Surface defect linear modes in one-dimensional photonic lattices

We report on the existence of surface defect linear modes at an interface between the defect of one-dimensional photonic lattices and the uniform media. The interface defect can significantly affect the properties of linear modes. Such new type of modes exists in the first bandgap for positive defects; while they exist in the second bandgap for negative defects. Particularly, when a Gaussian beam, which is similar to the linear mode, is launched at the defect site, we find that the Gaussian beam can be strongly confined at defect site and robustness along longitudinal direction for a long distance. When launched at a small angle into the defect site, the Gaussian beam exhibits stable snake propagation.