Abstract

Transmission through an opaque Au film with a single subwavelength aperture centered in a smooth cavity between linear grating structures is studied experimentally and with a finite element model. The model is in good agreement with measured results and is used to investigate local field behavior. It shows that a surface plasmon polariton (SPP) is launched along the metal surface, while interference of the SPP with the incident light along with resonant cavity effects give rise to suppression and enhancement in transmission. Based on experimental and modeling results, peak location and structure of the enhancement/suppression bands are explained analytically, confirming the primary role of SPPs in enhanced transmission through small apertures in opaque metal films.

© 2007 Optical Society of America

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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, 667 (1998).
    [CrossRef]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  3. T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, "Control of optical transmission through metals perforated with subwavelength hole arrays," Opt. Lett. 24, 256 (1999).
    [CrossRef]
  4. U. Schröter and D. Heitmann, "Surface-plasmon-enhanced transmission through metallic gratings," Phys. Rev. B 58, 15419 (1998).
    [CrossRef]
  5. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972 (2001).
    [CrossRef]
  6. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901 (2003).
    [CrossRef]
  7. H. F. Ghaemi, T. Thio, D. D. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmon enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779 (1998).
    [CrossRef]
  8. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  9. 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 (1999).
    [CrossRef]
  10. Ph. 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, Pure Appl. Opt. 2, 48 (2000).
    [CrossRef]
  11. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16,100 (2000).
    [CrossRef]
  12. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629 (2004).
    [CrossRef] [PubMed]
  13. G. Gay, O. Alloschery, B. V. de Lesegno, J. Weiner, and H. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by Far-Field Interferometry," Phys. Rev. Lett. 96, 213901/1-4 (2006).
    [CrossRef]
  14. F. Garcia, L. Martin-Moreno, H. Lezec, and T. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500 (2003).
    [CrossRef]
  15. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
    [CrossRef]
  16. P. Flammer, I. Schick, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Theoretical study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63231Z (2006).
  17. I. Schick, P. Flammer, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Experimental study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63230L (2006).
  18. P. Lalanne and J. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
    [CrossRef]
  19. O. Janssen, H. Urbach, and G. ’t Hooft, "On the phase of plasmons excited by slits in a metal film," Opt. Express 14, 11823 (2006).
    [CrossRef]

2006 (4)

P. Flammer, I. Schick, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Theoretical study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63231Z (2006).

I. Schick, P. Flammer, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Experimental study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63230L (2006).

P. Lalanne and J. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[CrossRef]

O. Janssen, H. Urbach, and G. ’t Hooft, "On the phase of plasmons excited by slits in a metal film," Opt. Express 14, 11823 (2006).
[CrossRef]

2004 (1)

2003 (3)

F. Garcia, L. Martin-Moreno, H. Lezec, and T. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef]

2001 (1)

2000 (2)

Ph. 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, Pure Appl. Opt. 2, 48 (2000).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16,100 (2000).
[CrossRef]

1999 (2)

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 (1999).
[CrossRef]

T. J. Kim, T. Thio, T. W. Ebbesen, D. E. Grupp, and H. J. Lezec, "Control of optical transmission through metals perforated with subwavelength hole arrays," Opt. Lett. 24, 256 (1999).
[CrossRef]

1998 (3)

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 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. D. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmon enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779 (1998).
[CrossRef]

U. Schröter and D. Heitmann, "Surface-plasmon-enhanced transmission through metallic gratings," Phys. Rev. B 58, 15419 (1998).
[CrossRef]

1994 (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

F. Garcia, L. Martin-Moreno, H. Lezec, and T. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. A, (1)

Ph. 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, Pure Appl. Opt. 2, 48 (2000).
[CrossRef]

Nat. Phys. (1)

P. Lalanne and J. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[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, 667 (1998).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (3)

U. Schröter and D. Heitmann, "Surface-plasmon-enhanced transmission through metallic gratings," Phys. Rev. B 58, 15419 (1998).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16,100 (2000).
[CrossRef]

H. F. Ghaemi, T. Thio, D. D. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmon enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef]

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 (1999).
[CrossRef]

SPIE (2)

P. Flammer, I. Schick, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Theoretical study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63231Z (2006).

I. Schick, P. Flammer, J. Yarbrough, C. Allen, G. Nuebel, E. Schick, J. Dahda, J. Martineau, M. Hurowitz, R. Hollingsworth, and R. Collins, "Experimental study of enhanced transmission through subwavelength linear apertures flanked by periodic corrugations," Proc. SPIE  6323, 63230L (2006).

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

G. Gay, O. Alloschery, B. V. de Lesegno, J. Weiner, and H. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by Far-Field Interferometry," Phys. Rev. Lett. 96, 213901/1-4 (2006).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic cross-section of structure geometry. Cavity width, wC , was varied from 800 – 2000 nm; tAu = 200 nm; tSiN = 200 nm; depth of grooves cut into SiN was 75 nm; P = 400 or 450 nm; and aperture width was 150 nm at substrate and 450 nm at air side. Light is normally incident on the glass side of the film. (b) Experimental absolute transmission spectra (top) and FEM transmission spectra (bottom), for varying cavity widths. All curves are for P = 400 nm. Note the red shift as wC is increased.

Fig. 2.
Fig. 2.

Peak location as a function of cavity width, wC . Gray scale background is a linearly-scaled density plot of transmission generated by the FEM; white represents highest transmission and black represents lowest transmission. Experimental peak positions are shown for P = 400 nm and P = 450 nm as triangles and boxes, respectively. Analytically predicted maxima (white lines) and minima (grey lines) taken from a modification of the interference theory by Lezec and Thio [12] and a resonant cavity theory are displayed as dashed and solid lines, respectively.

Fig. 3.
Fig. 3.

(a) Modeled geometry consisting of an Au film on glass with a single set of five 50 nm tall grooves cut into the glass forming raised ridges in the Au with 400 nm period at the glass/Au interface and a 100 nm wide aperture in the Au located 1.1 μm from the edge of the grooves. A TM-polarized plane wave is normally incident on the Au from above (through the glass). The power flow within the dashed box is shown in (b) and (c) for free space wavelengths of 660 nm and 730 nm, respectively. Gray-scale is the magnitude of time-average power flow and streamlines show the direction of the power flow.

Fig. 4.
Fig. 4.

Comparison of the dispersion relation (top) and propagation length (bottom) for surface waves observed in the FEM (shown as boxes) and the analytical expressions for SPPs [8] (shown as lines).

Fig. 5.
Fig. 5.

Calculated integrated energy density inside the cavity of the structure in Fig. 1(a) with a cavity width of 1450 nm are shown as a function of wavelength. The solid curve is without an aperture present. The dashed curve is with the aperture present. The vertical dotted lines are predicted cavity resonant wavelengths using Eq. 4 for m = 3, 4, and 5.

Equations (4)

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λ max = a 0 m n SP ; n SP = Re ( ( ε m ε d ε m + ε d ) 1 2 ) ,
A exp ( bx ) exp [ i ( k SW x + ϕ ) ] ,
λ 0 = w C + 200 nm 2 m ϕ π n SP .
λ 0 = w C m n SP ,

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