Physicists have found a very interesting solution to the well-known Maxwell Equations, one in which can form light into interesting geometries and knots.
In the late 1980s, a researcher discovered exact solutions of Maxwell’s
equations in free space (containing no electric charge) with the odd
property that every field line formed a closed loop, and each loop was
linked to another. This structure is called a Hopf fibration, which has
been found in other places such as liquid-crystal physics (see 3 June 2013 Viewpoint). Kedia et al.
now go a step further with their discovery of exact solutions that are
both linked and knotted: the field lines are tied around each other
inside a torus.
More coverage and explanation on Physics World.
Identified by Hridesh Kedia
at the University of Chicago, along with colleagues at the Polish
Academy of Sciences in Warsaw and the Spanish National Research Council
in Madrid, the new family of solutions to Maxwell's equations have field
lines describing all "torus knots" and "links". Torus knots are those
knots that can lie on the surface of a torus, whereas a link is a
collection of such knots.
One solution involves magnetic-field lines that trace out a familiar
"trefoil" knot around a torus that is aligned in the plane perpendicular
to the direction of propagation of the light (see figure). As the light
propagates, the knot is distorted but retains the topological property
of being a trefoil knot. The electric-field lines have the same
structure as the magnetic-field lines but are rotated about the
propagation axis by an angle that depends upon the knot. Other solutions
include cinquefoil knots and linked rings.
Still plenty of surprises and interesting solutions out of the old equations!
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