triangular projection between the slab waveguide and the PhC one, unlike structures 1-3, so that we find that the projection is necessary for obtaining better transmission characteristic. CONCLUSIONSWe applied topology optimization with the FEM to improve the coupling between a slab waveguide and a PhC waveguide and obtained an optimized structure with excellent transmission characteristic in a small design region for the coupling. Also, we simplified the optimized structure of the coupling region for easier fabrication and were able to find some core features of the optimized structure. ACKNOWLEDGMENTSThe authors thank Prof. K. Svanberg for his computer codes of MMA.