Abstract

We utilize three diffraction theories to investigate the focal-shift phenomena of plasmonic lenses. By taking the Fresnel number into account, a better accuracy in predicting the relative focal shift can be achieved for low-Fresnel-number systems. On the basis of this focal-shift effect, we present a method to realize an active plasmonic lens. Two-dimensional finite-difference time-domain simulation is performed to verify the method proposed.

© 2012 Optical Society of America

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  2. S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
    [CrossRef]
  3. S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
    [CrossRef]
  4. Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
    [CrossRef]
  5. Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
    [CrossRef]
  6. S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
    [CrossRef]
  7. G.-G. Zheng and X.-Y. Li, J. Opt. A 11, 075002 (2009).
    [CrossRef]
  8. N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
    [CrossRef]
  9. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
    [CrossRef]
  10. F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
    [CrossRef]
  11. X. M. Goh, L. Lin, and A. Roberts, Opt. Express 18, 11683 (2010).
    [CrossRef]
  12. M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
    [CrossRef]
  13. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
    [CrossRef]
  14. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
    [CrossRef]
  15. H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
    [CrossRef]
  16. P. Ruffieux, T. Scharf, H. P. Herzig, R. Völkel, and K. J. Weible, Opt. Express 14, 4687 (2006).
    [CrossRef]
  17. Y. Yu and H. Zappe, Opt. Express 19, 9434 (2011).
    [CrossRef]
  18. Y. Li and E. Wolf, Opt. Commun. 39, 211 (1981).
    [CrossRef]
  19. Y. Li, J. Opt. Soc. Am. 72, 770 (1982).
    [CrossRef]
  20. S. Szapiel, Opt. Lett. 8, 327 (1983).
    [CrossRef]
  21. Y. Li, J. Mod. Opt. 38, 1815 (1991).
    [CrossRef]
  22. Y. Li, J. Opt. Soc. Am. A 20, 234 (2003).
    [CrossRef]
  23. A. E. Çetin, K. Güven, and Ö. E. Müstecaplioğlu, Opt. Lett. 35, 1980 (2010).
    [CrossRef]

2011

2010

X. M. Goh, L. Lin, and A. Roberts, Opt. Express 18, 11683 (2010).
[CrossRef]

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

A. E. Çetin, K. Güven, and Ö. E. Müstecaplioğlu, Opt. Lett. 35, 1980 (2010).
[CrossRef]

2009

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

S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
[CrossRef]

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

G.-G. Zheng and X.-Y. Li, J. Opt. A 11, 075002 (2009).
[CrossRef]

2008

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

2007

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

2006

2005

2004

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

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Y. Li, J. Opt. Soc. Am. A 20, 234 (2003).
[CrossRef]

1991

Y. Li, J. Mod. Opt. 38, 1815 (1991).
[CrossRef]

1983

1982

1981

Y. Li and E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

Barnard, E. S.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Brantley, C.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Brongersma, M. L.

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

Çetin, A. E.

Chang, Y.-C.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Chen, M.-K.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Chen, Y.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Dong, X.

Du, C.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Edwards, E.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Fan, S.

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

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Fedotov, V. A.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Fu, Y.

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

Gao, H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef]

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

X. M. Goh, L. Lin, and A. Roberts, Opt. Express 18, 11683 (2010).
[CrossRef]

Guo, Y.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Güven, K.

Halas, N. J.

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

Herzig, H. P.

Huang, F. M.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Hyun, J. K.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

Inouye, Y.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
[CrossRef]

Kao, T. S.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Kawata, S.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
[CrossRef]

Kim, H.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Kim, H. K.

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

Kim, S.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Lal, S.

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

Lauhon, L. J.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

Lee, B.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Lee, M. H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

Li, X.-Y.

G.-G. Zheng and X.-Y. Li, J. Opt. A 11, 075002 (2009).
[CrossRef]

Li, Y.

