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Nonlinear Localization in Metamaterials

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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.

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  • DOI: 10.1007/978-3-319-08386-5_14
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References

  1. V.M. Shalaev, Nat. Photonics 1, 41 (2007)

    ADS  CrossRef  Google Scholar 

  2. C.M. Soukoulis, S. Linden, M. Wegener, Science 315, 47 (2007)

    CrossRef  Google Scholar 

  3. C.M. Soukoulis, M. Wegener, Nat. Photonics 5, 523 (2011)

    ADS  Google Scholar 

  4. N.I. Zheludev, Y.S. Kivshar, Nat. Mater. 11, 917 (2012)

    ADS  CrossRef  Google Scholar 

  5. J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)

    ADS  CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  7. N.I. Zheludev, Science 328, 582 (2010)

    ADS  CrossRef  Google Scholar 

  8. N.I. Zheludev, Opt. Photonics News 22, 31 (2011)

    ADS  CrossRef  Google Scholar 

  9. J.G. Caputo, I. Gabitov, A.I. Maimistov, Phys. Rev. B 85, 205446 (2012)

    ADS  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  11. D.A. Powell, I.V. Shadrivov, Y.S. Kivshar, M.V. Gorkunov, Appl. Phys. Lett. 91, 144107 (2007)

    ADS  CrossRef  Google Scholar 

  12. I.V. Shadrivov, A.B. Kozyrev, D.W. van der Weide, Y.S. Kivshar, Appl. Phys. Lett. 93, 161903 (2008)

    ADS  CrossRef  Google Scholar 

  13. B. Wang, J. Zhou, T. Koschny, C.M. Soukoulis, Opt. Express 16, 16058 (2008)

    ADS  CrossRef  Google Scholar 

  14. S.M. Anlage, J. Opt. 13, 024001 (2011)

    ADS  CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  16. M.C. Ricci, N. Orloff, S.M. Anlage, Appl. Phys. Lett. 87, 034102 (2005)

    ADS  CrossRef  Google Scholar 

  17. M.C. Ricci, H. Xu, R. Prozorov, A.P. Zhuravel, A.V. Ustinov, S.M. Anlage, IEEE Trans. Appl. Supercond. 17, 918 (2007)

    ADS  CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  21. B. Josephson, Phys. Lett. A 1, 251 (1962)

    CrossRef  MATH  Google Scholar 

  22. A. Barone, G. Patternó, Physics Applications of the Josephson Effect (Wiley, New York, 1982)

    CrossRef  Google Scholar 

  23. K.K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, Philadelphia, 1986)

    Google Scholar 

  24. N. Lazarides, G.P. Tsironis, Appl. Phys. Lett. 16, 163501 (2007)

    ADS  CrossRef  Google Scholar 

  25. N. Lazarides, G.P. Tsironis, M. Eleftheriou, Nonlinear Phenom. Complex Syst. 11, 250 (2008)

    Google Scholar 

  26. P. Jung, S. Butz, S.V. Shitov, A.V. Ustinov, Appl. Phys. Lett. 102, 062601 (2013)

    ADS  CrossRef  Google Scholar 

  27. S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Opt. Express 29(19), 22540 (2013)

    ADS  CrossRef  Google Scholar 

  28. S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Supercond. Sci. Technol. 26, 094003 (2013)

    ADS  CrossRef  Google Scholar 

  29. M. Trepanier, D. Zhang, O. Mukhanov, S.M. Anlage, Phys. Rev. X 3, 041029 (2013)

    Google Scholar 

  30. L. Esaki, Phys. Rep. 109, 603 (1958)

    Google Scholar 

  31. J. Schindler, A. Li, M.C. Zheng, F.M. Ellis, T. Kottos, Phys. Rev. A 84, 040101(R) (2011)

    ADS  CrossRef  Google Scholar 

  32. D.W. Hook, Ann. Phys. (Berlin) 524(6–7), A106 (2012)

    ADS  CrossRef  Google Scholar 

  33. R. El-Ganainy, K.G. Makris, D.N. Christodoulides, Z.H. Musslimani, Opt. Lett. 32, 2632 (2007)

    ADS  CrossRef  Google Scholar 

  34. K.G. Makris, R. El-Ganainy, D.N. Christodoulides, Z.H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008)

    ADS  CrossRef  Google Scholar 

  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. N. Lazarides, G.P. Tsironis, Phys. Rev. Lett. 110, 053901 (2013)

    ADS  CrossRef  Google Scholar 

  37. G.P. Tsironis, N. Lazarides, Appl. Phys. A 115, 449 (2014)

    Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  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)

