Abstract
A simple conserved quantity for electromagnetic fields in vacuum was discovered by Lipkin in 1964. In recent years, this “zilch” has been used as a measure of the chirality of light. The conservation of optical zilch is here derived from a simple symmetry of the standard electromagnetic action. The symmetry transformation allows the identification of circularly polarized plane waves as zilch eigenstates. The same symmetry is present for electromagnetism in a homogeneous, dispersive medium, allowing the derivation of the zilch density and flux in such a medium. Optical helicity density and flux are also derived for a homogeneous, dispersive medium. For monochromatic beams in vacuum, optical zilch is proportional to optical helicity. This monochromatic zilch-helicity relation acquires a factor of the square of the phase index in a dispersive medium.
- Received 4 March 2013
DOI:https://doi.org/10.1103/PhysRevA.87.043843
©2013 American Physical Society