▎ 摘　　要

The possibility of using hexagonal structures in general, and graphene in particular, to emulate the Dirac equation is the topic under consideration here. We show that Dirac oscillators with or without rest mass can be emulated by distorting a tight-binding model on a hexagonal structure. In the quest to make a toy model for such relativistic equations, we first show that a hexagonal lattice of attractive potential wells would be a good candidate. Firstly, we consider the corresponding one-dimensional (1D) model giving rise to a 1D Dirac oscillator and then construct explicitly the deformations needed in the 2D case. Finally, we discuss how such a model can be implemented as an electromagnetic billiard using arrays of dielectric resonators between two conducting plates that ensure evanescent modes outside the resonators for transversal electric modes, and we describe a feasible experimental setup.