Abstract

As is well-known, the sub-wavelength transmissions and field enhancement are related to the surface plasmon excitation. Here we demonstrate that in two-layer metallic gratings the deep sub-wavelength transmissions is supported with the TE polarization where the surface plasmon mode is forbidden. The new mechanism to the sub-wavelength transmission is discovered to be completely different from the findings in the literatures. we propose a simple resonance condition to classify the resonance types which are responsible for those sub-wavelength transmissions and confirm with numerical simulations. To give a complete explanation of underlying physics, we inspect the near-field phenomenon within the grating slits.

© 2009 OSA

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References

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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(6668), 667–669 (1998).
    [CrossRef]
  2. E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
    [CrossRef] [PubMed]
  3. 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(5582), 820–822 (2002).
    [CrossRef] [PubMed]
  4. S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
    [CrossRef]
  5. S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
    [CrossRef]
  6. F. J. Garcia de Abajo, “Full transmission through perfect-conductor subwavelength hole arrays,” Rev. Mod. Phys. 79, 1267 (2007).
  7. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
    [CrossRef] [PubMed]
  8. S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley & Sons, Inc., New York, 1994).
  9. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, Heidelberg, New York, 1980).
  10. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
    [CrossRef]
  11. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
    [CrossRef]
  12. S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
    [CrossRef]
  13. M. Chen, S. Lin, H. C. Chang, and A. S. P. Chang, “Physical origin of the resonant mode deep inside the stop band of a metallodielectric photonic crystal,” Phys. Rev. B 78(8), 085110 (2008).
    [CrossRef]
  14. A. S. P. Chang, Y. S. Kim, M. Chen, Z. P. Yang, J. A. Bur, S. Y. Lin, and K. M. Ho, “Visible three-dimensional metallic photonic crystal with non-localized propagating modes beyond waveguide cutoff,” Opt. Express 15(13), 8428–8437 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8428 .
    [CrossRef] [PubMed]
  15. M. Fox, Optical Properties of Solids (Oxford Univ. Press, New York, 2006).
  16. A. Taflove, and S. C. Hagness, “Computational Electrodynamics: The Finite-Differece Time-Domain Method”, (Artech House, Boston/London, 2005).
  17. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
    [CrossRef]
  18. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
    [CrossRef]

2008 (1)

M. Chen, S. Lin, H. C. Chang, and A. S. P. Chang, “Physical origin of the resonant mode deep inside the stop band of a metallodielectric photonic crystal,” Phys. Rev. B 78(8), 085110 (2008).
[CrossRef]

2007 (2)

2005 (1)

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
[CrossRef]

2004 (1)

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

2003 (2)

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

2002 (3)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[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(5582), 820–822 (2002).
[CrossRef] [PubMed]

2001 (2)

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

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(14), 2845–2848 (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(6668), 667–669 (1998).
[CrossRef]

Akarca-Biyikli, S. S.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
[CrossRef]

Altewischer, E.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[CrossRef] [PubMed]

Bishop, S. R.

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

Bulu, I.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
[CrossRef]

Bur, J. A.

Chang, A. S. P.

Chang, H. C.

M. Chen, S. Lin, H. C. Chang, and A. S. P. Chang, “Physical origin of the resonant mode deep inside the stop band of a metallodielectric photonic crystal,” Phys. Rev. B 78(8), 085110 (2008).
[CrossRef]

Chen, M.

Coe, J. V.

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

Collin, S.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[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(5582), 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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[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(6668), 667–669 (1998).
[CrossRef]

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, “Full transmission through perfect-conductor subwavelength hole arrays,” Rev. Mod. Phys. 79, 1267 (2007).

Garcia-Vidal, F. 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(5582), 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(14), 2845–2848 (1999).
[CrossRef]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

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(6668), 667–669 (1998).
[CrossRef]

Ho, K. M.

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Kim, Y. S.

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[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(6668), 667–669 (1998).
[CrossRef]

Lin, S.

