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Quantum Corrections in Plasmonics and Plasmon–Emitter Interactions

  • Paulo André Dias GonçalvesEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

Here, we introduce and extend a mesoscopic formalism for quantum nanoplasmonics that simultaneously incorporates quantum mechanical effects such as nonlocality, electronic spill-out/spill-in, and surface-enhanced Landau damping. Our approach is rooted on the Feibelman d-parameter formalism, through which quantum surface-response functions reintroduce the relevant electronic length scales of the plasmon-supporting electron gas that are neglected in classical descriptions. We derive analytic expressions for the nonclassical scattering coefficients associated with typical plasmonic systems and investigate the role of quantum corrections in their plasmonic response and in plasmon-empowered light–matter interactions, including the plasmonic enhancement of the spontaneous emission rates associated with both dipole-allowed and dipole-forbidden transitions, and plasmon-mediated energy transfer between two emitters.

References

  1. 1.
    Gonçalves PAD, Peres NMR (2016) An introduction to graphene plasmonics, 1st edn. World Scientific, Singapore.  https://doi.org/10.1142/9948
  2. 2.
    Maradudin AA, Barnes WL, Sambles JR (eds) (2014) Modern plasmonics, 1st edn. Elsevier, AmsterdamGoogle Scholar
  3. 3.
    Christensen T, Yan W, Jauho AP, Soljačić M, Mortensen NA (2017) Phys Rev Lett 118:157402.  https://doi.org/10.1103/PhysRevLett.118.157402ADSCrossRefGoogle Scholar
  4. 4.
    Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, New YorkzbMATHGoogle Scholar
  5. 5.
    Duffy DG (2015) Green’s functions with applications, 2nd edn. CRC Press, Boca RatonCrossRefGoogle Scholar
  6. 6.
    Feibelman PJ (1982) Prog Surf Sci 12(4):287.  https://doi.org/10.1016/0079-6816(82)90001-6ADSCrossRefGoogle Scholar
  7. 7.
    Liebsch A (1997) Electronic excitations at metal surfaces. Springer, New YorkCrossRefGoogle Scholar
  8. 8.
    Varas A, García-González P, Feist J, García-Vidal FJ, Rubio A (2016) Nanophotonics 5(3):409.  https://doi.org/10.1515/nanoph-2015-0141CrossRefGoogle Scholar
  9. 9.
    Zhu W, Esteban R, Borisov AG, Baumberg JJ, Nordlander P, Lezec HJ, Aizpurua J, Crozier KB (2016) Nat Commun 7:11495.  https://doi.org/10.1038/ncomms11495ADSCrossRefGoogle Scholar
  10. 10.
    Reiners T, Ellert C, Schmidt M, Haberland H (1995) Phys Rev Lett 74:1558.  https://doi.org/10.1103/PhysRevLett.74.1558ADSCrossRefGoogle Scholar
  11. 11.
    Mandal S, Wang J, Winans RE, Jensen L, Sen A (2013) J Phys Chem C 117(13):6741.  https://doi.org/10.1021/jp310514zCrossRefGoogle Scholar
  12. 12.
    Scholl JA, Koh AL, Dionne JA (2012) Nature 483(7390):421.  https://doi.org/10.1038/nature10904ADSCrossRefGoogle Scholar
  13. 13.
    Campos A, Troc N, Cottancin E, Pellarin M, Weissker HC, Lermé J, Kociakand M, Hillenkamp M (2018) Nat Phys  https://doi.org/10.1038/s41567-018-0345-z
  14. 14.
    Dias EJC, Iranzo DA, Gonçalves PAD, Hajati Y, Bludov YV, Jauho AP, Mortensen NA, Koppens FHL, Peres NMR (2018) Phys Rev B 97:245405.  https://doi.org/10.1103/PhysRevB.97.245405ADSCrossRefGoogle Scholar
  15. 15.
    Bozhevolnyi SI, Mortensen NA (2017) Nanophotonics 6:1185.  https://doi.org/10.1515/nanoph-2016-0179CrossRefGoogle Scholar
  16. 16.
    Marques MA, Ullrich CA, Nogueira F, Rubio A, Burke K, Gross EKU (2006) Time-dependent density functional theory. Lecture notes in physics. Springer, New YorkCrossRefGoogle Scholar
  17. 17.
    Gonçalves PAD, Christensen T, Rivera N, Jauho AP, Mortensen NA, Soljačić M (2020). Plasmon-emitter interactions at the nanoscale. Nat Commun 11:366.  https://doi.org/10.1038/s41467-019-13820-z
  18. 18.
