Electromagnetic density of states in complex plasmonic systems

Surface Science Reports

Volumn 70, Issue 1, 2015, Pages 1-41

  Carminati, R ^a   Caze A ^b   Cao, D ^a   Peragut, F ^a   Krachmalnicoff, V ^a   Pierrat, R ^a   De Wilde, Y ^a  

^a PSL RESEARCH UNIVERSITY   (France)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Cross density of states; Local density of states; Plasmonics; Spatial coherence; Spontaneous emission; Thermal radiation

Indexed keywords

HEAT RADIATION; NANOSTRUCTURES; SPONTANEOUS EMISSION; SURFACE PLASMONS;

COMPLEX NANOSTRUCTURES; DENSITY OF STATE; FLUORESCENCE MEASUREMENTS; LIGHT CONCENTRATION; LIGHT-MATTER INTERACTIONS; LOCAL DENSITY OF STATE; METALLIC NANOSTRUCTURE; SPATIAL COHERENCE;

PLASMONICS;

EID: 84921019781     PISSN: 01675729     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.surfrep.2014.11.001     Document Type: Review

References (162)

1. H. Raether Surface Plasmons 1988 Springer-Verlag Berlin
2. D. Mills Surface Polaritons 1982 North-Holland Amsterdam
3. L. Novotny, and B. Hecht Principle of Nano-Optics 2006 Cambridge University Press Cambridge
4. S.A. Maier Plasmonics: Fundamentals and Applications 2007 Springer New-York
5. W.L. Barnes, A. Dereux, and T.W. Ebbesen Nature 424 2003 824
6. S.A. Maier, and H.A. Atwater J. Appl. Phys. 98 2005 011101
7. D.K. Gramotnev, and S.I. Bozhevolnyi Nat. Photonics 4 2010 83
8. J.A. Schuller, E.S. Barnard, W. Cai, Y.C. Jun, J.S. White, and M.L. Brongersma Nat. Mater. 9 2010 193
9. H.A. Atwater, and A. Polman Nat. Mater. 9 2010 865
10. M.I. Stockman Opt. Express 19 2011 22029
11. L. Novotny, and N.F. van Hulst Nat. Photonics 5 2011 83
12. K.F. MacDonald, and N.I. Zheludev Laser Photonics Rev. 4 2010 562
13. M.S. Tame, K.R. McEnery, S.K. Ozdemir, J. Lee, S.A. Maier, and M.S. Kim Nat. Phys. 9 2013 329
14. R.J. Glauber, and M. Lewenstein Phys. Rev. A 43 1991 467 491
15. C. Sauvan, J.P. Hugonin, I.S. Maksymov, and P. Lalanne Phys. Rev. Lett. 110 2013 237401
16. C. Sauvan, J.P. Hugonin, R. Carminati, and P. Lalanne Phys. Rev. A 89 2014 043825
17. C.-A. Guérin, B. Gralak, and A. Tip Phys. Rev. E 75 2007 056601
18. J.D. Jackson Classical Electrodynamics 1962 John Wiley and Sons New-York
19. J. van Bladel Singular Electromagnetic Fields and Sources 1991 Oxford University Press New York
20. R. Carminati, J.J. Greffet, C. Henkel, and J.M. Vigoureux Opt. Commun. 261 2006 368
21. K. Joulain, R. Carminati, J.P. Mulet, and J.J. Greffet Phys. Rev. B 68 2003 245405
22. G.S. Agarwal Phys. Rev. A 11 1975 230 242
23. J.M. Wylie, and J.E. Sipe Phys. Rev. A 30 1984 1185
24. M. Born Atomic Physics 1936 Dover New York
25. E.M. Purcell Phys. Rev. 69 1946 681
26. S. Haroche J. Dalibard, J.M. Raimond, J. Zinn-Justin, Cavity Quantum Electrodynamics in Fundamental Systems in Quantum Optics 1992 Elsevier Science Publishers Amsterdam
