Some rules of the diffractive deep neural network (D2NN) are discovered. They reveal that the inner product of any two optical fields in D2NN is invariant and the D2NN 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 D2NN 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 D2NN performs well in applications like mode conversion, mode multiplexing/demultiplexing, and optical mode recognition.