## 3 Results and Discussion
This variation was well observed in the results that were obtained by varying the grating size. When the filling factor decreased, the resonance frequency was blue shifted from 844 to 912 GHz, and the Q-factor significantly increased to almost 700. By modulating the refractive index and the grating size, the resonance peak and Q-factor can be modulated perfectly. In particular, broad resonance-frequency modulation and very high Q-factors can be achieved by using the GMR structure with the circular shape. Consequently, our simulated results can provide highly sensitive and low-cost biochemical sensing platforms, using the GMR device. Figure 4: (**a**) Scheme of the simulated THz reflectance with varying refractive index of the grating layer; (**b**) peak frequency and Q-factor for the circular pattern, where \(F\) = 0.25. To apply the results to sensing platforms, however, GMR devices with a sensing layer must be considered. Such a sensing material or receptor for target material detection can be coated onto the GMR device. In a previous study, humidity sensing was conducted by using the GMR device with polymer and ceramic balls [10]. The mechanism of humidity sensing can be explained as follows: when the water vapor attaches to the sensing layer due to humidity, the refractive index of the sensing layer changes. Subsequently, the THz spectrum of the GMR device at high humidity is different from that at low humidity. We simulated the GMR device depending on thickness (t), and the real (n) and imaginary (k) parts of the refractive index of the sensing layer, because the optical parameters of the sensing layer could be changed by the properties of the sensing materials. The GMRs with the sensing layer were analyzed under the same boundary conditions as those used to obtain previous results. Figure 6 shows the simulated results as a function of the thickness of the layer. In this case, we fixed the refractive index of the layer to 1.4 and varied the thickness of the sensing layer from 0 to 30 \(\upmu\)m. As the thickness of the layer increased, the resonance frequency was significantly shifted to a lower frequency. In addition, the change of the ratio was slightly altered at thicker layers more than at thinner layers, which indicates that the sensing resolution would be good with thin layers of sensing material. The refractive index of the layer is another important factor that affects the detection of materials. We calculated the dependence of the refractive index on the thickness of the sensing layer, as shown in Figure 7. The refractive index changed from 1.4 to 1.5 (t = 10 um); however, when the refractive index of the layer was changed to a high value, the resonance frequency slightly decreased. Possibly, the resonance frequency was affected by the thickness of the material more than by the refractive index. The reflectivity of the GMR device was also affected by the absorption coefficient. Figure 5: (a) Scheme of the simulated THz reflectance with size dependency of the grating layer, where \(n_{\mathit{eff}}\) = 2.05; (b) peak frequency and Q-factor for the circular pattern. Figure 6: Dependence of the sensing-layer thickness on the (a) THz reflectance of the GMR device and (b) the resonance frequency. The inset shows the scheme of the sensing layer (blue layer) on the GMR structure. The variation in the absorption coefficients of the sensing layer was calculated from 0 to 0.1, where the thickness was 10 \(\upmu\)m; the real part of the refractive index was 1.45 for the GMR device, as shown in Figure 8. Interestingly, the resonance frequency was not changed as the absorption coefficient of the layer increased. However, variation in the absorption coefficient dramatically changed the Q-factor of the GMR device, indicating that when the absorption coefficient of the sensing materials is high in the THz region, then GMR with a high Q-factor can be applied for highly sensitive detection.