# Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning
## 1 Introduction
Although the aforementioned studies show the feasibility of encoding systems based on OAM modes, OAM does not increase the amount of information, nor does it exceed the multiple-input multiple-output (MIMO) transmission of current standards in optical communications [7; 27]. In fact, the number of spatial modes available for data encoding is limited by the space-bandwidth product of a given optical system [27; 28]. A solution to this problem is to use all spatial degrees of freedom offered by OAM modes. A commonly used OAM beam for this purpose is a Laguerre-Gaussian (LG) beam [7; 17], which provides eigen-modes dependent on both radial (\(p\)) and azimuthal (\(\ell\)) indices, being able to use the superposition of modes to increase the number of encoding data in a limited system. On the other hand, a decoding system (which is generally based on image detection and classification) can present strong signal distortion (both in the intensity profile and in the phase distribution) due to optical alignment, turbulence and scattering [29]. Recently, convolutional neural networks (CNNs) and machine learning techniques have been implemented in optical coding systems as an alternative solution for image detection and classification [30; 31; 32]. High-resolution recognition techniques based on deep learning to encode data in spatial modes have already been implemented [33]. The deep-learning-based approach has also been used to recover the sparse data from multiplexed OAM channels independent of phase information [34]. Although these studies demonstrate the feasibility of encoding systems based on OAM modes as well as various methods implemented for data decoding, there is still a gap concerning image detection and classification methods in decoding due to degradation effects that the medium induces in the transmitted signal, which brings the motivation for this research work. Motivated by previous statements, this paper proposes a comprehensive optical encoding-decoding system based on the intensity profile generated by a coherent superposition of two OAM-carrying Laguerre-Gaussian (LG) modes and a machine learning detection method. In the encoding process, an intensity profile for data encoding is generated based on the selection of \(p\) and \(\ell\) indices of LG beams, while the decoding process is performed using support vector machine (SVM). Different from other existing encoding systems that require the additional extraction of phase information, this paper proposesa novel optical encoder based on the number of spatial modes carrying data symbols increased in a limited optical system. Moreover, the proposed optical encoding model opens a pathway to a stable image detection and classification system based on machine learning that only uses the intensity profile for target modes. As a result, the main contributions of this paper are: (1) a comprehensive design of a coherent optical encoding system based on the superposition of LG modes carrying OAM that is independent of phase information and (2) a robust decoding system based on intensity profile recognition using the machine learning SVM method. Section 2 presents the concept and operating principle of the optical encoder. In Section 3, the SVM-based decoding method for image recognition and classification is explained in detail. In Section 4, a case study for a 4-bit coding system with different types of noise is considered to validate the robustness of the proposed encoder. Finally, Sections 5 and 6 exhibit the results and conclusion, respectively.