Abstract

We report on experimental observations of highly collimated beams of radiation generated when a periodic sub-wavelength grating interacts with surface bound plasmon-polariton modes of a thin gold film. We find that the radiation process can be fully described in terms of interference of emission from a dipole antenna array and modeling the structure in this way enables the far-field radiation pattern to be predicted. The directionality, multiplicity and divergence of the beams can be completely described within this framework. Essential to the process are the surface plasmon excitations: these are the driving mechanism behind the beam formation, phase-coupling radiation from the periodic surface structure and thus imposing a spatial coherence. Detailed fitting of the experimental and modeled data indicates the presence of scattering events involving the interaction of two surface plasmon polariton modes.

© 2007 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. 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 sub-wavelength aperture," Science 297, 820-822 (2002).
    [CrossRef] [PubMed]
  3. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
    [CrossRef]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  5. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
    [CrossRef]
  6. J. R. Lakowicz, "Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission," Anal. Biochem. 337, 171 (2005).
    [CrossRef] [PubMed]
  7. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
    [CrossRef] [PubMed]
  8. L. Martin-Moreno, F. L. Garcia-Vidal, H. J. Lezec, A. Degiron and T. W. Ebbesen, "Theory of higly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
    [CrossRef]
  9. D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh and C. K. Lee, "Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings," Opt. Express 14, 3503-3511 (2006).
    [CrossRef] [PubMed]
  10. A. A. Oliner and A. Hessel, "Guided waves on sinusoidally-modulated reactance surfaces," IRE Trans. Antennas Propag.AP- 7, S202-S208 (1959).
  11. A. A. Oliner and D. R. Jackson, "Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 1: basic features," IEEE Antennas and Propagation Society International Symposium, 2, 1091-1094 (2003).
  12. D. R. Jackson, T. Zhao, J. T. Williams and A. A. Oliner, "Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 2: Leaky-wave antenna model," IEEE Antennas and Propagation Society International Symposium 2, 1095-1098 (2003).
  13. E. Krestshmann, "Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185-187 (1972).
    [CrossRef]
  14. J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
    [CrossRef]
  15. L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. T. Yeh, J. M. Liu, C. S. Yeh and C. K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405-1-041405-4 (2005).
    [CrossRef]
  16. K. G. Sullivan, O. King, C. Sigg and D. G. Hall, "Directional enhanced fluorescence from molecules near a periodic surface," Appl. Opt. 33, 2447-2454 (1994).
    [CrossRef] [PubMed]
  17. H. Raether, Springer Tracts in Modern Physics, Vol. 111: Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Spinger-Verlag Berlin Heidelberg, 1988).
  18. J. D. Kraus and D. A. Fleisch, Electromagnetics with Applications (McGraw-Hill, 1999).
  19. E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
    [CrossRef] [PubMed]
  20. E. Hecht, Optics (Addison-Wesley, 2002).
  21. M. Born and E. WolfPrinciples of optics: electromagnetic theory of propagation, interference and diffraction of light (Pergamon Press, 1965).

2006

2005

J. R. Lakowicz, "Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission," Anal. Biochem. 337, 171 (2005).
[CrossRef] [PubMed]

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

2004

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

1998

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]

1994

1982

J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

1972

E. Krestshmann, "Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185-187 (1972).
[CrossRef]

1959

A. A. Oliner and A. Hessel, "Guided waves on sinusoidally-modulated reactance surfaces," IRE Trans. Antennas Propag.AP- 7, S202-S208 (1959).

1944

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

Adams, A.

J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bethe, H. A.

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

Chang, C. K.

Chang, S. H.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Chen, Y. C.

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

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]

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[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, 667-669 (1998).
[CrossRef]

Gray, S. K.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Hall, D. G.

Hansma, P. K.

J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

Henzie, J.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Hessel, A.

A. A. Oliner and A. Hessel, "Guided waves on sinusoidally-modulated reactance surfaces," IRE Trans. Antennas Propag.AP- 7, S202-S208 (1959).

King, O.

Krestshmann, E.

E. Krestshmann, "Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185-187 (1972).
[CrossRef]

Kuan, C. H.

Kwak, E. S.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Lakowicz, J. R.

J. R. Lakowicz, "Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission," Anal. Biochem. 337, 171 (2005).
[CrossRef] [PubMed]

Lee, C. K.

Lewen, G. D.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

Lezec, H. J.

