A high Q-factor metamaterial sensor based on electromagnetically induced transparency-like

This paper proposes an electromagnetically induced transparency-like (EIT-like) metamaterial with a high-quality factor (143.54), which is composed of a square ring resonator (SRR) and a cross-shaped resonator (CR). The designed metamaterial generates a sharp transparency peak at 15.79 GHz. The electric field distributions reveal that appearance of the transparency window results from the coupling between bright mode and dark mode. Moreover, analysis of the surface current distributions verifies that the EIT-like effect is induced by the destructive interference of the electric dipoles . Furthermore, the metamaterial is equated to a circuit model, which provides a better fit to the simulated transmission spectrum. These theories fully explain the generation mechanism of the EIT-like phenomenon. In addition, the EIT-like metamaterial is able to detect the dielectric constant of the target analyte (glucose solution), and the sensing performance is evaluated. The results demonstrate that the sensitivity (S) is 4.80 GHz R−1IU−1 and the figure of merit (FOM) reaches 43.71. The proposed EIT-like metamaterial shows prominent sensing abilities, consequently it has potential applications in environmental monitoring, biological and chemical measurements.


Introduction
Metamaterials [1,2] are artificially engineered composite materials that consist of subwavelength scale unit cells in periodic arrays.These metamaterials have exotic electromagnetic properties which do not exist in natural materials.The extraordinary electromagnetic parameters including negative permittivity and negative refractive index are achieved by designing the arrangement and geometrical parameters of the unit cells.Therefore, metamaterials have important applications in many fields, such as perfect absorbers [3][4][5], polarization converters [6][7][8], beam controllers [9,10].Electromagnetically induced transparency (EIT) is a physical phenomenon that was originally observed in an atomic system with multiple energy levels [11].It forms a narrow transparency window in the broad spectrum region because of the quantum interference, which means an opaque medium becomes transparent.However, the realization of EIT in the classical atomic system usually requires ultra-low temperature and strong laser.The harsh experimental conditions are inconvenient for practical applications.In the past decade, researchers have found that metamaterials can realize the analogy of the EIT.The metamaterials are easy to fabricate and the experimental environment requirements are relatively simple, and these advantages attract widespread attention.With further research, the EIT-like phenomenon is observed in metamaterials that range from microwave [12,13], terahertz [14,15], and optical [16,17] band.
The EIT-like metamaterials commonly have two approaches for implementation: bright-dark mode coupling [18,19] and bright-bright mode coupling [20,21].The bright mode directly couple with the incident electromagnetic wave and generates a strong resonance.Nevertheless, the interaction between the dark mode and the incident electromagnetic wave is extremely weak.Therefore, the dark mode is only indirectly excited by the bright mode.Owing to the significant dispersion properties and the narrow transparency window, the EITlike metamaterials have essential applications in optical switches [22,23], slow-light devices [24,25], sensors [26][27][28], and so on.Tian et al [29] numerically and experimentally demonstrated a high transmittance and lowlosses EIT-like metamaterial, whose unit structure is composed of two independent opening ring resonators.The designed EIT-like structure is used as a sensor, and the sensitivity achieves 1.69 GHz R −1 IU −1 as well as the figure of merit is 11.66 .Liu et al [30] utilized the multilayer EIT-like metamaterial to design a broad stopband filter.The metamaterial structure consists of components (a U-shaped resonator and a strip resonator) constructed on a polyimide substrate.The EIT-like spectrum features are utilized to accomplish the stopband filter.Ma et al [31] proposed and analyzed the characterization of a EIT-like metamaterial in slow light technology.The surface structure of the metamaterial units comprises a ring resonator and a rectangular bar.The all-optical tunable slow-light effect of the metamateiral is theoretically corroborated, and it can be used as tunable chip-scale slow-light devices.
In this work, a high quality factor (Q-factor) metamaterial based on the EIT-like phenomenon is designed.The simulation result shows that the metamaterial can produces a narrow transparency window, and the fabricated metamaterial sample is measured to validate this property.The mechanism of the EIT-like phenomenon production is clearly clarified by the electric field, the surface current distributions, and equivalent circuit model.Meanwhile, the effects of different geometrical parameters on the transparency window of the proposed metamaterial are investigated, and thus the spectrum properties are optimized.Moreover, the sensing performance of the EIT-like metamaterial is simulated and it is superior to some of the sensors proposed in recent years.), and the thickness is 0.035 mm.The specific geometry parameters are optimized as following: P = 20 mm, l 1 = 19 mm, w 1 = 1.5 mm l 2 = 7.1 mm, w 2 = 1 mm, h = 1.5 mm. Figure 1(c) exhibits the image of the manufactured sample of the designed metamaterial, which consists of 12 × 12 unit cells along the x-and y-directions.The practical physical dimension of the whole sample is 240 mm × 240 mm.The transmission spectrum characteristics of the designed metamaterial are obtained by using the full-wave numerical simulation software CST Microwave Studio 2021.The boundary conditions are set as unit cell in x-and y-directions and open (add space) in z-direction.The mesh is set as adaptive mesh refinement to improve the precision of the simulation results.

