ANALYSIS OF THE TIME-DOMAIN PML PROBLEM FOR THE ELECTROMAGNETIC SCATTERING BY PERIODIC STRUCTURES

This paper is concerned with the time-domain scattering of an electromagnetic plane wave by a periodic structure. An initial boundary value problem is formulated in a bounded domain by applying the perfectly matched layer (PML) technique to the scattering problem imposed in an unbounded domain. Based on the abstract inversion theorem of the Laplace transform and the analysis in the frequency domain, the well-posedness and stability are established for the truncated time-domain PML problem. Moreover, the exponential convergence of the solution for the truncated PML problem is proved by a careful study on the error for the Dirichlet-to-Neumann operators between the original scattering problem and the truncated PML problem.