## Fast modal method for crossed grating computation, combining finite formulation of Maxwell equations with polynomial approximated constitutive relations |

JOSA A, Vol. 30, Issue 4, pp. 573-581 (2013)

http://dx.doi.org/10.1364/JOSAA.30.000573

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### Abstract

We present a modal method for the fast analysis of 2D-layered gratings. It combines exact discrete formulations of Maxwell equations in 2D space with polynomial approximations of the constitutive equations, and provides a sparse formulation of the eigenvalue equations. In specific cases, the use of sparse matrices allows us to calculate the electromagnetic response while solving only a small fraction of the eigenmodes. This significantly increases computational speed up to

© 2013 Optical Society of America

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(250.5403) Optoelectronics : Plasmonics

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: October 19, 2012

Revised Manuscript: January 9, 2013

Manuscript Accepted: February 5, 2013

Published: March 6, 2013

**Citation**

Benjamin Portier, Fabrice Pardo, Patrick Bouchon, Riad Haïdar, and Jean-Luc Pelouard, "Fast modal method for crossed grating computation, combining finite formulation of Maxwell equations with polynomial approximated constitutive relations," J. Opt. Soc. Am. A **30**, 573-581 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-573

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