# Holographic Silicon Metasurfaces for Total Angular Momentum Demultiplexing Applications in Telecom
## 3 Results  
The output of the fabricated PBOEs has been analyzed and recorded for input circularly-polarized beams with well-defined OAM. For each PBOE, beams carrying OAM in the sorting set of the selected metasurface have been produced, in sequence, and circularly polarized before impinging on the optical element, according to the scheme in Figure 6. Using a Mach-Zehnder interferometric bench, as shown in Figure 6, the interference pattern between the generated OAM beam and a reference Gaussian beam was generated and collected in order to check the input OAM value. As a matter of fact, since the phase structure of an integer-OAM beam presents \(\ell\) intertwined helical phase fronts, being \(\ell\) the amount of OAM, the interference with a coaxial Gaussian beam generates a fringe pattern of \(\ell\) spirals, whose helicity is given by the sign of \(\ell\)[44] (Figure 7a, Figure 8a, and Figure 9a).  
Figure 8: Optical characterization of the demultiplexer in Figure 3. (**a**) Experimental interference pattern of the input beams. The twist-handedness and number of the spiral arms reveal the sign and value of orbital angular momentum, respectively. Experimental output intensity for input right-handed (**b**) and left-handed (**c**) circular polarization states. The position of the far-field bright spots is in accordance with the channel scheme depicted in Figure 3b.  
Figure 7: Optical characterization of the demultiplexer in Figure 2. (**a**) Experimental interference pattern of the input beams. The twist-handedness and number of the spiral arms reveal the sign and value of orbital angular momentum, respectively. Experimental output intensity for input right-handed (**b**) and left-handed (**c**) circular polarization states. The position of the far-field bright spots is in accordance with the channel scheme depicted in Figure 2b.  
When a beam carrying OAM illuminates the demultiplexer, the optical element performs the projection over the mode set for which the phase pattern has been calculated. Next, a bright spot is detected in correspondence of the input OAM value, when it is present, at the coordinates given by corresponding far-field channel scheme. Otherwise, a non-null OAM beam is generated, i.e., an annular intensity profile with a central dark singularity.  
In Figure 7, the optical characterization is reported for the PBOE performing OAM sorting in the range {-3,..., +3} with OAM step \(\Delta\ell\) = 1 (Figure 7a). In Figure 7b,c, the far field is shown for input beams with right-handed and left-handed circular polarizations, respectively. As expected, the demultiplexer can sort the orthogonal polarization states onto two different linear arrays, while the OAM value is detected correctly according to the scheme in Figure 2b. A similar analysis is reported in Figure 8, for the PBOE performing OAM demultiplexing in the range {-6,..., +6}, step \(\Delta\ell\) = 2, according to the scheme in Figure 3b. In Figure 8b,c, the far field is shown for input optical vortices with right-handed and left-handed circular polarizations, respectively. The demultiplexer separates the orthogonal polarization states onto two heptagons, while the OAM content is detected correctly. Figure 9 reports the optical analysis of the PBOE performing sorting in the OAM range {-9,..., +9}, step \(\Delta\ell\) = 3, over a circular configuration, as depicted in the scheme in Figure 4b. In Figure 9b,c, the far field is shown for input vortices with right-handed and left-handed circular polarization, respectively. As expected, the demultiplexer can distinguish between orthogonal polarization states, by projecting them onto two complementary, i.e., non-overlapping, semicircles.