Long-range elastic metamaterials

Abstract

The problem of wave propagation control in one-dimensional systems, including electrical charges and dipole magnetic moments is investigated. The waveguide is characterized by long-range and nonlinear interaction forces of Coulomb and Lorentz nature. Wave propagation properties are derived by a method based on an equivalent partial differential equation that replaces the discrete equation of motion of the chain. The paper shows how the waves propagating in these special systems have characteristics, such as phase and group velocity, that are function of the electrical and magnetic property distribution along the chain. Of interest are also possible wave-stopping phenomena. The paper presents an outline of some basic principles developed by some of the authors in recent theoretical papers and shows also numerical experiments illustrating wave propagation in metamaterials characterized by long-range elastic-electromagnetic interactions.