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Nonlinear Localization in Metamaterials

  • Nikos LazaridesEmail author
  • George P. Tsironis
Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 200)

Abstract

Metamaterials, i.e., artificially structured (“synthetic”) media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including Super-Resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tunability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete breather in metallic, SQUID-Based, and \({\fancyscript{PT}}\)-symmetric metamaterials. We review recent results demonstrating the generic appearance of breather excitations in these systems resulting from power-balance between intrinsic losses and input power, either by proper initialization or by purely dynamical procedures. Breather properties peculiar to each particular system are identified and discussed. Recent progress in the fabrication of Low-Loss, active and superconducting metamaterials, makes the experimental observation of breathers in principle possible with the proposed dynamical procedures. Recent experimental results on dynamical phenomena due to intrinsic nonlinearities in SQUID metamaterials are briefly summarized.

Keywords

Floquet Multiplier Discrete Breather Dime Chain Exact Phase Intrinsic Nonlinearity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was partially supported by the European Union’s Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement no 316165, and by the Thales Projects ANEMOS and MACOMSYS, cofinanced by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.

References

  1. 1.
    V.M. Shalaev, Nat. Photonics 1, 41 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    C.M. Soukoulis, S. Linden, M. Wegener, Science 315, 47 (2007)CrossRefGoogle Scholar
  3. 3.
    C.M. Soukoulis, M. Wegener, Nat. Photonics 5, 523 (2011)ADSGoogle Scholar
  4. 4.
    N.I. Zheludev, Y.S. Kivshar, Nat. Mater. 11, 917 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, D.R. Smith, Science 314, 977 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    N.I. Zheludev, Science 328, 582 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    N.I. Zheludev, Opt. Photonics News 22, 31 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    J.G. Caputo, I. Gabitov, A.I. Maimistov, Phys. Rev. B 85, 205446 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    S. Linden, C. Enkrich, G. Dolling, M.W. Klein, J. Zhou, T. Koschny, C.M. Soukoulis, S. Burger, F. Schmidt, M. Wegener, IEEE J. Selec. Top. Quant. Electron. 12, 1097 (2006)CrossRefGoogle Scholar
  11. 11.
    D.A. Powell, I.V. Shadrivov, Y.S. Kivshar, M.V. Gorkunov, Appl. Phys. Lett. 91, 144107 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    I.V. Shadrivov, A.B. Kozyrev, D.W. van der Weide, Y.S. Kivshar, Appl. Phys. Lett. 93, 161903 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    B. Wang, J. Zhou, T. Koschny, C.M. Soukoulis, Opt. Express 16, 16058 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    S.M. Anlage, J. Opt. 13, 024001 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    A.D. Boardman, V.V. Grimalsky, Y.S. Kivshar, S.V. Koshevaya, M. Lapine, N.M. Litchinitser, V.N. Malnev, M. Noginov, Y.G. Rapoport, V.M. Shalaev, Laser Photonics Rev. 5(2), 287 (2010)CrossRefGoogle Scholar
  16. 16.
    M.C. Ricci, N. Orloff, S.M. Anlage, Appl. Phys. Lett. 87, 034102 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    M.C. Ricci, H. Xu, R. Prozorov, A.P. Zhuravel, A.V. Ustinov, S.M. Anlage, IEEE Trans. Appl. Supercond. 17, 918 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M.X. He, J.W. Zhang, J. Han, H. Chen, W. Zhang, Appl. Phys. Lett. 97, 071102 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    V.A. Fedotov, A. Tsiatmas, J.H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, N.I. Zheludev, Opt. Express 18, 9015 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    H.T. Chen, H. Yang, R. Singh, J.F. OHara, A.K. Azad, A. Stuart, S.A. Trugman, Q.X. Jia, A.J. Taylor, Phys. Rev. Lett. 105, 247402 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    B. Josephson, Phys. Lett. A 1, 251 (1962)CrossRefzbMATHGoogle Scholar
  22. 22.
    A. Barone, G. Patternó, Physics Applications of the Josephson Effect (Wiley, New York, 1982)CrossRefGoogle Scholar
  23. 23.
    K.K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, Philadelphia, 1986)Google Scholar
  24. 24.
    N. Lazarides, G.P. Tsironis, Appl. Phys. Lett. 16, 163501 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    N. Lazarides, G.P. Tsironis, M. Eleftheriou, Nonlinear Phenom. Complex Syst. 11, 250 (2008)Google Scholar
  26. 26.
    P. Jung, S. Butz, S.V. Shitov, A.V. Ustinov, Appl. Phys. Lett. 102, 062601 (2013)ADSCrossRefGoogle Scholar
  27. 27.
    S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Opt. Express 29(19), 22540 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Supercond. Sci. Technol. 26, 094003 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    M. Trepanier, D. Zhang, O. Mukhanov, S.M. Anlage, Phys. Rev. X 3, 041029 (2013)Google Scholar
  30. 30.
