Amorphous Nanophotonics pp 89-117

Part of the Nano-Optics and Nanophotonics book series (NON) | Cite as

Multipole Analysis of Self-assembled Metamaterials

Abstract

We provide here a review on the theoretical description of the interaction of light with metamaterials fabricated by chemical self-assembling processes. Unique to the metamaterials accessible with such approaches is the amorphous arrangement of the unit-cells in space. This is in striking contrast to most of the structures previously considered, i.e. metamaterials fabricated by top-down process that usually lead to periodically arranged unit-cells. In consequence, novel concepts have to be established to describe the light interaction with their metamaterials and novel design rules have to be developed to suggest metamaterials that shall provide a desired optical response. A theoretical description based on Cartesian multipole moments is outlined in this chapter that fully satisfies these requirements. The description of the scattering response of the unit-cells is revealed as to be essential to understand amorphous metamaterials. Based on mixing rules, the propagation of light in amorphous metamaterials is properly described in terms of excited multipole moments of their unit-cells. The theoretical framework we outline here provides the methodology to discuss amorphous metamaterials and constitutes therefore an indispensable tool for the future development of optical components exploiting amorphous nanooptical materials.

References

  1. 1.
    A.P. Alivisatos, K.P. Johnsson, X. Peng, T.E. Wilson, C.J. Loweth, M.P. Bruchez, P.G. Schultz, Nature 382, 609–611 (1996) ADSGoogle Scholar
  2. 2.
    L.C. Brousseau III, J.P. Novak, S.M. Marinakos, D.L. Feldheim, Adv. Mater. 11, 447–449 (1999) Google Scholar
  3. 3.
    K.J.M. Bishop, C.E. Wilmer, S. Soh, B.A. Grzybowski, Small 5, 1600–1630 (2009) Google Scholar
  4. 4.
    C.L. Choi, A.P. Alivisatos, Annu. Rev. Phys. Chem. 61, 369–389 (2010) Google Scholar
  5. 5.
    J.M. Romo-Herrera, R.A. Alvarez-Puebla, L.M. Liz-Marzan, Nanoscale 3, 1304–1315 (2011) ADSGoogle Scholar
  6. 6.
    A. Guerrero-Martínez, J.L. Alonso-Gómez, B. Auguié, M.M. Cid, L.M. Liz-Marzán, Nano Today 6, 381–400 (2011) Google Scholar
  7. 7.
    J.Y. Cheng, C.A. Ross, E.L. Thomas, H.I. Smith, G.J. Vancso, Appl. Phys. Lett. 81, 3657–3659 (2002) ADSGoogle Scholar
  8. 8.
    S. Darling, Prog. Polym. Sci. 32, 1152–1204 (2007) Google Scholar
  9. 9.
    T. Smart, H. Lomas, M. Massignani, M.V. Flores-Merino, L.R. Perez, G. Battaglia, Nano Today 3, 38–46 (2008) Google Scholar
  10. 10.
    J. Bang, U. Jeong, D.Y. Ryu, T.P. Russell, C.J. Hawker, Adv. Mater. 21, 4769–4792 (2009) Google Scholar
  11. 11.
    J. Polleux, M. Rasp, I. Louban, N. Plath, A. Feldhoff, J.P. Spatz, ACS Nano 5, 6355–6364 (2011) Google Scholar
  12. 12.
    X. Wang, D.-H. Kwon, D.H. Werner, I.-C. Khoo, A.V. Kildishev, V.M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007) ADSGoogle Scholar
  13. 13.
    R. Pratibha, K. Park, I.I. Smalyukh, W. Park, Opt. Express 17, 19459–19469 (2009) ADSGoogle Scholar
  14. 14.
    R. Pratibha, W. Park, I.I. Smalyukh, J. Appl. Phys. 107, 063511 (2010) ADSGoogle Scholar
  15. 15.
    R.J. Macfarlane, B. Lee, M.R. Jones, N. Harris, G.C. Schatz, C.A. Mirkin, Science 334, 204–208 (2011) ADSGoogle Scholar
  16. 16.
    W. Cheng, M.J. Campolongo, J.J. Cha, S.J. Tan, C.C. Umbach, D.A. Muller, D. Luo, Nat. Mater. 8, 519–525 (2009) ADSGoogle Scholar
  17. 17.
    A.M. Hung, C.M. Micheel, L.D. Bozano, L.W. Osterbur, G.M. Wallraff, J.N. Cha, Nat. Nanotechnol. 5, 121–126 (2010) ADSGoogle Scholar
  18. 18.
