Negative refraction in crystals with spatial dispersion

We predict, on the basis of numerical simulations, that organic crystals with appropriate spatial dispersion can exhibit negative refraction at optical frequencies near excitonic transitions. In particular we demonstrate that a plane slab of such materials is able to focus light coming from an oscillating point dipole. The intensity of the resulting image and its sharpness are mainly limited by absorption but its very presence unambiguously demonstrates negative refraction at the slab/vacuum interface. In our approach the medium is characterized by a generalized dielectric constant and all the relevant fields are computed by solving Maxwell equations with appropriate boundary conditions.