# Hypersentized Metamaterials Based on a Corona-Shaped Resonator for Efficient Detection of Glucose
## 4 Numerical and Experimental Studies of the Proposed Sensor for Glucose Detection
The resonance frequency of the proposed sensor shifted down by increasing the concentration of glucose in water; the frequency shift also caused a change in the transmission coefficient (S\({}_{21}\)) level at a fixed frequency of 7.01 GHz, which is the resonance frequency for the 100 mg/dL glucose-water mixture. Therefore, both the resonance frequency shift (\(\Delta\)f\({}_{\rm r}\)) and the S\({}_{21}\) level can be used in the sensing mechanism. The resonance frequency shift versus the glucose concentration is plotted in Figure 13a. The resonance frequency shifts of the experimental results and fitted curve are plotted in Figure 13b. It  
Figure 5:0 (a) Simulated and (b) measured results of the glucose-water mixture of the proposed metamaterials sensor. Figure 5:1 A comparison of the glucose-blood mixture sample of the proposed metamaterials sensor: (a) simulated and (b) measured. was noticed that by increasing the glucose concentration in water, the resonance frequency shift was decreased. The lowest concentration of glucose which was reliably detected by the proposed sensor can be expressed by the limit of detection (LOD). The value of the LOD defines the lowest detectable quantity of an analyte when the concentration approaches to zero. The response of the sensor in the range of 200-500 mg/dL was found to be well fitted as y = 6.414 \(-\) 0.0048x (\(R^{2}\) = 0.972). Consequently, the LOD was determined to be 30.94 mg/dL using LOD = \(K\times S_{0}/S\)[42], where \(K\) was chosen as 3.3 with respect to the 95% confidence level, \(S_{0}\) is the standard deviation and \(S\) is the slope of the fitting curve. Figure 14 shows the frequency shift dependence of the glucose-blood mixtures for the simulated and measured results. It was seen that the fitted curve was in compliance with the resonance frequency shifts, concluding that the resonance frequency shifts are decreased by increasing the glucose concentration in blood. Figure 15a shows the change in the transmission level variation, \(\Delta\)\(\lvert\)S\({}_{21}\rvert\), with respect to the 100 mg/dL glucose-water mixture at 7.01 GHz for the simulation and fitted curve derived from the Debye formula. The results show a linear relationship between the resonance frequency shift and the glucose concentration in the solution. However, the S\({}_{21}\) level variation is a nonlinear function of the glucose concentration for the considered concentration ranges. The points in Figures 13a, 14a, 15a and 16a were obtained by repeating each simulation 10 times. As it can be seen from the figure, the variation in transmission level was increased when the glucose concentration in water was increased. To verify the simulated results, the  
To better understand the working principle of the proposed metamaterials sensor, the simulated surface current, electric field and magnetic field distribution was studied at two different resonance frequencies of 3.6 and 6.18 GHz, as shown in Figures 17-19, respectively. At the resonance frequency of 3.6 GHz, the current flowed into port one and exited from port two. Furthermore, at the lower part of the resonator, the direction of the current flow was clockwise, while at the upper part of the resonator, the current flow was in an anticlockwise direction, as shown in Figure 17a. At the resonance frequency of 6.18 GHz, the current was heavily distributed on the resonator, whereas currents on port one and two were flowing in opposite directions and both the resonator and transmission line were in parallel and anti-parallel directions. Nevertheless, the parallel currents control the electric response and the anti-parallel currents control the magnetic response, as shown in Figure 17b. Figure 18 depicts the simulated electric field distribution for the proposed metamaterials sensor at two different resonance frequencies of 3.6 and 6.18 GHz. From Figure 18a, it is apparent that the electric field intensity is mostly concentrated in the inner and outer rings of the resonator.