Helicity conservation of the Riemann–Silberstein vector

Abstract In this paper, we consider Riemann–Silberstein (RS) helicity (RSH) given by the sum of the electric and magnetic helicities. We show that this quantity is chiral under parity transformation and invariant under duality. In the case of null fields in free space, we prove that the electric field behaves as a material, frozen-in field, and demonstrate the conservation of the electric and magnetic helicities; as a corollary, the conservation of the RSH follows suit. These results can find applications in many areas of current research, from the study of knotted fields in electromagnetism to the applications of Hopfion solutions in chiral meta-matter.