  Topological structures of electromagnetic fields could give access to
nontrivial light-matter interactions and additional degrees of freedom for
information and energy transfer. A characteristic example of such
electromagnetic excitations are space-time non-separable single-cycle pulses,
the exact solutions of Maxwell equation of toroidal topology predicted by
Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we
introduce a new family of electromagnetic excitation of toroidal topology with
increasing complexity in which the Hellwarth-Nouchi pulse is just the simplest
member. The electromagnetic excitations of the new family can be parametrised
by a single real number and exhibit skyrmionic structures of various orders.
They feature multiple singularities in the electromagnetic and Poynting vector
fields are accompanied by the fractal-like distributions of energy backflow.
The generalized family of toroidal electromagnetic excitation with salient
topologies are of interest for transient light-matter interactions, ultrafast
optics, spectroscopy, and toroidal electrodynamics.
