# Plasmonic and Dielectric Metasurfaces: Design, Fabrication and Applications
## 2 Plasmonic Metasurfaces
By controlling the orientation angle of rectangular apertures, we can construct the desired spatially-variant polarizers to generate OAM-carrying vector beams with a right or left circularly-polarized input light beam. Figure 3c shows an example of the phase front and spatial polarization after passing though the metasurfaces, which indicates the generation of the OAM-carrying vector beam from the circularly-polarized beam. Figure 4 depicts the spatial distributions of phase, power and polarization of output beams under the excitation of input left circularly-polarized light (\(\mathbf{E}_{in}=[1\ \mathbf{i}]\ ^{T}\)). We set the wavelength at 1550 nm to characterize the properties of the generated OAM-carrying vector beams. The employed metasurfaces have an orientation angle of \(\alpha\) (\(\phi\)) = \(l\phi\) + \(\alpha_{0}\), where \(l\) varies from +3 to \(-\)3 and \(\alpha_{0}\) = 0. We use \(\mathbf{E}_{1}\) and \(\mathbf{E}_{2}\) to represent the electric field components along the directions of \(\mathbf{e}_{1}\) (\(\phi\)) and \(\mathbf{e}_{2}\) (\(\phi\)) in Figure 3b, respectively. The first row of Figure 4 shows the spatial phase distribution of \(\mathbf{E}_{1}\), indicating that output beams carry OAM with a charge number of \(l\) from +3 to \(-\)3. The second and third rows of Figure 4 show spatial power distributions (\(P_{1}\propto|\mathbf{E}_{1}\ ^{2}\), \(P_{2}\propto|\mathbf{E}_{2}\ ^{2}\)) along the directions of \(\mathbf{e}_{1}\) (\(\phi\)) and \(\mathbf{e}_{2}\) (\(\phi\)), respectively. It is found that the power component \(P_{1}\) is much larger than \(P_{2}\). The extinction ratio (ER), defined by 10 \(\times\) log\({}_{10}\)(\(P_{1}\)/\(P_{2}\)), exceeds 20 dB. Hence, the electric field component \(\mathbf{E}_{2}\) along the direction of \(\mathbf{e}_{2}\) (\(\phi\)) can be ignored. The fourth and fifth rows of Figure 4 show spatial power distributions (\(P_{x}\), \(P_{y}\)) along \(x\) and \(y\) axes, respectively. The alternative bright and dark power distribution implies that the polarization state rotates with the azimuthal angle \(\phi\). The sixth row of Figure 4 shows the calculated spatial polarization distribution, implying the generation of vector beams with a polarization order of \(l\) from +3 to \(-\)3. The obtained results shown in Figure 4 confirm the successful generation of OAM-carrying vector beams using metal-assisted metasurfaces. \begin{table}
\begin{tabular}{|p{142.3 pt}|p{142.3 pt}|} \hline \multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{Rectangular apertures arranged in an array with rotational symmetry in metal film to generate OAM beams. Reproduced with permission from [98], Copyright The Optical Society, 2012.} \\ \hline \multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{Metal nanorods to generate broadband OAM beams. Reproduced with permission from [99], Copyright American Chemical Society, 2012.} \\ \hline \multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{Split-ring resonators to generate the second harmonic. Reproduced with permission from [102], Copyright Nature Publishing Group, 2015.} \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. We also study the operation bandwidth. Metasurfaces with an orientation angle of \(\alpha\) (\(\phi\)) = \(l\phi\) + \(\alpha_{0}\) (\(l\) = 1, 2, 3) are considered. Left circularly-polarized light is adopted as the input excitation source. We use ER and purity to characterize the quality of the generated OAM-carrying vector beams. Figure 5a plots ER as a function of wavelength. One can clearly see the high-quality broadband generation of OAM-carrying vector beams ranging from 1000-2500 nm, i.e., from near-infrared to mid-infrared. For \(l\) = 1 and 2, the ER is kept above 20 dB over a 1500-nm bandwidth (1000-2500 nm).