Atmospheric transmission distortion is one of the main challenges hampering the practical application of a vortex beam (VB) which carries orbital angular momentum (OAM). In this work, we propose and investigate a deep learning based atmospheric turbulence compensation method for correcting the distorted VB and improving the performance of OAM multiplexing communication. A deep convolutional neural network (CNN) model, which can automatically learn the mapping relationship of the intensity distributions of input and the turbulent phase, is well designed. After trained with loads of studying samples, the CNN model possesses a good generalization ability in quickly and accurately predicting equivalent turbulent phase screen, including the untrained turbulent phase screens. The results show that through correction, the mode purity of the distorted VB improves from 39.52% to 98.34% under the turbulence intensity of $C_n^2$ = 1 × 10⁻¹³. Constructing an OAM multiplexing communication link, the bit-error-rate (BER) of the transmitted signals in each OAM channel is reduced by almost two orders of magnitude under moderate-strong turbulence, and the demodulated constellation diagram also converges well after compensated by the CNN model.

Vortex beams (VBs), possessing a helical phase front and carrying orbital angular momentum (OAM), have attracted considerable attention in optical communications for their mode orthogonality. A platform for achieving all-optical signal processing of VBs, however, remains elusive due to the limited light-field-manipulation capability. We introduce diffractive deep neural networks (${\mathrm{D}}^2$NNs) and their applications to process VBs. Exploiting the multiple-light-field-modulation ability of multilayer diffraction structures and the strong data-processing capability of deep neural networks, we reveal that ${\mathrm{D}}^2$NNs can manipulate multiple VBs by configuring the phase and amplitude distribution of diffractive screens. The diffraction efficiency and converted-mode purity are greater than 96%. After being trained, ${\mathrm{D}}^2$NNs with functions of hybrid-OAM-mode generation, identification, and conversion are obtained, and three typical types of all-optical signal-processing communication, (OAM-shift keying (OAM-SK), OAM multiplexing and demultiplexing, and OAM-mode switching) are successfully achieved. Our simulation results provide an approach that breaks the limitations of poor functionality and complex design in processing VBs, introducing the ${\mathrm{D}}^2$NN as a universal light-field-modulation platform.

Optical logical operations demonstrate the key role of optical digital computing, which can perform general-purpose calculations and possess fast processing speed, low crosstalk, and high throughput. The logic states usually refer to linear momentums that are distinguished by intensity distributions, which blur the discrimination boundary and limit its sustainable applications. Here, we introduce orbital angular momentum (OAM) mode logical operations performed by optical diffractive neural networks (ODNNs). Using the OAM mode as a logic state not only can improve the parallel processing ability but also enhance the logic distinction and robustness of logical gates owing to the mode infinity and orthogonality. ODNN combining scalar diffraction theory and deep learning technology is designed to independently manipulate the mode and spatial position of multiple OAM modes, which allows for complex multilight modulation functions to respond to logic inputs. We show that few-layer ODNNs successfully implement the logical operations of AND, OR, NOT, NAND, and NOR in simulations. The logic units of XNOR and XOR are obtained by cascading the basic logical gates of AND, OR, and NOT, which can further constitute logical half-adder gates. Our demonstrations may provide a new avenue for optical logical operations and are expected to promote the practical application of optical digital computing.