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.
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