Flat lensing by periodic loss-modulated materials

We propose a flat lensing effect using a periodic loss-modulated material. In particular, we consider a two-dimensional square and rhombic arrangement of lossy cylinders embedded in a host media with the same refractive index. The effect is predicted by the dispersion curves obtained by a coupled mode expansion of Maxwell equations and by numerical beam propagation experiments. From both analytical and numerical studies, we show that, for a range of frequencies, light beams undergo negative diffraction on propagation through the loss-modulated medium, providing a window of high transmission. The phase shifts accumulated by negative diffraction within the structure are then compensated by normal diffraction, leading to substantial focalization beyond it.