Nonlinear Metamaterials

  • Lei Xu
  • Mohsen Rahmani
  • David A. Powell
  • Dragomir Neshev
  • Andrey E. MiroshnichenkoEmail author
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 32)


Metamaterials are engineered structures designed to exhibit exotic electromagnetic properties. Early on in the development of metamaterials, these properties were extended to exotic regimes of nonlinear behaviour, unknown in classical nonlinear optics. In this chapter, we give a historical overview of metamaterials, considering first their exotic linear properties, and show how these give rise to exotic nonlinear properties, at frequency ranges from RF to visible. We overview the main attractive features of metamaterials for nonlinear applications, namely their strong local field enhancement, their ability to achieve exotic phase matching conditions, and the possibility to create inclusions with the correct symmetry to enhance a chosen nonlinear process. We then summarise the two most important classes of nonlinear optical metamaterials, plasmonic and all-dielectric.



This work was supported by the Australian Research Council and UNSW Scientia Fellowship.


  1. 1.
    U. Leonhardt, Nat. Photonics 1, 207 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    V.G. Veselago, Sov. Phys. Uspekhi 10, 509 (1968)ADSCrossRefGoogle Scholar
  3. 3.
    J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    H. Lamb, Proc. Lond. Math. Soc. 1, 473 (1904)Google Scholar
  5. 5.
    H.C. Pocklington, Nature 71, 607 (1905)ADSCrossRefGoogle Scholar
  6. 6.
    L. Mandel’shtam, Zh. Eksp. Teor. Fiz. 15, 475 (1945)Google Scholar
  7. 7.
    J.D. Joannopoulos, P. Villeneuve, S. Fan, Nature 386, 143 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    S.A. Maier, H.A. Atwater, J. Appl. Phys. 98, 011101 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    W. Rotman, IRE Trans. Antennas Propag. 10, 82 (1962)ADSCrossRefGoogle Scholar
  10. 10.
    P.A. Belov, R. Marqués, S.I. Maslovski, I.S. Nefedov, M. Silveirinha, C.R. Simovski, S.A. Tretyakov, Phys. Rev. B 67, 113103 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    C.R. Simovski, P.A. Belov, Phys. Rev. E 70, 046616 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    S.A. Schelkunoff, H.T. Friis, Antennas: Theory and Practice (Wiley, New York, 1952)zbMATHGoogle Scholar
  13. 13.
    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, IEEE Trans. Microw. Theory Tech. 47, 2075 (1999)Google Scholar
  14. 14.
    A.I. Kuznetsov, A.E. Miroshnichenko, Y.H. Fu, J. Zhang, B. Luk’yanchuk, Sci. Rep. 2, 492 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    A. Mackay, B. Sanz-Izquierdo, E.A. Parker, Forum Electromagn. Res. Methods Appl. Technol. 2, 1 (2014)Google Scholar
  16. 16.
    S. Narayan, R.M. Jha, IEEE Antennas Propag. Mag. 57, 135 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    J.B. Pendry, D. Schurig, D.R. Smith, Science 312, 1780 (2006)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    D.R. Smith, D. Schurig, Phys. Rev. Lett. 90, 5 (2003)Google Scholar
  19. 19.
    C. Holloway, M. Mohamed, E. Kuester, A. Dienstfrey, IEEE Trans. Electromagn. Compat. 47, 853 (2005)CrossRefGoogle Scholar
  20. 20.
    C.É. Kriegler, M.S. Rill, S. Linden, M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010)Google Scholar
  21. 21.
    R. Ro, V. Varadan, V. Varadan, IEE Proc. H – Microw. Antennas Propag. 139, 441 (1992)Google Scholar
  22. 22.
    M.C.K. Wiltshire, J.B. Pendry, J.V. Hajnal, J. Phys. Condens. Matter 21, 292201 (2009)CrossRefGoogle Scholar
  23. 23.
    M. Decker, M. Ruther, C.E. Kriegler, J. Zhou, C.M. Soukoulis, S. Linden, M. Wegener, Opt. Lett. 34, 2501 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    A. Serdyukov, I. Semchenko, S.A. Tretyakov, A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001)Google Scholar
  25. 25.
