Asymmetric Wave Propagation in a Modulated Magnetic Lattice

We investigate, numerically and analytically, the breakdown of reciprocity in a one-dimensional periodic system in which the elastic properties are modulated in time and space. The system is comprised of an array of repelling magnets, with the modulations caused by electromagnets that act on individual magnets in a controlled way. This provides an effective wave-like elastic foundation for the system. We show how directional wave propagation characteristics can be realized and tuned by dynamically modulating the elasticity of the foundation. Our theoretical findings complement the asymmetric wave propagation characteristics that are observed in experiments on this system.