Abstract

The plasmon analog of the self-imaging Talbot effect is described and theoretically analyzed. Rich plasmon carpets containing hot spots are shown to be produced by a row of periodically-spaced surface features. A row of holes drilled in a metal film and illuminated from the back side is discussed as a realizable implementation of this concept. Self-images of the row are produced, separated from the original one by distances up to several hundreds of wavelengths in the examples under consideration. The size of the image focal spots is close to half a wavelength and the spot positions can be controlled by changing the incidence direction of external illumination, suggesting the possibility of using this effect (and its extension to non-periodic surface features) for far-field patterning and for long-distance plasmon-based interconnects in plasmonic circuits, energy transfer, and related phenomena.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  2. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  3. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
    [CrossRef]
  4. J. A. Conway, S. Sahni, and T. Szkopek, "Plasmonic interconnects versus conventional interconnects: a comparison of latency, crosstalk and energy costs," Opt. Express 15, 4474-4484 (2007).
    [CrossRef] [PubMed]
  5. C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
    [CrossRef] [PubMed]
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  8. K. Patorski, "The self imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  12. M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. E. Noponen and J. Turunen, "Electromagnetic theory of Talbot imaging," Opt. Commun. 98, 132-140 (1993).
    [CrossRef]
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    [CrossRef]
  20. F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
    [CrossRef]
  21. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
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  26. F. J. Garc’ıa de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. (in press).
  27. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
    [CrossRef] [PubMed]
  28. M. V. Berry and S. Popescu, "Evolution of quantum superoscillations and optical superresolution without evanescent waves," J. Phys. A: Math Gen. 39, 6965-6977 (2006).
    [CrossRef]
  29. F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range coupled surface exciton polaritons," Phys. Rev. Lett. 64, 559-562 (1990).
    [CrossRef] [PubMed]
  30. R. Ulrich andM. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
    [CrossRef]
  31. A. Mugarza, A. Mascaraque, V. P’erez-Dieste, V. Repain, S. Rousset, F. J. Garc’ıa de Abajo, and J. E. Ortega, "Electron confinement in surface states on a stepped gold surface revealed by angle-resolved photoemission," Phys. Rev. Lett. 87, 107,601 (2001).
    [CrossRef]

2007

F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
[CrossRef]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

J. A. Conway, S. Sahni, and T. Szkopek, "Plasmonic interconnects versus conventional interconnects: a comparison of latency, crosstalk and energy costs," Opt. Express 15, 4474-4484 (2007).
[CrossRef] [PubMed]

2006

K. O’Holleran, M. J. Padgett, and M. R. Dennis, "Topology of optical vortex lines formed by the interference of three, four and five plane waves," Opt. Express 14, 3039-3044 (2006).
[CrossRef] [PubMed]

M. V. Berry and S. Popescu, "Evolution of quantum superoscillations and optical superresolution without evanescent waves," J. Phys. A: Math Gen. 39, 6965-6977 (2006).
[CrossRef]

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
[CrossRef]

2005

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

A. W. Lohmann, H. Knuppertz, and J. Jahns, "Fractional Montgomery effect: a self-imaging phenomenon," J. Opt. Soc. Am. A 22, 1500-1508 (2005).
[CrossRef]

2004

2003

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

2001

A. Mugarza, A. Mascaraque, V. P’erez-Dieste, V. Repain, S. Rousset, F. J. Garc’ıa de Abajo, and J. E. Ortega, "Electron confinement in surface states on a stepped gold surface revealed by angle-resolved photoemission," Phys. Rev. Lett. 87, 107,601 (2001).
[CrossRef]

1999

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

1996

M. V. Berry, "Quantum fractals in boxes," J. Phys. A: Math Gen. 29, 6617-6629 (1996).
[CrossRef]

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

1993

E. Noponen and J. Turunen, "Electromagnetic theory of Talbot imaging," Opt. Commun. 98, 132-140 (1993).
[CrossRef]

1990

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range coupled surface exciton polaritons," Phys. Rev. Lett. 64, 559-562 (1990).
[CrossRef] [PubMed]

1989

I. S. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 139, 449-453 (1989).
[CrossRef]

K. Patorski, "The self imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).
[CrossRef]

1988

A. W. Lohmann, "An array illuminator based on the Talbot effect," Optik 79, 41-45 (1988).

1984

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

R. Ulrich andM. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
[CrossRef]

1971

A. W. Lohmann and D. E. Silva, "An interferometer based on the Talbot effect," Opt. Commun. 2, 413-415 (1971).
[CrossRef]

1967

1881

Lord Rayleigh, "On copying diffraction-grating and on some phenomena connected with therewith," Philos.Mag. 11, 196-205 (1881).