    M.G. Silveirinha, Phys. Rev. B 75, 115104 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    M. Lapine, I.V. Shadrivov, Y.S. Kivshar, Rev. Mod. Phys. 86, 1093 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    P. Jung, A.V. Ustinov, S.M. Anlage, Supercond. Sci. Technol. 27, 073001 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    N. Lazarides, G. Neofotistos, G.P. Tsironis, Phys. Rev. B 91, 054303 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    S. Larouche, V. Radisic, Phys. Rev. A 97, 043863 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    X. Liu, S. Larouche, D.R. Smith, Opt. Commun. 410, 53 (2018)ADSCrossRefGoogle Scholar
  31. 31.
    D. Filonov, Y. Kramer, V. Kozlov, B.A. Malomed, P. Ginzburg, Appl. Phys. Lett. 109, 111904 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    L. Liu, L. Wu, J. Zhang, Z. Li, B. Zhang, Y. Luo, Adv. Sci. 5, 1800661 (2018)CrossRefGoogle Scholar
  33. 33.
    A. Rose, D. Huang, D.R. Smith, Phys. Rev. Lett. 107, 063902 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    N. Segal, S. Keren-Zur, N. Hendler, T. Ellenbogen, Nat. Photonics 9, 180 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    W.R.C. Somerville, D.A. Powell, I.V. Shadrivov, Appl. Phys. Lett. 98, 161111 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    K.E. Hannam, D.A. Powell, I.V. Shadrivov, Y.S. Kivshar, Appl. Phys. Lett. 100, 081111 (2012)ADSCrossRefGoogle Scholar
  37. 37.
    S.Y. Elnaggar, G.N. Milford, IEEE Trans. Antennas Propag. 66, 481 (2018)Google Scholar
  38. 38.
    M. Lapine, I.V. Shadrivov, D.A. Powell, Y.S. Kivshar, Nat. Mater. 11, 30 (2012)Google Scholar
  39. 39.
    M. Liu, D.A. Powell, I.V. Shadrivov, M. Lapine, Y.S. Kivshar, Nat. Commun. 5, 4441 (2014)Google Scholar
  40. 40.
    A. Li, Z. Luo, H. Wakatsuchi, S. Kim, D.F. Sievenpiper, IEEE Access 5, 27439 (2017)CrossRefGoogle Scholar
  41. 41.
    I.V. Shadrivov, S.K. Morrison, Y.S. Kivshar, Opt. Express 14, 9344 (2006)ADSCrossRefGoogle Scholar
  42. 42.
    Z. Luo, Q. Wang, X.G. Zhang, J.W. Wu, J.Y. Dai, L. Zhang, H.T. Wu, H.C. Zhang, H.F. Ma, Q. Cheng, T.J. Cui, Adv. Opt. Mater. 7, 1970071 (2019)CrossRefGoogle Scholar
  43. 43.
    I.V. Shadrivov, A.A. Sukhorukov, Y.S. Kivshar, A.A. Zharov, A.D. Boardman, P. Egan, Phys. Rev. E 69, 016617 (2004)Google Scholar
  44. 44.
    L.J. Zhang, L. Chen, C.H. Liang, J. Electromagn. Waves Appl. 22, 1031 (2008)CrossRefGoogle Scholar
  45. 45.
    T. Ozawa, H.M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M.C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019)ADSCrossRefGoogle Scholar
  46. 46.
    D.A. Dobrykh, A.V. Yulin, A.P. Slobozhanyuk, A.N. Poddubny, Y.S. Kivshar, Phys. Rev. Lett. 121, 163901 (2018)Google Scholar
  47. 47.
    W. Withayachumnankul, D. Abbott, IEEE Photonics J. 1, 99 (2009)ADSCrossRefGoogle Scholar
  48. 48.
    X. Zhao, J. Zhang, K. Fan, G. Duan, G.D. Metcalfe, M. Wraback, X. Zhang, R.D. Averitt, Photonics Res. 4, A16 (2016)CrossRefGoogle Scholar
  49. 49.