    ADS  CrossRef  Google Scholar 

  40. I. Sersić, M. Frimmer, E. Verhagen, A.F. Koenderink, Phys. Rev. Lett. 103, 213902 (2009)

    ADS  CrossRef  Google Scholar 

  41. N.N. Rosanov, N.V. Vysotina, A.N. Shatsev, I.V. Shadrivov, D.A. Powell, Y.S. Kivshar, Opt. Express 19, 26500 (2011)

    ADS  CrossRef  Google Scholar 

  42. S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)

    ADS  CrossRef  Google Scholar 

  43. R.S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)

    ADS  CrossRef  MATH  MathSciNet  Google Scholar 

  44. S. Aubry, Physica D 103, 201 (1997)

    ADS  CrossRef  MATH  MathSciNet  Google Scholar 

  45. P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, Y. Zolotaryuk, Phys. Rev. Lett. 84(4), 745 (2000)

    ADS  CrossRef  Google Scholar 

  46. E. Trías, J.J. Mazo, T.P. Orlando, Phys. Rev. Lett. 84, 741 (2000)

    ADS  CrossRef  Google Scholar 

  47. J.L. Marín, F. Falo, P.J. Martínez, L.M. Floría, Phys. Rev. E 63, 066603 (2001)

    ADS  CrossRef  Google Scholar 

  48. N. Lazarides, M. Eleftheriou, G.P. Tsironis, Phys. Rev. Lett. 97, 157406 (2006)

    ADS  CrossRef  Google Scholar 

  49. M. Eleftheriou, N. Lazarides, G.P. Tsironis, Phys. Rev. E 77, 036608 (2008)

    ADS  CrossRef  Google Scholar 

  50. N. Lazarides, G.P. Tsironis, Y.S. Kivshar, Phys. Rev. E 77(6), 065601(R) (2008)

    ADS  CrossRef  Google Scholar 

  51. M. Eleftheriou, N. Lazarides, G.P. Tsironis, Y.S. Kivshar, Phys. Rev. E 80, 017601 (2009)

    ADS  CrossRef  Google Scholar 

  52. G.P. Tsironis, N. Lazarides, M. Eleftheriou, Springer Ser. Opti. 150, 273 (2010)

    CrossRef  Google Scholar 

  53. G.P. Tsironis, N. Lazarides, M. Eleftheriou, PIERS Online 5, 26 (2009)

    CrossRef  Google Scholar 

  54. N. Lazarides, G.P. Tsironis, Proc. SPIE 8423, 84231K (2012)

    ADS  CrossRef  Google Scholar 

  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. I.V. Shadrivov, A.A. Zharov, N.A. Zharova, Y.S. Kivshar, Photonics Nanostruct. Fundam. Appl. 4, 69 (2006)

    ADS  CrossRef  Google Scholar 

  57. A.A. Zharov, I.V. Shadrivov, Y.S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003)

    ADS  CrossRef  Google Scholar 

  58. M. Lapine, M. Gorkunov, K.H. Ringhofer, Phys. Rev. E 67, 065601 (2003)

    ADS  CrossRef  Google Scholar 

  59. P.J. Martínez, M. Meister, L.M. Floria, F. Falo, Chaos 13, 610 (2003)

    ADS  CrossRef  MATH  MathSciNet  Google Scholar 

  60. M.I. Molina, N. Lazarides, G.P. Tsironis, Phys. Rev. E 80, 046605 (2009)

    ADS  CrossRef  Google Scholar 

  61. N. Lazarides, M.I. Molina, G.P. Tsironis, Acta Phys. Pol. A 116(4), 635 (2009)

    ADS  Google Scholar 

  62. N. Lazarides, G.P. Tsironis, Phys. Lett. A 374, 2179 (2010)

    ADS  CrossRef  Google Scholar 

  63. M. Sato, B.E. Hubbard, A.J. Sievers, B. Ilic, D.A. Czaplewski, H.G. Graighead, Phys. Rev. Lett. 90, 044102 (2003)

    ADS  CrossRef  Google Scholar 

  64. J.R. Kirtley, C.C. Tsuei, Ariando, H.J.H. Smilde, H. Hilgenkamp, Phys. Rev. B 72, 214521 (2005)

    Google Scholar 

  65. E. Shamonina, V.A. Kalinin, K.H. Ringhofer, L. Solymar, J. Appl. Phys. 92, 6252 (2002)

    ADS  CrossRef  Google Scholar 

  66. S. Poletto, F. Chiarello, M.G. Castellano, J. Lisenfeld, A. Lukashenko, P. Carelli, A.V. Ustinov, Phys. Scr. T137, 014011 (2009)

    ADS  CrossRef  Google Scholar 

  67. N. Lazarides, G.P. Tsironis, Supercond. Sci. Technol. 26, 084006 (2013)

    ADS  CrossRef  Google Scholar 

  68. N. Lazarides, V. Paltoglou, G.P. Tsironis, Int. J. Bifurc. Chaos 21, 2147 (2011)

    CrossRef  MATH  Google Scholar 

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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.

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Lazarides, N., Tsironis, G.P. (2015). Nonlinear Localization in Metamaterials. In: Shadrivov, I., Lapine, M., Kivshar, Y. (eds) Nonlinear, Tunable and Active Metamaterials. Springer Series in Materials Science, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-08386-5_14

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