Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
Iwo Bialynicki-Birula
Abstract
New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector ( E + i B)/2 is multiplied by a complex scalar function ϕ. 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 ϕ function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.
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