    H.R. Seren, J. Zhang, G.R. Keiser, S.J. Maddox, X. Zhao, K. Fan, S.R. Bank, X. Zhang, R.D. Averitt, Light Sci. Appl. 5, e16078 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    Y.C. Jun, I. Brener, J. Opt. 14, 114013 (2012)ADSCrossRefGoogle Scholar
  51. 51.
    M. Kauranen, A.V. Zayats, Nat. Photonics 6, 737 (2012)ADSCrossRefGoogle Scholar
  52. 52.
    V. Giannini, A.I. Fernández-Domínguez, S.C. Heck, S.A. Maier, Chem. Rev. 111, 3888 (2011)CrossRefGoogle Scholar
  53. 53.
    B. Metzger, M. Hentschel, T. Schumacher, M. Lippitz, X. Ye, C.B. Murray, B. Knabe, K. Buse, H. Giessen, Nano Lett. 14, 2867 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    H. Aouani, M. Rahmani, M. Navarro-Cía, S.A. Maier, Nat. Nanotechnol. 9, 290 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    B. Metzger, L. Gui, J. Fuchs, D. Floess, M. Hentschel, H. Giessen, Nano Lett. 15, 3917 (2015)ADSCrossRefGoogle Scholar
  56. 56.
    J. Butet, P.F. Brevet, O.J. Martin, ACS Nano 9, 10545 (2015)CrossRefGoogle Scholar
  57. 57.
    O. Wolf, S. Campione, A. Benz, A.P. Ravikumar, S. Liu, T.S. Luk, E.A. Kadlec, E.A. Shaner, J.F. Klem, M.B. Sinclair, I. Brener, Nat. Commun. 6, 7667 (2015)ADSCrossRefGoogle Scholar
  58. 58.
    M.W. Klein, C. Enkrich, M. Wegener, S. Linden, Science 313, 502 (2006)ADSCrossRefGoogle Scholar
  59. 59.
    H. Aouani, M. Navarro-Cia, M. Rahmani, T.P. Sidiropoulos, M. Hong, R.F. Oulton, S.A. Maier, Nano Lett. 12, 4997 (2012)ADSCrossRefGoogle Scholar
  60. 60.
    S.D. Gennaro, M. Rahmani, V. Giannini, H. Aouani, T.P. Sidiropoulos, M. Navarro-Cía, S.A. Maier, R.F. Oulton, Nano Lett. 16, 5278 (2016)ADSCrossRefGoogle Scholar
  61. 61.
    F. Niesler, N. Feth, S. Linden, J. Niegemann, J. Gieseler, K. Busch, M. Wegener, Opt. Lett. 34, 1997 (2009)ADSCrossRefGoogle Scholar
  62. 62.
    N. Panoiu, W. Sha, D. Lei, G. Li, J. Opt. 20, 083001 (2018)ADSCrossRefGoogle Scholar
  63. 63.
    M. Rahmani, A.S. Shorokhov, B. Hopkins, A.E. Miroshnichenko, M.R. Shcherbakov, R. Camacho-Morales, A.A. Fedyanin, D.N. Neshev, Y.S. Kivshar, ACS Photonics 4, 454 (2017)CrossRefGoogle Scholar
  64. 64.
    S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007)CrossRefGoogle Scholar
  65. 65.
    M. Rahmani, T. Tahmasebi, Y. Lin, B. Lukiyanchuk, T. Liew, M. Hong, Nanotechnology 22, 245204 (2011)ADSCrossRefGoogle Scholar
  66. 66.
    F. Lu, W. Zhang, L. Huang, S. Liang, D. Mao, F. Gao, T. Mei, J. Zhao, Opto-Electron. Adv. 1, 180010 (2018)Google Scholar
  67. 67.
    L. Chen, Y. Zhou, M. Wu, M. Hong, Opto-Electron. Adv. 1, 170001 (2018)Google Scholar
  68. 68.
    M. Rahmani, B. Luk’yanchuk, M. Hong, Laser Photonics Rev. 7, 329 (2013)ADSCrossRefGoogle Scholar
  69. 69.
    W. Zhang, M. Rahmani, W. Niu, S. Ravaine, M. Hong, X. Lu, Sci. Rep. 5, 8382 (2015)ADSCrossRefGoogle Scholar
  70. 70.
