# Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning
## 1 Introduction  
Since the study of [PERSON] et al. [1], optical beams with orbital angular momentum (OAM) have aroused growing interest from researchers around the world due to their wavefront helical shape properties that provide a new degree of freedom for exploration of new applications in particle manipulation [2, 3], image processing [4, 5] and optical communications [6, 7]. In this context, optical communications systems have found a possibility of exploring vortex beams properties in multiplexing [8, 9] and data encoding [10, 11] pathways. Concerning data encoding, OAM states to encode different data symbols are evidenced by [PERSON] et al. [12], where OAM holography is performed by OAM selectivity in a spatial-frequency domain without a theoretical helical mode index limit. In the area of holographic encryption, [PERSON] et al. [13] propose a two-coding information metasurface to achieve OAM-encrypted holography. OAM encoding has also been explored in multicasting links; for instance, [PERSON] et al. [14] encode digital signals through the OAM free space one-to-many multicasting link. Within the same research line, data coding has also been explored experimentally as demonstrated by [PERSON] et al. in [15], where data encoding at 20 Gb/s, using 4 possible OAM modes, is performed. High-dimensional data encoding through a hybrid OAM-radial index is also demonstrated in [14]. Optical encoding and multiplexing techniques in OAM channels for highly dispersive media have also been implemented [11], where a novel scattering-matrix-assisted retrieval technique was proposed to demultiplex OAM channels from highly scattered optical fields. There is a lot of evidence of OAM applications, for instance, in the data encoding field in free space and fiber-based transmission channels [16, 17], polarization-based [18, 19] and intensity and vortices in phase-based channels [20]. However, implementation of anOAM-based encoding system requires overcoming several challenges from the point of view of information medium propagation and system detection implementation. Due to the nature of information propagation, some effects can be induced in the medium, such as absorption, scattering and turbulence, spatial distortion (amplitude and phase), modal coupling and crosstalk. Some of these effects, as in the case of turbulence and modal crosstalk, have been potentially suppressed in coding and multiplexing systems through mitigation methods [21], but for the most part, these effects constitute a great challenge [11; 22]. Such challenges have captured the attention of the scientific community to focus their studies on designing more robust and flexible optical encoders and encryptors based on coding techniques that minimize noise and information distortion, while correctly maximizing the amount of data coded. In this way, the efforts to improve optical encoding systems are reflected in image recognition methods for encoded data, as in the case of [23], where an index modulation is implemented for OAM states with a uniform scheme circular array (OAM-UCA) to build low-intensity parity coding to improve error performance and transmit additional bits of information. Incoherent detection methods have also been implemented for data decoding [24], where an image information transfer method based on petal-like beam lattices for coding is used. In this case, a decoding system works directly with the identification of the intensity patterns captured. Another example of an image-based method is presented in [20] that employs the amplitude and the phase of an optical field into a phase-only hologram to control spatial transverse modes for data symbol mapping. A similar study can be found in [25] that uses an OAM array for a free-space communication encoding/decoding link with 625 states. A proposal for OAM light encoding in magnets has also been developed in [26], where the possible sub-wavelength magnetic phenomena induced by a vortex beam and their applications in the generation of topological defects in chiral magnets is discussed.