    Yan W, Wubs M, Asger Mortensen N (2015) Phys Rev Lett 115:137403.  https://doi.org/10.1103/PhysRevLett.115.137403ADSCrossRefGoogle Scholar
  19. 19.
    Persson BNJ, Apell P (1983) Phys Rev B 27:6058.  https://doi.org/10.1103/PhysRevB.27.6058ADSCrossRefGoogle Scholar
  20. 20.
    Jin D, Hu Q, Neuhauser D, von Cube F, Yang Y, Sachan R, Luk TS, Bell DC, Fang NX (2015) Phys Rev Lett 115:193901.  https://doi.org/10.1103/PhysRevLett.115.193901ADSCrossRefGoogle Scholar
  21. 21.
    Yang Y, Di Z, Yan W, Agarwal A, Zheng M, Joannopoulos JD, Lalanne P, Christensen T, Berggren KK, Soljačić M (2019) A general theoretical and experimental framework for nanoscale electromagnetism. Nature 576(7786):248–252.  https://doi.org/10.1038/s41586-019-1803-1
  22. 22.
    Gradshteyn IS, Ryzhik IM (2007) Table of integrals, series, and products, 7th edn. Academic, LondonzbMATHGoogle Scholar
  23. 23.
  24. 24.
    Ford GW, Weber WH (1984) Phys Rep 113(4):195.  https://doi.org/10.1016/0370-1573(84)90098-XADSCrossRefGoogle Scholar
  25. 25.
  26. 26.
  27. 27.
    Apell P, Monreal R, Flores F (1984) Solid State Commun 52(12):971.  https://doi.org/10.1016/0038-1098(84)90490-3ADSCrossRefGoogle Scholar
  28. 28.
    Christensen T, Yan W (2018) Private communicationGoogle Scholar
  29. 29.
    Johnson PB, Christy RW (1972) Phys Rev B 6:4370.  https://doi.org/10.1103/PhysRevB.6.4370ADSCrossRefGoogle Scholar
  30. 30.
    Tsuei KD, Plummer EW, Feibelman PJ (1989) Phys Rev Lett 63:2256.  https://doi.org/10.1103/PhysRevLett.63.2256ADSCrossRefGoogle Scholar
  31. 31.
    Tsuei KD, Plummer EW, Liebsch A, Kempa K, Bakshi P (1990) Phys Rev Lett 64:44.  https://doi.org/10.1103/PhysRevLett.64.44ADSCrossRefGoogle Scholar
  32. 32.
    Tsuei KD, Plummer EW, Liebsch A, Pehlke E, Kempa K, Bakshi P (1991) Surf Sci 247(2):302.  https://doi.org/10.1016/0039-6028(91)90142-FADSCrossRefGoogle Scholar
  33. 33.
    Sprunger PT, Watson GM, Plummer EW (1992) Surf Sci 269–270:551.  https://doi.org/10.1016/0039-6028(92)91307-WADSCrossRefGoogle Scholar
  34. 34.
    Bréchignac C, Cahuzac P, Kebaïli N, Leygnier J, Sarfati A (1992) Phys Rev Lett 68:3916.  https://doi.org/10.1103/PhysRevLett.68.3916ADSCrossRefGoogle Scholar
  35. 35.
    Bréchignac C, Cahuzac P, Leygnier J, Sarfati A (1993) Phys Rev Lett 70:2036.  https://doi.org/10.1103/PhysRevLett.70.2036ADSCrossRefGoogle Scholar
  36. 36.
    Kim BO, Lee G, Plummer EW, Dowben PA, Liebsch A (1995) Phys Rev B 52:6057.  https://doi.org/10.1103/PhysRevB.52.6057ADSCrossRefGoogle Scholar
  37. 37.
    Moresco F, Rocca M, Hildebrandt T, Zielasek V, Henzler M (1998) EPL 43(4):433.  https://doi.org/10.1209/epl/i1998-00377-0ADSCrossRefGoogle Scholar
  38. 38.
    Rocca M, Valbusa U (1993) Surf Sci 287–288:770.  https://doi.org/10.1016/0039-6028(93)91069-2. Proceedings of the 8th international conference on solid surfaces
  39. 39.
    Raza S, Kadkhodazadeh S, Christensen T, Di Vece M, Wubs M, Mortensen NA, Stenger N (2015) Nat Commun 6:8788.  https://doi.org/10.1038/ncomms9788ADSCrossRefGoogle Scholar
  40. 40.