    F. Della Picca, R. Berte, M. Rahmani, P. Albella, J.M. Bujjamer, M. Poblet, E. Cortés, S.A. Maier, A.V. Bragas, Nano Lett. 16, 1428 (2016)ADSCrossRefGoogle Scholar
  71. 71.
    P. Segovia, G. Marino, A.V. Krasavin, N. Olivier, G.A. Wurtz, P.A. Belov, P. Ginzburg, A.V. Zayats, Opt. Express 23, 30730 (2015)ADSCrossRefGoogle Scholar
  72. 72.
    G. Marino, P. Segovia, A.V. Krasavin, P. Ginzburg, N. Olivier, G.A. Wurtz, A.V. Zayats, Laser Photonics Rev. 12, 1700189 (2018)ADSCrossRefGoogle Scholar
  73. 73.
    P. Wang, A.V. Krasavin, M.E. Nasir, W. Dickson, A.V. Zayats, Nat. Nanotechnol. 13, 159 (2018)ADSCrossRefGoogle Scholar
  74. 74.
    E.P. Franken, A.E. Hill, C.E. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961)ADSCrossRefGoogle Scholar
  75. 75.
    J. Krauth, T. Schumacher, J. Defrance, B. Metzger, M. Lippitz, T. Weiss, H. Giessen, M. Hentschel, ACS Photonics 6, 2850 (2019)CrossRefGoogle Scholar
  76. 76.
    Y. Zhang, F. Wen, Y.R. Zhen, P. Nordlander, N.J. Halas, Proc. Natl. Acad. Sci. USA 110, 9215 (2013)ADSCrossRefGoogle Scholar
  77. 77.
    G. Bautista, C. Dreser, X. Zang, D.P. Kern, M. Kauranen, M. Fleischer, Nano Lett. 18, 2571 (2018)ADSCrossRefGoogle Scholar
  78. 78.
    H. Aouani, M. Navarro-Cía, M. Rahmani, S.A. Maier, Adv. Opt. Mater. 3, 1059 (2015)CrossRefGoogle Scholar
  79. 79.
    H. Linnenbank, Y. Grynko, J. Förstner, S. Linden, Light Sci. Appl. 5, e16013 (2016)ADSCrossRefGoogle Scholar
  80. 80.
    W. Fan, S. Zhang, N.C. Panoiu, A. Abdenour, S. Krishna, R. Osgood, K. Malloy, S. Brueck, Nano Lett. 6, 1027 (2006)ADSCrossRefGoogle Scholar
  81. 81.
    Y. Pu, R. Grange, C.L. Hsieh, D. Psaltis, Phys. Rev. Lett. 104, 207402 (2010)ADSCrossRefGoogle Scholar
  82. 82.
    T. Shibanuma, G. Grinblat, P. Albella, S.A. Maier, Nano Lett. 17, 2647 (2017)ADSCrossRefGoogle Scholar
  83. 83.
    V.F. Gili, L. Ghirardini, D. Rocco, G. Marino, I. Favero, I. Roland, G. Pellegrini, L. Duò, M. Finazzi, L. Carletti, A. Locatelli, A. Lemaître, D. Neshev, C. De Angelis, G. Leo, M. Celebrano, Beilstein J. Nanotech. 9, 2306 (2018)CrossRefGoogle Scholar
  84. 84.
    D. Smirnova, Y.S. Kivshar, Optica 3, 1241 (2016)ADSCrossRefGoogle Scholar
  85. 85.
    I. Staude, J. Schilling, Nat. Photonics 11, 274 (2017)ADSCrossRefGoogle Scholar
  86. 86.
    D.A. Smirnova, A.B. Khanikaev, L.A. Smirnov, Y.S. Kivshar, ACS Photonics 3, 1468 (2016)CrossRefGoogle Scholar
  87. 87.
    M.R. Shcherbakov, D.N. Neshev, B. Hopkins, A.S. Shorokhov, I. Staude, E.V. Melik-Gaykazyan, M. Decker, A.A. Ezhov, A.E. Miroshnichenko, I. Brener, A.A. Fedyanin, Y.S. Kivshar, Nano Lett. 14, 6488 (2014)ADSCrossRefGoogle Scholar
  88. 88.
