Abstract

We show that light tunneling inhibition may take place in suitable dynamically modulated waveguide arrays for light spots whose features are remarkably smaller than the wavelength of light. We found that tunneling between neighboring waveguides can be suppressed for specific frequencies of the out-of-phase refractive index modulation, affording undistorted propagation of the input subwavelength light spots over hundreds of Rayleigh lengths. Tunneling inhibition turns out to be effective only when the waveguide separation in the array is above a critical threshold. Inclusion of a weak focusing nonlinearity is shown to improve localization. We analyze the phenomenon in purely dielectric structures and also in arrays containing periodically spaced metallic layers.

© 2013 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef]
  4. S. Longhi and K. Staliunas, Opt. Commun. 281, 4343 (2008).
    [CrossRef]
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    [CrossRef]
  6. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
    [CrossRef]
  7. F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
    [CrossRef]
  8. G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
    [CrossRef]
  9. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
    [CrossRef]
  10. R. Iyer, J. S. Aitchison, J. Wan, M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
    [CrossRef]
  11. G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. S. Longhi, Phys. Rev. A 71, 065801 (2005).
    [CrossRef]
  15. X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
    [CrossRef]
  16. K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  17. K. Staliunas and C. Masoller, Opt. Express 14, 10669 (2006).
    [CrossRef]
  18. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
    [CrossRef]
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    [CrossRef]
  20. P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
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  21. S. Longhi, Laser Photonics Rev. 3, 243 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
    [CrossRef]
  27. A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 79, 053812 (2009).
    [CrossRef]
  28. F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
    [CrossRef]

2012 (3)

2011 (1)

P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
[CrossRef]

2010 (1)

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

2009 (5)

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 79, 053812 (2009).
[CrossRef]

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

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Opt. Lett. 34, 2700 (2009).
[CrossRef]

2008 (2)

2007 (6)

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tünnermann, and Y. S. Kivshar, Opt. Express 15, 9737 (2007).
[CrossRef]

R. Iyer, J. S. Aitchison, J. Wan, M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
[CrossRef]

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
[CrossRef]

E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674 (2007).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

2006 (3)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas and C. Masoller, Opt. Express 14, 10669 (2006).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

2005 (1)

S. Longhi, Phys. Rev. A 71, 065801 (2005).
[CrossRef]

2003 (2)

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

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

2000 (1)

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

1991 (1)

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

1986 (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Aitchison, J. S.

R. Iyer, J. S. Aitchison, J. Wan, M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
[CrossRef]

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

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Ceballos-Herrera, D. E.

Chauvet, M.

Christodoulides, D. N.

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

Cianci, E.

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Davoyan, A. R.

de Sterke, C. M.

R. Iyer, J. S. Aitchison, J. Wan, M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
[CrossRef]

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

Dignam, M.

Dittrich, T.

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

Doering, S.

Dreisow, F.

Dunlap, D. H.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Eisenberg, H. S.

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

Fahr, S.

Feigenbaum, E.

Ferrando, A.

Foglietti, V.

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Garanovich, I. L.

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 79, 053812 (2009).
[CrossRef]

Grossman, F.

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

Hanggi, P.

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

Heinrich, M.

Herrero, R.

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Hizanidis, K.

P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
[CrossRef]

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Iyer, R.

Jung, P.

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

Kartashov, Y. V.

Keil, R.

Kenkre, V. M.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tünnermann, and Y. S. Kivshar, Opt. Express 15, 9737 (2007).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Kominis, Y.

P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
[CrossRef]

Krolikowski, W.

Laporta, P.

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Lederer, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Opt. Lett. 34, 2700 (2009).
[CrossRef]

F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008).
[CrossRef]

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

Lenz, G.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

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

S. Longhi and K. Staliunas, Opt. Commun. 281, 4343 (2008).
[CrossRef]

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

S. Longhi, Phys. Rev. A 71, 065801 (2005).
[CrossRef]

Luo, X.

X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
[CrossRef]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Masoller, C.

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Milián, C.

Morandotti, R.

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

Nazabal, V.

Neshev, D.

Nolte, S.

Orenstein, M.

Ornigotti, M.

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Papagiannis, P.

P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
[CrossRef]

Parker, R.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tünnermann, and Y. S. Kivshar, Opt. Express 15, 9737 (2007).
[CrossRef]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

Renversez, G.

