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. 29, Iss. 2 — Feb. 1, 2012
  • pp: A127–A137

Theory and experiments of Bragg cavity modes in passive and active metallic nanoslit array devices

Ilai Schwarz, Moshe G. Harats, Nitzan Livneh, Shira Yochelis, Ayelet Strauss, Adiel Zimran, Uri Banin, Yossi Paltiel, and Ronen Rapaport  »View Author Affiliations

JOSA B, Vol. 29, Issue 2, pp. A127-A137 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (816 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Metallic nanoslit arrays exhibit several unique, surprising, and useful properties, such as resonant enhanced transmission and resonant local field enhancements. Here we present both a theoretical study of these static properties, as well as experiments showing the utilization of these features combined with active optical media. We develop an approximated, simple closed-form model for predicting and explaining the general emergence of enhanced transmission resonances through metallic gratings, in various configurations and polarizations. This model is based on an effective index approximation and it unifies in a simple way the underlying mechanism of all forms of enhanced transmission in such structures as emerging from standing wave resonances of the different diffraction orders of periodic structures. The known excitation of surface plasmon polaritons or slit cavity modes emerges as a limiting case of a more general condition. We also use this understanding of the resonant behavior of nanoslit arrays to design and fabricate such structures with embedded nanocrystal quantum dots, and show beaming of nonclassical light to a narrow angle of less than 4 deg, as well as an enhancement of the two-photon upconversion fluorescence process by a factor of 400.

© 2012 Optical Society of America

OCIS Codes
(190.7220) Nonlinear optics : Upconversion
(310.6628) Thin films : Subwavelength structures, nanostructures

Original Manuscript: October 11, 2011
Revised Manuscript: December 14, 2011
Manuscript Accepted: December 14, 2011
Published: February 1, 2012

Ilai Schwarz, Moshe G. Harats, Nitzan Livneh, Shira Yochelis, Ayelet Strauss, Adiel Zimran, Uri Banin, Yossi Paltiel, and Ronen Rapaport, "Theory and experiments of Bragg cavity modes in passive and active metallic nanoslit array devices," J. Opt. Soc. Am. B 29, A127-A137 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
  2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002). [CrossRef]
  3. N. Yu, R. Blanchard, J. Fan, Q. J. Wang, C. Pflugl, L. Diehl, T. Edamura, S. Furuta, M. Yamanishi, H. Kan, and F. Capasso, “Plasmonics for laser beam shaping,” IEEE Trans. Nanotechnol. 9, 11–29 (2010). [CrossRef]
  4. A. Y. Nikitin, F. J. Garca-Vidal, and L. Martn-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009). [CrossRef]
  5. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003). [CrossRef]
  6. N. Livneh, A. Strauss, I. Schwarz, I. Rosenberg, A. Zimran, S. Yochelis, G. Chen, U. Banin, Y. Paltiel, and R. Rapaport, “Highly directional emission and photon beaming from nanocrystal quantum dots embedded in metallic nanoslit arrays,” Nano Lett. 11, 1630–1635 (2011). [CrossRef]
  7. F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002). [CrossRef]
  8. M. G. Harats, I. Schwarz, A. Zimran, U. Banin, G. Chen, and R. Rapaport, “Enhancement of two photon processes in quantum dots embedded in subwavelength metallic gratings,” Opt. Express 19, 1617–1625 (2011). [CrossRef]
  9. X. Zhang, H. Liu, J. Tian, Y. Song, and L. Wang, “Band-selective optical polarizer based on gold-nanowire plasmonic diffraction gratings,” Nano Lett. 8, 2653–2658 (2008). [CrossRef]
  10. F. C. Chien, C. Y. Lin, J. N. Yih, K. L. Lee, C. W. Chang, P. K. Wei, C. C. Sun, and S. J. Chen, “Coupled waveguide surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007). [CrossRef]
  11. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]
  12. M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002). [CrossRef]
  13. P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A 2, 48 (2000). [CrossRef]
  14. J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70, 035101 (2004). [CrossRef]
  15. K. G. Lee and Q.-H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005). [CrossRef]
  16. 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]
  17. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef]
  18. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010). [CrossRef]
  19. A. M. Dykhne, A. K. Sarychev, and V. M. Shalaev, “Resonant transmittance through metal films with fabricated and light-induced modulation,” Phys. Rev. B 67, 195402 (2003). [CrossRef]
  20. S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface Plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003). [CrossRef]
  21. A. V. Kats and A. Y. Nikitin, “Analytical treatment of anomalous transparency of a modulated metal film due to surface plasmon-polariton excitation,” Phys. Rev. B 70, 235412 (2004). [CrossRef]
  22. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A 8, S94 (2006). [CrossRef]
  23. D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997). [CrossRef]
  24. P. Priambodo, T. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003). [CrossRef]
  25. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004). [CrossRef]
  26. D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427(2007). [CrossRef]
  27. H. Lochbihler, “Enhanced transmission of TE polarized light through wire gratings,” Phys. Rev. B 79, 245427 (2009). [CrossRef]
  28. 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]
  29. A. Benabbas, V. Halté, and J. Y. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005). [CrossRef]
  30. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005). [CrossRef]
  31. That is because, for ideal metals, for each Bloch mode inside the slits, the relative amplitude of each order of m is proportional to the Fourier transform of a rectangular box of width a/d. Since this Fourier transform ∼sinc(adm), we get a rapid decrease in the contributions of higher orders of m for a/d∼0.5. Even for real metals, this approximation still holds, as will be evident from our comparison to rigorous numerical calculations in Section 2 and from calculating the values of Hm (the relative amplitude for different orders of m) for different real metals.
  32. I. Schwarz, N. Livneh, and R. Rapaport, “General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations,” Opt. Express 20, 426–439 (2012). [CrossRef]
  33. M. Guillaumée, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martín-Moreno, F. J. García-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010). [CrossRef]
  34. H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644(2011). [CrossRef]
  35. Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011). [CrossRef]
  36. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010). [CrossRef]
  37. G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005). [CrossRef]
  38. Cao and U. Banin, “Growth and properties of semiconductor core/shell nanocrystals with InAs cores,” J. Am. Chem. Soc. 122, 9692–9702 (2000). [CrossRef]
  39. E. Verhagen, L. Kuipers, and A. Polman, “Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence,” Opt. Express 17, 14586–14598 (2009). [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