    G. Grinblat, Y. Li, M.P. Nielsen, R.F. Oulton, S.A. Maier, Nano Lett. 16, 4635 (2016)ADSCrossRefGoogle Scholar
  89. 89.
    G. Grinblat, Y. Li, M.P. Nielsen, R.F. Oulton, S.A. Maier, ACS Nano 11, 953 (2016)CrossRefGoogle Scholar
  90. 90.
    G. Grinblat, Y. Li, M.P. Nielsen, R.F. Oulton, S.A. Maier, ACS Photonics 4, 2144 (2017)CrossRefGoogle Scholar
  91. 91.
    R. Colom, L. Xu, L. Marini, F. Bedu, I. Ozerov, T. Begou, J. Lumeau, A.E. Miroshnishenko, D. Neshev, B.T. Kuhlmey, S. Palomba, N. Bonod, ACS Photonics 6, 1295 (2019)CrossRefGoogle Scholar
  92. 92.
    L. Xu, M. Rahmani, K.Z. Kamali, A. Lamprianidis, L. Ghirardini, J. Sautter, R. Camacho-Morales, H. Chen, M. Parry, I. Staude, G. Zhang, D. Neshev, A.E. Miroshnichenko, Light Sci. Appl. 7, 44 (2018)ADSCrossRefGoogle Scholar
  93. 93.
    L. Wang, S. Kruk, L. Xu, M. Rahmani, D. Smirnova, A. Solntsev, I. Kravchenko, D. Neshev, Y.S. Kivshar, Nanoscale 9, 2201 (2017)CrossRefGoogle Scholar
  94. 94.
    M.R. Shcherbakov, A.S. Shorokhov, D.N. Neshev, B. Hopkins, I. Staude, E.V. Melik-Gaykazyan, A.A. Ezhov, A.E. Miroshnichenko, I. Brener, A.A. Fedyanin, Y.S. Kivshar, ACS Photonics 2, 578 (2015)CrossRefGoogle Scholar
  95. 95.
    A.S. Shorokhov, E.V. Melik-Gaykazyan, D.A. Smirnova, B. Hopkins, K.E. Chong, D.Y. Choi, M.R. Shcherbakov, A.E. Miroshnichenko, D.N. Neshev, A.A. Fedyanin, Y.S. Kivshar, Nano Lett. 16, 4857 (2016)ADSCrossRefGoogle Scholar
  96. 96.
    M.K. Kroychuk, D.F. Yagudin, A.S. Shorokhov, D.A. Smirnova, I.I. Volkovskaya, M.R. Shcherbakov, G. Shvets, Y.S. Kivshar, A.A. Fedyanin, Adv. Opt. Mater. 7, 1900447 (2019)Google Scholar
  97. 97.
    Y. Yang, W. Wang, A. Boulesbaa, I.I. Kravchenko, D.P. Briggs, A. Puretzky, D. Geohegan, J. Valentine, Nano Lett. 15, 7388 (2015)ADSCrossRefGoogle Scholar
  98. 98.
    H. Liu, C. Guo, G. Vampa, J.L. Zhang, T. Sarmiento, M. Xiao, P.H. Bucksbaum, J. Vučković, S. Fan, D.A. Reis, Nat. Phys. 14, 1006 (2018)CrossRefGoogle Scholar
  99. 99.
    S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, Y.S. Kivshar, Nat. Nanotechnol. 14, 126 (2019)Google Scholar
  100. 100.
    D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.Y. Choi, Y.S. Kivshar, Phys. Rev. Lett. 123, 103901 (2019)Google Scholar
  101. 101.
    K. Koshelev, Y. Tang, K. Li, D.Y. Choi, G. Li, Y.S. Kivshar, ACS Photonics 6, 1639 (2019)CrossRefGoogle Scholar
  102. 102.
    L. Xu, K. Zangeneh Kamali, L. Huang, M. Rahmani, A. Smirnov, R. Camacho-Morales, Y. Ma, G. Zhang, M. Woolley, D. Neshev, A.E. Miroshnichenko, Adv. Sci. 6, 1802119 (2019)Google Scholar
  103. 103.
