Electromagnetic surface modes of a dielectric superlattice: the supercell method
- 1 February 1997
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America B
- Vol. 14 (2) , 370-381
- https://doi.org/10.1364/josab.14.000370
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.Keywords
This publication has 16 references indexed in Scilit:
- Photonic dispersion relation in a one-dimensional quasicrystalPhysical Review B, 1994
- Superlattice plasmon-polaritonsPhysics Reports, 1993
- Beat radiation from dipoles near a photonic band edgeJournal of the Optical Society of America B, 1993
- Study of Ge x Si1?x /Si superlattices by ellipsometryApplied Physics A, 1992
- Response functions in layered dielectric mediaSurface Science Reports, 1992
- Atomic emission rates in inhomogeneous media with applications to photonic band structuresPhysical Review A, 1992
- Electromagnetic Bloch waves at the surface of a photonic crystalPhysical Review B, 1991
- Collective excitations of semi-infinite superlattice structures: Surface plasmons, bulk plasmons, and the electron-energy-loss spectrumPhysical Review B, 1984
- Transverse elastic waves in periodically layered infinite and semi-infinite mediaPhysical Review B, 1983
- Electromagnetic propagation in periodic stratified media I General theory*Journal of the Optical Society of America, 1977