In many implementations of transparent boundary conditions for resonance problems, spurious modes arise.
We have developed a transparent boundary condition based on the pole condition that has one complex
tuning parameter. Numerical experiments suggest that the artificial eigenvalues are due to badly converged
solutions in the exterior domain and thus are strongly dependent on variations of this parameter while
physical solutions are well converged and thus almost invariant. Hence it is possible to differentiate between
spurious and physical solutions by doing a sensitivity analysis of the eigenvalues.
Light transmission through a 2D-periodic array of small rectangular apertures in a film of highly conductive
material is simulated using a finite-element method. It is demonstrated that well converged results are obtained
using higher-order finite-elements. The influence of the array periodicity and of corner roundings on transmission
properties is investigated.
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in these structures is modelled by Maxwell's equations. For a deeper numerical analysis one may compute the scattered field when the structure is illuminated or one may compute the resonances of the structure. We therefore address in this paper the electromagnetic scattering problem as well as the computation of resonances in an open system. For the simulation effcient and reliable numerical methods are required which cope with the infinite domain. We use transparent boundary conditions based on the Perfectly Matched Layer Method (PML) combined with a novel adaptive strategy to determine optimal discretization parameters like the thickness of the sponge layer or the mesh width. Further a novel iterative solver for time-harmonic Maxwell's equations is presented.