    Y. Chen, J. Fu, K.C. Ng, Y. Tang, W. Cheng, Cryst. Growth Des. 11, 4742–4746 (2011) Google Scholar
  19. 19.
    K.C. Ng, I.B. Udagedara, I.D. Rukhlenko, Y. Chen, Y. Tang, M. Premaratne, W. Cheng, ACS Nano 6, 925–934 (2012) Google Scholar
  20. 20.
    T. Wen, S.A. Majetich, ACS Nano 5, 8868–8876 (2011) Google Scholar
  21. 21.
    K.J. Stebe, E. Lewandowski, M. Ghosh, Science 325, 159–160 (2009) Google Scholar
  22. 22.
    J.H. Lee, Q. Wu, W. Park, Opt. Lett. 34, 443–445 (2009) ADSGoogle Scholar
  23. 23.
    T. Lerond, J. Proust, H. Yockell-Lelièvre, D. Gérard, J. Plain, Appl. Phys. Lett. 99, 123110 (2011) ADSGoogle Scholar
  24. 24.
    J. Henzie, M. Grünwald, A. Widmer-Cooper, P.L. Geissler, P. Yang, Nat. Mater. 11, 131–137 (2011) ADSGoogle Scholar
  25. 25.
    D.V. Talapin, E.V. Shevchenko, M.I. Bodnarchuk, X. Ye, J. Chen, C.B. Murray, Nature 461, 964–967 (2009) ADSGoogle Scholar
  26. 26.
    V.A. Tamma, J.-H. Lee, Q. Wu, W. Park, Appl. Opt. 49, A11–A17 (2009) ADSGoogle Scholar
  27. 27.
    J.A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N.J. Halas, V.N. Manoharan, P. Nordlander, G. Shvets, F. Capasso, Science 328, 1135–1138 (2010) ADSGoogle Scholar
  28. 28.
    L. Chuntonov, G. Haran, Nano Lett. 11, 2440–2445 (2011) ADSGoogle Scholar
  29. 29.
    J.A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N.J. Halas, V.N. Manoharan, G. Shvets, P. Nordlander, F. Capasso, Nano Lett. 10, 4680–4685 (2010) ADSGoogle Scholar
  30. 30.
    S.J. Tan, M.J. Campolongo, D. Luo, W. Cheng, Nat. Nanotechnol. 6, 268–276 (2011) ADSGoogle Scholar
  31. 31.
    C.A. Mirkin, R.L. Letsinger, R.C. Mucic, J.J. Storhoff, Nature 382, 607–609 (1996) ADSGoogle Scholar
  32. 32.
    O.I. Wilner, I. Willner, Chem. Rev. 112, 2528–2556 (2012) Google Scholar
  33. 33.
    S.A. Claridge, S.L. Goh, J.M.J. Fréchet, S.C. Williams, C.M. Micheel, A.P. Alivisatos, Chem. Mater. 17, 1628–1635 (2005) Google Scholar
  34. 34.
    C.M. Soto, A. Srinivasan, B.R. Ratna, J. Am. Chem. Soc. 124, 8508–8509 (2002) Google Scholar
  35. 35.
    S. Sheikholeslami, Y.-w. Jun, P.K. Jain, A.P. Alivisatos, Nano Lett. 10, 2655–2660 (2010) ADSGoogle Scholar
  36. 36.
    J.A. Fan, Y. He, K. Bao, C. Wu, J. Bao, N.B. Schade, V.N. Manoharan, G. Shvets, P. Nordlander, D.R. Liu, F. Capasso, Nano Lett. 11, 4859–4864 (2011) ADSGoogle Scholar
  37. 37.
    S.J. Barrow, A.M. Funston, D.E. Gómez, T.J. Davis, P. Mulvaney, Nano Lett. 11, 4180–4187 (2011) ADSGoogle Scholar
  38. 38.
    H. Xing, Z. Wang, Z. Xu, N.Y. Wong, Y. Xiang, G.L. Liu, Y. Lu, ACS Nano 6, 802–809 (2012) Google Scholar
  39. 39.
    D. Nykypanchuk, M.M. Maye, D. van der Lelie, O. Gang, Nature 451, 549–552 (2008) ADSGoogle Scholar
  40. 40.
    A.J. Mastroianni, S.A. Claridge, A.P. Alivisatos, J. Am. Chem. Soc. 131, 8455–8459 (2009) Google Scholar
  41. 41.
    O.-S. Lee, T.R. Prytkova, G.C. Schatz, J. Phys. Chem. Lett. 1, 1781–1788 (2010) Google Scholar
  42. 42.
