Surface Optical Waves in Semi-Infinite One-Dimensional Photonic Crystals Containing Alternating Layers of Positive and Negative Media with a Cap Layer

An analytical direct matching procedure within the Kronig-Penney model was applied to analyze the dispersion behavior of the localized surface states supported at the surface of a semi-infinite one-dimensional photonic crystals truncated with air or a cap layer. The photonic crystals contain alternating layers of positive and negative media. The present study demonstrates that by choosing some proper value for the photonic crystal parameters, zero and negative dispersion of surface modes emerge in a large range of parallel wave vector. New forward and backward surface waves are introduced. Due to the different nature of the band structure the surface modes are more localized compared to those appearing in the conventional photonic crystals