Energy Backflow in Unidirectional Monochromatic and Space–Time Waves

Backflow, or retropropagation, is a counterintuitive phenomenon whereby for a forward-propagating wave the energy locally propagates backward. In the context of backflow, physically most interesting are the so-called unidirectional waves, which contain only forward-propagating plane wave constituents. Yet, very few such waves possessing closed-form analytic expressions for evaluation of the Poynting vector are known. In this study, we examine energy backflow in a novel (2+time)-dimensional unidirectional monochromatic wave and in a (2+1)D spatiotemporal wavepacket, analytic expressions which we succeeded to find. We also present a detailed study of the backflow in the “needle” pulse. This is an interesting model object because well-known superluminal non-diffracting space–time wave packets can be derived from its simple factored wave function. Finally, we study the backflow in an unidirectional version of the so-called focus wave mode—a pulse propagating luminally and without spread, which is the first and most studied representative of the (3+1)D non-diffracting space–time wave packets (also referred to as spatiotemporally localized waves).