  Research on optical computing has recently attracted significant attention
due to the transformative advances in machine learning. Among different
approaches, diffractive optical networks composed of spatially-engineered
transmissive surfaces have been demonstrated for all-optical statistical
inference and performing arbitrary linear transformations using passive,
free-space optical layers. Here, we introduce a polarization multiplexed
diffractive processor to all-optically perform multiple, arbitrarily-selected
linear transformations through a single diffractive network trained using deep
learning. In this framework, an array of pre-selected linear polarizers is
positioned between trainable transmissive diffractive materials that are
isotropic, and different target linear transformations (complex-valued) are
uniquely assigned to different combinations of input/output polarization
states. The transmission layers of this polarization multiplexed diffractive
network are trained and optimized via deep learning and error-backpropagation
by using thousands of examples of the input/output fields corresponding to each
one of the complex-valued linear transformations assigned to different
input/output polarization combinations. Our results and analysis reveal that a
single diffractive network can successfully approximate and all-optically
implement a group of arbitrarily-selected target transformations with a
negligible 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 at
the input and output fields-of-view, respectively, and N_p refers to the number
of unique linear transformations assigned to different input/output
polarization combinations. This polarization-multiplexed all-optical
diffractive processor can find various applications in optical computing and
polarization-based machine vision tasks.
