Photonic realization of the kappa-deformed Dirac equation

Abstract

We show an implementation of a κ-deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to recreate the effects of a flat noncommutative spacetime -i.e., κ Minkowski spacetime-in simple experimental setups. We touch upon elastic realizations in the section of Conclusions.