Abstract: We have investigated the guide modes in two kinds of two-dimensional photonic crystal heterostructures by using the plane wave expansion method combined with the supercell technique. These heterostructures consist of different air cylinders embedded into host dielectric in different lattices. Namely, One heterostucture is composed of square cylinders in square lattice and hexagon cylinders in triangular lattice (SSTH heterostucture). The other heterostucture is composed of rectangular cylinders in rectangular lattice and circle cylinders in triangular lattice(RRTC heterostucture). We find that the SSTH heterostucture may produce guide modes in absolute photonic band gap (PBG) when introducing relative longitudinal gliding or transverse displacement of the sub-lattices along the interface of the heterostructure. But the RRTC heterostucture can produce guide modes in absolute PBG without any relative longitudinal gliding or transverse displacement. This feature is quite different from other pure dielectric photonic crystals heterostructures.

Keywords: 
• photonic crystal /
• heterostructure /
• guide modes /
• supercell