27. A.F. Koenderink Opt. Lett. 35 2010 4208
28. S.A. Maier Opt. Express 14 2010 1957
29. J.J. Greffet, M. Laroche, and F. Marquier Phys. Rev. Lett. 105 2010 117701
30. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa Phys. Rev. Lett. 69 1992 3314
31. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe Nature 432 2004 200
32. E. Peter, P. Senellart, D. Martrou, A. Lemai^tre, J. Hours, J.M. Gérard, and J. Bloch Phys. Rev. Lett. 95 2005 067401
33. A. Trügler, and U. Hohenester Phys. Rev. B 77 2008 115403
34. C. Van Vlack, P.T. Kristensen, and S. Hughes Phys. Rev B 85 2012 075303
35. D.E. Chang, A.S. Sørensen, E.A. Demler, and M.D. Lukin Nat. Phys. 3 2007 807
36. S. Aberra Guebrou, C. Symonds, E. Homeyer, J.C. Plenet, Y.N. Gartstein, V.M. Agranovich, and J. Bellessa Phys. Rev. Lett. 108 2012 066401
37. R. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau Nat. Photonics 7 2013 128
38. L. Sapienza, H. Thyrrestrup, S. Stobbe, P.D. Garcia, S. Smolka, and P. Lodahl Science 327 5971 2010 1352 1355 10.1126/science.1185080
39. J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D.L. Huffaker, A.D. Rossi, and C.W. Wong Sci. Rep. 3 2013 1994
40. A. Cazé, R. Pierrat, and R. Carminati Phys. Rev. Lett. 111 2013 053901
41. D. Cao, A. Cazé, M. Calabrese, R. Pierrat, N. Bardou, S. Collin, R. Carminati, V. Krachmalnicoff, Y. De Wilde, Mapping the radiative and non-radiative local density of states in the near field of a gold nanoantenna, 〈 http://arxiv.org/abs/1401.2858 〉.
42. E. Castanié, M. Boffety, and R. Carminati Opt. Lett. 35 2010 291
43. G.W. Ford, and W.H. Weber Phys. Rep. 113 1984 195
44. I.A. Larkin, M.I. Stockman, M. Achermann, and V.I. Klimov Phys. Rev. B 69 2004 121403(R)
45. G. Colas des Francs, A. Bouhelier, E. Finot, J.C. Weeber, A. Dereux, C. Girard, E. Dujardin, Opt. Express 16 (2008) 17654.
46. S. Albaladejo, R. Gómez-Medina, L.S. Froufe-Pérez, H. Marinchio, R. Carminati, J.F. Torrado, G. Armelles, A. García-Martín, and J.J. Sáenz Opt. Express 18 2010 3556
47. E. Castanié, V. Krachmalnicoff, A. Cazé, R. Pierrat, Y. De Wilde, and R. Carminati Opt. Lett. 37 2012 3006 3008
48. J.E. Sipe J. Opt. Soc. Am. B 4 1987 481
49. K. Joulain, J. Mulet, F. Marquier, R. Carminati, and J.J. Greffet Surf. Sci. Rep. 57 2005 59
50. P. Leung, and J. Vielma J. Chem. Phys. 126 2007 194704
51. P.O. Chapuis, S. Volz, C. Henkel, K. Joulain, and J.J. Greffet Phys. Rev. B 77 2008 035431
52. R. Esteban, A.G. Borisov, P. Nordlander, and J. Aizpurua Nat. Commun. 3 2012 825
53. K.J. Savage, M.M. Hawkeye, R. Esteban, A.G. Borisov, J. Aizpurua, and J. Baumberg Nature 491 2012 574
54. P.V. Ruijgrok, R. Wüest, A.A. Rebane, A. Renn, and V. Sandoghdar Opt. Express 18 6 2010 6360 6365 10.1364/OE.18.006360
55. M.D. Birowosuto, S.E. Skipetrov, W.L. Vos, and A.P. Mosk Phys. Rev. Lett. 105 2010 013904 10.1103/PhysRevLett.105.013904
