  In this note we have further developed the study of topologically non-trivial
solutions of vacuum electrodynamics. 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 CS charge in a class of solutions and it takes integer values.
