F. Ramosmendieta et P. Halevi, ELECTROMAGNETIC SURFACE-MODES OF A DIELECTRIC SUPERLATTICE - THE SUPERCELL METHOD, Journal of the Optical Society of America. B, Optical physics, 14(2), 1997, pp. 370-381
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.