Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion

States of light that are simultaneously eigenstates of orbital, intrinsic, and total angular momentum are found and eigenstates describing pairs of photons from spontaneous parametric down-conversion reveal classes of photon conversion with angular momentum conservation and cases where the initial angular momentum from the pump laser beam is shared between the converted photons and the generating medium. These angular momentum conservation laws open up a wide range of applications to be explored.