Abstract

Numerical analysis of diffraction by a single aperture surrounded by a circular shallow channel in a metallic screen shows the possibility of a 50-fold increase of the electric field intensity inside the central aperture, when compared to the incident field. Detailed analysis of cavity modes and their coupling through surface plasmon wave determine the parameters leading to maximum field enhancement. This effect can be used in high-efficiency single-molecule fluorescence analysis in attoliter volumes.

© 2008 Optical Society of America

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References

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  1. E. A. Ash and G. Nicholls, "Super-resolution aperture scanning microscope," Nature 237, 510-511 (1972).
    [CrossRef] [PubMed]
  2. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 Å spatial resolution light microscope I. Light is efficiently transmitted through λ/16 diameter apertures," Ultramicroscopy 13, 227-232 (1984).
    [CrossRef]
  3. E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, "Near-field scanning optical microscopy (NSOM), development and biophysical applications," J. Biophys. 49, 269-279 (1986).
    [CrossRef]
  4. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
    [CrossRef]
  5. J. D. Jackson, Classical Electrodynamics, 3rd ed., (John Wiley, New York, 1998).
  6. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  7. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
    [CrossRef]
  8. S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure and Applied Optics 4, S83-S87 (2002)
    [CrossRef]
  9. M. J. Levene, J. Kotach, S. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguide for single-molecule analysis at high concentrations," Science 209, 682-686 (2003).
    [CrossRef]
  10. H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. Ebbesen, and P. F. Lenne, "Detection enhancement of single molecules at high concentrations in subwavelength apertures," Phys. Rev. Lett. 95, 117401 (2005).
    [CrossRef] [PubMed]
  11. E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. Chaumet, N. Bonod, J. Dintinger, and T. Ebbesen, "Field enhancement in single subwavelength apertures," J. Opt. Soc. Am. A 23, 2342-2348 (2006).
    [CrossRef]
  12. E. Popov, M. Nevière, A.-L. Fehrembach, and N. Bonod, "Optimization of plasmon excitation at structured apertures," Appl. Opt. 44, 6141-6154 (2005).
    [CrossRef] [PubMed]
  13. N. Bonod, E. Popov, and M. Neviere, "Differential theory of diffraction by finite cylindrical objects," J. Opt. Soc. Am. A 22, 481-490 (2005).
    [CrossRef]
  14. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97-S101 (2005).
    [CrossRef]
  15. E. Popov, N. Bonod, and S. Enoch, "Comparison of plasmon surface wave on shallow and deep 1D and 2D gratings," Opt. Express 15, 4224-4237 (2007).
    [CrossRef] [PubMed]
  16. M. Nevière, The Homogeneous Problem in Electromagnetic Theory of Gratings, R. Petit, ed., (Springer, 1980) Chap. 5.
  17. F. I. Baida, "Enhanced transmission through subwavelength metallic coaxial apertures by excitation of the TEM mode," Appl. Phys. B 89,145-149 (2007).
    [CrossRef]
  18. A. Snyder and J. Love, Optical Waveguide Theory (Kluwert Academic, Boston, 1983).
  19. F. Baida, A. Belkhir, and D. Van Labeke, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
    [CrossRef]

2007 (2)

E. Popov, N. Bonod, and S. Enoch, "Comparison of plasmon surface wave on shallow and deep 1D and 2D gratings," Opt. Express 15, 4224-4237 (2007).
[CrossRef] [PubMed]

F. I. Baida, "Enhanced transmission through subwavelength metallic coaxial apertures by excitation of the TEM mode," Appl. Phys. B 89,145-149 (2007).
[CrossRef]

2006 (2)

F. Baida, A. Belkhir, and D. Van Labeke, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

E. Popov, M. Nevière, J. Wenger, P.-F. Lenne, H. Rigneault, P. Chaumet, N. Bonod, J. Dintinger, and T. Ebbesen, "Field enhancement in single subwavelength apertures," J. Opt. Soc. Am. A 23, 2342-2348 (2006).
[CrossRef]

2005 (4)

E. Popov, M. Nevière, A.-L. Fehrembach, and N. Bonod, "Optimization of plasmon excitation at structured apertures," Appl. Opt. 44, 6141-6154 (2005).
[CrossRef] [PubMed]

N. Bonod, E. Popov, and M. Neviere, "Differential theory of diffraction by finite cylindrical objects," J. Opt. Soc. Am. A 22, 481-490 (2005).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. Ebbesen, and P. F. Lenne, "Detection enhancement of single molecules at high concentrations in subwavelength apertures," Phys. Rev. Lett. 95, 117401 (2005).
[CrossRef] [PubMed]

2003 (1)

M. J. Levene, J. Kotach, S. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguide for single-molecule analysis at high concentrations," Science 209, 682-686 (2003).
[CrossRef]

2002 (1)

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure and Applied Optics 4, S83-S87 (2002)
[CrossRef]

2000 (1)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

1986 (1)

E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, "Near-field scanning optical microscopy (NSOM), development and biophysical applications," J. Biophys. 49, 269-279 (1986).
[CrossRef]

1984 (1)

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 Å spatial resolution light microscope I. Light is efficiently transmitted through λ/16 diameter apertures," Ultramicroscopy 13, 227-232 (1984).
[CrossRef]

1972 (1)

E. A. Ash and G. Nicholls, "Super-resolution aperture scanning microscope," Nature 237, 510-511 (1972).
[CrossRef] [PubMed]

