  Large-scale and high-dimensional permutation operations are important for
various applications in e.g., telecommunications and encryption. Here, we
demonstrate the use of all-optical diffractive computing to execute a set of
high-dimensional permutation operations between an input and output
field-of-view through layer rotations in a diffractive optical network. In this
reconfigurable multiplexed material designed by deep learning, every
diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each
unique combination of these rotatable layers represents a distinct rotation
state of the diffractive design tailored for a specific permutation operation.
Therefore, a K-layer rotatable diffractive material is capable of all-optically
performing up to 4^K independent permutation operations. The original input
information can be decrypted by applying the specific inverse permutation
matrix to output patterns, while applying other inverse operations will lead to
loss of information. We demonstrated the feasibility of this reconfigurable
multiplexed diffractive design by approximating 256 randomly selected
permutation matrices using K=4 rotatable diffractive layers. We also
experimentally validated this reconfigurable diffractive network using
terahertz radiation and 3D-printed diffractive layers, providing a decent match
to our numerical results. The presented rotation-multiplexed diffractive
processor design is particularly useful due to its mechanical
reconfigurability, offering multifunctional representation through a single
fabrication process.
