I. Introduction
Certain types of photonic crystals (PCs) can possess a photonic bandgap (PBG) and thus become equivalent to a photonic insulator [1], [2]. Such photonic insulators are expected to serve as a basic platform for photonic integrated circuits (PICs) because we can utilize the strong two-dimensional (2-D) or three-dimensional (3-D) confinement that results from the existence of the PBGs. By incorporating structural defects into PCs with PBGs, various functional components can be implemented, which is analogous with doping into insulators in electronic crystals [3]. Line defects can work as strongly confined waveguides and point defects work as ultrasmall high-Q resonators. These functional defects will be key components of PC-based integrated circuits.