Abstract

The Talbot effect of an Ag nanolens with five periodic concentric rings that are illuminated by the radially polarized light was numerically studied by means of rigorous finite-difference and time-domain (FDTD) algorithm. It was found that the Talbot effect occurs only when the incident wavelength is at the scale of less than half of period of the grating structures of the nanolenses. Specifically, in this work, the nanolenses with a 500 nm period grating structures has five focal points due to Talbot effect for the incident wavelength of λ = 248 nm. The diameter of the first focal spot after the exit plane in free space is 100 nm. In contrast, we analyzed the corresponding focal points on the basis of Talbot self-imaging by scalar diffraction theory. It was found that the scalar Talbot effect cannot interpret the Talbot effect phenomenon for the metallic nanolenses. It may attribute to the paraxial approximation applied in the Talbot effect theory in far-field region. However, the approximation does not hold in our nanolenses structures during the light propagation. In addition, the Talbot effect appears at the short-wavelength regime only, especially in the ultraviolet wavelength region.

© 2011 OSA

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References

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  1. F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2011 (1)

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

2010 (2)

Y. Liu, Y. Fu, and X. Zhou, “Polarization dependent of plasmonic lenses with variant periods on superfocusing,” Plasmonics 5(2), 117–123 (2010).
[CrossRef]

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef] [PubMed]

2009 (4)

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

S. Cherukulappurath, D. Heinis, J. Cesario, N. F. van Hulst, S. Enoch, and R. Quidant, “Local observation of plasmon focusingin Talbot carpets,” Opt. Express 17(26), 23772–23784 (2009).
[CrossRef] [PubMed]

F. I. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics 4(1), 51–59 (2009).
[CrossRef]

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (3)

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, “The plasmon Talbot effect,” Opt. Express 15(15), 9692–9700 (2007).
[CrossRef] [PubMed]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (3)

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

2003 (2)

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

N. Bonod, S. Enoch, L. Li, P. Evgeny, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11(5), 482–490 (2003).
[CrossRef] [PubMed]

1998 (1)

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

Alvarez-Palacio, D. C.

Baida, F. I.

F. I. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics 4(1), 51–59 (2009).
[CrossRef]

Belkhir, A.

F. I. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics 4(1), 51–59 (2009).
[CrossRef]

Bonod, N.

Cesario, J.

Chen, L.

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

Chen, W.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

Cherukulappurath, S.

Davis, C. C.

Dennis, M. R.

Dong, X.

Du, C.

Du, C. L.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Ebbesen, T. W.

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

Enoch, S.

Everett, P. N.

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

Evgeny, P.

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Fu, Y.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Y. Liu, Y. Fu, and X. Zhou, “Polarization dependent of plasmonic lenses with variant periods on superfocusing,” Plasmonics 5(2), 117–123 (2010).
[CrossRef]

Y. Fu, W. Zhou, and L. E. N. Lim, “Near-field behavior of zone-plate-like plasmonic nanostructures,” J. Opt. Soc. Am. A 25(1), 238–249 (2008).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Gao, H.

García de Abajo, F. J.

M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, “The plasmon Talbot effect,” Opt. Express 15(15), 9692–9700 (2007).
[CrossRef] [PubMed]

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

Garcia-Sucerquia, J.

García-Vidal, F. J.

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

Heinis, D.

Ishihara, T.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

Kreuzer, H. J.

Kuipers, L.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef] [PubMed]

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]

Lezec, H. J.

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

Li, L.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

N. Bonod, S. Enoch, L. Li, P. Evgeny, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11(5), 482–490 (2003).
[CrossRef] [PubMed]

Lim, L. E. N.

Y. Fu, W. Zhou, and L. E. N. Lim, “Near-field behavior of zone-plate-like plasmonic nanostructures,” J. Opt. Soc. Am. A 25(1), 238–249 (2008).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Liu, H.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Liu, Y.

Y. Liu, Y. Fu, and X. Zhou, “Polarization dependent of plasmonic lenses with variant periods on superfocusing,” Plasmonics 5(2), 117–123 (2010).
[CrossRef]

Liu, Z.

Lu, Z.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Luo, X.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

Luo, X. G.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

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]

Martin-Moreno, L.

