Orthogonality of diffractive deep neural network

Some rules of the diffractive deep neural network ((DNN)-N-2) are discovered. They reveal that the inner product of any two optical fields in (DNN)-N-2 is invariant and the (DNN)-N-2 acts as a unitary transformation for optical fields. If the output intensities of the two inputs are separated spatially, the input fields must be orthogonal. These rules imply that the (DNN)-N-2 is not only suitable for the classification of general objects but also more suitable for applications aimed at optical orthogonal modes. Our simulation shows the (DNN)-N-2 performs well in applications like mode conversion, mode multiplexing/demultiplexing, and optical mode recognition. (C) 2022 Optica Publishing Group