## 2 Dielectric Resonator Antenna  
A dielectric resonator antenna is a microwave antenna that consists of a high dielectric material and Q factor, which is mounted on top of a ground plane, as shown in Figure 3. A dielectric resonator can be in various shapes such as rectangular, cylindrical, spherical, and hemispherical [32]. The rectangular DRA has several benefits over the cylindrical, spherical, and hemispherical DRA. A rectangular DRA offers two degrees of freedom, where the aspect ratio of height to width and depth to width directly influence the impedance bandwidth and the radiation Q factor [33]. Such as most resonant antennas, one of the significant properties of a DRA is the resonant frequency of the fundamental mode. Figure 4 shows a rectangular DRA fed by a slot aperture. The antenna consists of a rectangular DR with where width is \(a\), length \(d\), and height \(b\). As it is characterized by three independent geometrical dimensions, \(a\), \(b\), and \(d\), it offers more design flexibility as compared to the cylindrical DRA. Additionally, the cross-polarization level of a rectangular DRA is low compared to the cylindrical DRA. TE modes are excited when the DRA is mounted on a ground plane. The resonant frequency of the fundamental mode, TE\({}_{111}\), is calculated using the following equations [34]. \[f_{0}=\frac{c}{2\pi\sqrt{\varepsilon_{r}}}\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{3}} \tag{1}\]  
\[k_{x}=\frac{\pi}{a} \tag{2}\]  
\[k_{z}=\frac{\pi}{2b} \tag{3}\]  
\[b=\frac{2}{k_{y}}\text{tanh}\left(\frac{k_{y0}}{k_{y}}\right) \tag{4}\]  
\[k_{y0}=\sqrt{k_{x}^{2}+k_{z}^{3}} \tag{5}\]  
where \(e_{r}\) is the relative dielectric constant of the resonator. For cylindrical DRAs, the antenna consists of a cylindrical dielectric resonator with height \(h\), radius \(a\), and dielectric constant. The main advantages of the cylindrical DRA are  
Figure 4: Rectangular DRA: (**a**) 3D view; (**b**) side view [33]. Figure 3: Typical configuration of DRA. the ease of fabrication and the ability to excite different modes. The resonant frequency of the modes can be calculated using Equations (6) and (7) [35]. \[f_{TE_{sym}}=\frac{c}{2\pi\sqrt{\varepsilon_{r}H_{r}}}\sqrt{\left(\frac{X_{np}}{a }\right)^{2}+\left(\frac{\left(2m+1\right)\,\pi}{2h}\right)^{3}} \tag{6}\]  
\[f_{TM_{sym}}=\frac{c}{2\pi\sqrt{\varepsilon_{r}H_{r}}}\sqrt{\left(\frac{X_{np}^ {\prime}}{a}\right)^{2}+\left(\frac{\left(2m+1\right)\,\pi}{2h}\right)^{3}} \tag{7}\]  
where \(X_{np}\) and \(X_{np}^{\prime}\) are the roots of the Bessel functions of the first kind and of the relevant first-order derivatives, respectively. Another important property of a DRA is its Q factor. The Q factor can be calculated analytically for canonical shapes, but for DRAs of arbitrary shape, the calculation of the Q factor relies on numerical methods or measurement. The Q factor of each mode can be calculated using the basis formulation derived by [36]. Considering only loss from radiation, the Q factor of each mode of the DRA is calculated using Equation (8). \[f_{0}=\frac{c}{2\pi\sqrt{\varepsilon_{r}}}\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{3}} \tag{1}\]0  
where \(W_{vac}^{e}\) and \(W_{vac}^{m}\) are the stored electric and magnetic energy in free space, \(W_{mat}^{e}\) is the stored electric energy in material, and \(P_{rad}\) is the radiated power. \(W_{vac}^{e}\), \(W_{vac}^{m}\), \(W_{mat}^{e}\), and \(P_{rad}\) can be evaluated using the current and charge density within the dielectric object. DRAs are an emerging antenna technology and a good option to fulfill the demands of being low profile and compact, while having a wideband characteristic. DRAs have small dissipation loss as they are made of a material with a high dielectric constant material and have no conducting parts. Therefore, DRAs can be highly efficient radiators. Moreover, DRA have small physical dimensions due to their high dielectric constant. Additionally, DRAs have wide bandwidth, high radiation efficiency, high gain, extra design flexibility, and simple excitation methods [37; 38].