Abstract

We report on the polarization-dependent optical response of elongated nanoholes in optically thin gold films. We measured elastic scattering spectra of spatially isolated ellipsoidal nanoholes with varying aspect ratio and compared the results to electrodynamic simulations. Both experiments and theory show that the plasmon mode that is polarized parallel to the short axis of the ellipsoidal hole red-shifts with increasing aspect ratio. This behavior is completely opposite to the case of elongated metal particles. We present a simple analytical model that qualitatively explains the observations in terms of the different orientations of the induced dipole moments in holes and particles.

© 2008 Optical Society of America

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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. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong polarization in the optical transmission through elliptical nanohole arrays," Phys. Rev. Lett. 92, 037401 (2004).
    [CrossRef] [PubMed]
  3. K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes," Phys. Rev. Lett. 92, 183901 (2004).
    [CrossRef] [PubMed]
  4. Z. C. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
    [CrossRef] [PubMed]
  5. M. W. Tsai, T. H. Chuang, H. Y. Chang, and S. C. Lee, "Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice," Appl. Phys. Lett. 89, 093102 (2006).
    [CrossRef]
  6. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Optics Commun. 239, 61-66 (2004).
    [CrossRef]
  7. A. Degiron and T. W. Ebbesen, "Analysis of the transmission process through single apertures surrounded by periodic corrugations," Opt. Express 12, 3694-3700 (2004).
    [CrossRef] [PubMed]
  8. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004).
    [CrossRef] [PubMed]
  9. F. J. G. de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  10. Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, "Optical antennas based on coupled nanoholes in thin metal films," Nature Phys. 3, 884-889 (2007).
    [CrossRef]
  11. T. Rindzevicius, Y. Alaverdyan, B. Sepúlveda, T. Pakizeh, M. Kall, R. Hillenbrand, J. Aizpurua, and F. J. Garcia de Abajo, "Nanohole plasmons in optically thin gold films," J. Phys. Chem. C 111, 1207 (2007).
    [CrossRef]
  12. J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Kall, "Optical spectroscopy of nanometric holes in thin gold films," Nano Lett. 4, 1003-1007 (2004).
    [CrossRef]
  13. T. H. Park, N. Mirin, J. B. Lassiter, C. L. Nehl, N. J. Halas, and P. Nordlander, "Optical properties of a nanosized hole in a thin metallic film," Acs Nano 2, 25-32 (2008).
    [CrossRef]
  14. L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Kall, S. L. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: Experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
    [CrossRef]
  15. P. Hanarp, M. Kall, and D. S. Sutherland, "Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography," J. Phys. Chem. B 107, 5768-5772 (2003).
    [CrossRef]
  16. O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
    [CrossRef]
  17. M. Paulus, P. Cay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
    [CrossRef]
  18. M. Paulus and O. J. F. Martin, "Light propagation and scattering in stratified media: a Green's tensor approach," J. Opt. Soc. Am. A 18, 854-861 (2001).
    [CrossRef]
  19. J. Alegret, M. Kall, and P. Johansson, "Top-down extended meshing algorithm and its applications to Green's tensor nano-optics calculations," Phys. Rev. E 75, 046702 (2007).
    [CrossRef]
  20. G. Arfken and H. Weber, Mathematical Methods for Physicists, 5th ed. (Academic Press, 2000).
  21. P. B. Johnson and R. W. Christy, "Optical-Constants of Noble-Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  22. C. F. Bohren and D. R. Huffman, Absorption and Scattering by small Particles, Wiley Science Paperback Series (Wiley -Interscience, New York, 1983).
  23. D. Stroud, "Generalized Effective-Medium Approach to Conductivity of an Inhomogeneous Material," Phys. Rev. B 12, 3368-3373 (1975).
    [CrossRef]
  24. B. Sepulveda, Y. Huttel, C. M. Boubeta, A. Cebollada, and G. Armelles, "Linear and quadratic magneto-optical Kerr effects in continuous and granular ultrathin monocrystalline Fe films," Phys. Rev. B 68 (2003).
    [CrossRef]
  25. A. Dahlin, M. Zach, T. Rindzevicius, M. Kall, D. S. Sutherland, and F. Hook, "Localized surface plasmon resonance sensing of lipid-membrane-mediated biorecognition events," J. Am. Chem. Soc. 127, 5043-5048 (2005).
    [CrossRef] [PubMed]
  26. T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, "Plasmonic sensing characteristics of single nanometric holes," Nano Lett. 5, 2335-2339 (2005).
    [CrossRef] [PubMed]

