Optical helicity of unpolarized light
Kayn A. Forbes
Abstract
Like energy and momentum, optical helicity is a fundamental dynamical property of light. In the prevalent plane wave and paraxial description of light the optical helicity is directly proportional to the degree of circular polarization, being zero for both linearly and unpolarized fields. Here it is shown that the nonparaxial fields generated by tightly focused optical vortices which have the phase factor $exp(i\ensuremath{\ell}\ensuremath{\phi})$ possess a contribution to the optical helicity density that is completely independent of the polarization state of the source paraxial field. In stark contrast to what is known in classical optics with plane waves and paraxial light, the physical consequence is that unpolarized light can exhibit optical activity and chiral light-matter interactions.