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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 9 — Sep. 1, 2008
  • pp: 1466–1473

Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice

Yumao Wu and Ya Yan Lu  »View Author Affiliations

JOSA B, Vol. 25, Issue 9, pp. 1466-1473 (2008)

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An efficient numerical method is developed for computing the transmission and reflection spectra of finite two-dimensional photonic crystals composed of circular cylinders in a triangular lattice. Our method manipulates a pair of operators defined on a set of curves, and it remains effective when the radius of the cylinders is larger than 3 4 of the lattice constant—a condition where different arrays of cylinders cannot be separated by planes without intersecting the cylinders. The method is efficient since it never calculates the wave field in the interiors of the (hexagon) unit cells and it approximates the operators by small matrices. This is achieved by using the Dirichlet-to-Neumann (DtN) maps of the unit cells, which map the wave field on the boundaries of the unit cells to its normal derivative.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

Original Manuscript: May 15, 2008
Revised Manuscript: July 5, 2008
Manuscript Accepted: July 5, 2008
Published: August 18, 2008

Yumao Wu and Ya Yan Lu, "Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice," J. Opt. Soc. Am. B 25, 1466-1473 (2008)

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