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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 7 — Jul. 1, 2009
  • pp: 1606–1614

Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps

Huan Xie and Ya Yan Lu  »View Author Affiliations

JOSA A, Vol. 26, Issue 7, pp. 1606-1614 (2009)

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For photonic crystals (PhCs) and related devices, it is useful to calculate the Dirichlet-to-Neumann (DtN) map of a unit cell, which maps the wave field to its normal derivative on the boundary. The DtN map can be used to avoid further calculations in the interiors of the unit cells and formulate mathematical problems on the cell boundaries. We develop a method to approximate the DtN map for two-dimensional PhCs involving anisotropic media, and we calculate band structures for PhCs involving liquid crystals. For band structures of triangular lattice PhCs, we also develop new eigenvalue problem formulations involving smaller matrices.

© 2009 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: February 23, 2009
Revised Manuscript: May 22, 2009
Manuscript Accepted: May 23, 2009
Published: June 18, 2009

Huan Xie and Ya Yan Lu, "Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps," J. Opt. Soc. Am. A 26, 1606-1614 (2009)

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