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. 18, Iss. 7 — Jul. 1, 2001
  • pp: 1495–1506

Modeling considerations for rigorous boundary element method analysis of diffractive optical elements

Jon M. Bendickson, Elias N. Glytsis, Thomas K. Gaylord, and Andrew F. Peterson  »View Author Affiliations


JOSA A, Vol. 18, Issue 7, pp. 1495-1506 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001495


View Full Text Article

Enhanced HTML    Acrobat PDF (763 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Critical modeling issues relating to rigorous boundary element method (BEM) analysis of diffractive optical elements (DOEs) are identified. Electric-field integral equation (EFIE) and combined-field integral equation (CFIE) formulations of the BEM are introduced and implemented. The nonphysical interior resonance phenomenon and thin-shape breakdown are illustrated in the context of a guided-mode resonant subwavelength grating. It is shown that modeling such structures by using an open geometric configuration eliminates these problems that are associated with the EFIE BEM. Necessary precautions in defining the incident fields are also presented for the analysis of multiple-layer DOEs.

© 2001 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics
(050.2770) Diffraction and gratings : Gratings
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: September 15, 2000
Manuscript Accepted: January 3, 2001
Published: July 1, 2001

Citation
Jon M. Bendickson, Elias N. Glytsis, Thomas K. Gaylord, and Andrew F. Peterson, "Modeling considerations for rigorous boundary element method analysis of diffractive optical elements," J. Opt. Soc. Am. A 18, 1495-1506 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-7-1495


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Feature issue on diffractive optics applications, Appl. Opt. 34, 2399–2559 (1995). [CrossRef]
  2. M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.
  3. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996). [CrossRef]
  4. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997). [CrossRef]
  5. E. N. Glytsis, M. E. Harrigan, K. Hirayama, T. K. Gaylord, “Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation,” Appl. Opt. 37, 34–43 (1998). [CrossRef]
  6. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998). [CrossRef]
  7. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999). [CrossRef]
  8. T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991). [CrossRef]
  9. D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997). [CrossRef]
  10. J.-C. Bolomey, W. Tabbara, “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propag. AP-21, 356–363 (1973). [CrossRef]
  11. C. A. Klein, R. Mittra, “An application of the ‘condition number’ concept to the solution of scattering problems in the presence of the interior resonant frequencies,” IEEE Trans. Antennas Propag. 23, 431–435 (1975). [CrossRef]
  12. A. F. Peterson, “The ‘interior resonance’ problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies,” Electromagnetics 10, 293–312 (1990). [CrossRef]
  13. R. Martinez, “The thin-shape breakdown (TSB) of the Helmholtz integral equation,” J. Acoust. Soc. Am. 90, 2728–2738 (1991). [CrossRef]
  14. G. Krishnasamy, F. J. Rizzo, Y. Liu, “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994). [CrossRef]
  15. T. W. Wu, “A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies,” J. Acoust. Soc. Am. 97, 84–91 (1995). [CrossRef]
  16. K. Hirayama, K. Igarashi, Y. Hayashi, E. N. Glytsis, T. K. Gaylord, “Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary element methods,” J. Opt. Soc. Am. A 16, 1294–1302 (1999). [CrossRef]
  17. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993). [CrossRef] [PubMed]
  18. A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett. 21, 1564–1566 (1996). [CrossRef] [PubMed]
  19. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995). [CrossRef] [PubMed]
  20. K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985). [CrossRef]
  21. N. Morita, “Analysis of scattering by a dielectric rectangular cylinder by means of integral equation formulation,” Electron. Commun. Jpn. 57-B, 72–80 (1974).
  22. J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).
  23. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings,” J. Opt. Soc. Am. A18 (to be published).
  24. P. M. Goggans, A. A. Kishk, A. W. Glisson, “A systematic treatment of conducting and dielectric bodies with arbitrarily thick or thin features using the method of moments,” IEEE Trans. Antennas Propag. 40, 555–560 (1992). [CrossRef]
  25. A. J. Poggio, E. K. Miller, “Integral equation solutions of three-dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, Oxford, UK, 1973), Chap. 4.

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