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[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, 667-669 (1998).
[CrossRef]

Lin, D. Z.

Lin, M. W.

Linke, R. A.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Liu, J. M.

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Moreland, J.

J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

Nahata, A.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

Odom, T. W.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Oliner, A. A.

A. A. Oliner and A. Hessel, "Guided waves on sinusoidally-modulated reactance surfaces," IRE Trans. Antennas Propag.AP- 7, S202-S208 (1959).

Pellerin, K. M.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

Shatz, G. C.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Sigg, C.

Sullivan, K. G.

Thio, T.

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

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]

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, 667-669 (1998).
[CrossRef]

Yang, D. L.

Yeh, C. S.

Yeh, J. T.

Anal. Biochem.

J. R. Lakowicz, "Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission," Anal. Biochem. 337, 171 (2005).
[CrossRef] [PubMed]

AP

A. A. Oliner and A. Hessel, "Guided waves on sinusoidally-modulated reactance surfaces," IRE Trans. Antennas Propag.AP- 7, S202-S208 (1959).

Appl. Opt.

Nano. Lett.

E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, "Surface plasmon standing waves in large-area subwavelength hole arrays," Nano. Lett. 5, 1963-1967 (2005).
[CrossRef] [PubMed]

Nanotechnology

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology,  13, 429-432 (2002).
[CrossRef]

Nature

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]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Commun.

E. Krestshmann, "Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results," Opt. Commun. 6, 185-187 (1972).
[CrossRef]

Opt. Express

Phys. Rev.

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

Phys. Rev. B

J. Moreland, A. Adams and P. K. Hansma, "Efficiency of light emission from surface plasmons," Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

Science

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 sub-wavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Other

L. Martin-Moreno, F. L. Garcia-Vidal, H. J. Lezec, A. Degiron and T. W. Ebbesen, "Theory of higly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. T. Yeh, J. M. Liu, C. S. Yeh and C. K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405-1-041405-4 (2005).
[CrossRef]

A. A. Oliner and D. R. Jackson, "Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 1: basic features," IEEE Antennas and Propagation Society International Symposium, 2, 1091-1094 (2003).

D. R. Jackson, T. Zhao, J. T. Williams and A. A. Oliner, "Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 2: Leaky-wave antenna model," IEEE Antennas and Propagation Society International Symposium 2, 1095-1098 (2003).

E. Hecht, Optics (Addison-Wesley, 2002).

M. Born and E. WolfPrinciples of optics: electromagnetic theory of propagation, interference and diffraction of light (Pergamon Press, 1965).

H. Raether, Springer Tracts in Modern Physics, Vol. 111: Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Spinger-Verlag Berlin Heidelberg, 1988).

J. D. Kraus and D. A. Fleisch, Electromagnetics with Applications (McGraw-Hill, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

(a) A bright wide-field image captured with a x5 objective lens of four 100×100 μm gratings. (b) A schematic diagram of SP excitation and beam formation. (c) The gratings structures under laser excitation.

Fig. 2.
Fig. 2.

Re-constructed images of the beams generated by (a) a 450 nm pitch grating, (b) a 550 nm pitch grating, (c) a 750 nm pitch grating and (d) a 900 nm pitch grating. In (a) and (b) it is also possible to make out beams from adjacent gratings in the periphery of the images.

Fig. 3.
Fig. 3.

A re-constructed image, plotted on a grey-scale of gratings with 10 and 50 lines located at 400 and 600 μm on the linescan distance axis. The solid white lines form a guide for the eye.

Fig. 4.
Fig. 4.

Polar plots of the normalized electric field of 550 (blue line), 650 (red line) and 750 nm (black line) pitch antenna arrays where the number of elements n is (a) 10 and (b) 50.

Fig 5.
Fig 5.

Far-field emission angle plotted as a function of grating pitch. The data points represent the experimental data while the solid lines show the fits generated by the antenna array model.

Fig 6.
Fig 6.

The far-field phase (blue line) and beam amplitude (red line) plotted as a function of angle. A maximum of the E-field occurs whenever ψ is a multiple of 2π.

Equations (5)

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

E = ( 1 n ) sin ( 2 ) sin ( ψ 2 )
ψ = 2 π Λ λ cos θ + δ
δ = 2 π Λ λ sp
m k g = k 0 cos θ + k sp
m k g = k 0 cos θ + 2 k sp

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