Electromagnetic vortex lines riding atop null solutions of the Maxwell equations

A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector (E + iB)/root2 is multiplied by a complex scalar function phi. 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, zeros of the phi function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.