56. R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N.F. van Hulst Phys. Rev. Lett. 106 2011 163902 10.1103/PhysRevLett.106.163902
57. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E.L. Hu, and A. Imamoglu Nature 445 2007 896 899
58. F.A. Inam, T. Gaebel, C. Bradac, L. Stewart, M.J. Withford, J.M. Dawes, J.R. Rabeau, and M.J. Steel New J. Phys. 13 7 2011 073012
59. S. Smolka, H. Thyrrestrup, L. Sapienza, T.B. Lehmann, K.R. Rix, L.S. Froufe-Pérez, P.D. Garcia, and P. Lodahl New J. Phys. 13 6 2011 063044
60. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati Phys. Rev. Lett. 105 2010 183901
61. I. Mallek-Zouari, S. Buil, X. Quélin, B. Mahler, B. Dubertret, and J.-P. Hermier Appl. Phys. Lett. 97 5 2010 doi: http://dx.doi.org/10.1063/1.3467264
62. D. Canneson, I. Mallek-Zouari, S. Buil, X. Quélin, C. Javaux, B. Mahler, B. Dubertret, and J.P. Hermier Phys. Rev. B 84 2011 245423 10.1103/PhysRevB.84.245423
63. S. Kühn, C. Hettich, C. Schmitt, J.-P. Poizat, and V. Sandoghdar J. Microsc. 202 1 2001 2 6 10.1046/j.1365-2818.2001.00829.x
64. A. Cuche, O. Mollet, A. Drezet, and S. Huant Nano Lett. 10 11 2010 4566 4570 10.1021/nl102568m
65. A.W. Schell, P. Engel, J.F.M. Werra, C. Wolff, K. Busch, and O. Benson Nano Lett. 14 5 2014 2623 2627 10.1021/nl500460c
66. M. Frimmer, Y. Chen, and A.F. Koenderink Phys. Rev. Lett. 107 2011 123602 10.1103/PhysRevLett.107.123602
67. V. Krachmalnicoff, D. Cao, A. Cazé, E. Castanié, R. Pierrat, N. Bardou, S. Collin, R. Carminati, and Y. De Wilde Opt. Express 21 9 2013 11536 11545 10.1364/OE.21.011536
68. J. Michaelis, C. Hettich, J. Mlynek, and V. Sandoghdar Nature 405 2000 325
69. P. Maletinsky, S. Hong, M.S. Grinolds, B. Hausmann, M.D. Lukin, R.-L. Walsworth, M. Loncar, and A. Yacoby Nat. Nanotechnol. 7 5 2012 320 324
70. B.C. Buchler, T. Kalkbrenner, C. Hettich, and V. Sandoghdar Phys. Rev. Lett. 95 2005 063003 10.1103/PhysRevLett.95.063003
71. J. Berthelot, S.S. Aćimović, M.L. Juan, M.P. Kreuzer, J. Renger, and R. Quidant Nat. Nanotechnol. 9 2014 295
72. J.N. Farahani, D.W. Pohl, H.J. Eisler, and B. Hecht Phys. Rev. Lett. 95 2005 017402 10.1103/PhysRevLett.95.017402
73. A. Singh, G. Calbris, and N.F. van Hulst Nano Lett. 14 2014 4715
74. T. van der Sar, E.C. Heeres, G.M. Dmochowski, G. de Lange, L. Robledo, T.H. Oosterkamp, and R. Hanson Appl. Phys. Lett. 94 17 2009 doi: http://dx.doi.org/10.1063/1.3120558
75. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M.D. Lukin Nano Lett. 10 10 2010 3922 3926 10.1021/nl101662v
76. A.W. Schell, G. Kewes, T. Hanke, A. Leitenstorfer, R. Bratschitsch, O. Benson, and T. Aichele Opt. Express 19 8 2011 7914 7920 10.1364/OE.19.007914
77. S. Kumar, N.I. Kristiansen, A. Huck, and U.L. Andersen Nano Lett. 14 2 2014 663 669 10.1021/nl403907w
78. F.J. García de Abajo Rev. Mod. Phys. 82 2010 209
