Abstract

We theoretically and experimentally demonstrate that the diffraction of microstructures based on silver nanowires leads to very efficient microfocusing effects. Pairs of parallel nanowires act as ultrasmall cylindrical microlenses with diffraction-limited resolution in the Fresnel region. This is a new diffraction scheme to make micron-sized optical lenses with higher transmittance than plasmonic microlens based on nano-aperture arrays. Calculations based on the scalar Rayleigh-Sommerfeld integral highlights the pure scalar diffractive contribution. Thus, the plasmon contribution is negligible in such micron-sized metallic geometry. We demonstrate that two-dimensional grids of nanowires can be used to fabricate dense arrays of microlenses, i.e. 10000x10000 DPI (dots per inch).

© 2012 OSA

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References

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  1. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
    [CrossRef] [PubMed]
  2. Q. Chen and D. R. S. Cumming, “Visible light focusing demonstrated by plasmonic lenses based on nano-slits in an aluminum film,” Opt. Express 18(14), 14788–14793 (2010).
    [CrossRef] [PubMed]
  3. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
    [CrossRef] [PubMed]
  4. Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5(3), 287–310 (2010).
    [CrossRef]
  5. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
    [CrossRef]
  6. M. Zhang, J. Du, H. Shi, S. Yin, L. Xia, B. Jia, M. Gu, and C. Du, “Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove,” Opt. Express 18(14), 14664–14670 (2010).
    [CrossRef] [PubMed]
  7. Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
    [CrossRef]
  8. H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
    [CrossRef] [PubMed]
  9. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lenses made of multiple concentric rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
    [CrossRef] [PubMed]
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, 1999).
  11. T. Baldacchini, A.-C. Pons, J. Pons, C. Lafratta, J. Fourkas, Y. Sun, and M. Naughton, “Multiphoton Laser Direct Writing of Two-Dimensional Silver Structures,” Opt. Express 13(4), 1275–1280 (2005).
    [CrossRef] [PubMed]
  12. M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
    [CrossRef]
  13. www.teemphotonics.com .
  14. L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
    [CrossRef]
  15. J. A. C. Veerman, J. J. Rusch, and H. P. Urbach, “Calculation of the Rayleigh-Sommerfeld diffraction integral by exact integration of the fast oscillating factor,” J. Opt. Soc. Am. A 22(4), 636–646 (2005).
    [CrossRef] [PubMed]
  16. www.lumerical.com .
  17. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]

2011 (2)

Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
[CrossRef]

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

2010 (5)

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5(3), 287–310 (2010).
[CrossRef]

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

M. Zhang, J. Du, H. Shi, S. Yin, L. Xia, B. Jia, M. Gu, and C. Du, “Three-dimensional nanoscale far-field focusing of radially polarized light by scattering the SPPs with an annular groove,” Opt. Express 18(14), 14664–14670 (2010).
[CrossRef] [PubMed]

Q. Chen and D. R. S. Cumming, “Visible light focusing demonstrated by plasmonic lenses based on nano-slits in an aluminum film,” Opt. Express 18(14), 14788–14793 (2010).
[CrossRef] [PubMed]

2009 (2)

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

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

2008 (1)

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

2005 (2)

2004 (1)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Abeysinghe, D. C.

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

Astilean, S.

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

Baldacchini, T.

Baldeck, L. P.

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

Baldeck, P. L.

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Chen, Q.

Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
[CrossRef]

Q. Chen and D. R. S. Cumming, “Visible light focusing demonstrated by plasmonic lenses based on nano-slits in an aluminum film,” Opt. Express 18(14), 14788–14793 (2010).
[CrossRef] [PubMed]

Chen, W.

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

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Cumming, D. R. S.

Du, C.

Du, J.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Fourkas, J.

Fu, Y.

Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5(3), 287–310 (2010).
[CrossRef]

Gao, H.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Giloan, M.

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Gu, M.

Hyun, J. K.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Jia, B.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Lafratta, C.

Lauhon, L. J.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Lee, M. H.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Lin, L.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Naughton, M.

Nelson, R. L.

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

Odom, T. W.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Pons, A.-C.

Pons, J.

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

Rusch, J. J.

Shi, H.

Stéphan, O.

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

Sun, Y.

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Urbach, H. P.

Veerman, J. A. C.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Vitrant, G.

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

Vurth, L.

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Xia, L.

Yang, J. C.

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

Yin, S.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

Zaiba, S.

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

Zhan, Q.

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

Zhang, M.

Zhou, X.

Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5(3), 287–310 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenim(II) dye as photoinitator,” Appl. Phys. Lett. 92(17), 171103 (2008).
[CrossRef]

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

Nano Lett. (4)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef] [PubMed]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[CrossRef] [PubMed]

H. Gao, J. K. Hyun, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

M. Giloan, S. Zaiba, G. Vitrant, P. L. Baldeck, and S. Astilean, “Light Transmission and Local Field Enhancement in Arrays of Silver Nanocylinders,” Opt. Commun. 284(14), 3629–3634 (2011).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Plasmonics (2)

Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5(3), 287–310 (2010).
[CrossRef]

Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6(1), 75–82 (2011).
[CrossRef]

Other (3)

www.teemphotonics.com .

M. Born and E. Wolf, Principles of Optics (Pergamon, 1999).

www.lumerical.com .

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental characterization set-up (b) Experimental and (c) simulated light patterns transmitted by two parallel nanowires with 300 nm width, and separated by D = 1, 2 and 4 µm. The inset shows the images of the microstructures.

Fig. 2
Fig. 2

Calculated (top) and experimental (bottom) diffracted and normalized intensity distributions along the propagation (left) and transversal (right) directions.

Fig. 3
Fig. 3

(a) Variations of the normalized focal length Zf/λ and depth of focus Df / λ, (b) lateral resolution ΔX/λ and (c) maximum intensity Imax as a function of normalized separating distance D/λ. The stars correspond to the experimental values and the vertical line correspond to the experimental depth of focus

Fig. 4
Fig. 4

(a) Experimental focusing pattern and (b) FDTD simulated focusing pattern for the 2-µm silver square.

Fig. 6
Fig. 6

Experimental intensity distributions along the x-axis at the focal point for a grid (square symbol) and for a single square (triangle symbol).Solid line corresponds to the square FDTD simulation.

Fig. 5
Fig. 5

Diffracted light patterns by 20X20 µm grid (a) at z = 0 and (b) at the focal plane.

Tables (1)

Tables Icon

Table 1 Calculated and experimental optical characteristics. Zf, Df, ΔX, and Imax/Io are respectively the focal length, the depth of focus, the lateral resolution, and the normalized intensity at the focal point. NA and ΔXd are the numerical aperture and the diffraction-limited resolution.

Equations (2)

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A(M)= 1 2π aperture e jk PM ¯ PM ¯ cos( n , PM )[ 1 PM ¯ jk ] A i (P) d 2 P
NA=n sinθ = n D 2 ( D 2 4 + Z f 2 )

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