Abstract

We demonstrate numerically, using a three-dimensional finite-difference frequency-domain method, the ability to design a phase front using an array of metallic pillars. We show that in such structures, the local phase delay upon transmission can be tuned by local geometry. We apply this knowledge to demonstrate a metallic microlens. The presented design principles apply to a wider range of wavelength-size integrated photonic components.

© 2010 Optical Society of America

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  1. N. Engheta, Science 317, 1698 (2007).
    [CrossRef] [PubMed]
  2. V. M. Shalaev, Nat. Photonics 1, 41 (2007).
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    [CrossRef]
  4. Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
    [CrossRef]
  5. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
    [CrossRef] [PubMed]
  6. T. Xu, C. Wang, C. Du, and X. Luo, Opt. Express 16, 4753 (2008).
    [CrossRef] [PubMed]
  7. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, Opt. Express 15, 9541 (2007).
    [CrossRef] [PubMed]
  8. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
    [CrossRef]
  9. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
    [CrossRef]
  10. Z. Sun, Appl. Phys. Lett. 89, 261119 (2006).
    [CrossRef]
  11. S. Yin, C. Zhou, X. Luo, and C. Du, Opt. Express 16, 2578 (2008).
    [CrossRef] [PubMed]
  12. Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
    [CrossRef]
  13. D.R.Lide, ed., CRC Handbook of Chemistry and Physics, 88th ed. (CRC, 2007).
  14. P. Ruffieux, T. Scharf, H. P. Herzig, R. Völkel, and K. J. Weible, Opt. Express 14, 4687 (2006).
    [CrossRef] [PubMed]
  15. G. Veronis and S. Fan, Opt. Lett. 30, 3359 (2005).
    [CrossRef]
  16. G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
    [CrossRef]
  17. A detailed description of the three-dimensional FDFD method will be published elsewhere.
  18. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  19. C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, Opt. Express 16, 20457 (2008).
    [CrossRef] [PubMed]
  20. R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
    [CrossRef]
  21. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
    [CrossRef] [PubMed]
  22. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
    [CrossRef] [PubMed]

2009 (5)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
[CrossRef]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (5)

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, Opt. Express 15, 9541 (2007).
[CrossRef] [PubMed]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

S. Lal, S. Link, and N. J. Halas, Nat. Photonics 1, 641 (2007).
[CrossRef]

2006 (2)

2005 (2)

2004 (1)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Barnard, E.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, Opt. Express 16, 20457 (2008).
[CrossRef] [PubMed]

Deng, Y.

Dong, X.

Du, C.

Du, C. L.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Engheta, N.

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

Evans, P.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

G. Veronis and S. Fan, Opt. Lett. 30, 3359 (2005).
[CrossRef]

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

Fesenmaier, C. C.

Fu, Y.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Gao, H.

Gargas, D.

R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
[CrossRef]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, Nat. Photonics 1, 641 (2007).
[CrossRef]

Hendren, W.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Herzig, H. P.

Huo, Y.

Jiao, X.

Kabashin, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Kim, H. K.

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, Nat. Photonics 1, 641 (2007).
[CrossRef]

Lim, L. E. N.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Link, S.

S. Lal, S. Link, and N. J. Halas, Nat. Photonics 1, 641 (2007).
[CrossRef]

Luo, X.

Luo, X. G.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Min, C.

Ming, H.

Pastkovsky, S.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Podolskiy, V. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Ruffieux, P.

Scharf, T.

Shalaev, V. M.

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Shi, H.

Sun, Z.

Z. Sun, Appl. Phys. Lett. 89, 261119 (2006).
[CrossRef]

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Veronis, G.

G. Veronis and S. Fan, Opt. Lett. 30, 3359 (2005).
[CrossRef]

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

Völkel, R.

Wang, C.

Wang, P.

Weible, K. J.

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Wurtz, G. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Xu, T.

Yan, R.

R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
[CrossRef]

Yang, P.

R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
[CrossRef]

Yin, S.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Zayats, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Zhou, C.

Zhou, W.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

Z. Sun, Appl. Phys. Lett. 89, 261119 (2006).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, Appl. Phys. Lett. 91, 061124 (2007).
[CrossRef]

Nano Lett. (1)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Nat. Mater. (1)

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Nat. Photonics (3)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

S. Lal, S. Link, and N. J. Halas, Nat. Photonics 1, 641 (2007).
[CrossRef]

R. Yan, D. Gargas, and P. Yang, Nat. Photonics 3, 569 (2009).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Science (1)

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

Other (3)

D.R.Lide, ed., CRC Handbook of Chemistry and Physics, 88th ed. (CRC, 2007).

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

A detailed description of the three-dimensional FDFD method will be published elsewhere.

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Figures (4)

Fig. 1
Fig. 1

Metallic nanoscale pillar array for two-dimensional phase front design. The entire structure is on the order of the wavelength size and consists of an array of 11 by 11 unit cells with 400 nm tall gold pillars of variable base width (between 25 and 75 nm) in unit cells of 100 nm by 100 nm.

Fig. 2
Fig. 2

Basic building block for two-dimensional phase front design. (a) Real and imaginary parts of the effective index as a function of the base width s of the metal pillar. The inset shows the metal pillar, centered in the 100 nm by 100 nm unit cell. (b) Vector plot of the electric field in a unit cell with s = 65   nm .

Fig. 3
Fig. 3

Phase front design for wavelength-size metallic microlens. (a) Phase delay calculated analytically from Eq. (1). (b) Phase delay approximated by an array of unit cells. (c) Phase delay measured underneath the lens in a three-dimensional FDFD simulation.

Fig. 4
Fig. 4

Two-dimensional focusing in a microlens application. (a) Electric field intensity | E y | 2 for an x y cross section through the center of the lens structure (from Fig. 1). Real part of the E y field for an (b) x y and (c) x z cross section near the center of the lens structure. (d)–(f) Electric field intensity | E y | 2 for (d) x y , (e) y z , and (f) x z cross sections of the focal spot. Where necessary, the field intensities inside the gaps are saturated.

Equations (1)

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ϕ ( x , y ) = 2 π f λ 2 π f 2 + x 2 + y 2 λ ,

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