79. M. Kociak, O. Stéphan, A. Gloter, L.F. Zagonel, L.H. Tizei, M. Tencé, K. March, J.D. Blazit, Z. Mahfoud, A. Losquin, S. Meuret, and C. Colliex C. R. Phys. 15 2014 158 175 http://dx.doi.org/http://dx.doi.org/10.1016/j.crhy.2013.10.003
80. M. Kociak, and O. Stephan Chem. Soc. Rev. 43 2014 3865 3883
81. A. Losquin, Surface plasmon modes revealed by fast electron based spectroscopies: from simple model to complex systems (Ph.D. thesis), Université Paris Sud, 2013.
82. A. Losquin, S. Camelio, D. Rossouw, M. Besbes, F. Pailloux, D. Babonneau, G.A. Botton, J.-J. Greffet, O. Stéphan, and M. Kociak Phys. Rev. B 88 2013 115427 10.1103/PhysRevB.88.115427
83. M. Kuttge, E.J.R. Vesseur, A.F. Koenderink, H.J. Lezec, H.A. Atwater, F.J. García de Abajo, and A. Polman Phys. Rev. B 79 2009 113405 10.1103/PhysRevB.79.113405
84. R. Sapienza, T. Coenen, J. Renger, M. Kuttge, N.F. Van Hulst, and A. Polman Nat. Mater. 11 2012 781
85. V.M. Shalaev Nat. Photonics 1 2007 41
86. C.M. Soukoulis, and M. Wegener Nat. Photonics 5 2011 523
87. J.B. Pendry, A. Aubry, D.R. Smith, and S.A. Maier Science 337 2012 549
88. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J.F. Zhou, T. Koschny, and C.M. Soukoulis Phys. Rev. Lett. 95 2005 203901
89. M. Husnik, M.W. Klein, N. Feth, M. Koenig, J. Niegemann, K. Busch, S. Linden, and M. Wegener Nat. Photonics 2 2008 614
90. I. Sersic, M. Frimmer, and A.F. Koenderink Phys. Rev. Lett. 103 2009 213902
91. I. Sersic, C. Tuambilangana, T. Kampfrath, and A.F. Koenderink Phys. Rev. B 83 2011 245102
92. A. Kwadrin, and A.F. Koenderink Phys. Rev. B 87 2013 125123
93. S. Karaveli, and R. Zia Opt. Lett. 35 2010 3318
94. S. Karaveli, and R. Zia Phys. Rev. Lett. 106 2011 193004
95. T.H. Taminiau, S. Karaveli, N.F. van Hulst, and R. Zia Nat. Commun. 3 2012 979
96. N. Noginova, R. Hussain, M.A. Noginov, J. Vella, and A. Urbas Opt. Express 21 2013 23087
97. L. Aigouy, A. Cazé, P. Gredin, M. Mortier, R. Carminati, Mapping and quantifying electric and magnetic dipole luminescence at the nanoscale, Phys. Rev. Lett. 113 (2014) 076101, http://dx.doi.org/10.1103/PhysRevLett.113.076101 〈 http://arxiv.org/abs/1404.1369 〉.
98. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.P. Mulet, Y. Chen, and J.J. Greffet Nature 444 2006 740
99. S.M. Rytov, Y.A. Kravtsov, and V.I. Tatarskii Principles of Statistical Radiophysics vol. 3 1989 Springer-Verlag Berlin
100. L.D. Landau, E.M. Lifshitz, and L.P. Pitaevskii Statistical Physics vol. 1 1980 Pergamon Press Oxford
101. A.V. Shchegrov, K. Joulain, R. Carminati, and J.J. Greffet Phys. Rev. Lett. 85 2000 1548
102. R. Carminati, and J.J. Greffet Phys. Rev. Lett. 82 1999 1660
103. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen Nature 416 2002 61
104. M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.J. Greffet, S. Collin, N. Bardou, and J.L. Pelouard Opt. Lett. 30 2005 2623
