wave passing through the metamaterial structure can be obtained, as shown in the following [28]:
In the formula, d represents the thickness of the structure and λ0 is the wavelength of the vacuum; ${\mathrm{\chi }_{eff}}$ is the equivalent magnetic susceptibility of the EIT metamaterial, calculated by formula (3) [28]:
As per the aforementioned discussions, the fitted analytical results of two EIT effects can be calculated by formula (2), and results are plotted in Fig. 4(a) and Fig. 4(b). The parameters corresponding to fitting curves of the first EIT window are δ=0.1638 THz, γ1=0.97 THz, γ2=0.0244 THz, ω0=0.90 THz, and k=0.0729 THz. The model fitting parameters of the second EIT window are δ=0.0688 THz, γ1=0.985 THz, γ2=0.014 THz, ω0=1.56 THz, and k=0.0312 THz. It can be seen from two figures that the fitting and simulation results are in good accordance, indicating the effectiveness of the “two particle” model. In addition, it is worth to notice that the values of γ1 and γ2 are several times different for the above cases. This means that the radiation losses of two resonant elements contributing to each EIT effect are obviously different, i.e., their Q values are significantly different, which is consistent with the results in the Fig. 2.
Fig. 4. Simulated transmission coefficient (red line) and calculated transmission coefficient (black line) by the “two particle” model describing for (a) the first EIT window, (b) the second EIT window.
4. Sensing performance analysis of the EIT sensor
In the following, we investigate the sensing performance of EIT sensor. In general, the sensing of the terahertz MS mainly refers to the sensing of refractive index of the analysis layer on the sensor surface [35]. The performance of sensor is usually characterized by quality factor Q, sensitivity S and FOM. For the first performance parameter of Q value, it is related to the resolution and sensitivity of the sensor [35].
The second performance parameter, sensitivity S, refers to the variation degree of the sensor's response to changes in the unit amount of analyte [36]. The main factor that affects the sensitivity of terahertz MS is the change in the refractive index of the surface analyte. The resonance frequency shift of the sensor per unit refractive index represents its sensitivity, and it is expressed as [36]:
Here, Δf is the resonance frequency variation, Δn is the change of refractive index.
In addition, In order to facilitate the comparison of sensor performance at different bands, the FOM value is defined as [37,38]:
Here, S is sensitivity, Q is quality factor. When the sensitivity S is same, the FOM value is higher, and then the sensor performance is better.
Based on the above analysis, we discuss the sensing performance of the designed EIT sensor with different parameters of the thickness, the coverage area (OR) of the analyte and the refractive index. Here, the analyte is placed on the top surface of sensor. To find the optimal coating thickness for the analyte, the transmission spectra of sensor with different thicknesses but the fixed refractive index of 1.3 are investigated, and results are shown in Figs. 5(a)-(b). As shown in Figs. 5(a)-(b), when the thickness of the analyte changes from 0 µm to 20 µm, there are obvious resonance shifts for two EIT transparency windows. However, when the thickness is greater than 15 µm, the resonance characteristic of the first transparent window is almost unchanged. That is to say, after this thickness, even if the thickness of the analyte continues to increase, the sensitivity remains almost unchanged. But for the second transparent window, the sensitivity of sensor can be further enhanced when the thickness of the analyte is more than 15 µm. In order to obtain the optimal detection effect for the analyte in two EIT windows, the thickness is selected as 15 µm in the next discussions.
Fig. 5. Transmission spectra at different thicknesses of the analyte with a refractive index of 1.3 for (a) the first transparent window, (b) the second transparent window. (c), (d) Transmission spectra for two transparent windows of the analyte under different coverage areas. (e), (f) Dependences of refractive indexes versus frequency shifts for two transparency windows of analyte under different coverage areas.
