Abstract

We report on the optimization of ultrasmall microlenses based on the diffraction of two parallel metallic nanowires. The Rayleigh–Sommerfeld integral is used in the visible range to simulate the near field diffraction patterns induced by single and paired planar silver wires. We demonstrate that the wire width w affects only the diffraction efficiency and the contrast of the diffraction pattern. The wire interdistance D controls the focal length and the depth of focus, which are equal and vary in the 0.1 to 10 μm range when D/λ increases from 1 to 8. The transversal FWHM increases from 200 to 700 nm, and a normalized intensity greater than 2.2 is obtained at the focal point when w is about 300 nm and D/λ=3. There is excellent agreement between these calculated properties and the experimental results obtained for single and paired parallel silver nanowires. We show that in our microsized geometry, the plasmon contribution is negligible with respect to pure diffraction effect. In addition, these nanowire microlenses have focusing properties similar to those of ideal refractive lenses limited by diffraction.

© 2012 Optical Society of America

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References

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  1. Q. Chen and D. R. S. Cumming, “Visible light focusing demonstrated by plasmonic lenses based on nano slits in aluminum film,” Opt. Express 18, 14788–14793 (2010).
    [CrossRef]
  2. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Bernard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
    [CrossRef]
  3. L. Ling, 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, 1936–1940 (2010).
    [CrossRef]
  4. M. Zhang, J. Du, H. Shi, L. Xia, S. Yin, 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, 14664–14670 (2010).
    [CrossRef]
  5. G. M. Lerman, A. Yanai, N. Ben-Yosef, and U. Levy, “Demonstration of an elliptical plasmonic lens illuminated with radially like polarized field,” Opt. Express 18, 10871–10877 (2010).
    [CrossRef]
  6. Q. Chen, “Effect of the number of zones in a one-dimensional plasmonic zone plate lens: simulation and experiment,” Plasmonics 6, 75–82 (2011).
    [CrossRef]
  7. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric rings under radially polarized illumination,” Nano Lett. 9, 4320–4325 (2009).
    [CrossRef]
  8. L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
    [CrossRef]
  9. H. Gao, J. K. Hyum, M. H. Lee, J. C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10, 4111–4116 (2010).
    [CrossRef]
  10. S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization selective design,” Opt. Lett. 36, 451–453 (2011).
    [CrossRef]
  11. Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5, 287–310 (2010).
    [CrossRef]
  12. S. Zaiba, T. Kouriba, O. Ziane, O. Stéphan, J. Bosson, G. Vitrant, and P. L. Baldeck, “Metallic nanowires can lead to wavelength-scale microlenses and microlens arrays,” Opt. Express 20, 15516–15521 (2012).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), Chap. 8.
  14. 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, 636–646 (2005).
    [CrossRef]
  15. L. Vurth, L. P. Baldeck, O. Stéphan, and G. Vitrant, “Two-photon induced fabrication of gold microstructures in polystyrene sulfonate thin films using a ruthenium(II) dye as photoiniatator,” Appl. Phys. Lett. 92, 171103 (2008).
    [CrossRef]
  16. www.teemphotonics.com .
  17. www.lumerical.com .

2012

2011

S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization selective design,” Opt. Lett. 36, 451–453 (2011).
[CrossRef]

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

2010

2009

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

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

2008

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

2005

Abeysinghe, D. C.

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

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 ruthenium(II) dye as photoiniatator,” Appl. Phys. Lett. 92, 171103 (2008).
[CrossRef]

Baldeck, P. L.

Ben-Yosef, N.

Bernard, E. S.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), Chap. 8.

Bosson, J.

Brongersma, M. L.

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

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef]

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

Chen, K. P.

Chen, Q.

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

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

Chen, W.

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

Cumming, D. R. S.

Drachev, V. P.

Du, C.

Du, J.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef]

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

Fu, Y.

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

Gao, H.

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

Goh, X. M.

L. Ling, 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, 1936–1940 (2010).
[CrossRef]

Gu, M.

Hyum, J. K.

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

Ishii, S.

Jia, B.

Kildishev, A. V.

Kouriba, T.

Lauhon, L. J.

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

Lee, M. H.

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

Lerman, G. M.

Levy, U.

Ling, L.

L. Ling, 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, 1936–1940 (2010).
[CrossRef]

McGuinness, L. P.

L. Ling, 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, 1936–1940 (2010).
[CrossRef]

Nelson, R. L.

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

Odom, T. W.

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

Roberts, A.

L. Ling, 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, 1936–1940 (2010).
[CrossRef]

Ruan, Z.

Rusch, J. J.

Shalaev, V. M.

Shi, H.

Shin, W.

Stéphan, O.

S. Zaiba, T. Kouriba, O. Ziane, O. Stéphan, J. Bosson, G. Vitrant, and P. L. Baldeck, “Metallic nanowires can lead to wavelength-scale microlenses and microlens arrays,” Opt. Express 20, 15516–15521 (2012).
[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 ruthenium(II) dye as photoiniatator,” Appl. Phys. Lett. 92, 171103 (2008).
[CrossRef]

Urbach, H. P.

