Orbital angular momentum (OAM) mode multiplexing provides a new strategy for reconstructing multiple holograms, which is compatible with other physical dimensions involving wavelength and polarization to enlarge information capacity. Conventional OAM multiplexing holography usually relies on the independence of physical dimensions, and the deep holography involving spatial depth is always limited for the lack of spatiotemporal evolution modulation technologies. Herein, we introduce a depth-controllable imaging technology in OAM deep multiplexing holography via designing a prototype of five-layer optical diffractive neural network (ODNN). Since the optical propagation with dimensional-independent spatiotemporal evolution offers a unique linear modulation to light, it is possible to combine OAM modes with spatial depths to realize OAM deep multiplexing holography. Exploiting the multi-plane light conversion and in-situ optical propagation principles, we simultaneously modulate both the OAM mode and spatial depth of incident light via unitary transformation and linear modulations, where OAM modes are encoded independently for conversions among holograms. Results show that the ODNN realized light field conversion and evolution of five multiplexed OAM modes in deep multiplexing holography, where the mean square error and structural similarity index measure are 0.03 and 86%, respectively. Our demonstration explores a depth-controllable spatiotemporal evolution technology in OAM deep multiplexing holography, which is expected to promote the development of OAM mode-based optical holography and storage.
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.
The identification of orbital angular momentum (OAM) modes with high-accuracy and-speed is always a difficult issue in practically applying optical vortex beams (OVs). In this work, we propose and experimentally investigate a convolutional neural network (CNN) method for optical OAM mode identification and shift-keying (SK) communications. The CNN model, including convolution and pooling layers, was designed to extract mode information from the diffraction patterns produced by diffracting the OVs with a cylindrical lens. After trained with loads of studying samples, the CNN model has a good generation ability in recognizing the OAM modes of OVs ranging from −15 to 15. The recognition accuracy reaches 99% with the turbulence intensity of C 2 n = 1 × 10 −13 m −2/3 , z = 50 m. Even under the turbulence of C 2 n = 1 × 10 −12 m −2/3 , z = 50 m, the accuracy still exceeds 89%. By mapping and encoding a Lena gray image with the size of 100 × 100 pixels to two OAM channels, the OAM-SK signals with 900 modulation orders were successfully demodulated by the CNN model, and the image was well recovered after transmission. With an I5-8500 Central Processing Unit, this recognition process only takes 1 × 10 −3 s per mode. It is anticipated that the CNN methods might provide an effective way for identifying OAM modes with high-accuracy and-speed, which may have great potentials in OAM communication, quantum information processing, and astronomical application, etc. INDEX TERMS Neural networks, optical vortices, optical signal detection.
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