OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 4 — Apr. 1, 2010
  • pp: 878–889

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

Guillaume Demésy, Frédéric Zolla, André Nicolet, and Mireille Commandré  »View Author Affiliations


JOSA A, Vol. 27, Issue 4, pp. 878-889 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000878


View Full Text Article

Enhanced HTML    Acrobat PDF (761 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A  12, 1068–1076 (1995). [CrossRef]
  2. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A  14, 2758–2767 (1997). [CrossRef]
  3. E. Noponen and J. Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A  11, 2494–2502 (1994). [CrossRef]
  4. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings,” J. Opt. Soc. Am. A  24, 2880–2890 (2007). [CrossRef]
  5. E. Popov and M. Nevière, “Maxwell’s equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A  18, 2886–2894 (2001). [CrossRef]
  6. P. Vincent, “A finite-difference method for dielectric and conducting crossed gratings,” Opt. Commun.  26, 293–296 (1978). [CrossRef]
  7. D. Maystre and M. Nevière, “Electromagnetic theory of crossed gratings,” J. Opt.  9, 301–306 (1978). [CrossRef]
  8. G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, “Crossed gratings: A theory and its applications,” Appl. Phys. B: Photophys. Laser Chem.  18, 39–52 (1979).
  9. R. C. McPhedran, G. H. Derrick, M. Neviere, and D. Maystre, “Metallic crossed gratings,” J. Opt.  13, 209–218 (1982). [CrossRef]
  10. G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: Application to multilayer crossed gratings,” J. Opt. Soc. Am. A  15, 1121–1131 (1998). [CrossRef]
  11. J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, and R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A  13, 2041–2049 (1996). [CrossRef]
  12. J. J. Greffet, C. Baylard, and P. Versaevel, “Diffraction of electromagnetic waves by crossed gratings: a series solution,” Opt. Lett.  17, 1740–1742 (1992). [CrossRef] [PubMed]
  13. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A  10, 2551–2562 (1993). [CrossRef]
  14. O. P. Bruno, and F. Reitich, “Boundary-variation solutions for bounded-obstacle scattering problems in three dimensions,” J. Acoust. Soc. Am.  104, 2579–2583 (1998). [CrossRef]
  15. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.  14, 302–307 (1966). [CrossRef]
  16. K. S. Yee and J. S. Chen, “The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell’s equations,” IEEE Trans. Antennas Propag.  45, 354–363 (1997). [CrossRef]
  17. J. L. Volakis, A. Chatterjee, and L. C. Kempel, “Review of the finite-element method for three-dimensional electromagnetic scattering,” J. Opt. Soc. Am. A  11, 1422–1422 (1994). [CrossRef]
  18. X. Wei, A. J. Wachters, and H. P. Urbach, “Finite-element model for three-dimensional optical scattering problems,” J. Opt. Soc. Am. A  24, 866–881 (2007). [CrossRef]
  19. E. Popov, M. Nevière, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A  19, 33–42 (2002). [CrossRef]
  20. J. J. Greffet and Z. Maassarani, “Scattering of electromagnetic waves by a grating: a numerical evaluation of the iterative-series solution,” J. Opt. Soc. Am. A  7, 1483–1493 (1990). [CrossRef]
  21. G. Demésy, F. Zolla, A. Nicolet, M. Commandré, and C. Fossati, “The finite element method as applied to the diffraction by an anisotropic grating,” Opt. Express  15, 18089–18102 (2007). [CrossRef] [PubMed]
  22. G. Demésy, F. Zolla, A. Nicolet, M. Commandré, C. Fossati, O. Gagliano, S. Ricq, and B. Dunne, “Finite element method as applied to the study of gratings embedded in complementary metal-oxide semiconductor image sensors,” Opt. Eng. (Bellingham)  48, 058002 (2009). [CrossRef]
  23. F. Zolla and R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical diffraction mounts,” J. Opt. Soc. Am. A  13, 796–802 (1996). [CrossRef]
  24. A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, “Modelling of electromagnetic waves in periodic media with finite elements,” J. Comput. Appl. Math.  168, 321–329 (2004). [CrossRef]
  25. Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, “On the use of PML for the computation of leaky modes: an application to gradient index MOF,” Compel  27, 95–109 (2008).
  26. P. Dular, A. Nicolet, A. Genon, and W. Legros, “A discrete sequence associated with mixed finite elements and its gauge condition for vector potentials,” IEEE Trans. Magn.  31, 1356–1359 (1995). [CrossRef]
  27. P. Ingelstrom, “A new set of H (curl)-conforming hierarchical basis functions for tetrahedral meshes,” IEEE Trans. Microwave Theory Tech.  54, 106–114 (2006). [CrossRef]
  28. A. Bossavit and I. Mayergoyz, “Edge-elements for scattering problems,” IEEE Trans. Magn.  25, 2816–2821 (1989). [CrossRef]
  29. T. V. Yioultsis and T. D. Tsiboukis, “The Mystery and Magic of Whitney Elements—An Insight in their Properties and Construction,” ICS Newsletter  3, 1389–1392 (1996).
  30. T. V. Yioultsis and T. D. Tsiboukis, “Multiparametric vector finite elements: a systematic approach to the construction of three-dimensional, higher order, tangential vector shape functions,” IEEE Trans. Magn.  32, 1389–1392 (1996). [CrossRef]
  31. R. Bräuer and O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun.  100, 1–5 (1993). [CrossRef]
  32. L. Arnaud, “Diffraction et diffusion de la lumière: modélisation tridimensionnelle et application à la métrologie de la microélectronique et aux techniques d’imagerie sélective en milieu diffusant,” Ph.D. thesis (Université Paul Cézanne, 2008).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited