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

  • Vol. 25, Iss. 12 — Dec. 1, 2008
  • pp: 3099–3110

Solutions of Maxwell’s equations in presence of lamellar gratings including infinitely conducting metal

Boris Gralak, Raphaël Pierre, Gérard Tayeb, and Stefan Enoch  »View Author Affiliations


JOSA A, Vol. 25, Issue 12, pp. 3099-3110 (2008)
http://dx.doi.org/10.1364/JOSAA.25.003099


View Full Text Article

Enhanced HTML    Acrobat PDF (3408 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Modal methods often used to model lamellar gratings that include infinitely or highly conducting metallic parts encounter numerical instabilities in some situations. In this paper, the origin of these numerical instabilities is determined, and then a stable algorithm solving this problem is proposed. In order to complete this analysis, the different geometries that can be handled without numerical instabilities are clearly defined. Numerical tests of the exact modal method implemented with the proposed solution are also presented. A test of convergence shows the efficiency of the method while the comparison with the fictitious sources method shows its accuracy.

© 2008 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 16, 2008
Revised Manuscript: September 18, 2008
Manuscript Accepted: September 25, 2008
Published: November 25, 2008

Citation
Boris Gralak, Raphaël Pierre, Gérard Tayeb, and Stefan Enoch, "Solutions of Maxwell's equations in presence of lamellar gratings including infinitely conducting metal," J. Opt. Soc. Am. A 25, 3099-3110 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-12-3099


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981). [CrossRef]
  2. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087-1102 (1981). [CrossRef]
  3. L. C. Botten, M. S. Craig, and R. C. McPhedran, “Highly conducting lamellar diffraction grating,” Opt. Acta 28, 1103-1106 (1981). [CrossRef]
  4. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-waves analysis of metallic surface-relief grating,” J. Opt. Soc. Am. A 3, 1780-1787 (1986). [CrossRef]
  5. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature (London) 391, 667-669 (1998). [CrossRef]
  6. S. Enoch, M. Nevière, E. Popov, and R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A, Pure Appl. Opt. 4, S83-S87 (2002). [CrossRef]
  7. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002). [CrossRef] [PubMed]
  8. P. Andrew and W. L. Barnes, “Molecular fluorescence above metallic gratings,” Phys. Rev. B 64, 125405 (2001). [CrossRef]
  9. J. Kalkman, C. Strohhöfer, B. Gralak, and A. Polman, “Surface plasmon polariton modified emission of erbium in a metallodielectric grating,” Appl. Phys. Lett. 83, 30 (2003). [CrossRef]
  10. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature (London) 444, 740-743 (2006). [CrossRef]
  11. M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, “Microstructured magnetic materials for RF flux guides in magnetic resonance imaging,” Science 291, 849-851 (2001). [CrossRef] [PubMed]
  12. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001). [CrossRef] [PubMed]
  13. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024-1035 (1996). [CrossRef]
  14. S. Campbell, L. C. Botten, C. Martijn De Sterke, and R. C. McPhedran, “Fresnel formulation for multi-element lamellar diffraction gratings in conical mountings,” Waves Random Complex Media 17, 455-475 (2007). [CrossRef]
  15. L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553-573 (1993). [CrossRef]
  16. B. Gralak, M. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003). [CrossRef]
  17. Z.-Y. Li and K.-M. Ho, “Analytic modal solution to light propagation through layer-by-layer metallic photonic crystals,” Phys. Rev. B 67, 165104 (2003). [CrossRef]
  18. G. Tayeb and S. Enoch, “Combined fictitious sources-scattering matrix method,” J. Opt. Soc. Am. A 21, 1417-1423 (2004). [CrossRef]
  19. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, 1990).
  20. G. Tayeb, “The method of fictitious sources applied to diffraction gratings,” Special issue on Generalized Multipole Techniques (GMT) of Applied Computational Electromagnetics Society Journal 9, 90-100 (1994).
  21. D. Maystre, M. Saillard, and G. Tayeb, Scattering (Academic, 2001).
  22. D. Kaklamani and H. Anastassiu, “Aspects of the method of auxiliary sources (MAS) in computational electromagnetics,” IEEE Antennas Propag. Mag. 44, 48-64 (2002). [CrossRef]
  23. G. Benelli, S. Enoch, and G. Tayeb, “Modelling of a single object embedded in a layered medium,” J. Mod. Opt. 54, 871-879 (2007). [CrossRef]

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