M. Chen, S. Lin, H. C. Chang, and A. S. P. Chang, “Physical origin of the resonant mode deep inside the stop band of a metallodielectric photonic crystal,” Phys. Rev. B 78(8), 085110 (2008).
[CrossRef]

Lin, S. Y.

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martin-Moreno, L.

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Ozbay, E.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
[CrossRef]

Pardo, F.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[CrossRef]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Pelouard, J. L.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

Pelouard, J.-L.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[CrossRef]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[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(14), 2845–2848 (1999).
[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(14), 2845–2848 (1999).
[CrossRef]

Rogers, T. M.

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

Stafford, A. D.

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

Suh, W.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[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(6668), 667–669 (1998).
[CrossRef]

van Exter, M. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[CrossRef] [PubMed]

Williams, S. M.

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

Woerdman, J. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[CrossRef] [PubMed]

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(6668), 667–669 (1998).
[CrossRef]

Yang, Z. P.

Appl. Phys. Lett. (1)

S. M. Williams, A. D. Stafford, T. M. Rogers, S. R. Bishop, and J. V. Coe, “Extraordinary infrared transmission of Cu-coated arrays with subwavelength apertures: Hole size and the transition from surface plasmon to waveguide transmission,” Appl. Phys. Lett. 85(9), 1472–1474 (2004).
[CrossRef]

J. Opt. A (2)

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A 7, S159 (2005).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A 4, S154 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

Nature (2)

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(6668), 667–669 (1998).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. (2)

M. Chen, S. Lin, H. C. Chang, and A. S. P. Chang, “Physical origin of the resonant mode deep inside the stop band of a metallodielectric photonic crystal,” Phys. Rev. B 78(8), 085110 (2008).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63(3), 033107 (2001).
[CrossRef]

Phys. Rev. B (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission Resonances on Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

F. J. Garcia de Abajo, “Full transmission through perfect-conductor subwavelength hole arrays,” Rev. Mod. Phys. 79, 1267 (2007).

Science (1)

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Other (4)

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley & Sons, Inc., New York, 1994).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, Heidelberg, New York, 1980).

M. Fox, Optical Properties of Solids (Oxford Univ. Press, New York, 2006).

A. Taflove, and S. C. Hagness, “Computational Electrodynamics: The Finite-Differece Time-Domain Method”, (Artech House, Boston/London, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the two-layer gratings. The plane-waves are incident from the top with electric fields oriented along the grating lines. Given this polarization, the surface plasmon is no longer excited.

Fig. 2.
Fig. 2.

(a) The transmission spectrum of the two-layer gratings. The resonances can be approximately decided by kres = ikν + jka , where (i, j) is the mode index. Those with j = 0 are categorized as Fabry-Perot resonances, while the others are Fano resonances as shown in (b).

Fig. 3.
Fig. 3.

(Color online) The Ey mode profiles of Fano resonances. The Fano resonances occur when the resonant fields have horizontal components, e.g. j ≠ 0. The color denotes the field strength. The red and blue represent the positive and negative maxima, respectively.

Fig. 4.
Fig. 4.

(Color online) The Ey mode profiles of Fabry-Perot resonances. The Fabry-Perot resonances occur when the resonant fields do not have horizontal components, meaning j = 0.

Fig. 5.
Fig. 5.

Examination of the tunneling strength. (a)(b) The FDTD-computed resonance wavelengths with respect to different slit widths, marked as “ *”. The dashed line indicates the results calculated from the proposed formula. The tunneling strength is weakened with narrower slit width. As a result, the FDTD-computed wavelengths approach the formula-computed ones. (c)(d) The FDTD-computed wavelengths versus the scaling factor δ.

Tables (1)

Tables Icon

Table 1. The resonance wavelengths obtained from both the formula and FDTD simulations

Equations (3)

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

kres=ikν+jka ,
kν=2πn0L/2 ; ka=2πn0a .
λres=[(2in0L)2+(jn0a)2]1/2

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