Rotating light, the orbital angular momentum paradox and relativistic complex scalar fields

Abstract

Recent studies show that the angular momentum, both spin and orbital, of rotating light beams possesses counter-intuitive characteristics. We present a new approach to the question of the orbital angular momentum of light based on the complex massless scalar field representation of light. The covariant equation for the scalar field is treated in a rotating system using the general relativistic framework. The equivalence of the U(1) gauge current for the scalar field with the Poynting vector continuity equation for paraxial light is used to apply the formalism to the calculation of the orbital angular momentum of rotating light beams. If the difference between the co-, contra- and physical quantities is properly accounted for there is no paradox in the orbital angular momentum of rotating light. An artificial analogue of the paradoxical situation could be constructed but it is wrong within the present formalism. It is shown that the orbital angular momentum of a rotating beam comprising modes with opposite azimuthal indices corresponds to that of rigid rotation. A plausible physical explanation of this feature is suggested in analogy with the rigid rotation of the vortex core in a rotating fluid.