Duplex symmetry and its relation to the conservation of optical helicity

Helicity is a familiar concept in particle physics and also appears in the physics of fluids and plasmas. In this paper, we present the optical helicity in a form readily applicable to both quantum and classical problems. We examine the relationship between the optical helicity and the more familiar optical spin and show that the conservation of helicity is an expression of the electric-magnetic symmetry for light. We show that helicity is distinct from Lipkin's 00-zilch; a simple relationship exists between the two only for monochromatic fields. It is only the optical helicity that has the correct dimensions of an angular momentum, thereby accurately describing the helicity of light. To illustrate the physical significance of the optical helicity, we consider a circularly polarized plane wave and the field emitted by a rotating electric dipole.

Figure 1

Optical helicity and optical spin are pseudoscalar and pseudovector quantities, respectively. Consider a left-handed circularly polarized wave incident upon a mirror as shown. Following reflection, both the handedness (and therefore helicity) and the direction of propagation of the wave are inverted. This leaves the spin of the wave unchanged.