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. Śliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schrödinger 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 Schrödinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of the Maxwell equations with embedded vortex lines are given. Vortex lines in the Laguerre-Gaussian beams are treated in some detail.
- Received 3 December 2002
DOI:https://doi.org/10.1103/PhysRevA.67.062114
©2003 American Physical Society
