Reactive energy in non-diffracting localized waves

TL;DR

This paper investigates reactive energy in non-diffracting localized electromagnetic waves, explaining how interference of plane waves influences energy flow and reactive energy densities in superluminal and subluminal pulses.

Contribution

It provides detailed calculations of energy and reactive energy densities for various structured light pulses, highlighting the physical origin of reactive energy due to wave interference.

Findings

Reactive energy is linked to interference of wave components.

Energy flow velocity is limited to c, despite superluminal group velocities.

Reactive energy density varies with wave structure and interference patterns.

Abstract

It is well known that although the group velocity of structured light pulses propagating in vacuum can be subluminal or superluminal, the upper limit of the energy flow velocity is c, the speed of light in vacuum. This inequality can be explained in terms of the reactive energy left behind by the fields. Energy and reactive energy densities have been calculated for vector-valued two-dimensional (light sheet) superluminal electromagnetic nondiffractive pulses, as well as scalar-valued and TM three-dimensional superluminal and subluminal spatiotemporally localized electromagnetic waves. Emphasis is placed on the physical formation of the reactive energy due to interference of the plane-wave constituents of the structured light waves.