Negative diffraction by a periodically modulated loss

We show how a periodic modulation of loss on the wavelength scale provides negative diffraction propagation. In particular, we consider a 2D square arrangement of lossy cylinders embedded in air, with no index contrast. The phase-shifts accumulated in propagation trough such a structure, with flat-flat interfaces, are then compensated by normal diffraction in air leading to a substantial focalization of a light beam behind the crystal. The transmitted light intensity map exhibits a window of high transmission as a result of anisotropic loss provided by the periodicity. The effect is accounted buy the dispersion curves obtained by a coupled mode expansion of Maxwell equations and numerical experiments. The predicted phenomenon is expected to be generic for spatially modulated materials, and indeed we show that the results can be extended to acoustics.