Open AccessReformulation of the plane wave method to model photonic crystals
Author(s) -
Rossella Zoli,
M. Gnan,
Davide Castaldini,
Gaetano Bellanca,
Paolo Bassi
Publication year - 2003
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.11.002905
Subject(s) - photonic crystal , superposition principle , supercell , optics , plane wave expansion , plane wave expansion method , dielectric , physics , dispersion (optics) , plane wave , finite difference time domain method , field (mathematics) , plane (geometry) , quantum mechanics , mathematics , geometry , thunderstorm , meteorology , pure mathematics
A new formulation of the plane-wave method to study the characteristics (dispersion curves and field patterns) of photonic crystal structures is proposed. The expression of the dielectric constant is written using the superposition of two regular lattices, the former for the perfect structure and the latter for the defects. This turns out to be simpler to implement than the classical one, based on the supercell concept. Results on mode coupling effects in two-dimensional photonic crystal waveguides are studied and successfully compared with those provided by a Finite Difference Time Domain method. In particular the approach is shown able to determine the existence of "mini-stop bands" and the field patterns of the various interfering modes.