Linked Electric and Magnetic Fields for Source-Free Maxwell Equations

This Demonstration shows the electric and magnetic field lines (in red and blue) of localized, time-dependent, finite-energy, rational solutions (in , , , and ) of the source-free Maxwell equations that can be interpreted as classical (nonquantum) photons. For all times, any pair of electric and magnetic field lines is linked.
  • Contributed by: Michael Trott
  • From: The Mathematica GuideBook for Programming, second edition by Michael Trott (© Springer, 2008).



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For details, see
W. T. M. Irvine and D. Bouwmeester, "Linked and Knotted Beams of Light," Nature Physics, 4(9), 2008 pp. 716–720.
The explicit forms of the fields are
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