Abstract

We report polarization tomography experiments on metallic nanohole arrays with square and hexagonal symmetry. As a main result we find that a fully polarized input beam is partly depolarized after transmission through a nanohole array. This loss of polarization coherence is found to be anisotropic; i.e., it depends on the polarization state of the input beam. The depolarization is ascribed to a combination of two factors: (i) the nonlocal response of the array as a result of surface-plasmon propagation and (ii) the non-plane-wave nature of a practical input beam.

© 2005 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [CrossRef]
  2. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
    [CrossRef]
  3. H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  4. J. Elliott, I. I. Smolyaninov, N. I. Zheludev, and A. V. Zayats, Opt. Lett. 29, 1414 (2004).
    [CrossRef] [PubMed]
  5. K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
    [CrossRef]
  6. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
    [CrossRef]
  7. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  8. F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
    [CrossRef]
  9. C. Genet, E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Depolarization induced by subwavelength metal hole arrays,” November28, 2003, arXiv:physics/0311137, http://xxx.lanl.gov .
  10. E. Altewischer, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. B 20, 1927 (2003).
    [CrossRef]
  11. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
    [CrossRef]
  12. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
    [CrossRef]
  13. E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
    [CrossRef] [PubMed]
  14. E. Altewischer, M. P. van Exter, and J. P. Woerdman are preparing a manuscript to be called “Analytic model of optical depolarization in square and hexagonal nanohole arrays.”

2004 (3)

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

J. Elliott, I. I. Smolyaninov, N. I. Zheludev, and A. V. Zayats, Opt. Lett. 29, 1414 (2004).
[CrossRef] [PubMed]

2003 (2)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. B 20, 1927 (2003).
[CrossRef]

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

2002 (1)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

1997 (1)

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Ahn, Y. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Altewischer, E.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. B 20, 1927 (2003).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
[CrossRef] [PubMed]

E. Altewischer, M. P. van Exter, and J. P. Woerdman are preparing a manuscript to be called “Analytic model of optical depolarization in square and hexagonal nanohole arrays.”

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Brolo, A. G.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Ebbesen, T. W.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Elliott, J.

Enoch, S.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

Ghaemi, H. F.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Gordon, R.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Hohng, S. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Kavanagh, K. L.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Kim, D. S.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Kim, J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Koerkamp, K. J. K.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

Kuipers, L.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

Le Jeune, B.

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Le Roy-Brehonnet, F.

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Leathem, B.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Lezec, H. J.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Lienau, C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Malyarchuk, V.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

McKinnon, A.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Park, J. W.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Park, Q. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

Rajora, A.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

Segerink, F. B.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

Smolyaninov, I. I.

Thio, T.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

van Exter, M. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. B 20, 1927 (2003).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
[CrossRef] [PubMed]

E. Altewischer, M. P. van Exter, and J. P. Woerdman are preparing a manuscript to be called “Analytic model of optical depolarization in square and hexagonal nanohole arrays.”

van Hulst, N. F.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

Woerdman, J. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. B 20, 1927 (2003).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
[CrossRef] [PubMed]

E. Altewischer, M. P. van Exter, and J. P. Woerdman are preparing a manuscript to be called “Analytic model of optical depolarization in square and hexagonal nanohole arrays.”

Wolff, P. A.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, J. Opt. Soc. Am. B 16, 1743 (1999).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Yee, K. J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Yoon, Y. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Zayats, A. V.

Zheludev, N. I.

J. Opt. Soc. Am. B (2)

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

E. Altewischer, M. P. van Exter, and J. P. Woerdman, Nature 418, 304 (2002).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (1)

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, Phys. Rev. B 58, 6779 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, Phys. Rev. Lett. 92, 037401 (2004).?Unfortunately, the authors employed the word “depolarization” in an improper way, using it to describe a change of a spatially uniform SOP.
[CrossRef]

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Prog. Quantum Electron. (1)

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Other (4)

C. Genet, E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Depolarization induced by subwavelength metal hole arrays,” November28, 2003, arXiv:physics/0311137, http://xxx.lanl.gov .

E. Altewischer, M. P. van Exter, and J. P. Woerdman are preparing a manuscript to be called “Analytic model of optical depolarization in square and hexagonal nanohole arrays.”

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

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Figures (2)

Fig. 1
Fig. 1

Transmission spectra of nanohole arrays under almost plane-wave illumination at normal incidence for the square and hexagonal array. The dashed vertical line indicates the resonance wavelength of 810 nm used in the experiments. The insets show scanning electron-beam micrographs of the arrays, with 2µm-scale bars.

Fig. 2
Fig. 2

Diagonal elements Mii of the Mueller matrix, normalized to M00, as a function of the NA of the incident light beam on the (a) square and (b) hexagonal hole array. Squares, M11; triangles, M22; circles, M33; dashed vertical lines indicate the NAs at which the full Mueller matrices were measured (see Table 1).

Tables (1)

Tables Icon

Table 1 Mueller Matrices Measured Under Four Different Conditionsa

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