Abstract

Resonances in subwavelength apertures are accompanied by wavelength-dependent phase shifts in the transmitted fields offering a potential for manipulation of wavefields. Here, we present Finite Element Method simulations and experiments investigating light passing through arrays of nanometric spatially varying near-resonant slits perforated in a silver film. We demonstrate that a one-dimensional focusing element can be obtained by tailoring the phase across the device through varying slit sizes around the resonant dimensions for a particular design wavelength.

©2010 Optical Society of America

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings. (Springer, 1988).
  2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
    [Crossref] [PubMed]
  3. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  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. F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
    [Crossref] [PubMed]
  7. 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]
  8. 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]
  9. Y. Chen, C. Zhou, X. Luo, and C. Du, “Structured lens formed by a 2D square hole array in a metallic film,” Opt. Lett. 33(7), 753–755 (2008).
    [Crossref] [PubMed]
  10. S. M. Orbons and A. Roberts, “Resonance and Extraordinary Transmission in Annular Aperture Arrays,” Opt. Express 14(26), 12623–12628 (2006).
    [Crossref] [PubMed]
  11. X. M. Goh, L. Lin, and A. Roberts, “Spatially Varying Near-resonant Aperture Arrays for Beam Manipulation,” in SPIE Nano Science + Engineering: Plasmonics: Metallic Nanostructures and Their Optical Properties VII, (2009).
  12. COMSOL. Multi-physics, http://www.comsol.com/ .
  13. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  14. E. Hecht, Optics. (Addison Wesley, 2002).
    [PubMed]
  15. P. Ruffieux, T. Scharf, H. P. Herzig, R. Völkel, and K. J. Weible, “On the Chromatic Aberration of Microlenses,” Opt. Express 14(11), 4687–4694 (2006).
    [Crossref] [PubMed]

2009 (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]

2008 (2)

Y. Chen, C. Zhou, X. Luo, and C. Du, “Structured lens formed by a 2D square hole array in a metallic film,” Opt. Lett. 33(7), 753–755 (2008).
[Crossref] [PubMed]

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

2006 (3)

2005 (1)

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]

2003 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[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]

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]

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]

Chen, Y.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Y. Chen, C. Zhou, X. Luo, and C. Du, “Structured lens formed by a 2D square hole array in a metallic film,” Opt. Lett. 33(7), 753–755 (2008).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Dong, X.

Du, C.

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

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]

Fedotov, V. A.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Gao, H.

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

Herzig, H. P.

Huang, F. M.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kao, T. S.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

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]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Luo, X.

Lv, Y.

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Orbons, S. M.

Roberts, A.

Ruffieux, P.

Scharf, T.

Shi, H.

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]

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]

Völkel, R.

Wang, C.

Weible, K. J.

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]

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]

Zheludev, N. I.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Zhou, C.

Appl. Phys. Lett. (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]

Nano Lett. (2)

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole array as a lens,” Nano Lett. 8(8), 2469–2472 (2008).
[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]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[Crossref] [PubMed]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[Crossref] [PubMed]

Other (4)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings. (Springer, 1988).

E. Hecht, Optics. (Addison Wesley, 2002).
[PubMed]

X. M. Goh, L. Lin, and A. Roberts, “Spatially Varying Near-resonant Aperture Arrays for Beam Manipulation,” in SPIE Nano Science + Engineering: Plasmonics: Metallic Nanostructures and Their Optical Properties VII, (2009).

COMSOL. Multi-physics, http://www.comsol.com/ .

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic illustration of a single slit aperture of slit width size C formed on a 400 nm thick Ag film below a glass substrate. A TE-polarized (electric field in the z-direction) plane wave is incident from above the slit array and glass substrate in the y-direction as indicated. Calculated (b) normalized transmission (total transmitted power normalized to incident power) and (c) phase shift for a range of single slit apertures each formed on a 400 nm thick Ag film over a range of slit width sizes and wavelengths. The cut-off wavelength for a perfectly conducting TE1 parallel-plate waveguide mode is shown.

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Fig. 2
Fig. 2

Calculated (a) normalized transmission (total transmitted power normalized to incident power) and (b) phase shift for a range of single slit apertures each formed on a 400 nm thick Ag film (εsilver = −29.98-i0.19) where λ = 800 nm and 300 nm ≤ C ≤ 700 nm.

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Fig. 3
Fig. 3

(a) Schematic illustration of a typical focusing element comprising a 400 nm thick Ag film, perforated with spatially varying slits C with equal slit interspacing d formed on a glass substrate. A TE-polarized plane wave at λ = 800 nm is incident from the left of the slit array in the y-direction. (b) The phase shift (green dotted line) and transmission (solid black line) across a focusing element with 7 slits, (with slit sizes 412 nm ≤ C ≤ 616 nm indicated by the asterisks) as a function of the distance x from the center of the structure. The position of each slit is indicated by the crosses. (c) x cross-section through the focal spot and the 2D FEM simulation corresponding to the (d) Poynting vector. Modeled device dimensions are 4.6 μm × 29.0 μm.

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Fig. 4
Fig. 4

(a) SEM image of the fabricated device. 2D FEM simulations for a focusing element for (b) TE and (c) TM-polarization. Modeled device x and y dimensions are 6.4 μm × 30.0 μm. Experimental results corresponding to a lens fabricated with the same design parameters as (b) and (c), showing transmission images taken in the xz-plane, obtained at different y-positions along the focal plane of the sample for TE (d)-(i) and TM-polarization (j)–(o). These images correspond to the transmission across the xz-plane along the y-axis in simulations. The fabricated lens x and z dimensions are 6.6 × 19.9 μm.

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Equations (1)

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φ ( x ) = 2 n π + 2 π λ f 2 + x 2 − 2 π f λ

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