1836

H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Aeschlimann, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Averbukh, I. S.

I. S. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 139, 449-453 (1989).
[CrossRef]

Barnes, W. L.

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

Bauer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Bayer, D.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry and S. Popescu, "Evolution of quantum superoscillations and optical superresolution without evanescent waves," J. Phys. A: Math Gen. 39, 6965-6977 (2006).
[CrossRef]

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

M. V. Berry, "Quantum fractals in boxes," J. Phys. A: Math Gen. 29, 6617-6629 (1996).
[CrossRef]

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).
[CrossRef]

Bodenschatz, E.

M. V. Berry and E. Bodenschatz, "Caustics, multiply reconstructed by Talbot interference," J. Mod. Opt. 46, 349-365 (1999).

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range coupled surface exciton polaritons," Phys. Rev. Lett. 64, 559-562 (1990).
[CrossRef] [PubMed]

Brixner, T.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
[CrossRef]

Chen, Y.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Conway, J. A.

Dennis, M. R.

Dereux, A.

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

Ford, G. W.

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
[CrossRef]

Garc’ia de Abajo, F. J.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
[CrossRef]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

F. J. Garc’ıa de Abajo, "Light scattering by particle and hole arrays," Rev. Mod. Phys. (in press).

Goncharenko, A. M.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Grady, N. K.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Halas, N. J.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Hollars, C. W.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Huang, F. M.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
[CrossRef]

Huser, T. R.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Jackson, J. B.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Jahns, J.

A. W. Lohmann, H. Knuppertz, and J. Jahns, "Fractional Montgomery effect: a self-imaging phenomenon," J. Opt. Soc. Am. A 22, 1500-1508 (2005).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Klein, S.

M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).
[CrossRef]

Knuppertz, H.

Lane, S. M.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Lohmann, A. W.

A. W. Lohmann, H. Knuppertz, and J. Jahns, "Fractional Montgomery effect: a self-imaging phenomenon," J. Opt. Soc. Am. A 22, 1500-1508 (2005).
[CrossRef]

A. W. Lohmann, "An array illuminator based on the Talbot effect," Optik 79, 41-45 (1988).

A. W. Lohmann and D. E. Silva, "An interferometer based on the Talbot effect," Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Mascaraque, A.

A. Mugarza, A. Mascaraque, V. P’erez-Dieste, V. Repain, S. Rousset, F. J. Garc’ıa de Abajo, and J. E. Ortega, "Electron confinement in surface states on a stepped gold surface revealed by angle-resolved photoemission," Phys. Rev. Lett. 87, 107,601 (2001).
[CrossRef]

Montgomery, W. D.

Mugarza, A.

A. Mugarza, A. Mascaraque, V. P’erez-Dieste, V. Repain, S. Rousset, F. J. Garc’ıa de Abajo, and J. E. Ortega, "Electron confinement in surface states on a stepped gold surface revealed by angle-resolved photoemission," Phys. Rev. Lett. 87, 107,601 (2001).
[CrossRef]

Noponen, E.

E. Noponen and J. Turunen, "Electromagnetic theory of Talbot imaging," Opt. Commun. 98, 132-140 (1993).
[CrossRef]

Nordlander, P.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

O’Holleran, K.

Oubre, C.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

Ozbay, E.

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Padgett, M. J.

Patorski, K.

K. Patorski, "The self imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).
[CrossRef]

Perelman, N. F.

I. S. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 139, 449-453 (1989).
[CrossRef]

Pfeiffer, W.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Popescu, S.

M. V. Berry and S. Popescu, "Evolution of quantum superoscillations and optical superresolution without evanescent waves," J. Phys. A: Math Gen. 39, 6965-6977 (2006).
[CrossRef]

Rohmer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Saastamoinen, T.

Sahni, S.

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range coupled surface exciton polaritons," Phys. Rev. Lett. 64, 559-562 (1990).
[CrossRef] [PubMed]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
[CrossRef]

Silva, D. E.

A. W. Lohmann and D. E. Silva, "An interferometer based on the Talbot effect," Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Spindler, C.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

Steeb, F.

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Talbot, H. F.

