Improved bends for two-dimensional photonic crystal waveguides

For two-dimensional photonic crystals involving infinitely long dielectric rods or air-holes on square or triangular lattices, a number of high performance 60 and 90 waveguide bends are obtained by solving optimization problems involving the radii of a few rods or air-holes as the degrees of freedom. In particular, the proposed 60 bends significantly outperform previous designs that insert three or five identical air-holes in the bend. The optimization problems are solved using a recently developed method based on the so-called Dirichlet-to-Neumann (DtN) maps of the unit cells.