Phys. Rev. Lett. 111, 150404 (2013)

Credit: © 2013 APS

Hridesh Kedia and colleagues from the USA, Poland and Spain have presented a family of exact knotted solutions to Maxwell's equations in free space. In these analytical solutions, the electric and magnetic field lines 'encoding' all torus knots and links persist in time. Knot theory has been around for a long time, and is applicable to a wide range of scientific fields, ranging from fluid dynamics to quantum field theory. The researchers describe the knotted structure of the field lines, and compute the set of conserved currents, the helicity and charges for the family of solutions. The evolution of the fields is analogous to a shear-free, compressible flow along the Poynting vector. The scientists raise the question of whether similar solutions exist for nonlinear systems such as the Euler flow of ideal fluids. It will be interesting to see if researchers can realize such solutions experimentally in systems such as plasmas and quantum fluids.