    J.P. Novak, D.L. Feldheim, J. Am. Chem. Soc. 122, 3979–3980 (2000) Google Scholar
  43. 43.
    S. Mühlig, C. Rockstuhl, V. Yannopapas, T. Bürgi, N. Shalkevich, F. Lederer, Opt. Express 19, 9607–9616 (2011) ADSGoogle Scholar
  44. 44.
    D.A. Walker, B. Kowalczyk, M.O. De la Cruz, B.A. Grzybowski, Nanoscale 3, 1316–1344 (2011) ADSGoogle Scholar
  45. 45.
    G. Decher, Science 277, 1232–1237 (1997) Google Scholar
  46. 46.
    A. Cunningham, S. Mühlig, C. Rockstuhl, T. Bürgi, J. Phys. Chem. C 115, 8955–8960 (2011) Google Scholar
  47. 47.
    L.V. Brown, H. Sobhani, J.B. Lassiter, P. Nordlander, N.J. Halas, ACS Nano 4, 819–832 (2010) Google Scholar
  48. 48.
    M.N. Hyder, S.W. Lee, F.C. Cebeci, D.J. Schmidt, Y. Shao-Horn, P.T. Hammond, ACS Nano 5, 8552–8561 (2011) Google Scholar
  49. 49.
    S. Mühlig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, F. Lederer, ACS Nano 5, 6586–6592 (2011) Google Scholar
  50. 50.
    M. Gellner, S. Niebling, H.Y. Kuschelmeister, C. Schmuck, S. Schlücker, Chem. Commun. 47, 12762–12764 (2011) Google Scholar
  51. 51.
    M. Gellner, D. Steinigeweg, S. Ichilmann, M. Salehi, M. Schütz, K. Kömpe, M. Haase, S. Schlücker, Small 7, 3445–3451 (2011) Google Scholar
  52. 52.
    D.A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, I. Vendik, Adv. Funct. Mater. 20, 1116–1124 (2010) Google Scholar
  53. 53.
    B. Senyuk, J.S. Evans, P.J. Ackerman, T. Lee, P. Manna, L. Vigderman, E.R. Zubarev, J.v.d. Lagemaat, I.I. Smalyukh, Nano Lett. 12, 955–963 (2012) ADSGoogle Scholar
  54. 54.
    H.O. Moser, C. Rockstuhl, Laser Photonics Rev. 6, 219–244 (2012) Google Scholar
  55. 55.
    D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Science 305, 788–792 (2004) ADSGoogle Scholar
  56. 56.
    V.M. Shalaev, Nat. Photonics 1, 41–48 (2007) ADSGoogle Scholar
  57. 57.
    C.M. Soukoulis, M. Wegener, Nat. Photonics 5, 523–530 (2011) ADSGoogle Scholar
  58. 58.
    T. Okamoto, Near-Field Optics and Surface Plasmon Polaritons (Springer, Berlin, 2001) Google Scholar
  59. 59.
    Y.-Y. Yu, S.-S. Chang, C.-L. Lee, C.R.C. Wang, J. Phys. Chem. B 101, 6661–6664 (1997) Google Scholar
  60. 60.
    C. Helgert, C. Menzel, C. Rockstuhl, E. Pshenay-Severin, E.-B. Kley, A. Chipouline, A. Tünnermann, F. Lederer, T. Pertsch, Opt. Lett. 34, 704–706 (2009) ADSGoogle Scholar
  61. 61.
    E. Prodan, C. Radloff, N.J. Halas, P. Nordlander, Science 302, 419–422 (2003) ADSGoogle Scholar
  62. 62.
    S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, S.R.J. Brueck, Phys. Rev. Lett. 95, 137404 (2005) ADSGoogle Scholar
  63. 63.
    J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A.M. Stacy, X. Zhang, Science 321, 930 (2008) ADSGoogle Scholar
  64. 64.
    G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, S. Linden, Science 312, 892–894 (2006) ADSGoogle Scholar
  65. 65.
    N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, Nat. Mater. 7, 31–37 (2008) ADSGoogle Scholar
  66. 66.
    J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D.A. Genov, G. Bartal, X. Zhang, Nature 455, 376–379 (2008) ADSGoogle Scholar
  67. 67.
    C. Menzel, A. Andryieuski, C. Rockstuhl, R. Iliew, R. Malureanu, F. Lederer, A. Lavrinenko, Phys. Rev. B 81, 195123 (2010) ADSGoogle Scholar
  68. 68.
    C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J.F. Zhou, Th. Koschny, C.M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005) ADSGoogle Scholar
  69. 69.
