ELECTROMAGNETIC SURFACE-MODES OF A DIELECTRIC SUPERLATTICE - THE SUPERCELL METHOD

We present a study of the reliability of the supercell method in calcu lations of surface electromagnetic modes. For a truncated superlattice constituted of nonabsorbing dielectric layers, we demonstrate that th e 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 yi elds satisfactory convergence to an analytic dispersion relation for t he surface modes. In addition, we apply the supercell method to study in detail the dependence of transverse-electric and transverse-magneti c surface waves on the cut-off position in the cell next to the surfac e. As a specific case, we choose a TiO2/SiO2 superlattice-layers with relatively high dielectric contrast in the visible spectrum. We find t he surface modes strongly dependent on the position of the surface. In fact, they appear only for certain terminations. By plotting the fiel d 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. (C) 1997 Optical Society of America.