Abstract

We present an intuitive reasoning and derivation leading to an approximated, simple closed-form model for predicting and explaining the general emergence of enhanced transmission resonances through rectangular, optically thick 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 enhanced transmission as emerging from standing wave resonances of the different diffraction orders of periodic structures. The model correctly predicts the conditions for the enhanced transmission resonances in various geometrical configurations, for both TE and TM polarizations, and in both the subwavelength and non-subwavelength spectral regimes, using the same underlying mechanism and one simple closed-form equation, and does not require explicitly invoking specific polarization dependent mechanisms. The known excitation of surface plasmons polaritons or slit cavity modes, emerge as limiting cases of a more general condition. This equation can be used to easily design and analyze the optical properties of a wide range of rectangular metallic transmission gratings.

© 2011 OSA

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  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. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
    [CrossRef] [PubMed]
  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: Pure Appl. Opt. 11, 125702 (2009).
    [CrossRef]
  5. 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] [PubMed]
  6. F. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66 (2002).
    [CrossRef]
  7. 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] [PubMed]
  8. 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] [PubMed]
  9. F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
    [CrossRef]
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    [CrossRef]
  11. M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66 (2002).
    [CrossRef]
  12. P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
    [CrossRef]
  13. J. Shen and P. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70 (2004).
    [CrossRef]
  14. K. G. Lee and Q. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).
    [CrossRef] [PubMed]
  15. 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]
  16. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
    [CrossRef] [PubMed]
  17. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
    [CrossRef]
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    [CrossRef]
  20. 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]
  21. E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
    [CrossRef]
  22. D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
    [CrossRef]
  23. P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
    [CrossRef]
  24. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004).
    [CrossRef] [PubMed]
  25. D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
    [CrossRef] [PubMed]
  26. H. Lochbihler, “Enhanced transmission of TE polarized light through wire gratings,” Phys. Rev. B 79 (2009).
    [CrossRef]
  27. M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
    [CrossRef]
  28. A. Benabbas, V. Halte, and J. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005).
    [CrossRef] [PubMed]
  29. 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] [PubMed]
  30. M. Guillaumee, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martin-Moreno, F. J. Garcia-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010).
    [CrossRef] [PubMed]

2011 (2)

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] [PubMed]

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] [PubMed]

2010 (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]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

M. Guillaumee, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martin-Moreno, F. J. Garcia-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010).
[CrossRef] [PubMed]

2009 (2)

H. Lochbihler, “Enhanced transmission of TE polarized light through wire gratings,” Phys. Rev. B 79 (2009).
[CrossRef]

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: Pure Appl. Opt. 11, 125702 (2009).
[CrossRef]

2008 (1)

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] [PubMed]

2007 (2)

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427 (2007).
[CrossRef] [PubMed]

2006 (1)

E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[CrossRef]

2005 (3)

A. Benabbas, V. Halte, and J. Bigot, “Analytical model of the optical response of periodically structured metallic films,” Opt. Express 13, 8730–8745 (2005).
[CrossRef] [PubMed]

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] [PubMed]

K. G. Lee and Q. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

2004 (4)

J. Shen and P. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70 (2004).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004).
[CrossRef] [PubMed]

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]

2003 (2)

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

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]

2002 (4)

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]

F. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66 (2002).
[CrossRef]

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66 (2002).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

2000 (1)

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

1999 (1)

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 (1999).
[CrossRef]

1998 (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]

1997 (1)

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

1986 (1)

Astilean, S.

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Banin, U.

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] [PubMed]

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] [PubMed]

Benabbas, A.

Bigot, J.

Blanchard, R.

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]

Cao, Q.

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]

Capasso, F.

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]

Catrysse, P. B.

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] [PubMed]

Chang, C.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Chen, G.

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] [PubMed]

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] [PubMed]

Chen, S.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Chien, F.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Crouse, D.

Darmanyan, S. A.

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]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

Diehl, L.

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]

Ding, Y.

Dunbar, L. A.

Dykhne, A. M.

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).

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

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]

Eckert, R.

Edamura, T.

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]

Fan, J.

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]

Fan, S.

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] [PubMed]

Friesem, A.

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Furuta, S.

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]

Garca-Vidal, F. J.

