Abstract

We investigate the focusing effect on circularly distributed planar tapered plasmonic waveguides by means of three-dimensional (3D) finite elements simulations. The proposed configuration allows nanofocusing on four faced planar nanotips, showing efficient condensation of surface plasmons polaritons (SPPs) at the silver/air interface toward the endpoint of the tips. By means of a plasmonic vortex lens it is possible to illuminate the tips with SPP waves carrying orbital angular momentum (OAM), namely plasmonic vortices. Our 3D simulations show that by acting on the topological charge of the plasmonic vortex the electric field charge distribution at the tips apex can be controlled accordingly to the input electric field phase distribution. The results for three particular OAM values are shown, along with a generalization for arbitrary plasmonic vortex angular momentum values.

© 2012 Optical Society of America

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    [CrossRef]
  2. S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).
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    [CrossRef]
  4. K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
    [CrossRef]
  5. Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
    [CrossRef]
  6. H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
    [CrossRef]
  7. L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
    [CrossRef]
  8. N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
    [CrossRef]
  9. S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, Opt. Lett. 34, 3047 (2009).
    [CrossRef]
  10. S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
    [CrossRef]
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    [CrossRef]
  12. P. Zilio, E. Mari, G. Parisi, F. Tamburini, and F. Romanato, Opt. Lett. 37, 3234 (2012).
    [CrossRef]
  13. D. K. Gramotnev and M. W. Vogel, Phys. Lett. A 375, 3464 (2011).
    [CrossRef]
  14. E. Verhagen, A. Polman, and L. Kuipers, Opt. Express 16, 45 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (3)

2011 (3)

2010 (2)

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

2009 (3)

S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, Opt. Lett. 34, 3047 (2009).
[CrossRef]

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

2008 (3)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

E. Verhagen, A. Polman, and L. Kuipers, Opt. Express 16, 45 (2008).
[CrossRef]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2005 (1)

R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).
[CrossRef]

2001 (1)

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Adam, A. J. L.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

Bretner, I.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Brok, J. M.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

Brongersma, M. L.

R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Chen, W.

Cho, S.-W.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Dereux, A.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Desiatov, B.

Gorodetski, Y.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

Goudonnet, J. P.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Goykhamn, I.

Gramotnev, D. K.

D. K. Gramotnev and M. W. Vogel, Phys. Lett. A 375, 3464 (2011).
[CrossRef]

Hasman, E.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

Hasman, H.

N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

He, X.

Kang, M.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Kim, H.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Kleiner, V.

N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

Krenn, J. R.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Kuipers, L.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

E. Verhagen, A. Polman, and L. Kuipers, Opt. Express 16, 45 (2008).
[CrossRef]

Lacroute, Y.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Lamprecht, B.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Lee, B.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Lee, S.-Y.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Levy, U.

Maier, S. A.

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Mari, E.

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Nechayev, S.

N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Nelson, R. L.

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Parisi, G.

Park, J.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, Opt. Express 20, 10083 (2012).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Planken, P. C. M.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

Polman, A.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

E. Verhagen, A. Polman, and L. Kuipers, Opt. Express 16, 45 (2008).
[CrossRef]

Romanato, F.

Selker, M. D.

R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Shitrit, N.

N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Spasenovic, M.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

Spreew, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Tamburini, F.

Urbach, H. P.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

Verhagen, E.

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

E. Verhagen, A. Polman, and L. Kuipers, Opt. Express 16, 45 (2008).
[CrossRef]

Vogel, M. W.

D. K. Gramotnev and M. W. Vogel, Phys. Lett. A 375, 3464 (2011).
[CrossRef]

Vuong, L. T.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

Weeber, J. Cs.

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yang, L.

Yang, S.

Yang, T.

Zhan, Q.

Zia, R.

R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Zilio, P.

Nano Lett. (3)

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

N. Shitrit, S. Nechayev, V. Kleiner, and H. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Lett. A (1)

D. K. Gramotnev and M. W. Vogel, Phys. Lett. A 375, 3464 (2011).
[CrossRef]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. B (2)

R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).
[CrossRef]

J. Cs. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, Phys. Rev. B 64, 045411 (2001).
[CrossRef]

Phys. Rev. Lett. (5)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef]

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, Phys. Rev. Lett. 104, 083903 (2010).
[CrossRef]

E. Verhagen, M. Spasenovic, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef]

Other (1)

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

PVL consists of m Archimedes’ spiral grooves milled in a 170 nm silver film on glass substrate, while at the center four silver planar rounded nanotips of thickness 70 nm are grown on a silver disk of thickness 100 nm in order to avoid direct nanotips illumination from the incoming radiation (λ=633nm). The refractive index of silver is nAg=0.13+i3.8. Inset: the tip base is curved. The tip is r=3.1μm in length, while the tip angle value is set to 12°. The PVL groove period for SPP coupling at silver/air interface is 617 nm with duty cycle of 50%.

Fig. 2.
Fig. 2.

Red line: SPP mode behavior for a silver stripe waveguide on a silver substrate for different widths value (w) for λ=633nm. The silver thickness is s=100nm. (a) Electric field intensity of the bound mode at silver/air interface for w=680nm. (b) Electric field intensity for single nanotip. The focusing effect is shown at silver/air interface. Color scale is saturated for better field visualization.

Fig. 3.
Fig. 3.

Intensity of the electric field for the structure of Fig. 1 illuminated with a PV with lPV=0. Lower inset shows the boundary mode used as input source. Color scale is saturated for better field visualization.

Fig. 4.
Fig. 4.

Color scale (a.u.) represents transverse electric field component Ez for lPV=1. Red arrows indicate the in plane electric field (Ex and Ey). Upper inset shows the boundary mode used as input source. (a) Charge distribution at T=0. (b) Charge distribution at T/4 time later.

Fig. 5.
Fig. 5.

Color scale (a.u.) represents transverse electric field component Ez for lPV=2. Red arrows indicate the in plane electric field (Ex and Ey). Upper inset shows the boundary mode used as input source. (a) Charge distribution at T=0. (b) Charge distribution at T/2 time later.

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