Abstract

The debate on the underlying physics of the extraordinary optical transmission (EOT) through a metallic nano-slit surrounded with periodic grooves is largely resolved. We clarify that the EOT originates from the interference between the slit modes excited by the incident light and by the groove-generated surface plasmon polaritons modulated by the horizontal Fabry–Perot resonance effect due to the surrounding grooves. The quantitative model derived will greatly simplify the design of such structures.

© 2010 Optical Society of America

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  1. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
    [CrossRef]
  2. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
    [CrossRef] [PubMed]
  3. O. T. A. Janssen, H. P. Urbach, and G. W. 't Hooft, Phys. Rev. Lett. 99, 043902 (2007).
    [CrossRef] [PubMed]
  4. B. Ung and Y. Sheng, Opt. Express 15, 1182 (2007).
    [CrossRef] [PubMed]
  5. P. Lalanne and J. P. Hugonin, Nat. Phys. 2, 551 (2006).
    [CrossRef]
  6. Y. X. Cui and S. L. He, Opt. Express 17, 13995 (2009).
    [CrossRef] [PubMed]
  7. P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
    [CrossRef]
  8. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  9. P. Lalanne, J. P. Hugonin, and J. C. Rodier, J. Opt. Soc. Am. A 23, 1608 (2006).
    [CrossRef]
  10. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, J. Opt. Soc. Am. A 18, 2865 (2001).
    [CrossRef]
  11. X. Wei, A. J. Wachters, and H. P. Urbach, J. Opt. Soc. Am. A 24, 866 (2007).
    [CrossRef]
  12. A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
    [CrossRef]

2009

Y. X. Cui and S. L. He, Opt. Express 17, 13995 (2009).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

2007

2006

2003

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

2001

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, J. Opt. Soc. Am. A 18, 2865 (2001).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Cao, Q.

Cui, Y. X.

Ebbesen, T. W.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Garcia-Vidal, F. J.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

He, S. L.

Hugonin, J. P.

Janssen, O. T. A.

O. T. A. Janssen, H. P. Urbach, and G. W. 't Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

Kima, T. J.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Krishnan, A.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Lalanne, P.

Lezec, H. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Linke, R. A.

Liu, H. T.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

Martin-Moreno, L.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Martín-Moreno, L.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Pellerin, K. M.

Pendry, J.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Rodier, J. C.

Sheng, Y.

Silberstein, E.

't Hooft, G. W.

O. T. A. Janssen, H. P. Urbach, and G. W. 't Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

Thio, T.

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Ung, B.

Urbach, H. P.

O. T. A. Janssen, H. P. Urbach, and G. W. 't Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

X. Wei, A. J. Wachters, and H. P. Urbach, J. Opt. Soc. Am. A 24, 866 (2007).
[CrossRef]

Wachters, A. J.

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

Wei, X.

Wolff, P. A.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Phys.

P. Lalanne and J. P. Hugonin, Nat. Phys. 2, 551 (2006).
[CrossRef]

Opt. Commun.

A. Krishnan, T. Thio, T. J. Kima, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Commun. 200, 1 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

O. T. A. Janssen, H. P. Urbach, and G. W. 't Hooft, Phys. Rev. Lett. 99, 043902 (2007).
[CrossRef] [PubMed]

Surf. Sci. Rep.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, Surf. Sci. Rep. 64, 453 (2009).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of the metallic nanoslit dressed by N periodic grooves on each side, with groove width w g , depth h, and period p. The electromagnetic quantities A 1 , B 1 , A 2 , B 2 , U , and D are all defined in the text. The scattering of incident SPP modes by (b) a nanoslit and (c) N periodic grooves with coefficients defined in the text.

Fig. 2
Fig. 2

| D | 2 (thick-blue curve), | G | 2 (thin-red curve), | H | 2 (dashed-black curve), and the transmission efficiency η calculated by FEM (dashed-dotted-green curve) as functions of d. The calculations are performed for (a) w g / p = 0.56 , p = 785   nm , h = 70   nm , N = 11 [3] with r g = 0.26 + 0.064 i ; (b) w g = 250   nm , p = 720   nm , h = 60   nm , N = 12 [6] with r g = 0.372 0.08 i ; (c) w g / p = 0.52 , p = 785   nm , h = 30   nm , N = 11 with r g = 0.045 + 0.058 i ; (d) w g / p = 0.56 , p = 785   nm , h = 30   nm , N = 11 with r g = 0.183 + 0.2 i . For all cases, ρ = 0.03 0.055 i and τ = 0.887 + 0.328 i .

Fig. 3
Fig. 3

(a) | I s p | calculated by FEM and | r g | calculated by a-FMM as functions of the duty cycle w g / p . (b) | D | 2 as a function of d for groove patterns with different duty cycles. The calculations are performed for p = 785   nm , h = 70   nm , N = 11 [3].

Equations (12)

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

B 1 = r g w A 1 + I s p 1 ,
A 1 = τ w A 2 + β I 0 + α v U + ρ w B 1 ,
A 2 = r g w B 2 + I s p 2 ,
B 2 = τ w B 1 + β I 0 + α v U + ρ w A 2 ,
D = t 0 I 0 + α w B 1 + α w A 2 + r s v U ,
U = r s v D ,
D = 1 1 r s 2 v 2 [ t 0 I 0 + 2 α w I s p 1 r g ( τ + ρ ) w 2 ] ,
G = 1 1 r s 2 v 2 1 1 r g ( τ + ρ ) w 2 2 α w I s p ,
H = 1 1 r s 2 v 2 [ t 0 I 0 + 2 α w I s p ] ,
2 k 0   Re ( n s p ) d + arg ( r g ) + arg ( τ + ρ ) = 2 n π ,
k 0   Re ( n s p ) d + arg ( α / t 0 ) + arg ( I s p ) = 2 m π ,
k 0   Re ( n s p ) d + arg ( I s p ) = 2 m π .

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