## Dirichlet-to-Neumann map method for analyzing crossed arrays of circular cylinders

JOSA B, Vol. 26, Issue 11, pp. 1984-1993 (2009)

http://dx.doi.org/10.1364/JOSAB.26.001984

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### Abstract

An efficient and accurate computational method is developed for analyzing finite layers of crossed arrays of circular cylinders, including woodpile structures as special cases. The method relies on marching a few operators (approximated by matrices) from one side of the structure to another. The marching step makes use of the Dirichlet-to-Neumann (DtN) maps for two-dimensional unit cells in each layer where the structure is invariant in the direction of the cylinder axes. The DtN map is an operator that maps two wave field components to their normal derivatives on the boundary of the unit cell, and they can be easily constructed by vector cylindrical waves. Unlike existing numerical methods for crossed gratings, our method does not require a discretization of the structure. Compared with the multipole method that uses vector cylindrical wave expansions and scattering matrices, our method is relatively simple since it does not need sophisticated lattice sums techniques.

© 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

**History**

Original Manuscript: July 10, 2009

Manuscript Accepted: August 24, 2009

Published: October 5, 2009

**Virtual Issues**

October 8, 2009 *Spotlight on Optics*

**Citation**

Yumao Wu and Ya Yan Lu, "Dirichlet-to-Neumann map method for analyzing crossed arrays of circular cylinders," J. Opt. Soc. Am. B **26**, 1984-1993 (2009)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-11-1984

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