Y. Li, J. Opt. Soc. Am. A 20, 234 (2003).
[CrossRef]

Y. Li, J. Mod. Opt. 38, 1815 (1991).
[CrossRef]

Y. Li, J. Opt. Soc. Am. 72, 770 (1982).
[CrossRef]

Y. Li and E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

Lim, Y.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Lin, L.

X. M. Goh, L. Lin, and A. Roberts, Opt. Express 18, 11683 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Link, S.

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

Luo, C.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Luo, X.

Mazurowski, J.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Mote, R. G.

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

Müstecaplioglu, Ö. E.

Odom, T. W.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

Park, J.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

X. M. Goh, L. Lin, and A. Roberts, Opt. Express 18, 11683 (2010).
[CrossRef]

Ruffieux, P.

Ruffin, P.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Scharf, T.

Shi, H.

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Sun, Z.

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

Szapiel, S.

Verma, P.

S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
[CrossRef]

Verslegers, L.

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

Völkel, R.

Wang, C.

Wang, Q.

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

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, Nano Lett. 9, 235 (2009).
[CrossRef]

Wolf, E.

Y. Li and E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

Yang, C.-E.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Yang, J.-C.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

Yin, S.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Yu, Y.

Yu, Z.

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

Zappe, H.

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Zheludev, N. I.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Zheng, G.-G.

G.-G. Zheng and X.-Y. Li, J. Opt. A 11, 075002 (2009).
[CrossRef]

Zhou, W.

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

Appl. Phys. Lett.

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

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

J. Mod. Opt.

Y. Fu, R. G. Mote, Q. Wang, and W. Zhou, J. Mod. Opt. 56, 1550 (2009).
[CrossRef]

Y. Li, J. Mod. Opt. 38, 1815 (1991).
[CrossRef]

J. Opt. A

G.-G. Zheng and X.-Y. Li, J. Opt. A 11, 075002 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Microw. Opt. Technol. Lett.

M.-K. Chen, Y.-C. Chang, C.-E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Nano Lett.

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

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, Nano Lett. 10, 4111 (2010).
[CrossRef]

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2469 (2008).
[CrossRef]

Nat. Photon.

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

S. Kawata, Y. Inouye, and P. Verma, Nat. Photon. 3, 388 (2009).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Opt. Commun.

Y. Li and E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

Opt. Express

Opt. Lett.

Science

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic focusing diagram when a plane wave propagates through a plasmonic lens composed of an array of nanoslits with variable widths.

Fig. 2.
Fig. 2.

Recalculation of the focal lengths considering the focal-shift effect using the three diffraction theories aforementioned, compared with the 2D FDTD simulation results (stars). The plasmonic lenses are f_3 (black) and f_5 (red), whose details can be found in Fig. 3, and in Tables 2 and 3 in Yu and Zappe [17]. The Fresnel numbers for f_3 are 0.67, 1.40, 2.19, and 2.93, respectively, and for f_5, they are 0.69, 1.71, 2.95, and 4.51, respectively.

Fig. 3.
Fig. 3.

Schematic of the active plasmonic lens with the microtunable pinhole in front of the plasmonic lens. The plasmonic lens is designed for a focal length of 5 μm. The nanoslits are symmetric about the x axis and have a width sequence (from y=0): 40, 40, 40, 45, 45, 50, 55, 65, 80, 115, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 25, 30, 35, 45, 65, 150, 15, 15, 15, 20, 20, 25, 35, 45 nm. All the gold walls are 80 nm in width.

Fig. 4.
Fig. 4.

2D FDTD simulation results of electric-field intensity for different w of the microtunable pinhole.

Fig. 5.
Fig. 5.

Simulation results of focal length for varying structural parameters.

Equations (3)

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

Δff=12(1+1/8γ2)π2N2×{1exp[π2N212(1+1/8γ2)11+N(11/16γ2)]},
Δff=(1+6/(γ12σT)1)/(1+6/(γ12σT)+2),
Δff=(1+N×1+(π2N/12)cc)1,

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