Theoretical Study On The Eigen States Of The Photonic Crystal Slab

The photonic crystal slab, a structure which is more amenable to fabrication than photonic crystals with full three-dimensional band gaps, but retains or approximates many of the latter's desirable properties, becomes an alternative of three-dimensional photonic crystals in many novel devices. In this paper, the plane wave method with super cell and the scattering-matrix method are used to calculate the band structures and eigen states of the photonic crystal slabs .The results of the plane wave method with super cell shows:(1) Photonic band gaps exist in the guided modes of the photonic crystal slabs.(2) A photonic crystal slab has an optimal thickness , which makes the photonic band gap maximum .The results of the scattering-matrix method shows:(1) The new method we provided in this paper is accord to the plane wavemethod with super cell in calculating the guided modes of the photonic crystal slabs , and accord to the FDTD method in calculating the leaky modes .(2) The new methods can apply to study the symmetry of the eigen modes .