  We experimentally study the propagation of microwaves in an artificial
honeycomb lattice made of dielectric resonators. This evanescent propagation is
well described by a tight-binding model, very much like the propagation of
electrons in graphene. We measure the density of states, as well as the wave
function associated with each eigenfrequency. By changing the distance between
the resonators, it is possible to modulate the amplitude of
next-(next-)nearest-neighbor hopping parameters and to study their effect on
the density of states. The main effect is the density of states becoming
dissymmetric and a shift of the energy of the Dirac points. We study the basic
elements: An isolated resonator, a two-level system, and a square lattice. Our
observations are in good agreement with analytical solutions for corresponding
infinite lattice.
