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: Stephen A. Burns
  • Vol. 24, Iss. 3 — Mar. 1, 2007
  • pp: 866–881

Finite-element model for three-dimensional optical scattering problems

Xiuhong Wei, Arthur J.H. Wachters, and H. Paul Urbach  »View Author Affiliations


JOSA A, Vol. 24, Issue 3, pp. 866-881 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000866


View Full Text Article

Enhanced HTML    Acrobat PDF (987 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a three-dimensional model based on the finite-element method for solving the time-harmonic Maxwell equation in optics. It applies to isotropic or anisotropic dielectrics and metals and to many configurations such as an isolated scatterer in a multilayer, bi-gratings, and crystals. We discuss the application of the model to near-field optical recording.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(210.4770) Optical data storage : Optical recording
(240.7040) Optics at surfaces : Tunneling
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 1, 2005
Revised Manuscript: August 14, 2006
Manuscript Accepted: August 16, 2006
Published: February 14, 2007

Citation
Xiuhong Wei, Arthur J. Wachters, and H. Paul Urbach, "Finite-element model for three-dimensional optical scattering problems," J. Opt. Soc. Am. A 24, 866-881 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-3-866


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am. 68, 1206-1210 (1978). [CrossRef]
  2. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982). [CrossRef]
  3. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 73, 1105-1112 (1983). [CrossRef]
  4. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
  5. V. Rokhlin, "Rapid solution of integral equations of scattering theory in two dimensions," J. Comput. Phys. 36, 414-439 (1990). [CrossRef]
  6. N. Enghetta, W. Murphy, V. Rokhlin, and M. Vassiliou, "The fast multipole method (FMM) for electromagnetic scattering problems," IEEE Trans. Antennas Propag. 40, 634-642 (1992). [CrossRef]
  7. J. Song, C. Lu, and W. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag. 45, 1488-1493 (1997). [CrossRef]
  8. W. Chew, C. Lu, and Y. Wang, "Efficient computation of three-dimensional scattering of vector electromagnetic waves," J. Opt. Soc. Am. A 11, 1528-1537 (1994). [CrossRef]
  9. K. Yee, "Numerical solutions of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966). [CrossRef]
  10. K. Shlager and J. Schneider, "A selective survey of the finite-difference time-domain literature," IEEE Antennas Propag. Mag. 37, 39-56 (1995). [CrossRef]
  11. A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, 1st ed. (Artech House, 1998).
  12. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
  13. J. Judkins and R. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A 12, 1974-1983 (1995). [CrossRef]
  14. W.-C. Liu and D. P. Tsai, "Optical tunneling effect of surface plasmon polaritons and localized surface plasmon resonance," Phys. Rev. B 65, 155423 (2002). [CrossRef]
  15. G. Bao, "Finite element approximation of time harmonic waves in periodic structures," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 32, 1155-1169 (1995). [CrossRef]
  16. G. Bao and H. Yang, "A least-squares finite element analysis for diffraction problems," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 37, 665-682 (2000).
  17. J. Nédélec, "Mixed finite elements in R3," Numer. Math. 35, 315-341 (1980). [CrossRef]
  18. J. Nédélec, "A new family of mixed finite elements in R3," Numer. Math. 50, 57-81 (1986). [CrossRef]
  19. G. Mur and A. de Hoop, "A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media," IEEE Trans. Magn. MAG-21, 2188-2191 (1985). [CrossRef]
  20. P. Monk, Finite Element Methods for Maxwell's Equations, 1st ed. (Oxford U. Press, 2003). [CrossRef]
  21. G. C. Cohen, High-Order Numerical Methods for Transient Wave Equations, 1st ed. (Springer, 2001).
  22. P. Monk and L. Demkowicz, "Discrete compactness and the approximation of Maxwell's equations in R3," Math. Comput. 70, 507-523 (2001). [CrossRef]
  23. W. Rachowicz and L. Demkowicz, "An hp-adaptive finite element method for electromagnetics. Part II: A 3D implementation," Int. J. Numer. Methods Eng. 53, 147-180 (2002). [CrossRef]
  24. C. Geuzaine, B. Meys, P. Dular, and W. Legros, "Convergence of high order curl-conforming finite elements," IEEE Trans. Magn. 35, 1442-1445 (1999). [CrossRef]
  25. C. Geuzaine, "High order hybrid finite element schemes for Maxwell's equations taking thin structures and global quantities into account," Ph.D. thesis (Université de Liège, Liège, Belgium, 2001).
  26. T. Eibert and V. Hansen, "3-D FEM/BEM-hybrid approach based on a general formulation of Huygen's principle for planar layered media," IEEE Trans. Microwave Theory Tech. 45, 1105-1112 (1997). [CrossRef]
  27. W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave Opt. Technol. Lett. 7, 599-604 (1994). [CrossRef]
  28. M. Benzi, "Preconditioning techniques for large linear systems: a survey," J. Comput. Phys. 182, 418-477 (2002). [CrossRef]
  29. Y. A. Erlangga, C. Vuik, and C. W. Oosterlee, "On a class of preconditioners for the study of the Helmholtz equation," Appl. Numer. Math. 50, 405-425 (2004). [CrossRef]
  30. G. Mur and A. de Hoop, "The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media," IEEE Trans. Magn. 28, 1130-1133 (1992). [CrossRef]
  31. J. Gozani, A. Nachshon, and E. Trukel, "Conjugate gradient coupled with multigrid for an indefinite problem," in Advances in Computer Methods for Partial Differential Equations V (Springfield, 1984), pp. 425-427.
  32. H. Elman, O. Ernst, and D. O'Leary, "A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations," SIAM J. Sci. Comput. (USA) 23, 1291-1315 (2002). [CrossRef]
  33. S. Kim, "Multigrid simulation for high-frequency solutions of the Helmholtz problem in heterogeneous media," SIAM J. Sci. Comput. (USA) 24, 684-701 (2003). [CrossRef]
  34. Y. A. Erlangga, C. W. Oosterlee, and C. Vuik, "A novel multigrid-based preconditioner for the heterogeneous Helmholtz equation," SIAM J. Sci. Comput. (USA) 27, 1471-1492 (2006). [CrossRef]
  35. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (Society for Industrial and Applied Mathematics, 2003). [CrossRef]
  36. A. Kononov, X. Wei, and H. Urbach, "An efficient preconditioner for the finite element method applied to the time-harmonic Maxwell equations," J. Comput. Phys. (to be published).
  37. F. Zijp, M. van der Mark, J. Lee, and C. Verschuren, "Near-field read-out of a 50-GB first-surface disk with NA=1.9 and a proposal for a cover-layer-incident, dual-layer near-field system," in Proc. SPIE 5380, 209-223 (2004).
  38. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959). [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