We also explore the influences of the OR of analyte on sensing performances for two EIT windows. The OR is the area of the analyte to the area of the sensor. In this case, the OR is set to 25%, 50%, and 100%, respectively, and corresponding results are shown in Figs. 5(c)-(d). As the OR of the analyte with a refractive index of 1.3 is varied, we observe a corresponding resonance shift for each EIT window, as shown in Fig. 5(c) and Fig. 5(d). Next, we analyze the sensitivities corresponding to two EIT resonances. The sensitivity of sensor is closely related to the refractive index of analyte. In order to obtain sensitivity, the refractive index of analyte varies from 1 to 1.5 with the step of 0.1 for each of the OR. We extract the refractive indexes versus frequency shifts for each transparency window, as shown in Fig. 5(e) and Fig. 5(f). Three linear lines indicate the properties of three different coverage areas of analyte for each EIT window. The slope of the line indicates the sensitivity. Obviously, as the OR increases, the sensitivity of the sensor enhances from 90 GHz/RIU to 180 GHz/RIU for the first EIT resonance and from 14.4 GHz/RIU to 201.6 GHz/RIU for the second EIT resonance. In comparison, the analyte with 100% of OR has the best sensing performance for two EIT resonant modes.
Through the above analyses, it is found that when the thickness and OR of the analyte are 15 µm and 100%, respectively, the sensing performance of sensor is the best. Under such parameter configuration, we discuss the sensing performances of two EIT windows for the sensor covered by the analyte with different refractive indexes, as shown in Figs. 6(a)–6(b). As the refractive index changes linearly, the peak frequency locations of the EIT windows and the frequencies corresponding to the left and right valleys also change regularly. As shown in Fig. 6(a), as the refractive index changes from 1 to 1.5, the frequency of the transmission peak of the first EIT window shifts by 90 GHz towards to the low frequency direction. The second EIT window also has the similar variation trend as the first EIT window, as shown in Fig. 6(b). When the refractive index changes from 1 to 1.5, the peak frequency of the second EIT window shifts by 100.8 GHz. In order to better describe the dependency relationship between the EIT resonance and the refractive index of analyte, a linear graph of the frequency shift of the EIT resonance with respect to the refractive index change of the analyte is drawn, as shown in Fig. 6(c). It is seen that the second EIT resonance has the better sensitivity (i.e. the higher slope) compared with the first EIT resonance for the refractive index from 1 to 1.5. To be specific, the sensitivity of the first EIT resonance is 180 GHz/ RIU, the average Q value is 12.1, and the FOM is 2.2. The sensitivity of the second EIT mode is 201.6 GHz/RIU, the average Q value is 56.9, and the FOM is 11.5. By comparison, it is found that the second EIT window has better sensing performance and it is more suitable for sensing the analyte with a refractive index from 1 to 1.5.
Fig. 6. (a),(b) Transmission spectra of two EIT resonances at different refractive indexes. (c) Frequency shifts of two EIT resonances at different refractive indexes of analyte extracted from panels (a) and (b). (d) Transmission spectra of the first EIT resonance at different refractive indexes. (e) Frequency shift of EIT resonance at different refractive indexes of analyte extracted from panel (d).
On the other hand, we study the sensing performances of two EIT resonances when the refractive index of the analyte is between 1.5 and 2, and the results are shown in the Figs. 6(d)-(e). As displayed in Fig. 6(d), the peak frequency of the first EIT window decreases from 0.8 THz to 0.66 THz while the performance of second transparent window is degraded (not shown) as the refractive index of analyte increases from 1.5 to 2. Figure 6(e) extracts the frequency shift Δf of the first EIT window at different refractive indexes. It can be seen that the maximum sensitivity of the first EIT resonance is 280.8 GHz/RIU, the average Q value is 14.3, and the FOM is 4.
The reasons for the above phenomena can be explained as followed: when the EIT effect occurs, the electric field is mainly concentrated in the EIT sensor. Once the surrounding medium environment changes slightly, the electric field around the sensor will be disturbed, which will cause the EIT resonance to shift. Therefore, when the dielectric constant, thickness, and OR of the analyte to be measured change, they will cause the EIT resonance to shift, which is used to realize sensing.
Based on the above analysis, we found that when the refractive index of the analyte is 1–1.5, the sensing effect of the second transparent window is better than that of the first transparent window. When the refractive index of the analyte is between 1.5–2, the transmittance of the second EIT window is reduced and its loss is increased, and thus it is not suitable for sensing. The reason why this case happens is because the further enhancement of refractive index for the analyte leads to the increasing of dielectric loss, which raises the overall loss of metamaterial and thus the performance of the second EIT window is degraded. Therefore, we say that the first EIT resonance is suitable for sensing the analyte with the refractive index from 1.5 to 2.
