Orthogonality of diffractive deep neural network

Some rules of the diffractive deep neural network (D NN) are discovered. They reveal that the inner product of any two optical fields in D NN is invariant and the D NN 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 D NN 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 D NN performs well in applications like mode conversion, mode multiplexing/demultiplexing, and optical mode recognition.