OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 3 — Mar. 1, 2010
  • pp: 560–566

A spectral element method calculation of extraordinary light transmission through periodic subwavelength slits

Ma Luo, Qing Huo Liu, and Junpeng Guo  »View Author Affiliations

JOSA B, Vol. 27, Issue 3, pp. 560-566 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (395 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A spectral element method together with a surface integral equation as the radiation boundary condition is used to simulate the scattering properties of periodic subwavelength slits. The surface integral equation utilizes the periodic Green’s function in the wave number space and is solved by the method of moments, while the interior inhomogeneous medium is modeled by the spectral element method. The solution convergence is found to be exponential; i.e., the error decreases exponentially with the order of basis functions. To our knowledge, such a fast solver with spectral accuracy is new in the scattering problem of periodic structures. Scattering properties of a gold slit grid within the whole wavelength-incidence angle parameter space are investigated, with the confirmation that strong transmission of light through subwavelength slits is achievable.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(160.5298) Materials : Photonic crystals

ToC Category:
Numerical Approximation and Analysis

Original Manuscript: October 20, 2009
Manuscript Accepted: November 30, 2009
Published: February 25, 2010

Ma Luo, Qing Huo Liu, and Junpeng Guo, "A spectral element method calculation of extraordinary light transmission through periodic subwavelength slits," J. Opt. Soc. Am. B 27, 560-566 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J.-H. Lee and Q. H. Liu, “An efficient 3-D spectral element method for Schrodinger equation in nanodevice simulation,” IEEE Trans. Comput.-Aided Des. 24, 1848-1858 (2005). [CrossRef]
  2. G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations (Springer, 2001).
  3. J.-H. Lee, T. Xiao, and Q. H. Liu, “A 3-D spectral element method using mixed-order curl conforming vector basis functions for electromagnetic fields,” IEEE Trans. Microwave Theory Tech. 54, 437-444 (2006). [CrossRef]
  4. M. Luo, Q. H. Liu, and Z. Li, “Spectral element method for band structures of two-dimensional anisotropic photonic crystals,” Phys. Rev. E 79, 026705 (2009). [CrossRef]
  5. J. Liu and Q. H. Liu, “A novel radiation boundary condition for finite-element method,” Microwave Opt. Technol. Lett. 49, 1995-2002 (2007). [CrossRef]
  6. F. Q. Hu, “A spectral boundary integral equation method for the 2D Helmholtz equation,” J. Comput. Phys. 120, 340-347 (1995). [CrossRef]
  7. J. Liu and Q. H. Liu, “A spectral integral method (SIM) for periodic and nonperiodic structures,” IEEE Microw. Wirel. Compon. Lett. 14, 97-99 (2004). [CrossRef]
  8. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  9. E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135-2136 (1968).
  10. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398-410 (1968). [CrossRef]
  11. Y.-Y. Teng and E. A. Stern, “Plasma radiation from metal grating surfaces,” Phys. Rev. Lett. 19, 511-514 (1967). [CrossRef]
  12. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530-1533 (1968). [CrossRef]
  13. C. J. Alleyne, A. G. Kirk, R. C. McPhedran, N.-A. P. Nicorovici, and D. Maystre, “Enhanced SPR sensitivity using periodic metallic structures,” Opt. Express 15, 8163-8169 (2007). [CrossRef] [PubMed]
  14. K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737-3742 (2005). [CrossRef] [PubMed]
  15. K. M. Byun, M. L. Shuler, S. J. Kim, S. J. Yoon, and D. Kim, “Sensitivity enhancement of surface plasmon resonance imaging using periodic metallic nanowires,” J. Lightwave Technol. 26, 1472-1478 (2008). [CrossRef]
  16. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006). [CrossRef] [PubMed]
  17. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901(E) (2007). [CrossRef]
  18. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271-5283 (1998). [CrossRef]
  19. H.-S. Leong, J. Guo, R. G. Lindquist, and Q. H. Liu, “Surface plasmon resonance in nanostructured metal films under the Kretschmann configuration” J. Appl. Phys. 106, 124314 (2009). [CrossRef]
  20. T. Tamir, H. C. Wang, and A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. 12, 323-335 (1964). [CrossRef]
  21. C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc. Am. 56, 1502-1508 (1966). [CrossRef]
  22. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780-1787 (1986). [CrossRef]
  23. 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 Opt. Image Sci. Vis 12, 1068-1076 (1995). [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