Discussion and analysis
where f is the resonance frequency of the transparency peak and FWHM represents the full width half maximum bandwidth.The Q-factor of the transparency peak is 143.54 by calculating, and this means that the metamaterial has a high Q-factor.A vector network analyzer (Agilent PNA E8362B) and a couple of horn antennas are used to measure the metamaterial sample in the experiment.The dotted line is the experimental result as displayed in figure 2(b).The EIT-like transmission spectrum is red-shifted, and the frequency of transmission dips shift to 14.37 GHz and 15.65 GHz.The first dip has a significant increase in transmission coefficient to 0.34, and the variations in second dip are small.The frequency of the transparency peak is 14.86 GHz and the transmission coefficient only reaches 0.54.As a result of these changes, the Q-factor of the experimental spectrum is calculated to 14.42.The possible several factors for the deviation are the follows: The metamaterial sample has defects in the manufacture, for example, the dielectric constant of the substrate does not match the simulation, besides the physical dimension of the practical sample has tiny differences compared to the simulation model.The laboratory is different from the ideal environment of simulation.Due to the limited experimental equipment, the metamaterial sample is not placed in the microwave anechoic chamber for measuring, which makes it subject to other electromagnetic interference and reduces the accuracy of the experimental result.In order to elucidate the physical mechanism of the EIT-like phenomenon, the electric field distributions and surface current distributions are simulated for analysis, with the simulation frequency of 15.90 GHz for individual the SRR and CR, while the unit cell is set at 15.79 GHz. Figure 3(a) shows the simulation results of the SRR, where the intense electric field energy is mainly distributed around the edges of the resonant ring arm.Obviously, the SRR is directly excited by the incident wave.In contrast, the CR has negligible interaction with the electromagnetic wave, and thus the electric field energy is very weak as displayed in figure 3(b).When the SRR is combined with the CR, the electric field energy of the SRR becomes quite faint, while the strong electric field energy distributions are clearly observed at the four ends of the CR in figure 3(c).From this, it suggests that the dark mode SRR receives energy from the bright mode CR through the near-field coupling effect.The energy radiation from the CR is almost suppressed, and the SRR becomes bright instead.The destructive interference between the two modes results in the sharp transparency window at 15.79 GHz. Figure 3(d) shows the surface current intensity of SRR is extremely weak and the current direction on the left and right ring arms is from top to bottom.Figure 3(e) illustrates the surface current distributions of the CR are mainly focused at corners, and the current direction is downward.After combining the two resonators as shown in figure 3(f), the intensity of the surface currents is enhanced, with the current direction in the CR reversing upward.Therefore, the surface current distributions of the SRR and CR are in the opposite direction, which can be regarded as two pairs of electric dipoles.As a result, this destructive interference effect between electric dipoles leads to the EIT-like phenomenon.
To further comprehend the the EIT-like phenomenon and verify the reliably of the proposed structure, the equivalent circuit of the metamaterial is given to fit EIT trasmission spectrum.Generally, the metal patch is equated to an inductor, while the gap between the metals is considered as a capacitor.For our designed structure, the SRR and the CR act as inductors in the circuit and the four ends of CR are capacitors [33,34].There are also gaps between the metamaterial unit cells, which also serve as capacitors in series with other components.These components are combined together to finally obtain the schematic diagram in figure 4 We analyze the influence of different geometrical parameters of the EIT-like metamaterial on the transmission spectra.Figures 5(a  drops to 0.79, the transparency peak becomes narrower and the Q-factor reaches 156.17.There is a trend in mutual inhibition between the transmission coefficient and the Q-factor.The reason is that the existence of loss in the metal on the surface of the metamaterial.When the Q-factor increases, the corresponding energy loss also increases, leading to a reduced transmission coefficient [36].Eventually, after optimizing the geometrical parameters, the metamaterial realizes the balance between an appropriate transmission coefficient and a high Q-factor. The above simulation results demonstrate that the proposed metamaterial has a high Q-factor, which is an important indicator of the sensing performance.A high Q-factor metamaterial is very sensitive to variations in surrounding dielectric environment, which offers significant advantage for designing sensors.Furthermore, the other sensing properties are explored in the simulation.As displayed in figure 6(a), a layer of homogeneous dielectric material is added on the surface of the metamaterial, and it is regarded as the target analyte.When its refractive index (n) is 1.1, the effect of the target analyte thicknesses on the metamaterial is investigated.figure 6(b) shows the transmission spectra under different thicknesses of the target analyte.Apparently, the metamaterial is sensitive to the changes in thickness.The thickness increases from 1.0 mm to 3.0 mm at 0.5 mm intervals, and the transparency peak appears a noticeable red-shift.The resonance frequency moves from 15.57 GHz to 15.39 GHz accompanied by a slight decrease in the transmission coefficient.
We further evaluate the refractive index sensing performance of the proposed metamaterial.The target analyte can be approximately considered as the glucose solution.The refractive index of the glucose solution in a room temperature environment (25 °C) is calculated from this equation = + n n aC w [37].The n w is the refractive index of water with a value of 1.33, a = 0.00143 is a constant and C represents the concentration of glucose per g/100ml.Table 1 demonstrates the specific refractive index of the glucose solution at different concentrations from 0% to 80%.The thickness of the glucose solution is fixed at 2.6 mm, and the concentrations is varied to obtain transmission spectra in figure 7. The transparency peak shifts from 14.51 GHz to 13.96 GHz with a total resonance frequency offset of 0.55 GHz, and transmission coefficient increases gradually.The sensitivity (S) and the figure of merit (FOM) are also crucial indicators for assessing sensing technologies.The S is defined as the resonance frequency shift per unit change in refractive index, while the FOM characterizes the overall performance of the sensor and its formula is [38].The calculated values for the S is 4.80 GHz R −1 IU −1 and the FOM is 43.71.In addition, table 2 intuitively displays the performance of the metamaterial, and its performance indicators are compared with different sensors proposed recently.The proposed EIT-like metamaterial performs excellently in terms of Q-factor and FOM, therefore it has remarkable applications in refractive index sensor.
The group velocity decreases as the incident wave passes through the EIT medium, which is known as the slow light effect and it is an important feature of the EIT phenomenon.The group delay / t j w = -d d g [39] is a common method for assessing the effect of slow light in metamaterials, where j represents the transmission phase and ω denotes the angular frequency of the incident wave.The group delay spectrum of the proposed EITlike metamaterial is illustrated in figure 8.The significant dispersion is observed at the transparency peak and transmission dips, where the group delay at the transparency peak (15.79 GHz) reaches 4.62 ns.

