Abstract

We addressed the existence of the nonlinear electromagnetic surface waves, the so-called Tamm states, that form at an interface separating a nonlinear uniform left-handed metamaterial and a conventional one-dimensional photonic crystal. We found two types of nonlinear surface waves, one with a hump at the interface and the other one with two humps. It was demonstrated that the nonlinear metamaterial can support the both type Tamm states with a backward energy flow and allows for a flexible control of the dispersion properties of surface states. We also, described the intensity-dependent properties of surface Tamm states for a nonlinear self-focusing medium.

©2008 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk92, 517–526 (1967) (in Russian) [English translation: Sov. Phys. Usp. 10, 509–513 (1968).
  2. D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [Crossref] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  4. M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
    [Crossref]
  5. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
    [Crossref] [PubMed]
  6. L. Venema, “Negative refraction: A lens less ordinary,” Nature (London)  420, 119–120 (2002).
    [Crossref] [PubMed]
  7. S. Kawata, ed., Near-Field Optics and Surface Plasmon Polaritons (Springer-Verlag, 2001).
    [Crossref]
  8. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).
  9. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
    [Crossref]
  10. P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
    [Crossref] [PubMed]
  11. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
    [Crossref] [PubMed]
  12. M. Lapine, M. Gorkunov, and K. H. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Phys. Rev. E67, 065601-4 (2003).
    [Crossref]
  13. I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
    [Crossref]
  14. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
    [Crossref]
  15. N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005).
    [Crossref] [PubMed]
  16. I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
    [Crossref]
  17. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
    [Crossref]
  18. S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
    [Crossref]
  19. S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
    [Crossref]
  20. N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schroinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614-4 (2005).
    [Crossref]
  21. I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626-5 (2005).
    [Crossref]
  22. A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
    [Crossref]
  23. P. Yeh, A. Yariv, and A. Y. Cho, Optical waves in Layered Media (John Wily & Sons, New York, 1998).
  24. J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
    [Crossref]

2007 (1)

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

2006 (4)

A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
[Crossref]

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
[Crossref]

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

2005 (4)

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schroinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614-4 (2005).
[Crossref]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626-5 (2005).
[Crossref]

2004 (3)

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

2003 (2)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
[Crossref] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

2002 (2)

L. Venema, “Negative refraction: A lens less ordinary,” Nature (London)  420, 119–120 (2002).
[Crossref] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

2000 (1)

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
[Crossref]

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

Aharov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

Aydin, K.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

Bayindir, M.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

Boardman, A. D.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, Optical waves in Layered Media (John Wily & Sons, New York, 1998).

Dai, X.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

Egan, P.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

Fan, D.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
[Crossref]

Fu, X.

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Gorkunov, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Phys. Rev. E67, 065601-4 (2003).
[Crossref]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

Irman, A.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
[Crossref] [PubMed]

Kivshar, Yu. S.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
[Crossref]

A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
[Crossref]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

Kourakis, I.

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626-5 (2005).
[Crossref]

Lapine, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Phys. Rev. E67, 065601-4 (2003).
[Crossref]

Lazarides, N.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schroinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614-4 (2005).
[Crossref]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

Lodahl, P.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Markos, P.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

Martorell, J.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

Morozov, G. V.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
[Crossref]

Namdar, A.

A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
[Crossref]

Nasser, S. C. Nemat

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Nikolaev, I. S.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Overgaag, K.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Ozbay, E.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

Padilla, W.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Phys. Rev. E67, 065601-4 (2003).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
[Crossref]

A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
[Crossref]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
[Crossref] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

Shukla, P. K.

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626-5 (2005).
[Crossref]

Shultz, S.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Soukoulis, C. M.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

Sprung, D. W. L.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
[Crossref]

Su, W.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

Tang, Z.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

Tsironis, G. P.

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schroinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614-4 (2005).
[Crossref]

van Driel, A. Floris

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Vanmaekelbergh, D.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Venema, L.

L. Venema, “Negative refraction: A lens less ordinary,” Nature (London)  420, 119–120 (2002).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk92, 517–526 (1967) (in Russian) [English translation: Sov. Phys. Usp. 10, 509–513 (1968).

Vier, D. C.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
[Crossref]

Vos, W. L.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Wang, Y.

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Wen, S.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

Xiang, Y.

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, Optical waves in Layered Media (John Wily & Sons, New York, 1998).