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: Pure Appl. Opt. 11, 125702 (2009).
[CrossRef]

Garcia-Vidal, F.

F. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66 (2002).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

M. Guillaumee, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martin-Moreno, F. J. Garcia-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010).
[CrossRef] [PubMed]

E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

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 (1999).
[CrossRef]

Gaylord, T.

Ghaemi, H. F.

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]

Guillaumee, M.

Halte, V.

Harats, M. G.

Hugonin, J.

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Kan, H.

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]

Kats, A. V.

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]

Keshavareddy, P.

Klein, M. J. K.

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Lalanne, P.

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]

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Lee, K.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Lee, K. G.

K. G. Lee and Q. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

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]

Lin, C.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

Liu, H.

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] [PubMed]

Livneh, N.

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] [PubMed]

Lochbihler, H.

H. Lochbihler, “Enhanced transmission of TE polarized light through wire gratings,” Phys. Rev. B 79 (2009).
[CrossRef]

Magnusson, R.

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004).
[CrossRef] [PubMed]

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

Maldonado, T. A.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

M. Guillaumee, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martin-Moreno, F. J. Garcia-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010).
[CrossRef] [PubMed]

E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

F. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66 (2002).
[CrossRef]

Martn-Moreno, L.

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: Pure Appl. Opt. 11, 125702 (2009).
[CrossRef]

Moharam, M.

Moller, K.

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Moreno, E.

E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[CrossRef]

Nikitin, A. Y.

M. Guillaumee, A. Y. Nikitin, M. J. K. Klein, L. A. Dunbar, V. Spassov, R. Eckert, L. Martin-Moreno, F. J. Garcia-Vidal, and R. P. Stanley, “Observation of enhanced transmission for s-polarized light through a subwavelength slit,” Opt. Express 18, 9722–9727 (2010).
[CrossRef] [PubMed]

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: Pure Appl. Opt. 11, 125702 (2009).
[CrossRef]

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]

Palamaru, M.

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Paltiel, Y.

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] [PubMed]

Park, Q.

K. G. Lee and Q. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
[CrossRef] [PubMed]

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 (1999).
[CrossRef]

Pflugl, C.

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]

Platzman, P.

J. Shen and P. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70 (2004).
[CrossRef]

Porto, J. A.

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 (1999).
[CrossRef]

Priambodo, P. S.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

Rapaport, R.

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] [PubMed]

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] [PubMed]

Rosenberg, I.

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] [PubMed]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Sarychev, A. K.

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).

Schwarz, I.

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] [PubMed]

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] [PubMed]

Shalaev, V. M.

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).

Sharon, A.

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Shen, J.

J. Shen and P. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70 (2004).
[CrossRef]

Shen, J. T.

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] [PubMed]

Song, Y.

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] [PubMed]

Spassov, V.

Stanley, R. P.

Strauss, A.

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] [PubMed]

Sun, C.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Thio, T.

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]

Tian, J.

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] [PubMed]

Treacy, M.

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66 (2002).
[CrossRef]

Wang, L.

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] [PubMed]

Wang, Q. J.

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]

Wei, P.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Wolff, P. A.

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]

Yamanishi, M.

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]

Yih, J.

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

Yochelis, S.

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] [PubMed]

Yu, N.

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]

Zayats, A. V.

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]

Zhang, X.

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] [PubMed]

Zimran, A.

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] [PubMed]

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] [PubMed]

Appl. Phys. Lett. (1)

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

Biosens. Bioelectron. (1)

F. Chien, C. Lin, J. Yih, K. Lee, C. Chang, P. Wei, C. Sun, and S. Chen, “Coupled waveguide-surface plasmon resonance biosensor with subwavelength grating,” Biosens. Bioelectron. 22, 2737–2742 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, and A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

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]

J. Opt. A: Pure Appl. Opt. (3)

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: Pure Appl. Opt. 11, 125702 (2009).
[CrossRef]

P. Lalanne, J. Hugonin, S. Astilean, M. Palamaru, and K. Moller, “One-mode model and airy-like formulae for one-dimensional metallic gratings,” J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nano Lett. (2)

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] [PubMed]

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] [PubMed]

Nature (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]

Opt. Express (5)

Phys. Rev. B (7)

H. Lochbihler, “Enhanced transmission of TE polarized light through wire gratings,” Phys. Rev. B 79 (2009).
[CrossRef]

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).

