Electromagnetic surface modes of a dielectric superlattice: the supercell method

Abstract

We present a study of the reliability of the supercell method in calculations of surface electromagnetic modes. For a truncated superlattice constituted of nonabsorbing dielectric layers, we demonstrate that the numerical solutions obtained by this method for transverse-electric waves agree with those based on the Bloch theory for the semi-infinite superlattice. A slab of superlattice with at least nine unit cells yields satisfactory convergence to an analytic dispersion relation for the surface modes. In addition, we apply the supercell method to study in detail the dependence of transverse-electric and transverse-magnetic surface waves on the cut-off position in the cell next to the surface. As a specific case, we choose a TiO2/SiO2 superlattice—layers with relatively high dielectric contrast in the visible spectrum. We find the surface modes strongly dependent on the position of the surface. In fact, they appear only for certain terminations. By plotting the field amplitudes, we show that there exist different possibilities for the guidance of surface waves. The variation of the penetration depth of these modes is also discussed.