Longitudinal electromagnetic waves in the framework of standard classical electrodynamics

TL;DR

This paper demonstrates the existence of longitudinal electromagnetic waves within standard classical electrodynamics by deriving exact solutions of Maxwell's equations, linking them to scalar waves, and discussing potential experimental implications.

Contribution

It provides the first exact solutions for longitudinal electric field components in Maxwell's equations with specific current and charge densities, connecting them to scalar waves and proposing new terminology.

Findings

Longitudinal electric wave components are exact solutions of Maxwell's equations.

Scalar wave counterparts to longitudinal electric waves are identified.

Discussion of potential experimental detection of these waves.

Abstract

Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is considered. The link between the longitudinal electromagnetic waves and the system of Maxwell equations is demonstrated. The longitudinal wave component of the electric field strength vector is found as the exact solution of the standard Maxwell equations with specific gradient-type case of electric current and charge densities. The corresponded scalar wave is found as well. The necessary comment on the paper of K.J. van Vlaenderen and A. Waser is given. The possible experimental situation is discussed briefly. Following the Bialynicki-Birula's proposition to give the name for the well known complex 3-vector of electromagnetic field strengths, the suggestion to call the much more interesting 4-vector of this kind as Riemann--Silberstein--Darwin vector is given.