Backward energy flow in simple four-wave electromagnetic fields

Abstract

Electromagnetic energy backflow is a phenomenon that occurs in regions where the direction of the Poynting vector is opposite to that of the propagation of the wave field. It is particularly remarkable in the nonparaxial regime and has been exhibited in the focal region of sharply-focused beams, for vector Bessel beams, and vector-valued spatiotemporally localized waves. A detailed study is undertaken of this phenomenon and the conditions for its appearance are examined in detail in the case of a superposition of four plane waves in free space, the simplest electromagnetic arrangement for the observation of negative energy flow, as well as its comprehensive and transparent physical interpretation. It is shown that the state of polarization of the constituent components of the electromagnetic plane wave quartet determines whether or not energy backflow takes place and what values the energy flow velocity assumes. Depending on the polarization angles, the latter can assume any value from c (the speed of light in vacuum) to −c in certain spatiotemporal regions of the field.