Abstract

We performed three-dimensional finite elements simulations of the optical response of holey plasmonic vortex lenses, i.e., spiral grooves milled on a thin gold film with a hole at the center. We focus in particular on the properties of the wave transmitted in the underlying half-space, which is shown to be a relevant part of the transmitted field. We find out that the angular momentum selection rule for this part of the field is different from the one for the transmitted plasmonic vortex, although closely related to the plasmonic interaction of the impinging wave with the chiral geometry.

© 2012 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. Spreew, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).
  3. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
    [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]
  11. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  12. E. D. Palik, Handbook of Optical Constants of Solids(Elsevier, 1998).
  13. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  14. S. M. Barnett, J. Opt. B 4, S7 (2002).
    [CrossRef]

2012 (2)

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

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

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 (2)

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]

2008 (2)

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]

2006 (1)

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

2002 (1)

S. M. Barnett, J. Opt. B 4, S7 (2002).
[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]

Barnett, S. M.

S. M. Barnett, J. Opt. B 4, S7 (2002).
[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]

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]

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]

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]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

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]

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]

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]

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]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Elsevier, 1998).

Paparo, D.

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

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]

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]

Spreew, R. J.

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

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]

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]

Woerdman, J. P.

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

Yang, S.

Zhan, Q.

J. Opt. B (1)

S. M. Barnett, J. Opt. B 4, S7 (2002).
[CrossRef]

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 (1)

Opt. Lett. (1)

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. Lett. (4)

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]

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

Other (3)

E. D. Palik, Handbook of Optical Constants of Solids(Elsevier, 1998).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

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

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of the gold plasmonic vortex lenses considered, i.e., a 2-PVL and a 0-PVL (bull’s eye structure). Laguerre–Gaussian beams coaxial with the structure are set as illumination (the red curve is a scheme of the intensity profile). In the presented simulations r0 is set to 3 μm, groove width and depth are, respectively, 360 nm and 30 nm. The maximal value of the azimuthal angle ϕ considered in Eq. (1) is 4π.

Fig. 2.
Fig. 2.

Field distributions in the central part (radius lower than 3 μm) of a 0-PVL illuminated by an LG beam with li=4 and si=1. Hole diameter is d=800nm. Ez and Ex are reported in a (a) y-z cross section and in (b) x-y cross sections located (c) 200 nm and (d) 1.7 μm under the hole [positions are marked with dashed lines in (a) and (b)]. Insets show Ez and Ex fields in an x-y cross section located in the mid of the gold film. All field values are normalized to max(|Ez|).

Fig. 3.
Fig. 3.

arg(Ez) and arg(Ex) in x-y cross sections under the hole (d=800nm), as in Fig. 2, in case of an LG beam with li=4 and si=±1 impinging on a 0-PVL (bull’s eye).

Fig. 4.
Fig. 4.

Ez and Ex and their phases for LG beam with li=4, si=1 impinging on an (a)–(d) m=2 PVL and on a (e)–(h) m=2 PVL. Hole diameter is d=1.2μm, x-y cross sections positions as in Fig. 2.

Equations (6)

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

rm(ϕ)=r0+m·λSPP·ϕ,
Ez,lPV(r,ϕ)JlPV(kSPPr)exp(ilPVϕ),
lPV=m+li+si.
Ex=α0kdκE(κ)exp(ilfϕ+ik2κ2z)Jlf(κr),Ey=β0kdκE(κ)exp(ilfϕ+ik2κ2z)Jlf(κr),Ez=0kdκE(κ)exp(ilfϕ+ik2κ2z)Jlf(κr)×(κ/2k2κ2)·[(iαβ)exp(iϕ)Jlf1(κr)(iα+β)exp(+iϕ)Jlf+1(κr)],
sf=i(αβ*α*β)
lf=jsgn(j)=lPVsgn(lPV)=m+li+sisgn(m+li+si).

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