# Holographic Silicon Metasurfaces for Total Angular Momentum Demultiplexing Applications in Telecom
## 4 Discussion  
In this work, we described the design, nanofabrication, and optical characterization of silicon metasurfaces for the parallel sorting of orbital angular momentum and polarization using the method of optical-mode projection. The samples were fabricated in the form of dielectric Pancharatnam-Berry optics, whose inhomogeneous anisotropy imparts a spatially-variant phase-change due to a local control of the input polarization. In particular, the phase is geometric in nature and equal to twice the rotation angle of the local extraordinary axis, corresponding to the direction of the subwavelength grating vector. Three different sorters have been designed and fabricated, performing combined PDM and OAM-MDM over different OAM sets and channel configurations, with the aim to exhibit the versatility of the demultiplexing method in terms of channels geometry and OAM values. In particular, we demonstrated the possibility to sort a symmetric range of OAM beams over a linear  
Figure 9: Optical characterization of the demultiplexer in Figure 4. (**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 4b.  
array and over 2D regular distributions, specifically a regular polygon and a semicircle. By properly designing the far-field channel scheme, fixed by the spatial frequency carriers in the phase pattern definition of the sorter, it was possible to originate two non-overlapping channel geometries for the two orthogonal polarizations. The optical characterization has been reported at the wavelength of 1310 nm, in the telecom O-band, showing the expected capability to distinguish between modes with different orbital angular momentum and spin values by using a single element. With respect to the diffractive counterpart [23], the number of available channels is redoubled without the need of additional optical elements.  
Metasurfaces have become one of the most rapidly expanding frontiers of nanophotonics to revolutionize optics by substituting refractive and diffractive optics in many widespread applications and introducing entirely altogether novel functionalities [45; 46]. In particular, the possibility to use silicon as optical material has promoted the flourishing of a new framework in which optics design and silicon photonics merge to create a new generation of optical elements with unprecedented levels of integration. In comparison with plasmonic metamaterials, the importance of silicon in optics design and fabrication is based not only on its optical properties, low-cost, and well-established nanofabrication techniques, but also on the peculiar and promising prospects that silicon nanostructures can provide in terms of integration into existing photonic architectures and complementary metal-oxide semiconductor (CMOS) compatibility [47; 48].  
By including optics design and silicon photonics, the presented metasurfaces pave the way to novel optical devices for combined polarization- and OAM-mode division multiplexing with an unprecedented combination of miniaturization and integration.  
Conceptualization, G.R. and F.R.; formal analysis, G.R.; investigation, G.R., M.M., and P.C.; software, G.R.; methodology, M.M., P.C.; writing--original draft preparation, G.R., P.C., and M.M.; writing--review and editing, F.R.; supervision, F.R.; funding acquisition, F.R. This work was supported by SM Optics S.r.l--SIAE Group, and by CEPOLISPE project 'VORTEX 2'. The authors gratefully thank [PERSON] and Ing. [PERSON] for the interesting discussions during this work. The authors declare no conflict of interest.