Abstract

This study investigates plasmonic Bloch oscillations (PBOs) in cylindrical metal–dielectric waveguide arrays (MDWAs) by performing numerical simulations and theoretical analyses. Optical conformal mapping is used to transform cylindrical MDWAs into equivalent chirped structures with permittivity and permeability gradients across the waveguide arrays, which is caused by the curvature of the cylindrical waveguide. The PBOs are attributed to the transformed structure. The period of oscillation increases with the wavelength of the incident Gaussian beam. However, the amplitude of oscillation is almost independent of wavelength.

© 2010 Optical Society of America

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    [CrossRef]
  2. C. M. de Sterke, J. E. Sipe, and L. A. Weller-Brophy, Opt. Lett. 16, 1141 (1991).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  18. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. J. A. Arnaud, Beam and Fiber Optics (Academic, 1976).
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    [CrossRef] [PubMed]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

2009 (4)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

2007 (3)

2006 (3)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

2004 (1)

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

1999 (3)

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

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

1991 (2)

1975 (1)

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

1929 (1)

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Agarwal, V.

V. Agarwal, J. A. de 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.

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Alekseyev, L. V.

Arnaud, J. A.

J. A. Arnaud, Beam and Fiber Optics (Academic, 1976).

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Brauer, A.

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

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Chan, C. T.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Coquillat, D.

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

Dannberg, P.

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

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

de Rio, J. A.

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

de Sterke, C. M.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

C. M. de Sterke, J. E. Sipe, and L. A. Weller-Brophy, Opt. Lett. 16, 1141 (1991).
[CrossRef] [PubMed]

Eisenberg, H. S.

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Elflein, W.

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

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Feng, Y.

Gil, B.

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

Harris, J. H.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Huang, Y.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Jacob, Z.

Jiang, T.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kavokin, A.

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

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Lederer, F.

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

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Lenz, G.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Lin, W.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Liu, Y.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

Malpuech, G.

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

Morandotii, R.

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Nenciu, G.

G. Nenciu, Rev. Mod. Phys. 63, 91 (1991).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Pertsch, T.

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

Peschel, U.

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Scalbert, D.

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

Schuring, D.

J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Silberberg, Y.

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Sipe, J. E.

Smith, D. R.

J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Talanina, I.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Vladimirova, M.

V. Agarwal, J. A. de 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, G. P.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Weller-Brophy, L. A.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Zamfirescu, M.

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

Zentgraf, T.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

Zhang, X.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

Zhou, X.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

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

Laser Photon. Rev. (1)

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

Nano Lett. (1)

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, Nano Lett. 10, 1991 (2010).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (6)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

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

R. Morandotii, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

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

Rev. Mod. Phys. (1)

G. Nenciu, Rev. Mod. Phys. 63, 91 (1991).
[CrossRef]

Science (2)

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schuring, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Z. Phys. (1)

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Other (1)

J. A. Arnaud, Beam and Fiber Optics (Academic, 1976).

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Figures (3)

Fig. 1
Fig. 1

Simulated structure in (a) x y coordinate system and (b) transformed u v coordinate system. Insets of (b), effective relative permittivity and permeability versus u for incident wavelength of 375 nm .

Fig. 2
Fig. 2

FDTD-simulated contours of magnetic field intensity | H | 2 and predicted ray trajectory (white line) in (a) x y coordinate system and (b) u v coordinate system. (c) Calculated equal- k v contours and predicted ray trajectory (white line) in k u P u space. Incident wavelength is 375 nm .

Fig. 3
Fig. 3

FDTD-simulated period and amplitude of oscillation against incident wavelength. Insets, predicted ray trajectories for incident wavelengths of 450 and 550 nm .

Equations (4)

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

u + i v = r c ln [ ( x + i y ) / r c ] .
cos [ k u ( a 1 + a 2 ) ] = cos ( k 1 a 1 ) cos ( k 2 a 2 ) ( ε m 2 μ m 2 k 1 2 + ε a 2 μ a 2 k 2 2 2 ε m μ m ε a μ a k 1 k 2 ) sin ( k 1 a 1 ) sin ( k 2 a 2 ) ,
H ( k u , k v , u ) = k v k v ( k u , u ) ,
d u d v = H ( k u , k v , u ) k u = k v ( k u , u ) k u , d k u d v = H ( k u , k v , u ) u = k v ( k u , u ) u .

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