  Backflow, or retro-propagation, is a counterintuitive phenomenon where for a
forward-propagating wave the energy or probability density locally propagates
backward. In this study the energy backflow has been examined in connection
with relatively simple causal unidirectional finite-energy solutions of the
wave equation which are derived from a factorization of the so-called basic
splash mode. Specific results are given for the energy backflow arising in
known azimuthally symmetric unidirectional wavepackets, as well as in novel
azimuthally asymmetric extensions. Using the Bateman-Whittaker technique, a
novel finite-energy unidirectional null localized wave has been constructed
that is devoid of energy backflow and has some of the topological properties of
the basic Hopfion.