1944 (1)

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

F. I. Baida, "Enhanced transmission through subwavelength metallic coaxial apertures by excitation of the TEM mode," Appl. Phys. B 89,145-149 (2007).
[CrossRef]

J. Biophys. (1)

E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, "Near-field scanning optical microscopy (NSOM), development and biophysical applications," J. Biophys. 49, 269-279 (1986).
[CrossRef]

J. Opt. A: Pure and Applied Optics (1)

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure and Applied Optics 4, S83-S87 (2002)
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97-S101 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

E. A. Ash and G. Nicholls, "Super-resolution aperture scanning microscope," Nature 237, 510-511 (1972).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. (1)

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. B (2)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

F. Baida, A. Belkhir, and D. Van Labeke, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. Ebbesen, and P. F. Lenne, "Detection enhancement of single molecules at high concentrations in subwavelength apertures," Phys. Rev. Lett. 95, 117401 (2005).
[CrossRef] [PubMed]

Science (1)

M. J. Levene, J. Kotach, S. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguide for single-molecule analysis at high concentrations," Science 209, 682-686 (2003).
[CrossRef]

Ultramicroscopy (1)

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 Å spatial resolution light microscope I. Light is efficiently transmitted through λ/16 diameter apertures," Ultramicroscopy 13, 227-232 (1984).
[CrossRef]

Other (3)

J. D. Jackson, Classical Electrodynamics, 3rd ed., (John Wiley, New York, 1998).

M. Nevière, The Homogeneous Problem in Electromagnetic Theory of Gratings, R. Petit, ed., (Springer, 1980) Chap. 5.

A. Snyder and J. Love, Optical Waveguide Theory (Kluwert Academic, Boston, 1983).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic representation of a screen with a circular aperture and a circular channel around it, made in an aluminum screen with thickness t=200 nm. The cladding is glass and the substrate is water. The channel width is R3-R2, its depth h, and it is filled with glass.

Fig. 2.
Fig. 2.

Field enhancement averaged in the entrance plane of the aperture as a function of the channel depth h for R1=75 nm, R2=200 nm, R3=280 nm.

Fig. 3.
Fig. 3.

Enhancement factor as a function of the radius R2 of the inner channel wall for three different channel widths taken for R1=75 nm and h=40 nm.

Fig. 4.
Fig. 4.

Enhancement factor IS (on the left) and the real and imaginary parts of the normalized mode propagation constants γ inside the coaxial channel (on the right) as a function of R3. R1=75 nm, R2=200 nm, ncl=1.5 and h=40 nm.

Fig. 5.
Fig. 5.

Comparison of the position in R2 of the maximum of the enhancement factor IS with the minimum of the surface plasmon electric field components tangential to the channel wall

Fig. 6.
Fig. 6.

Same as in Fig. 5 but for a higher cladding index ncl=2

Fig. 7.
Fig. 7.

Absolute value of the electric field amplitude of the plasmon surface wave (in blue) as a function of R3 when R2=200 nm and ncl=1.5, compared with the coupling between the incident light and the plasmon, as given in Eq. (9)

Fig. 8.
Fig. 8.

Response (as in Figs. 4 and 7) as a function of R3 of the structure with cladding index ncl=2 and R2=160 nm. (a) IS and γ, (b) incident wave - surface plasmon coupling integral according to Eq. (9).

Tables (2)

Tables Icon

Table 1. Radial and azimuthal dependence of the electric field for H- and E-mode, and incident wave. The coefficients aE and aH are constants.

Tables Icon

Table 2. The cut-off width R3-R2 (in nm) for the modes H12 and E11 of a coaxial waveguide with infinitely conducting walls at λ=488 nm and n=1.5, given for different values of R2.

Equations (11)

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

I S = 1 π R 2 S E 2 dS
exp ( i k z z ) exp ( i k 0 γ z )
k ρ 2 + k z 2 = k 2 = k 0 2 n 2
E ρ = J 1 ( k ρ , pl ρ ) cos φ 1 2 [ J 0 ( k ρ , pl ρ ) J 2 ( k ρ , pl ρ ) ] cos φ
E φ = J 1 ( k ρ , pl ρ ) k ρ , pl ρ sin φ 1 2 [ j 0 ( k ρ , pl ρ ) + J 2 ( k ρ , pl ρ ) ] sin φ
E z = J 1 ( k ρ , pl ρ ) i k z , pl ρ cos φ k ρ , pl 2 i k z , pl [ J 0 ( k ρ , pl ρ ) + J 2 ( k ρ , pl ρ ) ] cos φ
J 1 ( k ρ R 2 ) + a H Y 1 ( k ρ R 2 ) = 0 J 1 ( k ρ R 3 ) + a H Y 1 ( k ρ R 3 ) = 0 , H mode
J 1 ( k ρ R 2 ) + a E Y 1 ( k ρ R 2 ) = 0 J 1 ( k ρ R 3 ) + a E Y 1 ( k ρ R 3 ) = 0 , E   mode
abs [ J 0 ( k ρ , pl R 2 ) + J 2 ( k ρ , pl R 2 ) ]
1 2 π 0 2 π ρ d φ E pl . E ¯ inc = R 2 J 0 ( k ρ , pl R 2 )
1 2 π 0 2 π ρ d φ E pl · E ¯ inc R 2 , R 3 = R 2 J 0 ( k ρ , pl R 2 ) R 3 J 0 ( k ρ , pl R 3 )

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