Resampling the optical transmission matrix to accelerate the training of the diffractive deep neural network

The diffractive deep neural network (D 2 NN) enables all-optical implementation of machine learning tasks. During the training, the Rayleigh–Sommerfeld (RS) diffraction integral is employed for connecting neurons between neighboring hidden layers. The RS formula can be rewritten as a transmission matrix (TM), which allows for the parallel computation of multiple vectorized light fields. However, the TM has a large size, demanding substantial computational resources, and resulting in long training time. In this paper, we propose to resample the TM in free space based on the propagation invariant modes (PIMs), thereby reducing the size of the matrix, and accelerating the propagation simulations. This method enables the training of the large-scale D 2 NN with reduced memory requirements and fast speed.