Abstract

We have performed a theoretical study of various arrangements of one-dimensional heterostructures composed by bilayers made of nondispersive (A)/dispersive linear (B) materials and illuminated by an obliquely incident electromagnetic wave, which are shown to exhibit a robust bulk-like plasmon-polariton gap for frequencies below the plasma frequency. The origin of this gap stems from the coupling between photonic and plasmonic modes that may be of a magnetic (electric) origin in a transversal electric (traversal magnetic) configuration yielding a plasmon-polariton mode. By substituting the nondispersive linear layer by a nonlinear Kerr layer, we have found that, for frequencies close to the edge of the plasmon-polariton gap, the transmission of a finite superlattice presents a multistable behavior and it switches from very low values to the maximum transparency at particular values of the incident power. At these frequencies, for those singular points where transmission becomes maximum, we find localized plasmon-polariton-gap solitons of various orders depending on the particular value of the incident power. Present results reveal, therefore, new gap plasmon-soliton solutions that are hybrid modes stemming from the resonant coupling between the incoming electromagnetic wave and the plasmonic modes of the dispersive material, leading to the transparency of a stack with nonlinear inclusions.

© 2013 Optical Society of America

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. N. I. Zheludev, 2010 Science 328, 582 (2010).
    [CrossRef]
  3. A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
    [CrossRef]
  4. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
    [CrossRef]
  5. A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
    [CrossRef]
  6. N. I. Zheludev, Opt. Photon. News 22(3), 30 (2011).
    [CrossRef]
  7. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef]
  8. J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
    [CrossRef]
  9. H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
    [CrossRef]
  10. M. Liscidini and L. C. Andreani, Phys. Rev. E 73, 016613 (2006).
    [CrossRef]
  11. S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
    [CrossRef]
  12. J. Schilling, Nat. Photonics 5, 449 (2011).
    [CrossRef]
  13. E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
    [CrossRef]
  14. C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
    [CrossRef]
  15. E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
    [CrossRef]
  16. E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
    [CrossRef]
  17. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  18. W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
    [CrossRef]
  19. W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).
    [CrossRef]
  20. S. D. Gupta, J. Opt. Soc. Am. B 6, 1927 (1989).
    [CrossRef]
  21. R. S. Hedge and H. G. Winful, Microwave and Opt. Tech. Lett. 46, 528 (2005).
  22. R. S. Hedge and H. G. Winful, Opt. Lett. 30, 1852 (2005).
    [CrossRef]
  23. T. Peschel, P. Dannberg, U. Langbein, and F. Lederer, J. Opt. Soc. Am. B 5, 29 (1988).
    [CrossRef]
  24. U. Trutschel and F. Lederer, J. Opt. Soc. Am. B 5, 2530 (1988).
    [CrossRef]
  25. A thorough study of the effect of absorptive losses will be published elsewhere.

2013

E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
[CrossRef]

2012

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

2011

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

J. Schilling, Nat. Photonics 5, 449 (2011).
[CrossRef]

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

N. I. Zheludev, Opt. Photon. News 22(3), 30 (2011).
[CrossRef]

2010

N. I. Zheludev, 2010 Science 328, 582 (2010).
[CrossRef]

A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

2009

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

2006

M. Liscidini and L. C. Andreani, Phys. Rev. E 73, 016613 (2006).
[CrossRef]

2005

R. S. Hedge and H. G. Winful, Microwave and Opt. Tech. Lett. 46, 528 (2005).

R. S. Hedge and H. G. Winful, Opt. Lett. 30, 1852 (2005).
[CrossRef]

2003

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

1989

1988

1987

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef]

W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

1968

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Andreani, L. C.

M. Liscidini and L. C. Andreani, Phys. Rev. E 73, 016613 (2006).
[CrossRef]

Atwater, H. A.

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

Boltasseva, A.

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

Bruno-Alfonso, A.

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Carvalho, C. A. A.

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

Cavalcanti, S. B.

E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Chatterjee, R.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Chen, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Chen, W.

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef]

W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Dannberg, P.

de Carvalho, C. A. A.

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
[CrossRef]

Gupta, S. D.

Hedge, R. S.

R. S. Hedge and H. G. Winful, Opt. Lett. 30, 1852 (2005).
[CrossRef]

R. S. Hedge and H. G. Winful, Microwave and Opt. Tech. Lett. 46, 528 (2005).

Jiang, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Kocaman, S.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
[CrossRef]

Kwong, D. L.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Langbein, U.

Lederer, F.