    J.K. Gansel, M. Thiel, M.S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, M. Wegerner, Science 325, 1513–1515 (2009) ADSGoogle Scholar
  70. 70.
    C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, F. Lederer, Phys. Rev. B 81, 035320 (2010) ADSGoogle Scholar
  71. 71.
    J.B. Pendry, Phys. Rev. Lett. 85, 3966–3969 (2000) ADSGoogle Scholar
  72. 72.
    T. Paul, C. Menzel, C. Rockstuhl, F. Lederer, Adv. Mater. 22, 2354–2357 (2010) Google Scholar
  73. 73.
    M. Husnik, M.W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, M. Wegener, Nat. Photonics 2, 614–617 (2008) Google Scholar
  74. 74.
    T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, H. Giessen, Opt. Lett. 33, 848–850 (2008) ADSGoogle Scholar
  75. 75.
    I. Sersic, C. Tuambilangana, A.F. Koenderink, New J. Phys. 13, 083019 (2011) ADSGoogle Scholar
  76. 76.
    P. Banzer, U. Peschel, S. Quabis, G. Leuchs, Opt. Express 18, 10905–10923 (2010) ADSGoogle Scholar
  77. 77.
    F. von Cube, S. Irsen, J. Niegemann, C. Matyssek, W. Hergert, K. Busch, S. Linden, Opt. Mater. Express 1, 1009–1018 (2011) Google Scholar
  78. 78.
    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999) ADSGoogle Scholar
  79. 79.
    S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, C.M. Soukoulis, Science 306, 1351–1353 (2004) ADSGoogle Scholar
  80. 80.
    I. Sersic, M. Frimmer, E. Verhagen, A.F. Koenderink, Phys. Rev. Lett. 103, 213902 (2009) ADSGoogle Scholar
  81. 81.
    I. Sersic, C. Tuambilangana, T. Kampfrath, A.F. Koenderink, Phys. Rev. B 83, 245102 (2011) ADSGoogle Scholar
  82. 82.
    J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, T. Pertsch, Phys. Rev. A 78, 043811 (2008) ADSGoogle Scholar
  83. 83.
    C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, H. Giessen, Opt. Express 14, 8827–8836 (2006) ADSGoogle Scholar
  84. 84.
    T.D. Corrigan, P.W. Kolb, A.B. Sushkov, H.D. Drew, D.C. Schmadel, R.J. Phaneuf, Opt. Express 16, 19850 (2008) ADSGoogle Scholar
  85. 85.
    P.C. Waterman, Phys. Rev. D 3, 825–839 (1971) ADSGoogle Scholar
  86. 86.
    M.I. Mishchenko, L.D. Travis, D.W. Mackowski, J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996) ADSGoogle Scholar
  87. 87.
    T.A. Nieminen, N.R. Heckenberg, H. Rubinsztein-Dunlop, in SPIE Conference Series, vol. 5514, ed. by K. Dholakia, G.C. Spalding (2004), pp. 514–523 Google Scholar
  88. 88.
    D.W. Mackowski, M.I. Mishchenko, J. Opt. Soc. Am. A 13, 2266–2278 (1996) ADSGoogle Scholar
  89. 89.
    J.B. Schneider, I.C. Peden, IEEE Trans. Antennas Propag. 36, 1317–1321 (1988) ADSGoogle Scholar
  90. 90.
    T.A. Nieminen, V.L.Y. Loke, A.B. Stilgoe, G. Knöner, A.M. Brańczyk, N.R. Heckenberg, H. Rubinsztein-Dunlop, J. Opt. A, Pure Appl. Opt. 9, 196–203 (2007) ADSGoogle Scholar
  91. 91.
    S. Mühlig, C. Menzel, C. Rockstuhl, F. Lederer, Metamaterials 5, 64–73 (2011) ADSGoogle Scholar
  92. 92.
    Y.-l. Xu, Appl. Opt. 34, 4573–4588 (1995) ADSGoogle Scholar
  93. 93.
    S. Mühlig, C. Rockstuhl, J. Pniewski, C.R. Simovski, S.A. Tretyakov, F. Lederer, Phys. Rev. B 81, 075317 (2010) ADSGoogle Scholar
  94. 94.
    C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, (1998) Google Scholar
  95. 95.
    C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, F. Lederer, Phys. Rev. B 83, 245119 (2011) ADSGoogle Scholar
  96. 96.
    U. Leonhardt, T.G. Philbin, in Progress in Optics, vol. 53 (Elsevier, Amsterdam, 2009), pp. 69–152 Google Scholar
  97. 97.
    E.D. Palik, Handbook of Optical Constants of Solids, (1985) Google Scholar
  98. 98.
