## 2 Structure
### Design of the Nano-Antenna  
The geometry of the proposed novel broadband optical nano-antenna that operates in the infrared and visible window is depicted in Figure 2, in terms of the front and side outlook. The design consists of a landscape-inspired Canadian flag-like antenna of length and width represented as \(L\) and \(W\), respectively. The antenna is fed by a hybrid plasmonic waveguide which achieves a strong light confinement by coupling the guided light from the dielectric waveguide and plasmonic waveguide. The side view of the antenna in Figure 2b shows that the design comprises three consecutive layers namely metal, low refractive index material, and dielectric having a high refractive index. The low refractive index material is sandwiched between metal and dielectric. The parametric values for the different dimensions shown in the cross-section view of the waveguide are as follows: The thickness of the metallic (Ag) layer, thin SiO\({}_{2}\) layer, and the Si layer are defined as \(h_{Ag}=100\) nm, \(h_{SiO2}=10\) nm, and \(h_{si}=100\) nm, respectively. The height of the substrate (\(h\)) is kept as 200 nm. To cover all of the optical communication windows, we fix our target frequency range of operation as 50-450 THz with the center frequency at fc = 250 THz (\(\lambda\)c = 1200 nm). The length (\(L\)) and width (\(W\)) of the antenna can be calculated using Equations (1)-(6) (where the effective permittivity of Ag is \((-129+3.28\) j) [38]. Table 1 represents the parametric values used for the simulations to obtain optimum performance of the designed antenna. The impedance of the waveguide is determined as follows:  
\[Z_{waveguide}=\frac{Z_{0}}{n_{eff}}=\frac{377}{n_{eff}} \tag{1}\]  
where the effective refractive index (\(n_{eff}\)) depends on the permittivity of the medium (\(\varepsilon_{m}\)) and dielectric (\(\varepsilon_{m}\)), as well as, the function of width (\(W\)) and thickness of SiO2 (\(h_{SiO2}\)). \(Z_{0}\) is the impedance of the free-space (vacuum), equal to 377 \(\Omega\).  
\[n_{eff}=\sqrt{\frac{\varepsilon_{m}\varepsilon_{d}}{\varepsilon_{m}+ \varepsilon_{d}}}F(W,h) \tag{2}\]  
\[F(W,h_{SiO_{2}})=\frac{1+1798W+311h_{SiO_{2}}+10.55 Wh_{SiO_{2}}}{32,300+759.7W +3337h_{SiO_{2}}+10.55 Wh_{SiO_{2}}} \tag{3}\]  
Figure 1: (**a**) Perspective view of the structure; (**b**) basic geometry of HPWG; and (**c**) TM mode.  
Finally, the antenna impedance, in terms of conductance (\(G\)) can be found as:  
\[Z_{antenna}=\frac{1}{Y_{in}}=\frac{1}{2G} \tag{4}\]  
\[G=\frac{W}{120\lambda_{0}}\Bigg{[}1-\frac{1}{24}\left(\frac{2\pi h_{SiO_{2}}}{ \lambda_{0}}\right)^{2}\Bigg{]} \tag{5}\]  
where \(\lambda_{0}\) is the free-space wavelength. The effective resonant length of the radiating patch is given by:  
\[L=\frac{\lambda_{0}}{2n_{eff}} \tag{6}\]  
The development of the design is performed in the steps shown in Figure 3, which produce a different set of return loss characteristics, as will be discussed in the next section. Changes have been made for an improvement in the antenna performance in terms of the driving point impedance bandwidth and the return loss. Figure 3 depicts that step 1 is designed by introducing a rectangular rod, having two triangular cuts on top of the rod with an operating band of 350 and 450 THz. In step 2, the patch is embedded with the same-sized rod with a wide band of operating frequency of 50-450 THz. A complete male-leaf shape is achieved with better results in step 3 having a broadband of (50-450 THz) with the resonance of 193, 229, 353, and 390 THz.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values (nm)** & **Parameters** & **Values (nm)** \\ \hline W & 960 & L\({}_{6}\) & 155 \\ L & 780 & L\({}_{7}\) & 125 \\ W\({}_{\text{g}}\) & 1600 & L\({}_{8}\) & 200 \\ L\({}_{\text{g}}\) & 1600 & L\({}_{