## 2 Results and Discussion
### Farfield Radiation Pattern  
The farfield radiation patterns (3D and polar plot) of the one segment fractal antenna are shown in Figure 6a-d. The measured results of the antenna clearly show that the antenna radiation characteristics change upon the changes in permittivity of the liquid crystal (PDLC) from the ordinary to extraordinary state. In the extraordinary state, the farfield directivity of the antenna is obvious and quite high (highly directive), compared to the ordinary state. The directivity of the antenna in ordinary state is 7.35 dBi at 0.54 THz, and in the extraordinary state, it is 8.43 dBi at 0.504 THz. Under \(\varepsilon\) state changing, the patterns are slightly deviated (e.g., the beam width, side lobe level, and lobe magnitude), which can be understood from the polar plots (b) and (d) of the antenna. However, the most important point to highlight is that the antenna reconfigurability feature under the state change in the PDLC is well retained. On the other hand, the farfield radiation patterns (3D and polar plot) of the two segment fractal antenna under different physical length variations are shown in Figure 7a-f at the ordinary state of PDLC. The antenna radiation characteristics alter when the electrical length is varied by cutting some parts of the fractal, as observed in the radiation patterns. From Figure 7a,b, it is observed that without the cutting of the fractal arm (no change in electrical length), the directivity of the fractal antenna is 5.9 dBi at 0.558 THz, with a 3 dB bandwidth of 89.8 degree and main lobe direction of 3.0 degree. However, the magnitude of the directivity and main love direction dramatically changed when some of the fractal arm was cut into different electrical lengths. When the fractal geometry was cut into small physical lengths (large electrical length), the curve shifted towards the left and the peak directivity changed to 7.22 dBi at 0.555 THz with a 3 dB bandwidth of 59.7 degree and main lobe direction of 18 degree, as shown in Figure 7c,d. However, when the fractal geometry was cut into large physical lengths (small electrical length), the curve shifted towards the right and the directivity reached 7.21 dBi at 0.579 THz with a 3 dB bandwidth of 74.4 degree and main lobe direction of 30 degree, as depicted in Figure 7e,f. It is worth noting that all the proposed antennas radiate predominantly in the vertical or E plane (\(\theta\)-plane) for the respective frequency bands. In the operating frequency bands, the antenna radiates very efficiently at the resonant, with a high radiation efficiency of >90%. The farfield directivities of all the fractal antennas at resonant frequencies are summarized in Table 2.  
The finite integration approach (FIT) utilized in CST MWS is used to analyze the simulated gain plots of the designed antenna. The far-field gain (3D and polar plot) of the one segment fractal antenna is displayed in Figure 8a-d. The peak gain of the antenna in ordinary state is 1.73 dBi at the resonant frequency 0.54 THz and in the extraordinary state, it is 4.29 dBi at the resonant frequency 0.504 THz. On the other hand, the farfield gain (3D and polar plot) of the two segment fractal antenna under different physical length variations is shown in Figure 9a-f at the ordinary state of PDLC. Initially, a gain of 0.981 dBi was observed at 0.558 THz for the two segment antenna without the cutting of the fractal