# Plasmonic and Dielectric Metasurfaces: Design, Fabrication and Applications
## 2 Plasmonic Metasurfaces
For \(l\) = 3, ER > 16 dB over a bandwidth of 1500 nm (1000-2500 nm) and ER > 20 dB over a bandwidth  
Figure 4: Spatial distributions of the phase, power and polarization of the generated OAM-carrying vector beams (\(\sigma\) = 1: left circularly polarized input beam, \(\alpha_{0}\) = 0: along the direction of \(\mathbf{e}_{1}\) (\(\phi\))). Reproduced with permission from [118], Copyright The Optical Society, 2013. Figure 3: (**a**) Schematic structure of metasurfaces for generating the OAM-carrying vector beams; (**b**) geometric parameters: the radii are \(r_{i}\) = (\(i\) + 6.3) \(\times\) 700 nm (\(i\) = 0, 1), and the orientation angle is \(\alpha(\phi)\) = \(l\phi\) + \(\alpha_{0}\) (\(l\) = 2, \(\alpha_{0}\) = 0 as an example) with respect to the \(x\) axis; the rectangular aperture has a dimension of 600 \(\times\) 140 nm; (**c**) illustration of generating the OAM-carrying vector beam (OAM charge number: two, polarization order: two). Reproduced with permission from [118], Copyright The Optical Society, 2013.  
of 800 nm (1000-1800 nm) are achieved. Shown in Figure 5b is the wavelength-dependent purity for the OAM-carrying vector beam (\(l=3\)), which is larger than 0.85 over a bandwidth of 1500 nm (1000-2500 nm). The insets depict weight spectra as functions of OAM charge number and polarization order number at 1550 nm. High values of purity are achieved. In Figure 3a, two concentric rings are used to excite a single OAM-carrying vector beam. Actually, one ring can also enable the generation of one OAM-carrying vector beam. Hence, it is possible to generate multiple OAM-carrying vector beams by forming multiple concentric rings in a gold film, as shown in Figure 6, where each ring contains a rectangular aperture array with each aperture acting as a localized polarizer. In particular, it is expected to selectively generate different orders of OAM-carrying vector beams by shining the circularly-polarized light source onto different concentric rings. Figure 7a shows ER as a function of wavelength. One can see broadband operation from 1000-1550 nm with an extinction ratio above 20 dB, which indicates high-quality broadband (~500 nm) generation of OAM-carrying vector beams. We further study the fabrication tolerance by evaluating the performance dependence on the initial orientation angle \(\alpha_{i0}\) of the rectangular aperture. Figure 7b shows the extinction ratio as a function of the initial orientation angle \(\alpha_{20}\) of rectangular apertures in the second ring. The extinction ratio is kept above 20 dB when \(\alpha_{20}\) is varied from \(-1\) to 7 degrees. The obtained range of initial orientation angle around eight degrees implies the good fabrication tolerance of the designed metasurfaces. We use \(\mathbf{E}_{1i}\) and \(\mathbf{E}_{2i}\) to denote the electric field components on  
Figure 5: Wavelength-dependent (**a**) extinction ratio (ER); and (**b**) purity for the generation of OAM-carrying vector beams. Insets in (**b**) show the weight as functions of OAM charge number (left) and polarization order number (right) at 1550 nm. Reproduced with permission from [118], Copyright The Optical Society, 2013. Figure 6: (**a**) Schematic structure of metasurfaces; (**b**) geometric parameters: the radius of the ring is \(r_{i}=(2i+0.3)\times 700\) nm, where \(i=1\), 2 and 3. The rectangular aperture has dimensions of 600 \(\times\) 140 nm and an orientation angle of \(\alpha_{i}\) (\(\phi\)) = \(i\phi+\alpha_{i0}\) with respect to the \(x\) axis. Reproduced with permission from [119], Copyright The Optical Society, 2013.  
the directions of \(\mathbf{e}_{1i}\) (\(\phi\)) and \(\mathbf{e}_{2i}\) (\(\phi\)) (similar to \(\mathbf{e}_{1}\) (\(\phi\)) and \(\mathbf{e}_{2}\) (\(\phi\)) in Figure 3b), respectively. We calculate the phase of \(\mathbf{E}_{1i}\) and the power components on directions of \(\mathbf{e}_{1i}\) (\(\phi\)), \(\mathbf{e}_{2i}\) (\(\phi\)), \(x\) and \(y\) axes, which are represented by \(P_{1}\), \(P_{2}\), \(P_{x}\) and \(P_{y}\), respectively.