  High-dimensional encoding schemes have emerged as a novel way to perform
quantum information tasks. For high dimensionality, temporal and transverse
spatial modes of photons are the two paradigmatic degrees of freedom commonly
used in such experiments. Nevertheless, general devices for multi-outcome
measurements are still needed to take full advantage of the high-dimensional
nature of encoding schemes. We propose a general full-field mode sorting scheme
consisting only of up to two optimized phase elements based on evolutionary
algorithms that allows for joint sorting of azimuthal and radial modes in a
wide range of bases. We further study the performance of our scheme through
simulations in the context of high-dimensional quantum cryptography, where
high-fidelity measurement schemes are crucial.