105. C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J.L. Pelouard, and J.J. Greffet Phys. Rev. B 86 2012 035316
106. Y. Kajihara, K. Kosaka, and S. Komiyama Rev. Sci. Instrum. 81 2010 033706
107. A.C. Jones, and M.B. Raschke Nano Lett. 12 2012 1475
108. A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. De Wilde Phys. Rev. Lett. 110 2013 146103
109. A.C. Jones, B.T. OĆallahan, H.U. Yang, and M.B. Raschke Prog. Surf. Sci. 88 2013 349
110. F. Peragut, J.-B. Brubach, P. Roy, and Y. De Wilde Appl. Phys. Lett. 104 2014 251118
111. B.T. OĆallahan, W.E. Lewis, A.C. Jones, and M.B. Raschke Phys. Rev. B 89 2014 245446
112. R. Carminati1, and J.J. Sáenz Phys. Rev. Lett. 84 2000 5156
113. K. Joulain, P. Ben-Abdallah, P.-O. Chapuis, Y. De Wilde, A. Babuty, and C. Henkel J. Quant. Spectrosc. Radiat. Transfer 136 2014 1
114. R.L. Olmon, B. Slovick, T.W. Johnson, D. Shelton, S.-H. Oh, G.D. Boreman, and M.B. Raschke Phys. Rev. B 86 2012 235147
115. J.P. Tetienne, A. Bousseksou, D. Costantini, R. Colombelli, A. Babuty, I. Moldovan-Doyen, Y. De Wilde, C. Sirtori, G. Beaudoin, L. Largeau, O. Mauguin, and I. Sagnes Appl. Phys. Lett. 97 2010 211110
116. M. Schnell, A. Garcia-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand Nano Lett. 10 2010 3524
117. P.O. Chapuis, M. Laroche, S. Volz, and J.J. Greffet Appl. Phys. Lett. 92 2008 201906
118. W. Spitzer, D. Kleinman, and D. Walsh Phys. Rev. 113 1959 127
119. A. Bousseksou, A. Babuty, J.P. Tetienne, I. Moldovan-Doyen, R. Braive, G. Beaudoin, I. Sagnes, Y. De Wilde, and R. Colombelli Opt. Exp. 20 2012 13738
120. L. Mandel, and E. Wolf Optical Coherence and Quantum Optics 1995 Cambridge University Press Cambridge
121. R.L. Weaver, and O.I. Lobkis Phys. Rev. Lett. 87 2001 134301
122. E. Larose, L. Margerin, A. Derode, B.A. van Tiggelen, M. Campillo, N. Shapiro, A. Paul, L. Stehly, and M. Tanter Geophysics 71 2006 SI11 SI21
123. T. Setala, K. Blomstedt, M. Kaivola, and A.T. Friberg Phys. Rev. E 67 2003 026613
124. P. Sheng Introduction to Wave Scattering, Localization and Mesoscopic Phenomena 1995 Academic Press San Diego
125. R. Carminati Phys. Rev. A 81 2010 053804
126. K. Vynck, R. Pierrat, and R. Carminati Phys. Rev. A 89 2014 013842
127. A. Dogariu, R. Carminati, Electromagnetic field correlations in three-dimensional speckles, Phys. Rep., http://dx.doi.org/10.1016/j.physrep.2014.11.003, in press.
128. A. Cazé, R. Pierrat, and R. Carminati Phys. Rev. Lett. 110 2013 063903
129. T. Setälä, K. Blomstedt, M. Kaivola, and A.T. Friberg Phys. Rev. E 67 2003 026613
130. G. Boudarham, and M. Kociak Phys. Rev. B 85 2012 245447
131. V.A. Markel J. Phys.: Condens. Matter 18 2006 11149
132. E. Wolf Introduction to the Theory of Coherence and Polarization of Light 2007 Cambridge University Press Cambridge
133. S. Buil, J. Aubineau, J. Laverdant, and X. Quélin J. Appl. Phys. 100 6 2006 http://dx.doi.org/10.1063/1.2335664
