Time Dependent Scattering from a Grating
This work addresses the theoretical foundation for time-domain electromagnetic simulations of periodic gratings, which is critical for thin-film solar cell and antenna design, but remains incremental as it extends existing methods to a new class of materials.
The paper provides a first proof of existence and uniqueness for time-dependent scattering from periodic gratings with frequency-dependent material coefficients, and proves time-stepping error estimates using Convolution Quadrature, with preliminary numerical results demonstrating convergence and stability.
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.