# Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces
## 3 Metasurfaces for OAM Generation
### Ultrathin Complementary Metasurface  
The efficiency of reflective metasurface could be very high by placing a reflector beneath it, while for transmissive metasurface, high efficiency cannot be easily achieved due to the reflection at the metasurface-air interface stemming from the impedance mismatch. In the following, we show our designed double-layer complementary metasurface for OAM generation with high efficiency [85].  
The unit cell is shown in Figure 4a. Each unit cell consists of four complementary split-ring resonators (CSRRs) with two different sizes and orientations. The equivalent circuit and its response for each pair are drawn in Figure 4b. It is clear that the double-layer structure offers two parallel inductor-capacitor (LC) resonant circuits so that we have a sufficient tunable range to achieve the design objective, i.e., the same high transmittance from the two pairs as well as the \(\pi\) phase difference between their transmission coefficients. Figure 4c presents the full-wave simulation results of unit cell. At 17.85 GHz, magnitudes of the co-transmission coefficients are both 0.91 and their phase difference is \(\pi\), indicating a 81% circular polarization conversion efficiency. This double-layer structure can be fabricated on a conventional PCB.  
Then a whole metasurface is built by arranging the unit cells with varying orientations. Two metasurfaces with topological charges of 1 and 2 are designed. The top view of the designed metasurface is shown in Figure 5. Each metasurface includes 24 scatterers, whose centers describe two circles with the radius of \(r_{1}\) and \(r_{2}\).  
Figure 3: The amplitude and phase distributions of reflected electric fields from the discrete PEC-PMC metasurface. For the generation of OAM of order \(-2\), (**a**) amplitude; (**b**) phase at a transverse plane \(z=40\) mm. For the generation of OAM of order \(-4\), (**c**) amplitude; (**d**) phase at a transverse plane \(z=100\) mm. Reproduced with permission from [84], Copyright AIP Publishing LLC, 2016.  
The EM responses from the metasurfaces are calculated by an equivalent dipole model and CST MWS. In the equivalent dipole model, each unit cell is considered to be two orthogonal magnetic dipole sources with the orientations aligned with the long side of the CSRRs. Therefore, the EM response from the whole metasurface is considered to be a sum of the response from magnetic dipoles with varying orientations. This approach is useful to simulate a metasurface comprising a great number of scatterers that can be treated as point sources with arbitrary strengths, locations and orientations. The calculated field distributions are shown in Figure 6. The results verify the successful generation of OAM. The divergence between the results from the dipole model and the full-wave simulation comes from the coupling between unit cells.  
Figure 4: Schematic and the response of the proposed unit cell: (**a**) Schematic; (**b**) Equivalent circuit model of one pair of complementary split-ring resonators (CSRRs) and simulated \(S_{21}\). The purple and green curves are obtained by the translation of the original blue (magnitude) and red (phase) curves. The distance between the two layers is \(h=1.25\) mm. Characteristic impedance of free space is \(Z_{0}=377\)\(\Omega\). The capacitance and inductance are \(C_{0}=0.09\) pF and \(L_{0}=1.03\) nH; (**c**) Full-wave simulation results. The period of the unit cell is \(7\times 7\) mm\({}^{2}\). Side lengths of the two types of square CSRRs are \(a_{l}=5.2\) mm and \(a_{s}=3.9\) mm. The length of the gap is \(g=0.2\) mm. The width of the slots is \(t=0.2\) mm. Reproduced with permission from [85], Copyright IEEE, 2017.  
Figure 5: Geometric structure of the metasurface. Topological charge is (**a**) \(q=1\); (**b**) \(q=2\). The radius of the inner ring is \(r_{1}=14\) mm and that of the outer ring is \(r_{2}=21\) mm. Reproduced with permission from [85], Copyright IEEE, 2017.