134. M.I. Stockman Phys. Rev. E 56 1997 6494 6507 10.1103/PhysRevE.56.6494
135. S. Grésillon, L. Aigouy, A.C. Boccara, J.C. Rivoal, X. Quelin, C. Desmarest, P. Gadenne, V.A. Shubin, A.K. Sarychev, and V.M. Shalaev Phys. Rev. Lett. 82 1999 4520
136. A.K. Sarychev, and V.M. Shalaev Phys. Rep. 335 6 2000 275 371 http://dx.doi.org/10.1016/S0370-1573(99)00118-0
137. M.I. Stockman, S.V. Faleev, and D.J. Bergman Phys. Rev. Lett. 87 2001 167401
138. K. Seal, D.A. Genov, A.K. Sarychev, H. Noh, V.M. Shalaev, Z.C. Ying, X. Zhang, and H. Cao Phys. Rev. Lett. 97 2006 206103
139. V M. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films, Springer Tracts in Modern Physics, Berlin, Heidelberg, 2000.
140. A.D. Mirlin Phys. Rep. 326 5-6 2000 259 382 doi: http://dx.doi.org/10.1016/S0370-1573(99)00091-5
141. L. Zekri, R. Bouamrane, N. Zekri, and F. Brouers J. Phys.: Condens. Matter 12 3 2000 283
142. D.A. Genov, A.K. Sarychev, and V.M. Shalaev Phys. Rev. E 67 2003 056611
143. A. Cazé, R. Pierrat, and R. Carminati Photonics Nanostruct. Fundam. Appl. 10 2012 339 344
144. J. Aubineau, Modélisation de couches minces métalliques fractales et calculs d'exaltations de champs électromagnétiques (Ph.D. thesis), Université de Versailles Saint-Quentin, 2005.
145. R. Ferrando, and G. Tréglia Phys. Rev. B 50 1994 12104 12117
146. C. Mottet, R. Ferrando, F. Hontinfinde, and A.C. Levi Surf. Sci. 417 1998 220 237
147. F. Cleri, and V. Rosato Phys. Rev. B 48 1993 22 33
148. J. Hoshen, and R. Kopelman Phys. Rev. B 14 1976 3438 3445
149. R.F. Voss, R.B. Laibowitz, and E.I. Allessandrini Phys. Rev. Lett. 49 1982 1441 1444
150. B. Mandelbrot The Fractal Geometry of Nature 1983 Freeman New York, USA
151. P. Gadenne, Croissance de couches minces d'or: propriétés optiques, conductivité électrique et étude morphologique (Ph.D. thesis), University of Paris VI, 1986.
152. E. Castanié, Émission dipolaire et absorption en champ proche de nanostructures (Ph.D. thesis), Université Pierre et Marie Curie, 2011.
153. S.I. Bozhevolnyi, B. Vohnsen, A.V. Zayats, and I.I. Smolyaninov Surf. Sci. 356 1996 268 274
154. R.F. Harrington, Field Computations by Moment Methods, IEEE Press, New-York, 1992.
155. E.D. Palik Handbook of Optical Constants of Solids 1985 Academic Press New-York
156. P.C. Chaumet, and A. Rahmani Phys. Rev. E 70 2004 036606
157. R.R. Chance, A. Prock, and R. Silbey Adv. Chem. Phys. 37 1978 1
158. J. Laverdant, S. Buil, B. Bérini, and X. Quélin Phys. Rev. B 77 2008 165406
159. A.K. Sarychev, V.A. Shubin, and V.M. Shalaev Phys. Rev. B 60 1999 16389 16408
160. C.M. Soukoulis, Q. Li, and G.S. Grest Phys. Rev. B 45 1992 7724 7729
161. I. Chang, Z. Lev, A.B. Harris, J. Adler, and A. Aharony Phys. Rev. Lett. 74 1995 2094 2097
162. C. Awada, G. Barbillon, F. Charra, L. Douillard, and J.J. Greffet Phys. Rev. B 85 2012 045438