# Plasmonic and Dielectric Metasurfaces: Design, Fabrication and Applications
## 3 Dielectric Metasurfaces
### OAM Beam Generation Using a Nanophotonic Dielectric Metasurface Array [123]  
We design and fabricate a kind of chip-scale dielectric metasurface array on a silicon-on-insulator (SOI) platform. Figure 19 shows the schematic drawing of the proposed dielectric metasurface units, consisting of rectangle or ellipse silicon resonators with various dimensions. The working principle of these proposed dielectric resonators can be explained as follows: the polarization of incident light is along the \(x\) axis, which can be decomposed into two perpendicular components corresponding to the long and short axis of the resonator, respectively; the reflection amplitudes of the response for a resonator in both components are almost the same, while the relative phase retardation is around \(\pi\), where the linear polarization conversion occurs, resulting in a \(y\)-polarized reflected light. OAM beam generation using the dielectric metasurface at 1064 nm: Then, we simulate the amplitude and phase responses of the near-field of reflected light of a rectangle dielectric metasurface unit with various dimensions using the FDTD method at a wavelength of 1064 nm. The simulated \begin{table}
\begin{tabular}{|p{142.3 pt}|p{142.3 pt}|} \hline Silicon nanodiscs to achieve high transmission and full phase control in visible wavelengths. Reproduced with permission from [125], Copyright John Wiley and Sons, 2015. \\ Silicon cut-wire array in combination with a silver ground plane to achieve high linear polarization conversion efficiency in the near-infrared band. Reproduced with permission from [126], Copyright American Chemical Society, 2014. \\ Silicon nano-pillar array to realize low loss micro-lenses in the near-infrared band. Reproduced with permission from [127], Copyright The Optical Society, 2014. \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 19: Schematic diagram of the top view of the designed reflective dielectric rectangle/ellipse metasurface units based on a silicon-on-insulator (SOI) platform. results indicate that the response of the proposed resonator can cover a full phase varying over 0-2\(\pi\) and a wide shift of amplitude. It is relatively easy to find out a series of resonators covering full-phase control while maintaining approximately constant amplitude, which is considerably important for OAM beam generation. Then, eight kinds of resonators with different geometric dimensions are chosen to provide an equal-spacing phase shift from 0 to 2\(\pi\) and nearly constant amplitude, as plotted in Figure 20. Figure 21 plots the simulated intensity and phase distributions of OAM beams of topological charge number \(l\) = 1-4 generated using the rectangle dielectric metasurface array consisting of the eight chosen resonators. The results indicate that the generated OAM beams match the theoretical ones well. OAM beam generation using the dielectric metasurface at 632.8 nm: Moreover, we also design the dielectric ellipse metasurface arrays at a wavelength of 632.8 nm. Figure 22 shows the concept of OAM beam generation through a dielectric ellipse metasurface array consisting of a series of resonators covering a full-phase modulation. When a Gaussian beam of vertical polarization is incident to the metasurface, the reflected beam can be transformed into OAM beams of horizontal polarization. In view of the polarization conversation happening on the proposed metasurface, one can easily separate the incident and reflected lights. Figure 23 plots the simulated intensity and phase distributions of OAM beams of topological charge number \(l\) = 1-4 generated using the dielectric ellipse metasurface array consisting of the eight chosen resonators at a wavelength of 632.8 nm. The results indicate that the generated OAM beams match the theoretical ones well. Figure 21: Simulated intensity and phase distributions of the generated OAM beams by the proposed rectangle dielectric metasurface array at a wavelength of 1064 nm.