Orbital angular momentum transformations by non-local linear systems

A matrix description of orbital angular momentum (OAM) transformations in scalar optical beams by non-local, linear systems is introduced and the amplitude transfer function (ATF) is generalized to include information about mode-to-mode OAM coupling. In particular, the analysis of radially independent systems suggests the existence of unexplored types of OAM transforming systems. The results are extended to random beams and random non-local systems and the optical transfer function (OTF) is generalized to the OAM space.