Li, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Liscidini, M.

M. Liscidini and L. C. Andreani, Phys. Rev. E 73, 016613 (2006).
[CrossRef]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

McMillan, J. F.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Mills, D. L.

W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef]

Mogilevtsev, D.

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Oliveira, L. E.

E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

Osgood, R. M.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Panoiu, N. C.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Peschel, T.

Reyes-Gómez, E.

E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

Schilling, J.

J. Schilling, Nat. Photonics 5, 449 (2011).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Soukoulis, C. M.

A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
[CrossRef]

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Trutschel, U.

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Winful, H. G.

R. S. Hedge and H. G. Winful, Microwave and Opt. Tech. Lett. 46, 528 (2005).

R. S. Hedge and H. G. Winful, Opt. Lett. 30, 1852 (2005).
[CrossRef]

Wong, C. W.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Zhang, Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, Opt. Photon. News 22(3), 30 (2011).
[CrossRef]

N. I. Zheludev, 2010 Science 328, 582 (2010).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Zhu, S.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Appl. Phys. Lett.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, Appl. Phys. Lett. 83, 5386 (2003).
[CrossRef]

Europhys. Lett.

E. Reyes-Gómez, D. Mogilevtsev, S. B. Cavalcanti, C. A. A. Carvalho, and L. E. Oliveira, Europhys. Lett. 88, 24002 (2009).
[CrossRef]

J. Opt.

A. Fang, T. Koschny, and C. M. Soukoulis, J. Opt. 12, 024013 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Microwave and Opt. Tech. Lett.

R. S. Hedge and H. G. Winful, Microwave and Opt. Tech. Lett. 46, 528 (2005).

Nat. Photonics

J. Schilling, Nat. Photonics 5, 449 (2011).
[CrossRef]

Nature

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
[CrossRef]

Opt. Lett.

Opt. Photon. News

N. I. Zheludev, Opt. Photon. News 22(3), 30 (2011).
[CrossRef]

Phys. Rev. B

W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

C. A. A. de Carvalho, S. B. Cavalcanti, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 83, 081408(R) (2011).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Phys. Rev. E

M. Liscidini and L. C. Andreani, Phys. Rev. E 73, 016613 (2006).
[CrossRef]

Phys. Rev. Lett.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, R. M. Osgood, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef]

Rev. Mod. Phys.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Science

A. Boltasseva and H. A. Atwater, Science 331, 290 (2011).
[CrossRef]

N. I. Zheludev, 2010 Science 328, 582 (2010).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Superlattices Microstruct.

E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, Superlattices Microstruct. 64, 590 (2013).
[CrossRef]

Other

A thorough study of the effect of absorptive losses will be published elsewhere.

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Figures (5)

Fig. 1.
Fig. 1.

Transmission through a periodic lossless (γ=0) structure composed by 32 AB bilayers (A and B with equal widths of 10 mm), for an incidence angle θ=π/24. The following parameters were chosen: for the linear [a=0 in Eq. (2a)] RHM layer, ϵA=2.0, μA=1.0, and, for the linear LHM, the parameters are the same as in the study by Hedge and Winful [21,22] [cf. Eqs. (2c) and (2d)]. The red vertical line is at f=5.0662GHz, for which T0.0056 (see text).

Fig. 2.
Fig. 2.

Transmission through the same structure and linear parameters as in Fig. 1, as a function of increasing power of a defocusing nonlinearity. Several transparency (transmission T=1) points for f=5.0662GHz, occurring at values (see arrows) of a|Ei|2 equal to 0.00003, 0.0044, 0.022, 0.064, 0.14, 0.24, and 0.36.

Fig. 3.
Fig. 3.

Spatial profile for the electric field for the lowest three intensities where T=1 (cf. Fig. 2). In (a), (b), and (c) there are one, two, and three stable branches, respectively.

Fig. 4.
Fig. 4.

As in Fig. 3, for the next four higher intensities where T=1. In (a), (b), (c), and (d), there are four, five, six, and seven stable branches, respectively.

Fig. 5.
Fig. 5.

Plasmon polariton-gap solitons for the case of γ=0 [no loss, solid curve, cf. Fig. 3(a)] compared with the result for a γ=105 lossy structure (dashed line).

Equations (6)

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

ddz1μdEdz=[ω2ϵc2q2μ]E.
ϵA=ϵ0+a|E|2,
μA=μ0,
ϵB=1.6+400.81f2ifγ,
μB=1.0+250.814f2ifγ,
d2Edζ2+(εμβ2)E=0.

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