2008 (1)

T. H. Park, N. Mirin, J. B. Lassiter, C. L. Nehl, N. J. Halas, and P. Nordlander, "Optical properties of a nanosized hole in a thin metallic film," Acs Nano 2, 25-32 (2008).
[CrossRef]

2007 (4)

F. J. G. de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, "Optical antennas based on coupled nanoholes in thin metal films," Nature Phys. 3, 884-889 (2007).
[CrossRef]

T. Rindzevicius, Y. Alaverdyan, B. Sepúlveda, T. Pakizeh, M. Kall, R. Hillenbrand, J. Aizpurua, and F. J. Garcia de Abajo, "Nanohole plasmons in optically thin gold films," J. Phys. Chem. C 111, 1207 (2007).
[CrossRef]

J. Alegret, M. Kall, and P. Johansson, "Top-down extended meshing algorithm and its applications to Green's tensor nano-optics calculations," Phys. Rev. E 75, 046702 (2007).
[CrossRef]

2006 (2)

Z. C. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

M. W. Tsai, T. H. Chuang, H. Y. Chang, and S. C. Lee, "Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice," Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

2005 (3)

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Kall, S. L. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: Experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

A. Dahlin, M. Zach, T. Rindzevicius, M. Kall, D. S. Sutherland, and F. Hook, "Localized surface plasmon resonance sensing of lipid-membrane-mediated biorecognition events," J. Am. Chem. Soc. 127, 5043-5048 (2005).
[CrossRef] [PubMed]

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, "Plasmonic sensing characteristics of single nanometric holes," Nano Lett. 5, 2335-2339 (2005).
[CrossRef] [PubMed]

2004 (6)

A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004).
[CrossRef] [PubMed]

A. Degiron and T. W. Ebbesen, "Analysis of the transmission process through single apertures surrounded by periodic corrugations," Opt. Express 12, 3694-3700 (2004).
[CrossRef] [PubMed]

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Kall, "Optical spectroscopy of nanometric holes in thin gold films," Nano Lett. 4, 1003-1007 (2004).
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Optics Commun. 239, 61-66 (2004).
[CrossRef]

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong polarization in the optical transmission through elliptical nanohole arrays," Phys. Rev. Lett. 92, 037401 (2004).
[CrossRef] [PubMed]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes," Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

2003 (2)

P. Hanarp, M. Kall, and D. S. Sutherland, "Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography," J. Phys. Chem. B 107, 5768-5772 (2003).
[CrossRef]

B. Sepulveda, Y. Huttel, C. M. Boubeta, A. Cebollada, and G. Armelles, "Linear and quadratic magneto-optical Kerr effects in continuous and granular ultrathin monocrystalline Fe films," Phys. Rev. B 68 (2003).
[CrossRef]

2001 (1)

2000 (1)

M. Paulus, P. Cay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

1998 (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, 667-669 (1998).
[CrossRef]

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

1975 (1)

D. Stroud, "Generalized Effective-Medium Approach to Conductivity of an Inhomogeneous Material," Phys. Rev. B 12, 3368-3373 (1975).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical-Constants of Noble-Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Acs Nano (1)

T. H. Park, N. Mirin, J. B. Lassiter, C. L. Nehl, N. J. Halas, and P. Nordlander, "Optical properties of a nanosized hole in a thin metallic film," Acs Nano 2, 25-32 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

M. W. Tsai, T. H. Chuang, H. Y. Chang, and S. C. Lee, "Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice," Appl. Phys. Lett. 89, 093102 (2006).
[CrossRef]

J. Am. Chem. Soc. (1)

A. Dahlin, M. Zach, T. Rindzevicius, M. Kall, D. S. Sutherland, and F. Hook, "Localized surface plasmon resonance sensing of lipid-membrane-mediated biorecognition events," J. Am. Chem. Soc. 127, 5043-5048 (2005).
[CrossRef] [PubMed]

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

J. Phys. Chem. B (2)

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Kall, S. L. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: Experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

P. Hanarp, M. Kall, and D. S. Sutherland, "Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography," J. Phys. Chem. B 107, 5768-5772 (2003).
[CrossRef]

J. Phys. Chem. C (1)

T. Rindzevicius, Y. Alaverdyan, B. Sepúlveda, T. Pakizeh, M. Kall, R. Hillenbrand, J. Aizpurua, and F. J. Garcia de Abajo, "Nanohole plasmons in optically thin gold films," J. Phys. Chem. C 111, 1207 (2007).
[CrossRef]

Nano Lett. (2)

