Energy backflow in unidirectional spatiotemporally localized wavepackets

TL;DR

This paper investigates energy backflow in unidirectional wavepackets, revealing conditions under which backflow occurs or is absent, and introduces a new wave solution without backflow with topological features.

Contribution

It provides a detailed analysis of energy backflow phenomena in wavepackets and constructs a novel wave solution that lacks backflow and exhibits topological properties.

Findings

Energy backflow occurs in certain azimuthally symmetric wavepackets.

A new wave solution is constructed that has no energy backflow.

The new wave has topological properties similar to the Hopfion.

Abstract

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.