Figure 1

Properties of surface modes lying within the radiation continuum. (a and b) Projected band structures for a square lattice (period a) of cylindrical dielectric rods (ε=8.9, r=0.2a) in air, with terminations as shown in the insets. In a, the surface rods are cut in half, while in b, the surface rods have increased radii, r_s=0.33a. Gray shaded regions represent the light cone where there is a continuum of radiation modes. The light and dark khaki regions are the projected bulk bands of the photonic crystal. Surface modes that do not couple to radiation are shown as blue lines (these are the well known states) and a blue cross (this is an embedded eigenstate); those that do couple to radiation are shown as a red line. (c) Quality factor Q for the leaky surface modes along the red line in b. At k_y=0.2768×2π/a, the lifetime goes to infinity, and the leaky mode becomes an eigenmode. (d–f) E_z field patterns of the surface modes at the specified wavevectors, where k_ya/2π=0.260, 0.2768 and 0.290, respectively.