Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses

We investigate the electromagnetic response of a periodic checkerboard consisting of alternating rectangular cells of positive refractive index (epsilon=+1, mu=+1) and negative refractive index (epsilon=-1, mu=-1). We show that the system has peculiar imaging properties in that it reproduces images of a source in one cell in every other cell. Using coordinate transformations, we map this system into a class of imaging systems in three dimensions consisting of three orthogonal planes delimiting eight alternating cubical regions of positive and negative index media sharing the same vertex. We also generalize these results to more general checkerboards that are inhomogeneous and anisotropic that can then be used to generate a class of three-dimensional (3D) corner imaging systems.