M. Leumüller:

"Computing resonances in metallic photonic crystals";

Supervisor: L. Nannen; Institut für Analysis und Scientific Computing, 2018; final examination: 2018-10-08.

Resonance problems arise in many fields of research. An example are photonic crystals, in which the propagation of waves is defined by resonances. Photonic crystals with band gaps are of special interest.

Band gaps are regions of frequencies which cannot propagatate through the crystal. To calculate the band structure of photonic crystals many linear resonance problems need to be solved. Fast and reliable linear eigenvalue solves are needed. Lately, metallic photonic crystals have become more interestng. Differently from photonic crystals the electric permittivity of metallic photonic crystals depends on the frequency leading to rational resonance problems. These problems come with a high computational cost.

In this thesis, we introduce an efficient eigenvalue solver for large rational eigenvalue problems. At first, the resonance problems for two and three dimensional metallic photonic crystal are derived from Maxwell's equations. Then, they are discretised with Bloch periodic high order finite elements in Netgen/NGSolve. The arising large rational matrix eigenvalue problems are linearised with a rational linearisation schema and solved by the shift-and-invert Arnoldi method. By combining liearisation with the shift-and-invert Arnoldi, systems of linear equations with dimensions larger than the original matrix size have to be solve in each iteration. With the introduced rational linearisation these large systems of linear equations can be reduced to the original prolem size.

Created from the Publication Database of the Vienna University of Technology.