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. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2919–2924

Analytical solution of the fundamental waveguide mode of one-dimensional transmission grating for TM polarization

A. T. M. Anishur Rahman, Krasimir Vasilev, and Peter Majewski  »View Author Affiliations

JOSA B, Vol. 28, Issue 12, pp. 2919-2924 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (337 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This article presents an analytical solution of the effective index of the fundamental waveguide mode of one- dimensional (1D) metallodielectric grating for TM polarization. In contrast to the existing numerical solution involving a transcendental equation, it is shown that the square of the effective index ( n Eff ) of the fundamental waveguide mode of 1D grating is inversely proportional to the slit width (w) and the refractive index ( n m ) of the ridge material and varies linearly with the incident wavelength (λ). Further, it has also been demonstrated that the dependence of n Eff on the grating period (P) and the incidence angle (θ) is minimal. Agreement between the results obtained using the solution presented in this article and published data is excellent.

© 2011 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(260.3910) Physical optics : Metal optics

ToC Category:
Diffraction and Gratings

Original Manuscript: August 4, 2011
Revised Manuscript: October 12, 2011
Manuscript Accepted: October 12, 2011
Published: November 10, 2011

A. T. M. Anishur Rahman, Krasimir Vasilev, and Peter Majewski, "Analytical solution of the fundamental waveguide mode of one-dimensional transmission grating for TM polarization," J. Opt. Soc. Am. B 28, 2919-2924 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48–51 (2000). [CrossRef]
  2. S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000). [CrossRef]
  3. Y. Pang, C. Genet, and T. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007). [CrossRef]
  4. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, “Control of optical transmission through metals perforated with subwavelength hole arrays,” Opt. Lett. 24, 256–258 (1999). [CrossRef]
  5. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]
  6. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002). [CrossRef] [PubMed]
  7. P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916(1982). [CrossRef]
  8. A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005). [CrossRef]
  9. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001). [CrossRef] [PubMed]
  10. F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metal,” Phys. Rev. B 66, 155412 (2002). [CrossRef]
  11. T. Gaylord and M. Moharam, “Analysis and applications of optical diffraction by gratings,” in Proceedings of the IEEE (IEEE, 1985), pp. 894–937. [CrossRef]
  12. T. Clausnitzer, T. Kämpfe, E. B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, “An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings,” Opt. Express 13, 10448–10456(2005). [CrossRef] [PubMed]
  13. K. R. Catchpole, “A conceptual model of the diffuse transmittance of lamellar diffraction gratings on solar cells,” J. Appl. Phys. 102, 013102 (2007). [CrossRef]
  14. N. M. Lyndin, O. Parriaux, and A. V. Tishchenko, “Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings,” J. Opt. Soc. Am. A 24, 3781–3788(2007). [CrossRef]
  15. M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal–dielectric gratings: the decisive role of hidden modes,” J. Opt. Soc. Am. A 23, 2501–2509 (2006). [CrossRef]
  16. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Pearson Addison-Wesley, 2006), Vol.  2.
  17. A. T. M. A. Rahman, K. Vasilev, and P. Majewski, “Designing 1D grating for extraordinary optical transmission for TM polarization,” Photon. Nanostr. Fundam. Appl., doi:10.1016/j.photonics.2011.08.002 (posted 17 August 2011, in press). [CrossRef]
  18. E.D.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1985).

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