    L. Carletti, S.S. Kruk, A.A. Bogdanov, C. De Angelis, Y.S. Kivshar, Phys. Rev. Res. 1, 023016 (2019)Google Scholar
  104. 104.
    K.I. Okhlopkov, P.A. Shafirin, A.A. Ezhov, N.A. Orlikovsky, M.R. Shcherbakov, A.A. Fedyanin, ACS Photonics 6, 189 (2018)CrossRefGoogle Scholar
  105. 105.
    S. Chen, M. Rahmani, K.F. Li, A. Miroshnichenko, T. Zentgraf, G. Li, D. Neshev, S. Zhang, ACS Photonics 5, 1671 (2018)CrossRefGoogle Scholar
  106. 106.
    E.V. Melik-Gaykazyan, S.S. Kruk, R. Camacho-Morales, L. Xu, M. Rahmani, K.Z. Kamali, A. Lamprianidis, A.E. Miroshnichenko, A.A. Fedyanin, D.N. Neshev, Y.S. Kivshar, ACS Photonics 5, 728 (2017)CrossRefGoogle Scholar
  107. 107.
    Y. Gao, Y. Fan, Y. Wang, W. Yang, Q. Song, S. Xiao, Nano Lett. 18, 8054 (2018)ADSCrossRefGoogle Scholar
  108. 108.
    M.R. Shcherbakov, P.P. Vabishchevich, A.S. Shorokhov, K.E. Chong, D.Y. Choi, I. Staude, A.E. Miroshnichenko, D.N. Neshev, A.A. Fedyanin, Y.S. Kivshar, Nano Lett. 15, 6985 (2015)ADSCrossRefGoogle Scholar
  109. 109.
    L. Wang, S. Kruk, K. Koshelev, I. Kravchenko, B. Luther-Davies, Y.S. Kivshar, Nano Lett. 18, 3978 (2018)ADSCrossRefGoogle Scholar
  110. 110.
    B. Reineke, B. Sain, R. Zhao, L. Carletti, B. Liu, L. Huang, C. De Angelis, T. Zentgraf, Nano Lett. 19, 6585 (2019)ADSCrossRefGoogle Scholar
  111. 111.
    K.M. Dani, Z. Ku, P.C. Upadhya, R.P. Prasankumar, S. Brueck, A.J. Taylor, Nano Lett. 9, 3565 (2009)ADSCrossRefGoogle Scholar
  112. 112.
    S. Makarov, S. Kudryashov, I. Mukhin, A. Mozharov, V. Milichko, A. Krasnok, P. Belov, Nano Lett. 15, 6187 (2015)ADSCrossRefGoogle Scholar
  113. 113.
    G. Li, S. Zhang, T. Zentgraf, Nat. Rev. Mater. 2, 17010 (2017)ADSCrossRefGoogle Scholar
  114. 114.
    Y.S. Kivshar, Natl. Sci. Rev. 5, 144 (2018)Google Scholar
  115. 115.
    A. Krasnok, M. Tymchenko, A. Alù, Mater. Today 21, 8 (2018)CrossRefGoogle Scholar
  116. 116.
    B. Sain, C. Meier, T. Zentgraf, Adv. Photonics 1, 024002 (2019)ADSCrossRefGoogle Scholar
  117. 117.
    L. Carletti, A. Locatelli, O. Stepanenko, G. Leo, C. De Angelis, Opt. Express 23, 26544 (2015)ADSCrossRefGoogle Scholar
  118. 118.
    R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D.A. Smirnova, A.S. Solntsev, A. Miroshnichenko, H.H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y.S. Kivshar, D.N. Neshev, Nano Lett. 16, 7191 (2016)ADSCrossRefGoogle Scholar
  119. 119.
    J.D. Sautter, L. Xu, A.E. Miroshnichenko, M. Lysevych, I. Volkovskaya, D.A. Smirnova, R. Camacho-Morales, K. Zangeneh Kamali, F. Karouta, K. Vora, H.H. Tan, M. Kauranen, I. Staude, C. Jagadish, D.N. Neshev, M. Rahmani, Nano Lett. 19, 3905 (2019)ADSCrossRefGoogle Scholar
  120. 120.