Conclusions
In summary, we present a microwave metamaterial that realizes the EIT-like phenomenon.The electromagnetic properties of the designed metamaterial are verified by numerical simulations and experiments.Numerical results exhibit that the metamaterial has a sharp transparency peak at 15.79GHz.Meanwhile, the transmission spectrum features of the metamaterial is discussed through varying its geometrical parameters.These parameter values are finally optimized to achieve the transmission coefficient higher than 0.8 with a high Q-factor of 143.54.The glucose solution is covered on its surface in simulation to validate the sensing performance.The metamaterial proves to be highly sensitive to changes in the refractive index of the dielectric material, which yield the S and the FOM of 4.80 GHz R −1 IU −1 and 43.71, respectively.Furthermore, the slow light effect of the metamaterial is also demonstrated, with a maximum group delay of 4.62 ns.It is believed that the proposed EIT-

Figures 1 (
Figures 1(a) and (b) illustrate the geometrical structure of the unit cell.The designed metal pattern comprises of a square ring resonator (SRR) and a cross-shaped resonator (CR), which is etched on F4B dielectric substrate (e d = = 2.2, tan 0.001).The metal pattern is copper (the conductivity of copper, / s = ´S m 5.96 10 7), and the thickness is 0.035 mm.The specific geometry parameters are optimized as following: P = 20 mm, l 1 = 19 mm, w 1 = 1.5 mm l 2 = 7.1 mm, w 2 = 1 mm, h = 1.5 mm.Figure1(c) exhibits the image of the manufactured sample of the designed metamaterial, which consists of 12 × 12 unit cells along the x-and y-directions.The practical physical dimension of the whole sample is 240 mm × 240 mm.The transmission spectrum characteristics of the designed metamaterial are obtained by using the full-wave numerical simulation software CST Microwave Studio 2021.The boundary conditions are set as unit cell in x-and y-directions and open (add space) in z-direction.The mesh is set as adaptive mesh refinement to improve the precision of the simulation results.

