We perform a simple sensitivity analysis of a W1 waveguide bend in a photonic crystal (PhC) where we use the information obtained to optimize the PhC bend's frequency response. Within a single optimization step we already achieve very low power reflection coefficients over almost the entire frequency range of the photonic bandgap (PBG), i.e., an achromatic bend. A further analysis shows that there is a single critical rod in the optimized bend structure that exhibits an extraordinary high sensitivity at a given frequency. Hence power reflection becomes tunable from 0 % up to 100 % involving only small changes in the critical rod's properties. This opens the door to novel topologies for compact switches and sensor applications.

Using some simple plasmonic structures, we compare various numerical methods

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A novel h-ϕ approach for solving 3-D time-harmonic eddy current problems is presented. It makes it possible to limit the number of degrees of freedom required for the discretization such as the T-Ω method, while overcoming topological issues related to it when multiply connected domains are considered. Global basis functions, needed for representing magnetic field in the insulating region, are obtained by a fast iterative solver. The computation of thick cuts by high-complexity computational topology tools, typically required by the T-Ω method, is thus avoided. The final matrix system turns out to be symmetric and fullrank unlike the more classical A-A method, which requires gauging of magnetic vector potential to ensure uniqueness. Numerical tests show that the proposed method is accurate and the field problem solution is obtained in a reasonable computational time even for 3-D models with millions of mesh elements. INDEX TERMS Eddy currents, Finite element method, Cell Method, Multiply connected, Cut.

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