Contents I. Introduction
Two-Dimensional (2-D) photonic crystal (PC) waveguides have the strong potential for constructing ultra-compact photonic integrated circuits due to their abilities of controlling lightwaves. In general, the waveguides are formed by introducing line defects into the lattices of air holes in dielectric slabs. Lightwaves are confined in-plane by the photonic band gap, in which propagation of photons is forbidden. Utilizing this attractive advantage, waveguiding in straight channels [1]–[7] and even sharp bends [8]–[11] with low losses can be realized. In the vertical direction, there have been two types of guiding mechanisms demonstrated in the previous literatures. First, the 2-D PC slab waveguides of high-index-contrast type are implemented by means of suspending the thin core membrane in air [1] or patterning structures in silicon-on-insulator (SOI) wafers [2], [3] for providing strong confinement. However, the low propagation loss have been achieved only in the narrow bandwidth in this configuration. Second, the low-index-contrast PC slab waveguides are usually investigated in InP-based [4] or GaAs-based [5] heterostructures. Since the guided modes of PC waveguides exist above the light lines of cladding layers, severe vertical radiation losses exhibit in the single-line-defect waveguides [12]. To obtain high transmission, the multimode propagation is unavoidable.