    A.B. Evlyukhin, C. Reinhardt, A. Seidel, B.S. Luk’Yanchuk, B.N. Chichkov, Phys. Rev. B 82, 045404 (2010) ADSGoogle Scholar
  99. 99.
    A. García-Etxarri, R. Gómez-Medina, L.S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, J.J. Sáenz, Opt. Express 19, 4815–4826 (2011) ADSGoogle Scholar
  100. 100.
    Q. Zhao, J. Zhou, F. Zhang, D. Lippens, Mater. Today 12, 60–69 (2009) Google Scholar
  101. 101.
    V. Yannopapas, A. Moroz, J. Phys. Condens. Matter 17, 3717–3734 (2005) ADSGoogle Scholar
  102. 102.
    M.S. Wheeler, J.S. Aitchison, M. Mojahedi, Phys. Rev. B 72, 193103 (2005) ADSGoogle Scholar
  103. 103.
    B.-J. Seo, T. Ueda, T. Itoh, H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006) ADSGoogle Scholar
  104. 104.
    L. Jylhä, I. Kolmakov, S. Maslovski, S. Tretyakov, J. Appl. Phys. 99, 043102 (2006) ADSGoogle Scholar
  105. 105.
    V. Yannopapas, Phys. Rev. B 75, 035112 (2007) ADSGoogle Scholar
  106. 106.
    V. Yannopapas, Appl. Phys. A 87, 259–264 (2007) ADSGoogle Scholar
  107. 107.
    J.A. Schuller, R. Zia, T. Taubner, M.L. Brongersma, Phys. Rev. Lett. 99, 107401 (2007) ADSGoogle Scholar
  108. 108.
    M.S. Wheeler, J.S. Aitchison, J.I.L. Chen, G.A. Ozin, M. Mojahedi, Phys. Rev. B 79, 073103 (2009) ADSGoogle Scholar
  109. 109.
    P. Nordlander, C. Oubre, E. Prodan, K. Li, M.I. Stockman, Nano Lett. 4, 899–903 (2004) ADSGoogle Scholar
  110. 110.
    S. Riikonen, I. Romero, F.J. Garcia de Abajo, Phys. Rev. B 71, 235104 (2005) ADSGoogle Scholar
  111. 111.
    N. Shalkevich, A. Shalkevich, L. Si-Ahmed, T. Bürgi, Phys. Chem. Chem. Phys. 11, 10175 (2009) Google Scholar
  112. 112.
    J. Dintinger, S. Mühlig, C. Rockstuhl, T. Scharf, Opt. Mater. Express 2, 269–278 (2012) Google Scholar
  113. 113.
    C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, T. Scharf, Phys. Rev. Lett. 99, 017401 (2007) ADSGoogle Scholar
  114. 114.
    C.R. Simovski, S.A. Tretyakov, Phys. Rev. B 79, 045111 (2009) ADSGoogle Scholar
  115. 115.
    D.R. Smith, S. Schultz, P. Markoš, C.M. Soukoulis, Phys. Rev. B 65, 195104 (2002) ADSGoogle Scholar
  116. 116.
    C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, Phys. Rev. B 77, 195328 (2008) ADSGoogle Scholar
  117. 117.
    S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, S.R.J. Brueck, Phys. Rev. Lett. 95, 137404 (2005) ADSGoogle Scholar
  118. 118.
    V.P. Drachev, W. Cai, U. Chettiar, H.-K. Yuan, A.K. Sarychev, A.V. Kildishev, G. Klimeck, V.M. Shalaev, Laser Phys. Lett. 3, 49–55 (2006) ADSGoogle Scholar
  119. 119.
    E. Pshenay-Severin, F. Setzpfandt, C. Helgert, U. Hübner, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, T. Pertsch, J. Opt. Soc. Am. B 27, 660–666 (2010) Google Scholar
  120. 120.
    C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, F. Lederer, Phys. Rev. B 78, 155102 (2008) ADSGoogle Scholar
  121. 121.
    T. Paul, C. Rockstuhl, C. Menzel, F. Lederer, Phys. Rev. B 79, 115430 (2009) ADSGoogle Scholar
  122. 122.
    T. Paul, C. Menzel, W. Śmigaj, C. Rockstuhl, P. Lalanne, F. Lederer, Phys. Rev. B 84, 115142 (2011) ADSGoogle Scholar
  123. 123.
    C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, T. Pertsch, Phys. Rev. B 79, 233107 (2009) ADSGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Abbe Center of Photonics, Institute of Condensed Matter Theory and Solid State OpticsFriedrich-Schiller-Universität JenaJenaGermany

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