Abstract
Backflow, or retropropagation, is a counterintuitive phenomenon in which for a forward-propagating wave the energy locally propagates backward. In this study the energy backflow is 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 wave packets, as well as in some azimuthally asymmetric extensions. Using the Bateman-Whittaker technique, a 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.
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