Variational Effective Index Method for 3D Vectorial Scattering Problems in Photonics: TE Polarization

In order to reduce the computational effort we develop a method for 3D-to-2D dimensionality reduction of scattering problems in photonics. Contrary to the ‘standard’ Effective Index Method the effective parameters of the reduced problem are always rigorously defined using the variational technique, based on the vectorial 3D Maxwell equations. Results for a photonic crystal slab waveguide show that this approach predicts the location of the bandgap and other spectral features much more precisely than any ‘standard’ EIM approximation.