    L. Xu, G. Saerens, M. Timofeeva, D.A. Smirnova, I. Volkovskaya, M. Lysevych, R. Camacho-Morales, M. Cai, K. Zangeneh Kamali, L. Huang, F. Karouta, H.H. Tan, C. Jagadish, A.E. Miroshnichenko, R. Grange, D.N. Neshev, M. Rahmani, ACS Nano (2020). Scholar
  121. 121.
    I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, R. Ito, J. Opt. Soc. Am. B 14, 2268 (1997)ADSCrossRefGoogle Scholar
  122. 122.
    M. Ohashi, T. Kondo, R. Ito, S. Fukatsu, Y. Shiraki, K. Kumata, S. Kano, J. Appl. Phys. 74, 596 (1993)ADSCrossRefGoogle Scholar
  123. 123.
    M. Rahmani, G. Leo, I. Brener, A.V. Zayats, S.A. Maier, C. De Angelis, H. Tan, V.F. Gili, F. Karouta, R. Oulton, K. Vora, M. Lysevych, I. Staude, L. Xu, A.E. Miroshnichenko, C. Jagadish, D.N. Neshev, Opto-Electron. Adv. 1, 180021 (2018)CrossRefGoogle Scholar
  124. 124.
    L. Carletti, A. Locatelli, D. Neshev, C. De Angelis, ACS Photonics 3, 1500 (2016)CrossRefGoogle Scholar
  125. 125.
    L. Carletti, D. Rocco, A. Locatelli, C. De Angelis, V.F. Gili, M. Ravaro, I. Favero, G. Leo, M. Finazzi, L. Ghirardini, M. Celebrano, G. Marino, A.V. Zayats, Nanotechnology 28, 114005 (2017)ADSCrossRefGoogle Scholar
  126. 126.
    M. Guasoni, L. Carletti, D. Neshev, C. De Angelis, IEEE J. Quantum Electron. 53, 1 (2017)CrossRefGoogle Scholar
  127. 127.
    V.F. Gili, L. Carletti, A. Locatelli, D. Rocco, M. Finazzi, L. Ghirardini, I. Favero, C. Gomez, A. Lemaître, M. Celebrano, C. De Angelis, G. Leo, Opt. Express 24, 15965 (2016)ADSCrossRefGoogle Scholar
  128. 128.
    S. Liu, M.B. Sinclair, S. Saravi, G.A. Keeler, Y. Yang, J. Reno, G.M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, I. Brener, Nano Lett. 16, 5426 (2016)ADSCrossRefGoogle Scholar
  129. 129.
    S. Liu, G.A. Keeler, J.L. Reno, M.B. Sinclair, I. Brener, Adv. Opt. Mater. 4, 1457 (2016)CrossRefGoogle Scholar
  130. 130.
    L. Ghirardini, L. Carletti, V. Gili, G. Pellegrini, L. Duò, M. Finazzi, D. Rocco, A. Locatelli, C. De Angelis, I. Favero, M. Ravaro, G. Leo, A. Lemaître, M. Celebrano, Opt. Lett. 42, 559 (2017)ADSCrossRefGoogle Scholar
  131. 131.
    S.S. Kruk, R. Camacho-Morales, L. Xu, M. Rahmani, D.A. Smirnova, L. Wang, H.H. Tan, C. Jagadish, D.N. Neshev, Y.S. Kivshar, Nano Lett. 17, 3914 (2017)ADSCrossRefGoogle Scholar
  132. 132.
    J. Cambiasso, G. Grinblat, Y. Li, A. Rakovich, E. Cortés, S.A. Maier, Nano Lett. 17, 1219 (2017)ADSCrossRefGoogle Scholar
  133. 133.
    R. Camacho-Morales, G. Bautista, X. Zang, L. Xu, L. Turquet, A. Miroshnichenko, H.H. Tan, A. Lamprianidis, M. Rahmani, C. Jagadish, D.N. Neshev, M. Kauranen, Nanoscale 11, 1745 (2019)CrossRefGoogle Scholar
  134. 134.
    F. Koyama, J. lightwave Technol. 24, 4502 (2006)ADSCrossRefGoogle Scholar
  135. 135.
