  Non-classicality criteria for general N-dimensional optical fields are
derived. They involve intensity moments, the probabilities of photon-number
distributions or combinations of both. The Hillery criteria for the sums of the
probabilities of even or odd photon numbers are generalized to N-dimensional
fields. As an example, the derived non-classicality criteria are applied to an
experimental 3-mode optical field containing two types of photon-pair
contributions. The accompanying non-classicality depths are used to mutually
compare their performance.
