Diffractive neural networks for mode-sorting with flexible detection regions

Mode-sorting is a procedure that decomposes a light field into a basis of transverse modes, directing each mode into a separate spatial location, allowing the constituent mode intensities to be measured simultaneously. We demonstrate a mode-sorter based on a diffractive optical neural network and show that it is advantageous to include the output detection regions in the trainable set of parameters of that network. This approach outperforms traditional mode-sorting methods, achieving lower crosstalk levels for the same efficiency. For example, in sorting 25 Hermite-Gaussian modes with a 3 plate sorter, at 12 % efficiency, the experimentally measured crosstalk decreases from 37.5 % for fixed detection to 8.7 % for flexible detection.