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, Optical waves in Layered Media (John Wily & Sons, New York, 1998).

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
[Crossref]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction,” Opt. Express 13, 1291–1298 (2005).
[Crossref] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
[Crossref] [PubMed]

Zharov, N. A.

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

Zharova, N. A.

Appl. Phys. Lett. (2)

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120–122 (2002).
[Crossref]

A. Namdar, I. V. Shadrivov, and Yu. S. Kivshar, “Backward Tamm states in left-handed metamaterials,” Appl. Phys. Lett. 89, 114104-3 (2006).
[Crossref]

J. Opt. A: pure Appl. Opt. (1)

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals” J. Opt. A: pure Appl. Opt. 8, 630–638 (2006).
[Crossref]

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

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B (Optical Physics) 23, 529–534 (2006).
[Crossref]

Nature (3)

L. Venema, “Negative refraction: A lens less ordinary,” Nature (London)  420, 119–120 (2002).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light” Nature (London)  386, 143–149 (1997).
[Crossref]

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London)  430, 654–657 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. A (1)

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815-8 (2007).
[Crossref]

Phys. Rev. B (1)

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B 69, 165112–165117 (2004).
[Crossref]

Phys. Rev. E (4)

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schroinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614-4 (2005).
[Crossref]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626-5 (2005).
[Crossref]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617-6 (2006).
[Crossref]

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Aharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617-9 (2004).
[Crossref]

Phys. Rev. Lett. (3)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Phys. Rev. Lett. 91, 037401-4 (2003).
[Crossref] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snells law,” Phys. Rev. Lett. 90, 107401-4 (2003).
[Crossref] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Radio Science (1)

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, “Nonlinear left-handed metamaterials,” Radio Science 40, RS3S90-10 (2005).
[Crossref]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Other (5)

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Phys. Rev. E67, 065601-4 (2003).
[Crossref]

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk92, 517–526 (1967) (in Russian) [English translation: Sov. Phys. Usp. 10, 509–513 (1968).

S. Kawata, ed., Near-Field Optics and Surface Plasmon Polaritons (Springer-Verlag, 2001).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).

P. Yeh, A. Yariv, and A. Y. Cho, Optical waves in Layered Media (John Wily & Sons, New York, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) Geometry of the problem. In our calculations we take the following values: d 1=1cm, d 2=1.65cm, ε 1=4, µ 1=1, ε 2=2.25, µ 2=1, ε 0=-1, and µ 0=-1, dc =0.01cm.

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Fig. 2.
Fig. 2.

(Color online) Dispersion properties of the Tamm states in the first spectral gap. The solid and dashed curves correspond to the one-humped and two-humped structures of surface modes. The corresponding values of the intensity Ĩs for the curves 1–3 are 0.3, 0.6, 0.9, respectively and the curve 0 show the dispersion of linear regime where Ĩs →0. Points (a), (b), correspond to the mode profiles shown in Fig.3. The other parameters are the same as the Fig. 1.

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Fig. 3.
Fig. 3.

(Color online) Examples of the nonlinear surface Tamm states; Ĩs =0.3, β=1.19; (a) Backward nonlinear two hump LHM mode, k=1.141 cm-1; (b) Forward nonlinear one hump LHM mode, k=0.879 cm-1 ; Modes (a), (b) correspond to the points (a), (b) in FIG. 2. The other parameters are the same as the Fig. 1.

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Fig. 4.
Fig. 4.

(Color online) Total energy flow in nonlinear one-humped (dashed) and two-humped (solid) structures of surface Tamm modes vs β for different intensity.

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Fig. 5.
Fig. 5.

(Color online) Existence regions for the nonlinear surface Tamm modes ; the modes exist in the shaded regions. the region 1 with dark color show the corresponding regions for the backward nonlinear surface Tamm states whilst the region 2 with light color show the corresponding regions for the forward nonlinear surface Tamm states. (a) and (b) show the modes with one-humped and two-humped structures, respectively. The other parameters are the same as the Fig. 1.

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Equations (3)

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ε LH = ε 0 + α ∣ E ∣ 2 ,
∂ 2 E ∂ z 2 + ∂ 2 E ∂ x 2 + ω 2 c 2 ( ε μ + μ α ∣ E ∣ 2 ) E = 0 .
Ψ ( z ) = ( η 2 αμ ) sech [ ( ω c ) η ( z − z 0 ) ] ,

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