Abstract

We predict multiband vector plasmonic lattice solitons (PLSs) in metal–dielectric waveguide arrays, in both focusing and defocusing nonlinearities. Such vector solitons consist of two components originating from different transmission bands. By simulating the full nonlinear Maxwell’s equations, we demonstrate the diffractionless propagation of vector PLSs and their discrete diffraction when only one component is present. Their subwavelength size characteristics and the influences of metallic losses are also studied.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. S. H. Nam, A. J. Taylor, and A. Efimov, Opt. Express 18, 10120 (2010).
    [CrossRef]
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    [CrossRef]

2012

2011

2010

2009

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

2007

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

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

2006

2003

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

2001

A. Moroz, A. Tip, and J. M. Combes, Synth. Met. 116, 481 (2001).
[CrossRef]

1997

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

1988

1972

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Agrawal, G.

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

Aitchison, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Bartal, G.

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

Belov, P. A.

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Ceballos-Herrera, D. E.

Chauvet, M.

Chen, X.

Y. Kou, F. Ye, and X. Chen, Opt. Lett. 37, 3822 (2012).
[CrossRef]

Y. Kou, F. Ye, and X. Chen, Phys. Rev. A 84, 033855 (2011).
[CrossRef]

Christodoulides, D.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

D. Christodoulides and R. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef]

Christodoulides, D. N.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Combes, J. M.

A. Moroz, A. Tip, and J. M. Combes, Synth. Met. 116, 481 (2001).
[CrossRef]

Coskun, T. H.

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Efimov, A.

Feigenbaum, E.

Ferrando, A.

C. Milián, D. E. Ceballos-Herrera, D. V. Skryabin, and A. Ferrando, Opt. Lett. 37, 4221 (2012).
[CrossRef]

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Genov, D. A.

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

Gorbach, A. V.

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Opt. Lett. 36, 1179 (2011).
[CrossRef]

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

Hudock, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Iorsh, I. V.

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Joseph, R.

Kartashov, Y.

Kartashov, Y. V.

Kivshar, Y.

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

Kivshar, Y. S.

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Kou, Y.

Y. Kou, F. Ye, and X. Chen, Opt. Lett. 37, 3822 (2012).
[CrossRef]

Y. Kou, F. Ye, and X. Chen, Phys. Rev. A 84, 033855 (2011).
[CrossRef]

Liu, Y.

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

Marini, A.

Meier, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Opt. Lett. 36, 1179 (2011).
[CrossRef]

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

Milián, C.

Mitchell, M.

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Morandotti, R.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Moroz, A.

A. Moroz, A. Tip, and J. M. Combes, Synth. Met. 116, 481 (2001).
[CrossRef]

Nam, S. H.

Nazabal, V.

Orenstein, M.

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Opt. Lett. 36, 1179 (2011).
[CrossRef]

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

Renversez, G.

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

Segev, M.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Shadrivov, I. V.

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

Silberberg, Y.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Skryabin, D. V.

Stegeman, G.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Taylor, A. J.

Tip, A.

A. Moroz, A. Tip, and J. M. Combes, Synth. Met. 116, 481 (2001).
[CrossRef]

Torner, L.

Walasik, W.

Ye, F.

Zhang, X.

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

Zharov, A. A.

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

I. V. Iorsh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. A 86, 023819 (2012).
[CrossRef]

Y. Kou, F. Ye, and X. Chen, Phys. Rev. A 84, 033855 (2011).
[CrossRef]

Phys. Rev. B

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett.

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

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

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef]

Synth. Met.

A. Moroz, A. Tip, and J. M. Combes, Synth. Met. 116, 481 (2001).
[CrossRef]

Other

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Bandgap structure of the plasmonic lattice. tm=50nm, td=240nm. The solid (open) circles represent the location of self-focusing (defocusing) PLSs. (b) Bandgap spectrum versus metallic layer thickness tm, for td=240nm, λ=1550nm. The inset is a sketch of the present system. (c)–(f) Bloch waves (Ex). The gray (white) regions stand for metallic (dielectric) layers.

Fig. 2.
Fig. 2.

(a), (b) Normalized electric field profiles of the self-focusing vector PLSs for td=240nm, tm=50nm, Δn1=Δn2=0.025, λ1=1310nm, λ2=1550nm. (c) Soliton effective diameter versus Δn1, for Δn2=0.025. (d) Propagation length versus Δn1, for Δn2=0.025.

Fig. 3.
Fig. 3.

(a), (b) Propagation of vector PLSs in lossless plasmonic lattices. (c), (d) Propagation of single component when the other is switched off. (e), (f) Propagation in real (lossy) plasmonic lattices. The first (second) row of panels corresponds to the Component 1 (Component 2).

Fig. 4.
Fig. 4.

(a), (b) Normalized electric field (Ex) profiles of the self-defocusing vector PLSs for td=240nm, tm=50nm, Δn1=Δn2=0.025, λ1=1310nm, and λ2=1550nm. (c), (d) Propagation of the same modes in real (lossy) plasmonic lattices.

Equations (3)

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

k0,mεNLz0um=βmvm,
z0[ddx(1εNLddx)+1]vm=βmk0,mum,
εNL=nNL2=[nlinear,m+n2·m(|Ex,m2|+|Ez,m2|)]2.

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