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

Summary form only given. 2D photonic crystals with finite height that are embedded in slab waveguides are paid great attention as alternatives of 3D ones, because the former can be fabricated without serious difficulty on appropriate semiconductor substrates by means of sophisticated lithography techniques. According to the relative magnitude of the eigenfrequency and the wave vector parallel to the surface of the substrate, the eigenmodes of the radiation field are classified into two categories, that is, guided modes and leaky modes. The former are real eigenmodes, whereas the latter are metastable states with complex eigenfrequencies. K. Inoue et al. (1999) reported the fabrication and optical transmittance of a 2D triangular photonic crystal embedded in a waveguide formed on a GaAs substrate. The lattice constant was 0.4 /spl mu/m, and the transmission spectra were measured around 1.0 /spl mu/m. Because of the large refractive index of the substrate, all relevant modes were leaky. Further, some groups have studied 2D photonic crystals embedded in air-bridged slabs. However, they do not pay attention to leaky modes. In this paper, we report the photonic band structure and the transmission spectra of these systems calculated by the FDTD method. To calculate the band structure, we imposed the Bloch boundary condition on a parallelogram unit cell and Mur´s absorptive boundary condition in the vertical direction.