Electromagnetic Shocks and the Self-Annihilation of Intense Linearly Polarized Radiation in an Ideal Dielectric Material

Abstract

Maxwell's equations are studied for linearly polarized plane waves of intense electromagnetic radiation with the displacement field given by a nonlinear cubic function of the electric field. Analysis shows that electromagnetic shocks, surfaces of discontinuity for the electric and magnetic fields, are physically admissible and can indeed develop from an initially continuous field of radiation. Under ordinary conditions, the shocks proceed to "sweep up" and eventually dissipate all of the radiation field energy, giving rise theoretically to the complete self-annihilation of the electromagnetic radiation field. Under rather special conditions, a steady electromagnetic shock wave train (with some dissipation of the radiation field energy but only by the tail shock in the train) may possibly evolve dynamically. There is a rigorous mathematical correspondence between the theory here for intense linearly polarized electromagnetic plane waves in an ideal dielectric material and the theory of large-amplitude one-dimensional pressure waves in an ideal solid material.