We investigate the short pulse laser induced damage initiation mechanism on multilayer dielectric pulse compression gratings. We report that damages initiate at the edge of the grating pillars opposite to the incoming wave. It demonstrates, at a nanometer scale, the role of the electric field in the damage process coupled with periodic ripple pattern developing along the polarization direction. We avoid the formation of ripples by illuminating the diffraction grating in TM polarization and measure a significantly improved laser induced damage threshold associated with a strong decrease of the electric field in the grating structure