    L. Esaki, Phys. Rep. 109, 603 (1958)Google Scholar
  31. 31.
    J. Schindler, A. Li, M.C. Zheng, F.M. Ellis, T. Kottos, Phys. Rev. A 84, 040101(R) (2011)ADSCrossRefGoogle Scholar
  32. 32.
    D.W. Hook, Ann. Phys. (Berlin) 524(6–7), A106 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    R. El-Ganainy, K.G. Makris, D.N. Christodoulides, Z.H. Musslimani, Opt. Lett. 32, 2632 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    K.G. Makris, R. El-Ganainy, D.N. Christodoulides, Z.H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    C.E. Rüter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, D. Kip, Nat. Phys. 6, 192–195 (2010)Google Scholar
  36. 36.
    N. Lazarides, G.P. Tsironis, Phys. Rev. Lett. 110, 053901 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    G.P. Tsironis, N. Lazarides, Appl. Phys. A 115, 449 (2014)Google Scholar
  38. 38.
    O. Sydoruk, A. Radkovskaya, O. Zhuromskyy, E. Shamonina, M. Shamonin, C. Stevens, G. Faulkner, D. Edwards, L. Solymar, Phys. Rev. B 73, 224406 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A.A. Radkovskaya, M. Shamonin, T. Hao, C.J. Stevens, G. Faulkner, D.J. Edwardds, E. Shamonina, Phys. Stat. Sol. (b) 244, 1170 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    I. Sersić, M. Frimmer, E. Verhagen, A.F. Koenderink, Phys. Rev. Lett. 103, 213902 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    N.N. Rosanov, N.V. Vysotina, A.N. Shatsev, I.V. Shadrivov, D.A. Powell, Y.S. Kivshar, Opt. Express 19, 26500 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    R.S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  44. 44.
    S. Aubry, Physica D 103, 201 (1997)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  45. 45.
    P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, Y. Zolotaryuk, Phys. Rev. Lett. 84(4), 745 (2000)ADSCrossRefGoogle Scholar
  46. 46.
    E. Trías, J.J. Mazo, T.P. Orlando, Phys. Rev. Lett. 84, 741 (2000)ADSCrossRefGoogle Scholar
  47. 47.
    J.L. Marín, F. Falo, P.J. Martínez, L.M. Floría, Phys. Rev. E 63, 066603 (2001)ADSCrossRefGoogle Scholar
  48. 48.
    N. Lazarides, M. Eleftheriou, G.P. Tsironis, Phys. Rev. Lett. 97, 157406 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    M. Eleftheriou, N. Lazarides, G.P. Tsironis, Phys. Rev. E 77, 036608 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    N. Lazarides, G.P. Tsironis, Y.S. Kivshar, Phys. Rev. E 77(6), 065601(R) (2008)ADSCrossRefGoogle Scholar
  51. 51.
    M. Eleftheriou, N. Lazarides, G.P. Tsironis, Y.S. Kivshar, Phys. Rev. E 80, 017601 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    G.P. Tsironis, N. Lazarides, M. Eleftheriou, Springer Ser. Opti. 150, 273 (2010)CrossRefGoogle Scholar
  53. 53.
    G.P. Tsironis, N. Lazarides, M. Eleftheriou, PIERS Online 5, 26 (2009)CrossRefGoogle Scholar
  54. 54.
    N. Lazarides, G.P. Tsironis, Proc. SPIE 8423, 84231K (2012)ADSCrossRefGoogle Scholar
  55. 55.
    P. Jung, S. Butz, M. Marthaler, M.V. Fistul, J. Leppäkangas, V.P. Koshelets, A.V. Ustinov, Nat. Commun. 5, 3730 (2014)Google Scholar
  56. 56.
    I.V. Shadrivov, A.A. Zharov, N.A. Zharova, Y.S. Kivshar, Photonics Nanostruct. Fundam. Appl. 4, 69 (2006)ADSCrossRefGoogle Scholar
  57. 57.
    A.A. Zharov, I.V. Shadrivov, Y.S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003)ADSCrossRefGoogle Scholar
  58. 58.
    M. Lapine, M. Gorkunov, K.H. Ringhofer, Phys. Rev. E 67, 065601 (2003)ADSCrossRefGoogle Scholar
  59. 59.
    P.J. Martínez, M. Meister, L.M. Floria, F. Falo, Chaos 13, 610 (2003)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  60. 60.
    M.I. Molina, N. Lazarides, G.P. Tsironis, Phys. Rev. E 80, 046605 (2009)ADSCrossRefGoogle Scholar
  61. 61.
    N. Lazarides, M.I. Molina, G.P. Tsironis, Acta Phys. Pol. A 116(4), 635 (2009)ADSGoogle Scholar
  62. 62.
    N. Lazarides, G.P. Tsironis, Phys. Lett. A 374, 2179 (2010)ADSCrossRefGoogle Scholar
  63. 63.
    M. Sato, B.E. Hubbard, A.J. Sievers, B. Ilic, D.A. Czaplewski, H.G. Graighead, Phys. Rev. Lett. 90, 044102 (2003)ADSCrossRefGoogle Scholar
  64. 64.
    J.R. Kirtley, C.C. Tsuei, Ariando, H.J.H. Smilde, H. Hilgenkamp, Phys. Rev. B 72, 214521 (2005)Google Scholar
  65. 65.
    E. Shamonina, V.A. Kalinin, K.H. Ringhofer, L. Solymar, J. Appl. Phys. 92, 6252 (2002)ADSCrossRefGoogle Scholar
  66. 66.
    S. Poletto, F. Chiarello, M.G. Castellano, J. Lisenfeld, A. Lukashenko, P. Carelli, A.V. Ustinov, Phys. Scr. T137, 014011 (2009)ADSCrossRefGoogle Scholar
  67. 67.
    N. Lazarides, G.P. Tsironis, Supercond. Sci. Technol. 26, 084006 (2013)ADSCrossRefGoogle Scholar
  68. 68.
    N. Lazarides, V. Paltoglou, G.P. Tsironis, Int. J. Bifurc. Chaos 21, 2147 (2011)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Crete Center for Quantum Complexity and Nanotechnology, Department of PhysicsUniversity of CreteHeraklionGreece
  2. 2.Institute of Electronic Structure and LaserFoundation for Research and Technology-HellasHeraklionGreece
  3. 3.Department of Physics, School of Science and TechnologyNazarbayev UniversityAstanaKazakhstan

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