Figure 1 .
Figure 1.(a) Schematic of the unit cell.(b) Geometrical parameters of the unit cell.(c) Photograph of the fabricated sample.

Figure 2 (
Figure 2(a) shows the simulation transmission spectra of the single structure (SRR, or CR).It observes that SRR produces a sharp resonance dip at 15.90 GHz, while single CR has weak coupling with the y-polarization waves and the transmission spectrum is a slowly declining curve.Therefore, the SRR is defined as the bright mode resonator, and the CR plays the dark mode resonator.When the SRR and CR are arranged into a unit cell, the solid curve represents the simulation result in figure 2(b).A clear transparency window occurs in the transmission spectrum, which ranges from 15.58 GHz to 16.02 GHz and the transparency peak locates at 15.79 GHz with the transmission coefficient of 0.81.The Q-factor is calculated by the formula/ = Q f FWHM [32],where f is the resonance frequency of the transparency peak and FWHM represents the full width half maximum bandwidth.The Q-factor of the transparency peak is 143.54 by calculating, and this means that the metamaterial has a high Q-factor.A vector network analyzer (Agilent PNA E8362B) and a couple of horn antennas are used to measure the metamaterial sample in the experiment.The dotted line is the experimental result as displayed in figure 2(b).The EIT-like transmission spectrum is red-shifted, and the frequency of transmission dips shift to 14.37 GHz and 15.65 GHz.The first dip has a significant increase in transmission coefficient to 0.34, and the variations in second dip are small.The frequency of the transparency peak is 14.86 GHz and the transmission coefficient only reaches 0.54.As a result of these changes, the Q-factor of the experimental spectrum is calculated to 14.42.The possible several factors for the deviation are the follows: The metamaterial sample has defects in the manufacture, for example, the dielectric constant of the substrate does not match the simulation, besides the physical dimension of the practical sample has tiny differences compared to the simulation model.The laboratory is different from the ideal environment of simulation.Due to the limited experimental equipment, the metamaterial sample is not placed in the microwave anechoic chamber for measuring, which makes it subject to other electromagnetic interference and reduces the accuracy of the experimental result.
(a).The software employed for modeling the equivalent circuit and calculating the transmission spectrum is Advanced Design System (ADS).The initial values of inductance and capacitance are first calculated by / p = f 1 2 LC [35], and then optimized through ADS to acquire the final inductance and capacitance parameters: L 1 = 1.09 nH, L 2 = 0.99 nH, L 3 = 2.0 nH, C 1 = 0.097 pf, C 2 = 0.099 pf, C 3 = 0.16 pf. Figure 4(b) displays a comparison between the calculated and the simulated result.It shows that the frequency of the transmission spectrum peak slightly shifts to 15.77 GHz and the transmission coefficient increases to 0.82.The calculation result is excellent agreement with that obtained from CST simulation.The causes for the discrepancies between the two curves are that the ADS is only for the Floquet mode, whereas the CST result is based on a variety of electromagnetic responses.
) and (b) depict the transmission spectra with varying l 1 and w 1 , respectively.When l 1 gradually increases from 19.0 mm to 19.2 mm by a step of 0.1 mm and other parameters held constant, the transparency window shifts to a lower frequency.The transparency peak moves to 15.64 GHz and the transmission coefficient rises to 0.84 at l 1 of 19.2 mm, meanwhile the Q-factor of the transparency peak is calculated to 111.71.Apparently, the increase in l1 changes the characterizations of the transmission spectrum.The transparency peak progressively shifts to 15.67 GHz by changing w 1 from 1.4 mm to 1.6 mm, while l 1 is 19 mm and the rest of parameters remain same.As w 1 increases to 1.6 mm, although the transmission coefficient

Figure 4 .
Figure 4. (a) Diagram of the equivalent circuit.(b) The results of CST simulated and ADS calculated.

Figure 5 .
Figure 5.The simulation results of transmission spectra with different geometrical parameters.(a) l 1 .(b) w 1 .

Figure 6 .
Figure 6.(a) Schematic of the target analytes.(b) Simulation results at different analyte thicknesses.

Figure 7 .
Figure 7. Simulation results at different refractive indices.

Figure 8 .
Figure 8. Group delay spectra of the EIT-like metamaterial.

Table 1 .
Refractive index of glucose solutions of different concentrations.
like metamaterial will be a promising candidate for sensors and contribute to the fields of environmental monitoring, biology, and chemistry.

Table 2 .
Comparison with other sensors in recent years.