Investigation of self-collimation frequencies in 2-D photonic crystals

Abstract

The self-collimation frequencies (SCFs) in two-dimensional photonic crystals (2-D PhC) have been investigated systematically by the plane-wave expansion method. In the wave-vector space, the square-lattice 2-D PhCs have some square-shaped equifrequency contours (EFCs) both for TE modes and for TM modes. Narrow-beam lights with these frequencies can propagate in the directions normal to the flat borders of the EFCs without any significant broadening, which is known as self-collimation effect. We consider the 2-D PhCs consisting of a square lattice of air cylinders in a dielectric material and the 2-D PhCs consisting of a square lattice of dielectric cylinders in air respectively. Calculation results show how SCFs of TM and TE modes change with the radius of cylinders and the refractive index of the material. These results can be applied to designing the PhC devices based on self-collimation effect.