Abstract

The Talbot effect of the surface plasmon polaritons (SPPs) using SPP launching gratings is studied experimentally. Talbot carpets are obtained and the Talbot distance is given when the paraxial approximation is not satisfied. Multi-layer and multi-level-phase launching gratings are designed to enhance the intensities of the amplitude-modulated revivals. Effective focusing of SPPs with multiple focal spots and a subwavelength full width at half maximum is obtained by using a three-layer four-level-phase launching grating.

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  1. H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401–407 (1836).
  2. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
    [CrossRef] [PubMed]
  3. S. Nowak, C. Kurtsiefer, T. Pfau, and C. David, “High-order Talbot fringes for atomic matter waves,” Opt. Lett. 22(18), 1430–1432 (1997).
    [CrossRef]
  4. H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer-Verlag: Berlin, 1988).
  5. M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, “The plasmon Talbot effect,” Opt. Express 15(15), 9692–9700 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9692 .
    [CrossRef] [PubMed]
  6. G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
    [CrossRef]
  7. A. A. Maradudin and T. A. Leskova, “The Talbot effect for a surface plasmon polariton,” N. J. Phys. 11(3), 033004 (2009).
    [CrossRef]
  8. A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
    [CrossRef]
  9. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
    [CrossRef] [PubMed]
  10. A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
    [CrossRef]
  11. C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
    [CrossRef]
  12. E. D. Palik, Handbook of Optical Constant of Solids (Academic: Florida, 1985).
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    [CrossRef] [PubMed]
  14. J. R. Leger and G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional-Talbot planes,” Opt. Lett. 15(5), 288–290 (1990).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29(29), 4337–4340 (1990).
    [CrossRef] [PubMed]
  17. C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
    [CrossRef]
  18. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [CrossRef] [PubMed]
  19. Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
    [CrossRef]

2009

A. A. Maradudin and T. A. Leskova, “The Talbot effect for a surface plasmon polariton,” N. J. Phys. 11(3), 033004 (2009).
[CrossRef]

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

2008

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

2007

2006

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2001

Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
[CrossRef]

1997

1996

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

1995

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

1993

1992

1990

1836

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

Arrizon, V.

Aussenegg, F. R.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Barnes, W. L.

A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Chang, S.

Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
[CrossRef]

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Da, X.

David, C.

Dennis, M. R.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ditlbacher, H.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Drezet, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Galler, N.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

García de Abajo, F. J.

Giannattasio, A.

A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
[CrossRef]

Hammond, T. D.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Han, B.

Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
[CrossRef]

Hecht, B.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Hohenau, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Hooper, I. R.

A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
[CrossRef]

Inouye, Y.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Krenn, J. R.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Kurtsiefer, C.

Leger, J. R.

Leija, A. P.

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

Leitner, A.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Leskova, T. A.

A. A. Maradudin and T. A. Leskova, “The Talbot effect for a surface plasmon polariton,” N. J. Phys. 11(3), 033004 (2009).
[CrossRef]

Liu, L.

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

Lohmann, A. W.

Maradudin, A. A.

A. A. Maradudin and T. A. Leskova, “The Talbot effect for a surface plasmon polariton,” N. J. Phys. 11(3), 033004 (2009).
[CrossRef]

Niconoff, G. M.

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

Novotny, L.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Nowak, S.

Pfau, T.

Pohl, D. W.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Pritchard, D. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Sanchez, H. H.

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

Sanchez-Gil, J. A.

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

Schmiedmayer, J.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Song, Y.

Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
[CrossRef]

Steinberger, B.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Stepanov, A. L.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

Swanson, G. J.

Szwaykowski, P.

Talbot, H. F.

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

Tannian, B. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Thomas, J. A.

Wang, J.

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

Wehinger, S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Wu, X.

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

Zhang, J.

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

Zhao, C.

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

Zheludev, N. I.

Zhou, C.

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006).
[CrossRef]

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94(11), 111105 (2009).
[CrossRef]

N. J. Phys.

A. A. Maradudin and T. A. Leskova, “The Talbot effect for a surface plasmon polariton,” N. J. Phys. 11(3), 033004 (2009).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Commun.

Y. Song, B. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001).
[CrossRef]

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006).
[CrossRef]

G. M. Niconoff, J. A. Sanchez-Gil, H. H. Sanchez, and A. P. Leija, “Self-imaging and caustics in two-dimensional surface plasmon optics,” Opt. Commun. 281(8), 2316–2320 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Mag.

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

Phys. Rev. A

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local Excitation, Scattering, and Interference of Surface Plasmons,” Phys. Rev. Lett. 77(9), 1889–1892 (1996).
[CrossRef] [PubMed]

Other

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

E. D. Palik, Handbook of Optical Constant of Solids (Academic: Florida, 1985).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the SPPLG. (b) Scanning electron micrograph of the SPPLG with period d = 6λ SPP and α = 1/2 (only 2.5 periods are shown).

Fig. 2
Fig. 2

Experimental Talbot carpets for the SPPLGs with d = 3λ SPP (a) and 6λ SPP (b), respectively. (c) Experimental and theoretical transversal intensity distributions at Z t /2 for the SPPLG with d = 6λ SPP. (d) Theoretical Talbot carpet for the SPPLG with d = 6λ SPP; white dashed lines from left to right indicate the positions of Z t /2, d 2/λ, Z t and 2d 2/λ, respectively.

Fig. 3
Fig. 3

(a) Schematic of the multi-layer SPPLG with the distance between two adjacent layers Δ. (b) Schematic of a two-level-phase SPPLG with an optical path difference δ (only 2.5 periods are shown).

Fig. 4
Fig. 4

(a) Scanning electron micrograph of the three-layer two-level-phase SPPLG (only three periods are shown). (b) SPP image.

Fig. 5
Fig. 5

(a) Schematic of one period of the three-layer four-level-phase SPPLG. (b) SPP image. (c) Experimental and theoretical transverse intensity profiles of one focal spot atl –Z t/6.

Equations (1)

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Zn=λSPP/{1[1(nλSPP/d)2]1/2}   n=1,2,3,.

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