The orbital angular momentum of light, and also of waves beyond the electromagnetic spectrum, is a powerful
concept in all systems with cylindrical or rotational symmetry. Expressing quantum images in terms of orbital
angular momentum modes allows one to describe image rotations in terms of OAM dependent phase shifts.
We discuss image rotations, and in particular Faraday rotations in optical systems, and predict a Faraday
rotation for electron vortices. Our considerations highlight connections between orbital angular momentum
features in different systems, in particular between image rotations in optical and electron systems, and also
between parametric processes in parametric down-conversion and atomic cascades. We compare the phasematching
conditions of the two latter systems and demonstrate the efficient transfer of OAM modes and their
superpositions from near-infrared pump light to blue light in a four-wave mixing process in rubidium vapour.