# Holographic Silicon Metasurfaces for Total Angular Momentum Demultiplexing Applications in Telecom
## 1 Introduction  
In the last decades, the possibility to structure the spatial degree of freedom of light has acquired increasing interest, with applications in a wide range of fields. In particular, the exploitation of light beams with helical phase-fronts has provided disruptive achievements in microscopy [1, 2], astronomy [3], particle manipulation [4], holography [5], and information and communication technology (ICT) [6, 7]. Since the seminal paper of [PERSON] and coworkers [8] demonstrated that such beams carry orbital angular momentum (OAM), the study on methods and devices to generate and control this still unexploited degree of freedom has given rise to a flourishing research field [9]. It is especially in the ICT that the orbital angular momentum of light has demonstrated the most promising applications, in combination with other degrees of freedom of light [10]. As a matter of fact, the OAMdegree of freedom opens to an unbounded state space, in which light beams carrying different integer OAM values are orthogonal to each other and can be exploited for the transmission of different data streams at the same frequency with no interference [11]. The aggregate combination of OAM-mode division multiplexing (OAM-MDM) with other well-established multiplexing methods, e.g., time, polarization, wavelength, and amplitude/phase, has demonstrated to provide a significant increase in the spectral efficiency of today's optical networks [12], both in free-space [13] and optical fibers [14; 15], offering a solution to the problem of optical network saturation [16]. Both in the classical and quantum regimes, the combined manipulation of OAM and polarization has acquired paramount importance, and novel devices are required for the parallel detection in a compact and effective way. As a matter of fact, optical vortices propagating in multi-mode fibers have been demonstrated to be circularly polarized [15]. In the single-photon regime, the combination of orbital angular momentum and polarization opens to a wider state space for quantum-key distribution (QKD) applications [17], in which higher security and robustness against errors and eavesdropping are guaranteed with respect to standard protocols limited to polarization [7]. Novel formulations and innovative implementations of standard QKD protocols have been developed and demonstrated [18], both in discrete variable (DV-QKD) and continuous variable (CV-QKD) scenarios [19]. Concurrently, research efforts have focused on the design and realization of polarization-sensitive OAM (de)multiplexers, in order to generate and sort the state space exploited for high-dimensional QKD [20; 21]. In the last decade, several methods have been conceived for demultiplexing, i.e., the separation, of a superposition of beams with different values of OAM [22]. In particular, increasing interest has been devoted to solutions which could offer high miniaturization and integration levels, fabrication protocols suitable for mass-production, and backward compatibility with different multiplexing techniques. In order to improve the miniaturization level, we recently disclosed the realization of 3D multi-level phase-only diffractive optical elements [23; 24; 25; 26] performing OAM-mode generation and detection in the visible range, based either on _log-pol_ optical transformation [27] or OAM-mode projection [28; 29]. In comparison with bulky refractive elements, the diffractive version provides a miniaturized and almost flat implementation, in particular, when shorter focal lengths are necessary, i.e., for high miniaturization. On the other hand, the design of diffractive optics turns out to be optimized within a narrow bandwidth, therefore they exhibit a decrease in efficiency when operating far from the optimal wavelength. The optical thickness is inversely proportional to the refractive index of the material, and increases proportionally to the design wavelength.