Finite-Energy Unidirectional Hopfion-Like Space-Time Localized Electromagnetic Fields in Vacuum

Based on two novel Bateman conjugate functions, a class of finite-energy spatiotemporally localized null electromagnetic fields in vacuum have been constructed. These wavepackets share with the basic Hopfion, as well as higher-order Hopf-Ranada solutions, topological properties dealing with linked and knotted electromagnetic field lines. Contrary to the Hopf-Ranada solutions, however, they are unidirectional and devoid of energy backflow, the latter being a counterintuitive phenomenon whereby, even for a forward-propagating plane wave components, the energy locally propagates backward. Conservation laws for electromagnetic chirality and helicity for these novel wavepackets have been studied.<p></p>