Electromagnetic vortex lines riding atop null solutions of the Maxwell equations

Abstract

New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector $(\mathbf{E}+i\mathbf{B})/\sqrt{2}$ is multiplied by a complex scalar function $\varphi$. Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeroes of the $\varphi$ function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.

NATO Workshop on Singular Optics 2003 To appear in Journal of Optics A