## 3 Numerical Results and Discussion  
### Temperature Dependance of the Semiconductor Permitivity  
InSb, a semiconductor with tunable permittivity in the THz frequency spectrum, plays a pivotal role in the proposed structure. Specifically, we focus on the unique tunability, arrangements, and properties of InSb for our investigation. Notably, InSb is utilized in its undoped form, a deliberate choice driven by specific considerations. In intrinsic InSb, the narrow bandgap between the conduction and valence bands (0.18 eV at room temperature) enables the unrestricted movement of charge carriers. By adjusting the external temperature, the intrinsic carrier density (\(N\)) can be precisely controlled. In contrast, lightly and moderately doped semiconductors tend to exhibit significant absorption of THz radiation by free carriers. To minimize the loss of the transmitted THz incident beam, this study strictly adheres to the use of undoped InSb. Within the specified frequency and temperature ranges, we accurately describe InSb's permittivity using the Drude model, which is presented as follows in our analysis [28]:  
\[\varepsilon_{A}(\omega)=\varepsilon_{\infty}-\frac{\omega_{ps}^{2}}{\omega^{2 }+i\gamma\omega}\;. \tag{11}\]  
where \(\varepsilon_{\infty}=15.68\) denotes the static dielectric constant. \(\omega_{ps}=\sqrt{Ne^{2}/\varepsilon_{0}m^{*}}\), and \(\gamma\) are relevant to the plasma frequency and damping constant, respectively. Here, \(e\) is the electronic charge, \(m^{*}=0.015m_{e}\) is the effective mass, where \(m_{e}=9.1\times 10^{-31}\), and \(N\) (in cm\({}^{-3}\)) is the intrinsic carrier density, which demonstrates the dependence of \(\omega_{ps}\) and, eventually, the permittivity of InSb on temperature by given relation as follows:  
\[N=5.67\times 10^{14}Temp^{\frac{3}{2}}exp\bigg{(}\frac{-0.13}{k_{B}Temp} \bigg{)}. \tag{12}\]  
where \(Temp\) refers to the temperature in Kelvin. Here, all the evaluations are performed based on a particular temperature. As evident from Equations (11) and (12), the permittivity of InSb is temperature dependent; thus, it facilitates our objectives regarding the thermal tunability of the proposed structure. Despite the limitations and inaccuracies of the Drude model, describing the permittivity of InSb in the THz frequency range by this model could be advantageous due to the following reasons [48]. First, this model explains the dependence of the permittivity on the temperature and magnetic field. Plus, it is suitable for describing the interaction of geometrical light with the 1 DPC medium to predict the reflection, transmission, and absorption spectra of the 1 DPC, as well as the thermal emission and the PBG. More importantly, this model can also be easily incorporated into the transfer matrix method, which is a common numerical technique for analyzing the optical properties of 1 DPCs. According to the aforementioned relations, it could be noticed that InSb's intrinsic carrier density considerably depends on the temperature. Plus, this dependency has a direct effect on the plasma frequency and permittivity. Therefore, the variation in temperature causes the variation in permittivity and refractive index of InSb. This change in the refraction index leads to a new difference path inside the proposed photonic medium; thus, temperature tunability could be achieved. The ENG metamaterial can considerably tune our PBGs and manipulate the incident waves. In truth, changing the lattice constant corresponding to the applied ENG metamaterial can make our structure efficiently tunable toward the lattice constants. Furthermore, the dependency of its refractive index on the frequency amounts also makes our medium tunable towards the frequency domains. More importantly, the damping in our structure, which is mainly caused by our ENG metamaterial due to its complex refractive index, helps us to have a more efficient radiation spectrum. Metamaterials are categorized and namedin accordance with the sign of their permittivity and permeability.