H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

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C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
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M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
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R. Ulrich andM. Tacke, "Submillimeter waveguiding on periodic metal structure," Appl. Phys. Lett. 22, 251-253 (1972).
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G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
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F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range coupled surface exciton polaritons," Phys. Rev. Lett. 64, 559-562 (1990).
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F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
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R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Materials Today 9, 20-27 (2006).
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Appl. Phys. Lett.

F. M. Huang, N. Zheludev, Y. Chen, and F. J. Garc’ıa de Abajo, "Focusing of light by a nano-hole array," Appl. Phys. Lett. 90, 091,119 (2007).
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[CrossRef]

Nano Lett.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates," Nano Lett. 5, 1569-1574 (2005).
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Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
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M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garc’ıa de Abajo,W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, "Adaptive sub-wavelength control of nano-optical fields," Nature 446, 301-304 (2007).
[CrossRef] [PubMed]

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M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
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Philos. Mag.

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the plasmon Talbot effect above a metal surface. Light is transmitted through a one-dimensional array of nanoholes, setting up a Talbot carpet of interfering plasmon waves. At approximately the Talbot distance τ from the array, the propagating plasmons revive, giving an array of plasmon focal spots. Plasmon revival at half that distance is also observed, with the foci displaced by half the period along the array direction. The dependence of the field on height z above the metal is also shown, with the intensity of the z component of the plasmons at fixed height superimposed. The carpet plotted is as for Fig. 2(b).

Fig. 2.
Fig. 2.

Plasmon Talbot carpets, numerically computed (a–c) from Eqs. (7)(8) and analytically approximated (d) from Eqs. (7) and (9) for different choices of the lattice spacing a: (a) a=λ SP; (b) a=5λ SP; (c,d) a=20λ SP. The amplitude of the Ez component of the plasmon field is plotted at a height z=0.5 µm over a silver surface for a free-space wavelength λ 0=1.55 µm, with λ SP=1.544 µm the surface plasmon wavelength. Different scales along horizontal and vertical directions are used in each plot: horizontal double arrows show the period a, while vertical arrows signal the paraxial Talbot distance τ=2a 2/λ SP (long arrows) and half that distance (short arrows). The hole array is represented by circles in the lower part of each plot. The incident light wavevector is along z and its polarization along y (see axes in the center of the figure).

Fig. 3.
Fig. 3.

Shape of a plasmon focal spot near half the Talbot distance in Fig. 2(c). The contour plot (left) shows a square of side 2λ SP centered at (x, y)=(a/2,b), with a=20λ SP and b=τ/2-5λ SP=395λ SP. Plasmon intensities at cross sections of the spot are given on the right along directions parallel (solid curve) and perpendicular (broken curve) with respect to the hole array.

Fig. 4.
Fig. 4.

Lattice-period dependence of the intensity near half the Talbot distance at x=a/2-in the paraxial Talbot effect [Eq. (3)] the focal spot occurs at exactly y=τ/2. The plasmon intensity is represented along y (vertical axis) as a function of lattice period a at a height z=0.5 µm over a silver surface for a free-space wavelength λ 0=1.55 µm. The intensity is normalized to the maximum within the plotted range of y for each period.

Equations (10)

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f ( x , y ) = m f m exp ( i 2 π mx a ) exp ( i 2 π ζ m y λ ) ,
ζ m λ = 1 λ m 2 τ ( λ a ) 2 m 4 4 τ ( λ a ) 4 m 6 8 τ
f ( x , y ) exp ( i 2 π y λ ) m f m exp ( i 2 π mx a ) exp ( i 2 π m 2 y τ ) ,
f ( x , τ ) exp ( i 2 π y λ ) f ( x , 0 ) ,
f ( x , τ 2 ) exp ( i 2 π y λ ) f ( x a 2 , 0 ) .
E sin gle ( r ) = d 2 Q exp [ ik · ( r R 0 ) ] F ( Q ) ,
F ( Q ) = i λ 0 2 Q k z [ e ̂ p k z k y ( 1 r p ) + e ̂ s k k x ( 1 + r s ) ] ,
E total ( r ) = 2 π a m exp ( i 2 π mx a ) d k y exp ( i k y y + i k y z ) F ( Q m )
= m exp ( i 2 π mx a ) F m ( y , z ) ,
F m ( y , z ) 2 λ 0 ( 2 π ) 3 ε 2 a ( ε + 1 ) 2 ( ε 1 ) exp ( i kz ε + 1 ) exp ( i Q SP ζ m y ) ( m λ 0 a ε + 1 ε , ζ m ε , 1 ) ,

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