Vortex lines of the electromagnetic field

Iwo Bialynicki-Birula and Zofia Bialynicka-Birula

A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann–Silberstein vector is multiplied by a complex scalar function . 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 function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.

Phys. Rev. A vol. 67, 062114-1-8 (2003)