## All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack

JOSA A, Vol. 27, Issue 4, pp. 878-889 (2010)

http://dx.doi.org/10.1364/JOSAA.27.000878

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### Abstract

We propose a novel formulation of the finite element method adapted to the calculation of the vector field diffracted by an arbitrarily shaped crossed-grating embedded in a multilayered stack and illuminated by an arbitrarily polarized plane wave under oblique incidence. A complete energy balance (transmitted and reflected diffraction efficiencies and losses) is deduced from field maps. The accuracy of the proposed formulation has been tested using classical cases computed with independent methods. Moreover, to illustrate the independence of our method with respect to the shape of the diffractive object, we present the global energy balance resulting from the diffraction of a plane wave by a lossy thin torus crossed-grating. Finally, computation time and convergence as a function of the mesh refinement are discussed. As far as integrated energy values are concerned, the presented method shows a remarkable convergence even for coarse meshes.

© 2010 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

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: November 6, 2009

Revised Manuscript: February 5, 2010

Manuscript Accepted: February 10, 2010

Published: March 29, 2010

**Citation**

Guillaume Demésy, Frédéric Zolla, André Nicolet, and Mireille Commandré, "All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack," J. Opt. Soc. Am. A **27**, 878-889 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-4-878

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