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]

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]

F. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66 (2002).
[CrossRef]

J. Shen and P. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70 (2004).
[CrossRef]

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

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 (1999).
[CrossRef]

K. G. Lee and Q. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

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]

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] [PubMed]

Rev. Mod. Phys. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 –848 (2004).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 –822 (2002).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

A Cross section of a general metallic grating configuration. The incident plane wave vector, as well as the transmitted wave vector are represented by the arrows. All the relevant physical parameters are explained in the text.

Fig. 2
Fig. 2

A schematic illustration of the EBC model. (a) Numerically calculated near field intensity in a unit cell of the grating at a wavelength corresponding to an ET maximum in three different configurations, as explained in the text and in Table 1. The rectangular gray area indicates the metal and the white line marks the boundary of the dielectric layer n2 (when present). (b) The corresponding EBC model mapping. The same model applies to all the configurations, the only difference is the area in which the standing wave appears in the structure, depicted schematically for each configuration.

Fig. 3
Fig. 3

Transmission in the TM polarization with no added thin dielectric layer, in the symmetric configuration n1 = n3 = ns, for different wavelengths and grating thicknesses. The dotted white lines are the transmission maxima according to the EBC model for m = 1 (the first diffraction order) only. The yellow line is the first transmission maximum according to the EBC model with all the diffraction orders taken into account. The periodicity is d = 0.9 μm and the slit width is a = 0.35 μm. (a) The configuration in which the metal is a perfectly conducting metal, and (b) the configuration in which the metal is Ag, approximated by the Drude model, with artificially added large losses.

Fig. 4
Fig. 4

Transmission in the TE polarization with no added dielectric layer for different wavelengths and grating thicknesses. The dashed lines are the transmission maxima according to the EBC model. The periodicity is d = 0.9 μm, the slit width is a = 0.55 μm, so that 2a > d in the configuration corresponding to Fig. 2(3). The black dashed lines mark the boundaries between the different wavelength regimes.

Fig. 5
Fig. 5

Transmission in the TE polarization with a thin dielectric layer for different wavelengths and grating thicknesses. The dashed lines are the transmission maxima according to the EBC model (dotted line). The periodicity is d = 0.9 μm, the slit width is a = 0.35 μm and w2 = 0.93 μm. Because n2 = 1.52 and the metal is Al (approximated by the Drude model), the cutoff is at λ = 1.12 μm. The black dashed line marks the boundary between the wavelength regimes.

Fig. 6
Fig. 6

Transmission maxima according to the RCWA (full blue line) and the EBC model (black dotted line) for different slit widths. The transmission minimum is at λ = 1.266 μm. The periodicity is d = 0.9 μm, the grating thickness is w = 0.25 μm and the dielectric layer thickness is w2 = 0.25 μm.

Tables (1)

Tables Icon

Table 1 Summary of the different cases in Fig. 2

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

× [ 1 μ ( r ) × E ( r ) ] k 2 ɛ ( r ) E ( r ) = 0 ,
× [ 1 ɛ ( r ) × H ( r ) ] k 2 μ ( r ) H ( r ) = 0 ,
Δ E ( r ) + k 2 ɛ μ E ( r ) = 0 , Δ H ( r ) + k 2 ɛ μ H ( r ) = 0 ,
H ( j ) ( r ) = m H m j e i [ ( k x + g m ) x + k z ( j ) z ] y ^ ,
H ( r ) = j ψ ( j ) m H m j e i [ ( k x + g m ) x + k z ( j ) z ] y ^ .
H 1 , 3 ( r ) = m A m 1 , 3 e i [ ( k x + g m ) x + k z 1 , 3 z ] y ^ ,
H ( r ) = m H m e i [ ( k x + g m ) x + k z prop z ] y ^ ,
n eff = ( k z prop ) 2 + g 2 k .
2 k z prop w 2 ϕ 12 2 ϕ 23 = 2 π l ,
ϕ 12 = ϕ 23 = tan 1 ( ( χ 2 + 1 ) χ 2 1 ) ,
k z prop = μ ɛ c 2 ω 2 γ 2 ,
w = λ 0 l 2 n s ,

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