  Computing the electromagnetic field due to a periodic grating is critical for
assessing the performance of thin film solar voltaic devices. In this paper we
investigate the computation of these fields in the time domain (similar
problems also arise in simulating antennas). Assuming a translation invariant
periodic grating this reduces to solving the wave equation in a periodic
domain. Materials used in practical devices have frequency dependent
coefficients, and we provide a first proof of existence and uniqueness for a
general class of such materials. Using Convolution Quadrature we can then prove
time stepping error estimates. We end with some preliminary numerical results
that demonstrate the convergence and stability of the scheme.