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

Mondol, M. K.

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

Moon, E. E.

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

Nelson, R. L.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

Nevière, M.

Quidant, R.

Shi, H.

Smith, H. I.

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

Smolyaninov, I. I.

Spasenovic, M.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef] [PubMed]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Steele, J. M.

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Sun, Q.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

van Hulst, N. F.

van Oosten, D.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef] [PubMed]

Wang, C.

Wang, Y.

Yu, W.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Zhan, Q.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

Zhang, H.

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Zhang, X.

Zheludev, N. I.

Zhou, W.

Y. Fu, W. Zhou, and L. E. N. Lim, “Near-field behavior of zone-plate-like plasmonic nanostructures,” J. Opt. Soc. Am. A 25(1), 238–249 (2008).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Zhou, X.

Y. Liu, Y. Fu, and X. Zhou, “Polarization dependent of plasmonic lenses with variant periods on superfocusing,” Plasmonics 5(2), 117–123 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

F. J. García-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4503 (2003).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

E. E. Moon, L. Chen, P. N. Everett, M. K. Mondol, and H. I. Smith, “Nanometer gap measurement and verification via chirped-Talbot effect,” J. Vac. Sci. Technol. B 22(6), 3378–3381 (2004).
[CrossRef]

N. J. Phys. (1)

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

Nano Lett. (3)

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef] [PubMed]

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Plasmonics (3)

Y. Liu, Y. Fu, and X. Zhou, “Polarization dependent of plasmonic lenses with variant periods on superfocusing,” Plasmonics 5(2), 117–123 (2010).
[CrossRef]

F. I. Baida and A. Belkhir, “Superfocusing and light confinement by surface plasmon excitation through radially polarized beam,” Plasmonics 4(1), 51–59 (2009).
[CrossRef]

W. Yu, Y. Fu, L. Li, H. Zhang, H. Liu, Z. Lu, and Q. Sun, “Computational study of influence of structuring of plasmonic nanolens on superfocusing,” Plasmonics 6(1), 35–42 (2011).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the nanolenses.

Fig. 2
Fig. 2

E-field intensity distribution at (a) Y–Z plane and (b) X–Z plane at λ = 248 nm.

Fig. 3
Fig. 3

Electric field transmission at the incident wavelength λ = 248 nm in Y–Z plane, X = 0, Y = 0. The propagation is from left to right as shown in the picture. The exit plane is in the Z = 0.1μm plane.

Fig. 4
Fig. 4

Distributions of electric field intensity |E|2 at λ = 248 nm at the focal positions of Z = 0.396 μm, 0.841 μm, 1.309 μm, 1.901 μm, and 2.963 μm, respectively. Inset, zoom in plot of the central peaks.

Fig. 5
Fig. 5

Self-imaging of the grating structure with the same geometrical parameters as the nanolens mentioned before.

Fig. 6
Fig. 6

E-field intensity distribution in Y–Z plane for the incident wavelength of (a) 633 nm, (b) 532 nm, (c) 448 nm, (d) 325 nm, (e) 300 nm, (f) 248 nm, and (g) 193 nm, respectively. The intensity distribution in X–Z plane is the same as that of Y–Z plane due to symmetrical circular focused beam spot under illumination of radial polarization and hence omitted here.

Fig. 7
Fig. 7

E-field intensity profiles at Y–Z plane, X = 0, Y = 0 for the different wavelengths of 633 nm, 532 nm, 448 nm, 325 nm, 300 nm, 248 nm, and 193 nm.

Equations (7)

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

U ( x ) = n = c n exp ( j 2 π n d x ) ,
U z ( x ) = n = c n exp ( j 2 π n d x ) exp [ j π λ z ( n d ) 2 ] exp ( j k z ) .
z = 2 m d 2 λ     ( m = 1 , 2 , 3 )
exp [ j π λ z ( n d ) 2 ] = 1.
U z ( x ) = n = c n exp ( j 2 π n d x ) exp ( j k z ) = U ( x ) exp ( j k z ) .
I = | U z ( x ) | 2 = | U ( x ) | 2 .
z T = 2 d 2 λ .

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