Non-linear electromagnetic wave propagation in an isotropic material

Abstract

It is shown that small departures from the classical linear constitutive relations can have significant cumulative effects on the propagation of electromagnetic waves. A non-linear far field theory is developed for holohedral isotropic materials. It is found that the amplitude of the signal propagates independently of the direction, although the local direction field depends strongly on this amplitude. The evolution of weak electromagnetic shocks is also discussed.