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Research on optical computing has recently attracted significant attentiondue to the transformative advances in machine learning. Among differentapproaches, diffractive optical networks composed of spatially-engineeredtransmissive surfaces have been demonstrated for all-optical statisticalinference and performing arbitrary linear transformations using passive,free-space optical layers. Here, we introduce a polarization multiplexeddiffractive processor to all-optically perform multiple, arbitrarily-selectedlinear transformations through a single diffractive network trained using deeplearning. In this framework, an array of pre-selected linear polarizers ispositioned between trainable transmissive diffractive materials that areisotropic, and different target linear transformations (complex-valued) areuniquely assigned to different combinations of input/output polarizationstates. The transmission layers of this polarization multiplexed diffractivenetwork are trained and optimized via deep learning and error-backpropagationby using thousands of examples of the input/output fields corresponding to eachone of the complex-valued linear transformations assigned to differentinput/output polarization combinations. Our results and analysis reveal that asingle diffractive network can successfully approximate and all-opticallyimplement a group of arbitrarily-selected target transformations with anegligible error when the number of trainable diffractive features/neurons (N)approaches N_p x N_i x N_o, where N_i and N_o represent the number of pixels atthe input and output fields-of-view, respectively, and N_p refers to the numberof unique linear transformations assigned to different input/outputpolarization combinations. This polarization-multiplexed all-opticaldiffractive processor can find various applications in optical computing andpolarization-based machine vision tasks.

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Polarization Multiplexed Diffractive Computing: All-Optical  Implementation of a Group of Linear Transformations Through a  Polarization-Encoded Diffractive Network