Band structure of guided and leaky modes in two-dimensional photonic crystals of a slab type

Summary form only given. Two-dimensional photonic crystals with finite height that are embedded in slab waveguides are considered as alternatives to three-dimensional ones. According to the relative magnitude of the eigenfrequency and the wave vector parallel to the surface of the slab, the eigenmodes of the radiation field are classified into two categories, that is, guided mode and leaky mode. The former are real eigenmodes, whereas the latter are meta-stable state with complex eigenfrequencies. Some groups have studied two-dimensional photonic crystals embedded in slabs. However, they did not pay attention to leaky modes. In this paper, we will report the photonic band structure of the slab including both the guided modes and the leaky modes by the FDTD method and a group theoretical argument.