Light slowing down in Moiré fiber gratings and its implications for nonlinear optics

A theory of the dispersion in the Moir\'e gratings is developed and it is shown that the group velocity of light in them can be reduced by up to three orders of magnitude. A conceptual similarity between Moir\'e grating and the electro-magnetic-induced transparency medium is demonstrated, and it is argued that for some applications the Moir\'e gratings present a simple viable alternative to electromagnetically induced transparency.