Open AccessLCAO approximation for scaling properties of the Menger sponge fractal
Author(s) -
Kazuaki Sakoda
Publication year - 2006
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.14.011372
Subject(s) - linear combination of atomic orbitals , finite difference time domain method , physics , eigenfunction , fractal , scaling , quantum mechanics , optics , atomic orbital , mathematical analysis , eigenvalues and eigenvectors , mathematics , geometry , electron
The electromagnetic eigenmodes of a three-dimensional fractal called the Menger sponge were analyzed by the LCAO (linear combination of atomic orbitals) approximation and a first-principle calculation based on the FDTD (finite-difference time-domain) method. Due to the localized nature of the eigenmodes, the LCAO approximation gives a good guiding principle to find scaled eigenfunctions and to observe the approximate self-similarity in the spectrum of the localized eigenmodes.