Local Dispersion of Guiding Modes in Photonic Crystal Waveguide Interfaces and Hetero-Structures

Recently, we have introduced a numerical method for calculating local dispersion of arbitrary shaped optical waveguides, which is based on the Finite-Difference Time-domain and filter diagonalization technique. In this paper we present a study of photonic crystal waveguides at interfaces and double hetero-structure waveguides. We have studied the waveguide stretching effect, which is the change in lattice constant of photonic crystals along waveguiding direction. Hybrid modes at photonic crystal heterostructure interfaces are observed, which are the results of superposition of existing modes in adjacent waveguides. The dispersion at the interfaces of a double hetero-structure waveguide tends to the dispersion of outer waveguides. The effective area still holding the dispersion of the middle waveguide is shorter than the geometrical length of the middle waveguide. The results of this study present a clear picture of dispersion at interfaces and the transmission in photonic crystal hetero-structures.