## 2 Results and Discussion
### Large Frequency Shift or Tuning  
The electromagnetic characteristics of the fractal antenna are manipulated at both the level of fractal geometry and electrical length. Due to its unique repeated fractal pattern, it allows for the design of relatively smaller antenna dimensions for a relatively long wavelength operation. One of the features in our proposed antenna design is to utilize this length reduction in the Hilbert fractal antenna to create a medium to large discrete frequency shift (Figure 4a). As one can observe from Figure 4a, for a large frequency shift, one can simply disconnect a larger section of the antenna's electrical length (or disconnect a large segment of fractal pattern) in the antenna, hence reducing the overall size of the antenna and generating an upward frequency shift. On the other hand, if more fractal patterns are added or the electrical length is increased, the frequency will decrease due to a longer antenna. For a finer frequency shift, one can simply disconnect fewer fractal patterns or change the electrical length (Figure 4b,c). The effect can either increase the electrical length, which decreases the frequency, or vice versa. A simulation performed on a CST numerical software shows that a 0 to >21% frequency shift can be generated by this  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Parameters** & **L1** & **L2** & **L3** & **L4** & **L5** & **L6** & **L7** & **L8** & **L9** & **L10** & **W** & **g** & **\(I_{s}\)** & \(S_{s}\)** \\ \hline
**Dimension (\(\mu\)m)** & 25 & 35 & 30 & 30 & 25 & 20 & 40 & 30 & 60 & 90 & 5 & 30 & 450 & 7650 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimum values for fractal geometric dimensions of the proposed reconfigurable antenna.  
Figure 3: Geometric dimensions of (**a**) one segment unit cell (4 th iteration) and (**b**) magnified view of the 2 nd iteration of the unit cell antenna.  
reconfigurable Hilbert fractal antenna design when it operates at the 0.3 to 0.4 THz region (Figure 4d). The finesse of the frequency shift and tuning range is highly dependent on the fractal antenna design. For the demonstration of the concept, the Hilbert fractal pattern is utilized and only a slight modification is carried out on the dimension to show the potential of using a reconfigurable fractal antenna. However, many more unique fractal pattern designs will be investigated later using a generic algorithm or wavelet technique to search for the best frequency reconfigurability and performance. PIN diodes, varactors, FETs or other transistors will be used as switches to allow for frequency re-configurability between 0.2 and 0.6 THz [30]. Note that the position of varactors on the antenna will be optimized for obtaining a wide range of frequency tunability. These diodes can be fabricated along with the rectifier or subsequent supporting electronics separately, then anodic bonded together later.  
Figure 4: Reconfigurable Hilbert fractal antenna: (**a**) two segments without cut arm, (**b**) two segments with longer electrical length, (**c**) two segments with shorter electrical length and (**d**) large frequency shift by disconnecting or removing some part of the fractal pattern or electrical length. Here, we observe a left ward shift in frequency when the size of the fractal pattern is reducing and when size is increasing, we observe a rightward shift in frequency. This is clearly shown by the switching between one segment and two segment fractal design. Medium range frequency shift can be achieved by removing a smaller portion of the fractal pattern in the design. Here, three arms are cut from each segment, which means that the electrical length increases. A \(\sim\)0.02 THz downward shifted is observed (leftward shift). With even larger cut and arm length reduction, a rightward frequency shift is observed. Both techniques can be easily implemented by embedding diode-based switches at the junctions in the antenna to turn certain parts of the antenna on and off [30].