Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane

Abstract

A semi-infinite photonic crystal can support electromagnetic wave propagation at its surface. By using the supercell method, we studied in detail the properties of these (nonradiative) modes in crystals of two-dimensional periodicity constituted by parallel rods of square cross section. The rods cut the plane of periodicity (001) at the sites of a square lattice, and the sides of the rods have the same orientation as the lattice. We have performed calculations for crystals of air cylinders in a dielectric background. The Bloch-type surface waves are assumed to propagate at the (100) surface in the [010] direction. For both transverse electric and transverse magnetic polarizations, we found that the dispersion curves of the surface modes and their field confinements at the surface are strongly dependent on the crystal termination, that is, on the position of the cut plane through the rods. We also found that the degree of localization of the fields at the surface depends on the position of the mode within the band gap. Plots of the field intensity show that the TM waves are more strongly localized than the TE waves.