Abstract

Propagation of surface plasmon polaritons (SPPs) through a set of nanoscale metal waveguide arrays (MWGAs) is numerically simulated by using the finite-difference time-domain method. The results reveal that MWGAs show an interesting lens effect on SPPs: SPPs can be strongly focused or defocused by the MWGAs, which we attribute to anomalous coupling of SPPs in MWGAs. Our results imply interesting potential for MWGAs in, for example, nonlinear optics, optical imaging, and nanosensing.

© 2006 Optical Society of America

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2004 (4)

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

B. Wang and G. P. Wang, Appl. Phys. Lett. 85, 3599 (2004).
[CrossRef]

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, Opt. Lett. 29, 1992 (2004).
[CrossRef] [PubMed]

2003 (4)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

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

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

2002 (3)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, and G. Pennelli, J. Opt. Soc. Am. B 19, 2938 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (4)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 86, 3966 (2000).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1999 (1)

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

1998 (4)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

C. Z. Zao, Semiconductor Guided-Wave Optical Devices Theory and Technology (National Defense Industry Press, 1998).

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

1994 (1)

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1991 (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

1989 (1)

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

1988 (2)

1985 (1)

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

1983 (1)

H. Haus and L. Molter-Orr, IEEE J. Quantum Electron. 19, 840 (1983).
[CrossRef]

Agarwal, V.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Arnold, J. M.

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Barnes, W. L.

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

Berenger, J. P.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Coquillat, D.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

del Rio, J. A.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Dereux, A.

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

Ebbesen, T. W.

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

Eisenberg, H. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, and G. Pennelli, J. Opt. Soc. Am. B 19, 2938 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Enoch, S.

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Gil, B.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Gralak, B.

Haus, H.

H. Haus and L. Molter-Orr, IEEE J. Quantum Electron. 19, 840 (1983).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Kavokin, A.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Kim, H. K.

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

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Malpuech, G.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Molter-Orr, L.

H. Haus and L. Molter-Orr, IEEE J. Quantum Electron. 19, 840 (1983).
[CrossRef]

Morandotti, R.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, and G. Pennelli, J. Opt. Soc. Am. B 19, 2938 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 86, 3966 (2000).
[CrossRef]

Pennelli, G.

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Raether, H.

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

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Scalbert, D.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, and G. Pennelli, J. Opt. Soc. Am. B 19, 2938 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Sun, Z.

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

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Tanaka, K.

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

Tayeb, G.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Vladimirova, M.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Wang, B.

B. Wang and G. P. Wang, Opt. Lett. 29, 1992 (2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, Appl. Phys. Lett. 85, 3599 (2004).
[CrossRef]

Wang, G. P.

B. Wang and G. P. Wang, Appl. Phys. Lett. 85, 3599 (2004).
[CrossRef]

B. Wang and G. P. Wang, Opt. Lett. 29, 1992 (2004).
[CrossRef] [PubMed]

Zamfirescu, M.

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

Zao, C. Z.

C. Z. Zao, Semiconductor Guided-Wave Optical Devices Theory and Technology (National Defense Industry Press, 1998).

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

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

B. Wang and G. P. Wang, Appl. Phys. Lett. 85, 3599 (2004).
[CrossRef]

K. Tanaka and M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. Haus and L. Molter-Orr, IEEE J. Quantum Electron. 19, 840 (1983).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (3)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

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

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003), and references therein.
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. B (3)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Phys. Rev. Lett. (7)

J. B. Pendry, Phys. Rev. Lett. 86, 3966 (2000).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Other (5)

C. Z. Zao, Semiconductor Guided-Wave Optical Devices Theory and Technology (National Defense Industry Press, 1998).

As its dielectric counterparts, there are also symmetric and asymmetric models exist (represented by ?s and ?a, respectively) in two coupled metal waveguides. However, in coupled metal waveguides ?a>?s. Thus following the definition of the coupling coefficient of two coupled waveguides, C=??/2=(?s??a)/2, the coupling coefficient of the coupled metal waveguides is negative.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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

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Figures (3)

Fig. 1
Fig. 1

(a) Scheme of the MWGAs structure. The H y 2 distribution of SPPs in the MWGA is shown for a light source placed (b) on the input facet and (c) 250 nm from the input facet of the MWGA. (d) Normalized intensity profiles of the light source (dashed curve) and the SPP field at the focusing spot (solid curve) in (c).

Fig. 2
Fig. 2

(a) Propagation direction and (b) phase wavefront of H y 2 of the incident light beam and SPPs in a MWGA. (c), (d) Relation between the propagation direction and the phase wavefront of the SPPs in a MWGA as in Figs. 1b, 1c, respectively.

Fig. 3
Fig. 3

(a), (d) Schemes of the MWGA structures with a curved input facet and (b), (e) their SPP field intensity distributions. (a), (b) Concave and (d), (e) convex input facets. (c) Normalized H y 2 distribution profiles of the light source (dashed curve) and the SPP field at the focusing spot (solid curve) of (b).

Equations (2)

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i d a n ( z ) d z + C [ a n 1 ( z ) + a n + 1 ( z ) ] = 0 ,
γ = 2 C sin ( κ 0 ) ,

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