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Kall, "Optical spectroscopy of nanometric holes in thin gold films," Nano Lett. 4, 1003-1007 (2004).
[CrossRef]

T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sutherland, and M. Kall, "Plasmonic sensing characteristics of single nanometric holes," Nano Lett. 5, 2335-2339 (2005).
[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]

Nature Phys. (1)

Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, "Optical antennas based on coupled nanoholes in thin metal films," Nature Phys. 3, 884-889 (2007).
[CrossRef]

Opt. Express (2)

Optics Commun. (1)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Optics Commun. 239, 61-66 (2004).
[CrossRef]

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, "Optical-Constants of Noble-Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

D. Stroud, "Generalized Effective-Medium Approach to Conductivity of an Inhomogeneous Material," Phys. Rev. B 12, 3368-3373 (1975).
[CrossRef]

B. Sepulveda, Y. Huttel, C. M. Boubeta, A. Cebollada, and G. Armelles, "Linear and quadratic magneto-optical Kerr effects in continuous and granular ultrathin monocrystalline Fe films," Phys. Rev. B 68 (2003).
[CrossRef]

Phys. Rev. E (3)

J. Alegret, M. Kall, and P. Johansson, "Top-down extended meshing algorithm and its applications to Green's tensor nano-optics calculations," Phys. Rev. E 75, 046702 (2007).
[CrossRef]

O. J. F. Martin and N. B. Piller, "Electromagnetic scattering in polarizable backgrounds," Phys. Rev. E 58, 3909-3915 (1998).
[CrossRef]

M. Paulus, P. Cay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong polarization in the optical transmission through elliptical nanohole arrays," Phys. Rev. Lett. 92, 037401 (2004).
[CrossRef] [PubMed]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes," Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Z. C. Ruan and M. Qiu, "Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances," Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

F. J. G. de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Other (2)

G. Arfken and H. Weber, Mathematical Methods for Physicists, 5th ed. (Academic Press, 2000).

C. F. Bohren and D. R. Huffman, Absorption and Scattering by small Particles, Wiley Science Paperback Series (Wiley -Interscience, New York, 1983).

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Figures (4)

Fig. 1.
Fig. 1.

(a) SEM image of an elongated hole with a=80 nm and b=160 nm. Experimental scattering spectra of the nanoholes in 20 nm gold films as a function of the length of the long axis b for the case of the polarization parallel (b) or perpendicular (c) to the short axis a. All spectra are normalized by the peak scattering intensity of the circular hole with a=b=80.

Fig. 2.
Fig. 2.

Calculated forward scattering cross section spectra for elongated nanoholes in a 20 nm gold film as a function of the length of the long axis b for the case of incident polarization parallel (a) and perpendicular (b) to the short axis a for various aspect ratios but constant a=80 nm. (c) Scattering spectra for a nanohole with a=60 nm and b=90 nm for different polarizations.

Fig. 3.
Fig. 3.

(a) Real part of the dielectric constant of gold in the visible and near-infrared regions. (b) Schematics of the localized dipolar surface-plasmon excitation in a gold disk (left) or hole in a thin gold film (right).

Fig. 4.
Fig. 4.

Schematics of the induced charges and fields for different polarizations of the incoming light, assuming a frequency below resonance, for (a–b) elongated nanoholes and (c–d) nanoparticles.

Equations (11)

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

× × E ( r ) k 0 2 ε B ( r ) E ( r ) = k 0 2 Δ ε ( r ) E ( r )
E ( r ) = E 0 ( r ) + V d r G ( r , r ) k 0 2 Δ ε ( r ) E ( r )
× × G ( r , r ) k 0 2 ε B ( r ) G ( r , r ) = δ ( r r ) ,
G ( r , r ) = e i kR 4 π R g ( θ , ϕ , r )
E scatt = e i kR 4 π R d r k 0 2 g ( θ , ϕ , r ) k 0 2 Δ ε ( r ) E ( r ) = e i kR 4 π R E scatt ( θ , ϕ )
S i = 1 2 c n i ε 0 E i 2
d σ d Ω ( θ , ϕ ) = S 3 S 1 R 2 = 1 4 π n 3 E scatt ( θ , ϕ ) 2 E 0 2
α i ε int ε ext ( 1 L i ) ε ext + L i ε int
L i = abc 2 0 dq ( s i 2 + q ) ( q + a 2 ) ( q + b 2 ) ( q + c 2 )
Re [ ε int ] = Re [ ε m ] = ε d 1 L i L i
Re [ ε ext ] = Re [ ε m ] = ε d L i 1 L i

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