The proposed sensor can sensing different types of analytes at different frequency bands, which makes that the sensor has a wider range of applications, such as obtaining highly specific information about molecular specificity [39]. In addition, the sensing performances of different EIT sensors are compared, and results are plotted in Table 2. It is seen that the proposed sensor can achieve the dual-band refractive index sensing and its sensing range for refractive index is superior to the schemes in Refs. [18,21,40,41] and inferior to the results in Ref. [25]. But the sensitivity and FOM value of proposed sensor is better than the results in Refs. [25,40,41] except the FOM of its first EIT resonance. Compared to the Refs. [21,42], where the single-band refractive index sensor working at near-infrared region, or tunable sensor are achieved, while this paper proposes a sensor based on the double EIT effects. In our scheme, the two transparent windows of sensor are far apart and thus it has a wider working frequency band. Both transparent windows of sensor can be used for refractive index sensing and it owns the following advantages: Firstly, dual-band sensor has larger sensing ranges for the refractive index of the analyte to be measured. In this way, different working frequency bands of sensor can be selected to obtain the best sensing effect for different refractive index ranges. Secondly, if the specific vibration frequency band of the biomolecule to be measured matches the working frequency band of the sensor, the sensor has better performance [39]. The sensor proposed in this paper has more working frequency bands to ensure the specificity of biomolecules [39].
Table 2. Comparisons of the proposed sensor with the other reported sensors
In future fabrication, we will use 200 µm quartz or 10 µm PI as substrate. The analyte could be insulin [43] which is dripped to the surface of the sensor by using a micro-pipette and then a uniform film at room temperature is formed, or it may be cancer cells [18] that are cultured on the surface of our sensor.
5. Conclusion
In this paper, a dual-band MS composed of a metal bar, two FSs, and a SR was designed in THz frequency range. Couplings among resonant structures induce dual-band EIT effects at the frequencies of 0.89 THz and 1.56 THz, respectively. Resonance natures of EIT effects are analyzed by numerical simulations and the “two particle” model, and their results are in good agreements. Owing to the properties of low losses and high Q values of EIT effects, the proposed metamaterial can be used to the sensor based on refractive index. The sensitivity and FOM of EIT resonances are analyzed with respect to different thicknesses, ORs and refractive indexes of the coated analyte film. Results show that when the refractive index of the analyte is between 1.5 and 2, the sensing performance of the first EIT resonance is better, and its maximum of sensitivity is 280.8 GHz/RIU, the average Q value is 14.3, and the FOM value is 4; While the second EIT resonance is more suitable for sensing the refractive index of the analyte from 1 to 1.5, and its sensitivity is 201.6 GHz/RIU, the average Q value is 56.9, and the FOM value is 11.5. The dual-band sensor has not only good sensitivity, but also high resolution rate. With the properties of dual-band high refractive index sensitivity, the proposed MS would play important roles for promoting the developments of multi-band/broadband terahertz sensing and detection technology.
Funding
National Natural Science Foundation of China (61501275, 61604133, 61701141, 62075052); China Postdoctoral Science Special Foundation (2018T110274); China Postdoctoral Science Foundation (2017M611357); Science Foundation Project of Heilongjiang Province of China (QC2015073); Postdoctoral Science Foundation of Heilongjiang Province of China (LBH-Z17045); Young Creative Talents Training Plan of General Universities of Heilongjiang Province of China (UNPYSCT-2017152); Technology Bureau of Qiqihar City of Heilongjiang Province of China (GYGG-201511, GYGG-201905); Fundamental Research Funds in Heilongjiang Provincial Universities of China (135509227); Higher Education Teaching Reform Project of Heilongjiang Province of China (SJGY20190726); Cooperative Education Program of Ministry of Education, China 201902076029; Degree and Postgraduate Education Reform Research Project of Qiqihar University, China (JGXM_QUG_2019019); Educational Science Research Project of Qiqihar University in 2020, China (GJZRYB202003).
Disclosures
The authors declare no conflicts of interest.
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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