Shadrivov, I. V.

Silberberg, Y.

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

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

Skryabin, D. V.

Staliunas, K.

S. Longhi and K. Staliunas, Opt. Commun. 281, 4343 (2008).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas and C. Masoller, Opt. Express 14, 10669 (2006).
[CrossRef]

Sukhorukov, A. A.

Szameit, A.

Torner, L.

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Opt. Lett. 34, 2700 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

Tuennermann, A.

Tunnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

Tünnermann, A.

Valle, G.

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Vysloukh, V. A.

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

A. Szameit, Y. V. Kartashov, M. Heinrich, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Opt. Lett. 34, 2700 (2009).
[CrossRef]

Walasik, W.

Wan, J.

Wanke, M. C.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

Wu, B.

X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
[CrossRef]

Xie, Q.

X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
[CrossRef]

Ye, F.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Zhang, X.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Laser Photonics Rev. (1)

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

Nature (1)

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

Opt. Commun. (2)

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

S. Longhi and K. Staliunas, Opt. Commun. 281, 4343 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Phys. Rep. (1)

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

Phys. Rev. A (4)

S. Longhi, Phys. Rev. A 71, 065801 (2005).
[CrossRef]

X. Luo, Q. Xie, and B. Wu, Phys. Rev. A 76, 051802(R) (2007).
[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, Phys. Rev. A 84, 013820 (2011).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 79, 053812 (2009).
[CrossRef]

Phys. Rev. B (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Phys. Rev. E (1)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (7)

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, F. Lederer, and L. Torner, Phys. Rev. Lett. 102, 153901 (2009).
[CrossRef]

G. Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

F. Grossman, T. Dittrich, P. Jung, and P. Hanggi, Phys. Rev. Lett. 67, 516 (1991).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef]

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

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

Transverse and longitudinal electric field distributions in linear modes supported (a) by the purely dielectric waveguide when εr(x)=εbg+pexp(x2/w2) for x/d(,+) and (b) by the dielectric waveguide sandwiched between semi-infinite metal layers when εr(x)=εbg+pexp(x2/w2) for |x/d|0.464 and εr(x)=εm for |x/d|>0.464.

Fig. 2.
Fig. 2.

Evolution of the modulus of the transverse Ex (top row) and longitudinal Ez (bottom row) electric field components for modulation frequencies (a) ωz/ωb=0; (b) ωz/ωb=7.4; (c) ωz/ωb=3.19; and (d) ωz/ωb=6. In all cases the propagation distance is 200 μm, while the transverse width of the depicted window is 7.7 μm.

Fig. 3.
Fig. 3.

(a) Distance-averaged power in the excited waveguide versus ωz/ωb in the linear waveguide array; (b) Uav versus ωz/ωb at δnnl=0 (curve 1) and δnnl=0.0025 (curve 2); and (c) width of the primary resonance as a function of the nonlinear contribution to the refractive index. In all cases, z=200μm.

Fig. 4.
Fig. 4.

Evolution of |Ex| (top row) and |Ez| (bottom row) upon propagation in the nonlinear modulated waveguide array for δnnl=0 (a), δnnl=0.00063 (b), δnnl=0.00188 (c), and δnnl=0.00301 (d). In all cases ωz/ωb=6.7, while the transverse and longitudinal scales are the same as in Fig. 2.

Fig. 5.
Fig. 5.

(a) Maximal distance-averaged power and (b) primary resonance frequency, versus separation between waveguides. In all cases the propagation distance is z=200μm. Dashed line corresponds to separation used in Figs. 14.

Fig. 6.
Fig. 6.

Inhibition of tunneling in dielectric-metal waveguide arrays. The top row shows |Ex|, while the bottom row shows |Ez|. (a) Unmodulated array, (b) modulated array with ωz/ωb=2.09 without losses in the metal, (c) modulated array with losses in the metal, and (d) modulated array with ωz/ωb=3. In all cases, the propagation distance is 50 μm, while the transverse width of the depicted window is 7.7 μm.

Equations (2)

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iExz=1ε0ωx(1εrHyx)μ0ωHy,iHyz=ε0εrωEx,
Uav=(UL)10Ldzd/2+d/2(|Ex(x,z)|2+|Ez(x,z)|2)dx,U=d/2+d/2(|Ex(x,0)|2+|Ez(x,0)|2)dx,

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