Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice

An efficient semi-analytic method is developed for computing the band structures of two-dimensional photonic crystals which are triangular lattices of circular cylinders. The problem is formulated as an eigenvalue problem for a given frequency using the Dirichlet-to-Neumann (DtN) map of a hexagon un...

Full description

Saved in:
Bibliographic Details
Published inOptics communications Vol. 273; no. 1; pp. 114 - 120
Main Authors Yuan, Jianhua, Lu, Ya Yan
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.05.2007
Elsevier Science
Subjects
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Optical materials
Optics
Photonic bandgap materials
Physics
Eigenvalues
Band structure
Bloch wave
Two dimensional structure
Photonic crystals
Cylindrical waves
Online AccessGet full text

Cover

More Information
Summary:An efficient semi-analytic method is developed for computing the band structures of two-dimensional photonic crystals which are triangular lattices of circular cylinders. The problem is formulated as an eigenvalue problem for a given frequency using the Dirichlet-to-Neumann (DtN) map of a hexagon unit cell. This is a linear eigenvalue problem even if the material is dispersive, where the eigenvalue depends on the Bloch wave vector. The DtN map is constructed from a cylindrical wave expansion, without using sophisticated lattice sums techniques. The eigenvalue problem can be efficiently solved by standard linear algebra programs, since it involves only matrices of relatively small size.
ISSN:0030-4018
1873-0310
DOI:10.1016/j.optcom.2007.01.005