Orthogonality of diffractive deep neural network.

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