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!

Zz.

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