Vortex lines of the electromagnetic field

Abstract

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.

Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere

“…It can also be shown [13,22] that the real vector iν(ζ) * ×ν(ζ) is parallel to the ζ-direction; such vectors in the electromagnetic field E + iB have relativistically distinguished status (see e.g. [13,23] and [24], p 258).…”

<title>Optical vortex interferometry: AD 2007</title>

“…Nye and Nicholls have used them as a kind of reference system for studying phase singularities in electromagnetic field [44]. Bialynicki-Birula has proposed the similar step for studying the electromagnetic fields in quantum electrodynamics [45]. Although the field defined by Bialynicki-Birula is not classical optical fields it is still complex fields and represents electromagnetic field.…”

Interferometry with Vortices

“…The relations between vortex lattices and polarization singularities have also been described [29]. The papers concerning general questions in the theory of electromagnetic fields have also been published in the last decade [30,31]. The three-or more plane waves interference can also be used for photonics crystal manufacturing [32,33].…”