Reverse time migration for imaging periodic obstacles with electromagnetic plane wave

We propose reverse time migration (RTM) methods for the imaging of periodic obstacles using only measurements from lower or upper side of the obstacle arrays at a fixed frequency. We analyze the resolution of the lower side and upper side RTM methods in terms of the propagating part of the Rayleigh expansion, Helmholtz-Kirchhoff equation and the distance of the measurement surface to the obstacle arrays. We give some numerical experiments to justify the competitive efficiency of our imaging functionals and the robustness against noises.