  This paper is devoted to the mathematical analysis of a time-domain
electromagnetic scattering by periodic structures which are known as
diffraction gratings. The scattering problem is reduced equivalently into an
initial-boundary value problem in a bounded domain by using an exact
transparent boundary condition. The well-posedness and stability of the
solution are established for the reduced problem. Moreover, a priori energy
estimates are obtained with minimum regularity requirement for the data and
explicit dependence on the time.