    L. Carletti, G. Marino, L. Ghirardini, V.F. Gili, D. Rocco, I. Favero, A. Locatelli, A.V. Zayats, M. Celebrano, M. Finazzi, G. Leo, C. De Angelis, D.N. Neshev, ACS Photonics 5, 4386 (2018)CrossRefGoogle Scholar
  136. 136.
    P.P. Vabishchevich, S. Liu, M.B. Sinclair, G.A. Keeler, G.M. Peake, I. Brener, ACS Photonics 5, 1685 (2018)CrossRefGoogle Scholar
  137. 137.
    L. Ghirardini, G. Marino, V.F. Gili, I. Favero, D. Rocco, L. Carletti, A. Locatelli, C. De Angelis, M. Finazzi, M. Celebrano, D.N. Neshev, G. Leo, Nano Lett. 18, 6750 (2018)ADSCrossRefGoogle Scholar
  138. 138.
    G. Marino, C. Gigli, D. Rocco, A. Lemaître, I. Favero, C. De Angelis, G. Leo, ACS Photonics 6, 1226 (2019)CrossRefGoogle Scholar
  139. 139.
    F.J.F. Löchner, A.N. Fedotova, S. Liu, G.A. Keeler, G.M. Peake, S. Saravi, M.R. Shcherbakov, S. Burger, A.A. Fedyanin, I. Brener, T. Pertsch, F. Setzpfandt, I. Staude, ACS Photonics 5, 1786 (2018)CrossRefGoogle Scholar
  140. 140.
    S. Liu, P.P. Vabishchevich, A. Vaskin, J.L. Reno, G.A. Keeler, M.B. Sinclair, I. Staude, I. Brener, Nat. Commun. 9, 2507 (2018)ADSCrossRefGoogle Scholar
  141. 141.
    G. Marino, A.S. Solntsev, L. Xu, V.F. Gili, L. Carletti, A.N. Poddubny, M. Rahmani, D.A. Smirnova, H. Chen, A. Lemaître, G. Zhang, A.V. Zayats, C.D. Angelis, G. Leo, A.A. Sukhorukov, D.N. Neshev, Optica 6, 1416 (2019)ADSCrossRefGoogle Scholar
  142. 142.
    D. Rocco, V.F. Gili, L. Ghirardini, L. Carletti, I. Favero, A. Locatelli, G. Marino, D.N. Neshev, M. Celebrano, M. Finazzi, G. Leo, C. De Angelis, Photonics Res. 6, B6 (2018)CrossRefGoogle Scholar
  143. 143.
    B. Gao, M. Ren, W. Wu, H. Hu, W. Cai, J. Xu, Laser Photonics Rev. 13, 1800312 (2019)ADSCrossRefGoogle Scholar
  144. 144.
    F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M.T. Buscaglia, V. Buscaglia, R. Grange, ACS Photonics 6, 545 (2019)CrossRefGoogle Scholar
  145. 145.
    L. Carletti, C. Li, J. Sautter, I. Staude, C.D. Angelis, T. Li, D.N. Neshev, Opt. Express 27, 33391 (2019)ADSCrossRefGoogle Scholar
  146. 146.
    K. Koshelev, S. Kruk, E. Melik-Gaykazyan, J.H. Choi, A. Bogdanov, H.G. Park, Y.S. Kivshar, Science 367, 288 (2020)ADSCrossRefGoogle Scholar
  147. 147.
    D.N. Neshev, in Frontiers in Optics \(+\) Laser Science APS/DLS. OSA Technical Digest (Optical Society of America, 2019), paper FM5B.1Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Lei Xu
    • 1
  • Mohsen Rahmani
    • 2
    • 3
  • David A. Powell
    • 1
  • Dragomir Neshev
    • 4
  • Andrey E. Miroshnichenko
    • 1
    Email author
  1. 1.School of Engineering and Information TechnologyUniversity of New South WalesCanberraAustralia
  2. 2.Research School of PhysicsNonlinear Physics Centre, The Australian National UniversityCanberraAustralia
  3. 3.Advanced Optics and Photonics Laboratory, Department of EngineeringNottingham Trent UniversityNottinghamUK
  4. 4.Research School of PhysicsARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), The Australian National UniversityCanberraAustralia

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