In this talk I will decribe  topologically non-trivial solutions of vacuum Maxwell electrodynamics.

In our recent work (J.Phys. A48 (2015) 255204), we have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman’s variables. This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of the Bateman’s construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of SU(2) gauge theory. We have computed the corresponding Chern-Simons charge in a class of solutions and it takes integer values.