For a plane electromagnetic wave, where the electric and magnetic fields are precisely disposed in the transverse plane and the Poynting vector is parallel to the propagation vector, it is well known that the classical text-book analysis of angular momentum density gives a vanishing result for any longitudinal component. In particular, under these assumptions, a circularly-polarized wave (or photon) might be construed to have no angular momentum in the propagation direction. Of course this is untrue; indeed it is the basis of Beth’s famous measurement of spin angular momentum for circularly polarized light that a torque is exerted about the beam axis. This presentation reviews some of the calculational aspects, and the associated physics, involved in a resolution of the issue. In particular it is shown unnecessary to artificially impose on the beam a transverse intensity profile, vanishing at infinity, to resolve the matter. For optical beams of arbitrary structure, promotion of the electromagnetic fields, and associated potentials, to operator form gives non-zero values to each of the commonly deployed electromagnetic measures of physical significance; with a quantum optical formulation, results are cast in terms of Hermitian operators and duly relate to physical observables. Thus, not only energy and angular momentum, but also measures of chirality such as the ‘Lipkin zilch’, acquire a consistent physical interpretation

Date Published: 5 March 2013
PDF: 9 pages
Proc. SPIE 8637, Complex Light and Optical Forces VII, 863707 (5 March 2013); doi: 10.1117/12.2004430

Published in SPIE Proceedings Vol. 8637:
Complex Light and Optical Forces VII
Jesper Glückstad; David L. Andrews; Enrique J. Galvez, Editor(s)