Multi-stage optoelectronic hybrid recognition of signed high-order orbital angular momentum modes

Vortex beams carrying orbital angular momentum (OAM) enable high-dimensional encoding capabilities and thus offer significant potential for enhancing optical communication capacity. Nevertheless, their vulnerability to disturbances during free-space propagation poses substantial challenges for accurate OAM mode recognition at the receiver. As an all-optical artificial intelligence framework, the diffractive deep neural network (D²NN) exploits the advantages of all-optical computation and provides a promising solution for OAM mode recognition in complex environments. In this work, we designed a multi-stage optoelectronic hybrid D²NN model for signed high-order OAM vortex beams, referred to as the D²NN-HoOAM mode recognition model. This architecture integrates all-optical diffractive computing units with an electronic decision-making logic, enabling accurate recognition of signed high-order OAM modes. The influence of atmospheric turbulence (AT) intensity, radial index, and propagation distance on the recognition accuracy was investigated systematically. Furthermore, the model's robustness against physical misalignments, its generalization capability, and key optical metrics were also analyzed. The results demonstrate that, across a wide range of AT intensities (1 × 10^-16m^-2/3-1 × 10^-14m^-2/3), the proposed D²NN-HoOAM mode recognition model can achieve accurate recognition of 100 signed high-order OAM modes (topological charges l = -50 to +50, excluding zero), with an average recognition accuracy above 95.7%. The proposed signed high-order OAM mode recognition method based on a multi-stage optoelectronic hybrid D²NN model provides a promising solution for high-capacity free-space optical communication.