(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
Scattering of time-harmonic electromagnetic plane waves by a doubly
periodic surface structure in R3 can be simulated by a boundary value
problem of the time-harmonic curl-curl equation. For a truncated FEM domain,
non-local boundary value conditions are required in order to satisfy the
radiation conditions for the upper and lower half spaces. Alternatively to
boundary integral formulations, to approximate radiation conditions and
absorbing boundary methods, Huber et al. [11] have proposed a coupling method
based on an idea of Nitsche. In the case of profile gratings with perfectly
conducting substrate, the authors have shown previously that a slightly
modified variational equation can be proven to be equivalent to the boundary
value problem and to be uniquely solvable. Now it is shown that this result
can be used to prove convergence for the FEM coupled by truncated wave mode
expansion. This result covers transmission gratings and gratings bounded by
additional multi-layer systems.