Veerman, J. A. C.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef]

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

Vitrant, G.

S. Zaiba, T. Kouriba, O. Ziane, O. Stéphan, J. Bosson, G. Vitrant, and P. L. Baldeck, “Metallic nanowires can lead to wavelength-scale microlenses and microlens arrays,” Opt. Express 20, 15516–15521 (2012).
[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 ruthenium(II) dye as photoiniatator,” Appl. Phys. Lett. 92, 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 ruthenium(II) dye as photoiniatator,” Appl. Phys. Lett. 92, 171103 (2008).
[CrossRef]

White, J. S.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), Chap. 8.

Xia, L.

Yanai, A.

Yang, J. C.

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

Yin, S.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef]

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

Zaiba, S.

Zhan, Q.

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

Zhang, M.

Zhou, X.

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

Ziane, O.

Appl. Phys. Lett.

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

J. Opt. Soc. Am. A

Nano Lett.

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

L. Ling, 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, 1936–1940 (2010).
[CrossRef]

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

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

Opt. Express

Opt. Lett.

Plasmonics

Y. Fu and X. Zhou, “Plasmonic lenses: a review,” Plasmonics 5, 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, 75–82 (2011).
[CrossRef]

Other

www.teemphotonics.com .

www.lumerical.com .

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), Chap. 8.

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Figures (15)

Fig. 1.
Fig. 1.

Diffraction light patterns simulated for a single planar nanowire of (a) 50, (b) 100, (c) 200, (d) 300, (e) 400, and (f) 500 nm width.

Fig. 2.
Fig. 2.

(a) Normalized intensity diffracted in the z-direction behind the nanowire (at x=0) when the width w varies from 50 to 500 nm and (b) characteristic recovery length lC versus w.

Fig. 3.
Fig. 3.

(a) Normalized intensity diffracted at z=2μm in the x-direction for λ=430nm (dashed curve), λ=500nm (solid curve), and λ=630nm (dotted curve) and (b) maximum intensity for the three first diffraction orders (solid, dashed and doted curves, respectively) when w varies from 50 to 500 nm.

Fig. 4.
Fig. 4.

(a) Experimental diffraction light patterns and (b) dispersion effect at an arbitrary value of z induced by a silver single nanowire.

Fig. 5.
Fig. 5.

Experimental normalized intensity diffracted at λ=500nm at x=0 in the z-direction, FDTD simulation for w=300nm, and scalar near field calculations when w=300nm.

Fig. 6.
Fig. 6.

(a) Experimental intensities diffracted by the fabricated nanowire in the x-direction at z=2μm for λ=430 (solid curve), 500 (dashed curve), and 630 nm (dotted curve) and (b) comparison between the experimental (solid curve) and simulated intensity distribution (dotted curve) when the width is 300 nm.

Fig. 7.
Fig. 7.

Transmitted light pattern in the (x-z) plane calculated for a pair of nanowires separated by D=2μm for (a) w=100, (b) 200, and (c) 300 nm.

Fig. 8.
Fig. 8.

Normalized light intensity distributions along the propagation direction for (a) w=100nm and (b) 300 nm for different separating distances D.

Fig. 9.
Fig. 9.

Normalized focal length Zf/λ and depth of focus FWHM/λ for (a) w=100 and (b) 300 nm and for different values of D/λ. The stars in (b) are the normalized experimental focal length values for silver nanowires.

Fig. 10.
Fig. 10.

Focal length Zf for different widths w when D/λ varies from 1 to 8.

Fig. 11.
Fig. 11.

Maximal (solid curve) and minimal (dashed curve) normalized intensities Imax and Imin at the focal point for different widths w when D/λ varies from 1 to 8.

Fig. 12.
Fig. 12.

NA versus D/λ for different values of w.

Fig. 13.
Fig. 13.

Intensity distributions along the x-direction for (a) w=100 and (b) 300 nm for different values of D.

Fig. 14.
Fig. 14.

Normalized extension ΔX/λ when w and D/λ vary respectively from 50 to 400 nm and from 1 to 8. The stars are the experiment values of a pair of silver nanowires separated by D=2μm.

Fig. 15.
Fig. 15.

Theoretical (solid curve) and measured (dashed curve) transversal extension r and Δx versus D/λ for w=100 and 300 nm.

Tables (1)

Tables Icon

Table 1. Optimal Values of Imax and D/λ for the Corresponding Width w of the Microlens

Equations (5)

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

A(M)=ejkddcos(θ)(1djk)·Ai(P)dxodyo.
A(M)=Aiejkixoejkdodozdo(1jkdo)Fc(ko)dxo.
do=(xxo)2+z2.
Fc(ko)=+eiko[1+yo21]1+yo211+yo2jko1jkodyo.
NA=nsinθ=nD2(D24+Zf2),

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