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 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 rotating system using the general relativistic framework. First we show the equivalence of the U(1) gauge current for the scalar field with the Poynting vector continuity equation for paraxial light, and then 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 does not result any 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 rotating beam comprising of modes with opposite azimuthal indices corresponds to that of rigid rotation. A short review on the electromagnetism in noninertial systems is presented to motivate a fully covariant Maxwell field approach in rotating system to address the rotating light phenomenon. PACS numbers:1

Differential Electromagnetic Forms in Rotating Frames

“…A second response comes from the analysis of the Wilsons' experiments in which was measured the electric potential between the inner and outer surfaces of a cylinder rotating in an external axially directed magnetic field: an analysis with many different approaches [6,23,24,25] (the TrocherisTakeno des-cription of rotations is used in [25]). Finally, a third response is provided by the increasing at-tention paid to paraxial optical beams with an helicoidal geometrical structure [26], [27] lea-ding to a discussion of light propagation in rotating media: a problem object of some dispu-tes [28][29][30][31][32].The relativistic theory of geometrical optics [15] is still a challenge to which it would be interesting to see what could be the differential form contribution.…”

Do phonons carry spin?

“…Interestingly the scalar field description of light not only proved useful in several optical phenomena in the past, recent studies on the orbital angular momentum of light beams also underline the utility of this approach [14]. In this case there could be an unambiguous analogy to ascribe orbital angular momentum to phonons.…”