    Lipparini E, Pederiva F (1993) Z Phys D: At Mol Clust 27(3):281.  https://doi.org/10.1007/BF01436545ADSCrossRefGoogle Scholar
  41. 41.
  42. 42.
    Teperik TV, Nordlander P, Aizpurua J, Borisov AG (2013) Phys Rev Lett 110:263901.  https://doi.org/10.1103/PhysRevLett.110.263901ADSCrossRefGoogle Scholar
  43. 43.
  44. 44.
    Zwillinger D (1997) Handbook of differential equations, 3rd edn. Academic, LondonzbMATHGoogle Scholar
  45. 45.
    Pelton M, Bryant GW (2013) Introduction to metal-nanoparticle plasmonics. Wiley, New YorkGoogle Scholar
  46. 46.
    Christensen T, Yan W, Raza S, Jauho AP, Mortensen NA, Wubs M (2014) ACS Nano 8(2):1745.  https://doi.org/10.1021/nn406153kCrossRefGoogle Scholar
  47. 47.
    Novotny L, Hecht B (2012) Principles of nano-optics, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  48. 48.
    Kreibig U, Vollmer M (1995) Optical properties of metal clusters. Springer, BerlinCrossRefGoogle Scholar
  49. 49.
    Bohren CF, Huffman DR (1983) Absorption and scattering of light by small particles. Wiley, New YorkGoogle Scholar
  50. 50.
    Genzel L, Martin TP, Kreibig U (1975) Z Phys B Condens Matter 21(4):339.  https://doi.org/10.1007/BF01325393ADSCrossRefGoogle Scholar
  51. 51.
    Gramotnev DK, Bozhevolnyi SI (2010) Nat Photonics 4(2):83.  https://doi.org/10.1038/nphoton.2010.282, https://www.nature.com/articles/nphoton.2009.282
  52. 52.
    Fernández-Domínguez AI, García-Vidal FJ, Martín-Moreno L (2017) Nat Photonics 11(1):8. https://www.nature.com/articles/nphoton.2016.258
  53. 53.
    Flick J, Rivera N, Narang P (2018) Nanophotonics 7(9):1479.  https://doi.org/10.1515/nanoph-2018-0067CrossRefGoogle Scholar
  54. 54.
    Fernández-Domínguez AI, Bozhevolnyi SI, Mortensen NA (2018) ACS Photonics 5(9):3447.  https://doi.org/10.1021/acsphotonics.8b00852CrossRefGoogle Scholar
  55. 55.
    Ciracì C, Hill RT, Mock JJ, Urzhumov Y, Fernández-Domínguez AI, Maier SA, Pendry JB, Chilkoti A, Smith DR (2012) Science 337(6098):1072.  https://doi.org/10.1126/science.1224823ADSCrossRefGoogle Scholar
  56. 56.
    Alcaraz Iranzo D, Nanot S, Dias EJC, Epstein I, Peng C, Efetov DK, Lundeberg MB, Parret R, Osmond J, Hong JY, Kong J, Englund DR, Peres NMR, Koppens FHL (2018) Science 360(6386):291.  https://doi.org/10.1126/science.aar8438CrossRefGoogle Scholar
  57. 57.
    Purcell EM (1946) Phys Rev 69:681CrossRefGoogle Scholar
  58. 58.
    Anger P, Bharadwaj P, Novotny L (2006) Phys Rev Lett 96:113002.  https://doi.org/10.1103/PhysRevLett.96.113002ADSCrossRefGoogle Scholar
  59. 59.
    Kinkhabwala A, Yu Z, Fan S, Avlasevich Y, Müllen K, Moerner W (2009) Nat Photonics 3(11):654.  https://doi.org/10.1038/nphoton.2009.187ADSCrossRefGoogle Scholar
  60. 60.
    Vasa P, Wang W, Pomraenke R, Lammers M, Maiuri M, Manzoni C, Cerullo G, Lienau C (2013) Nat Photonics 7(2):128.  https://doi.org/10.1038/nphoton.2012.340ADSCrossRefGoogle Scholar
  61. 61.
    Akselrod GM, Argyropoulos C, Hoang TB, Ciracì C, Fang C, Huang J, Smith DR, Mikkelsen MH (2014) Nat Photonics 8:835.  https://doi.org/10.1038/nphoton.2014.228ADSCrossRefGoogle Scholar
  62. 62.
  63. 63.
    Kneipp K, Wang Y, Kneipp H, Perelman LT, Itzkan I, Dasari RR, Feld MS (1997) Phys Rev Lett 78:1667.  https://doi.org/10.1103/PhysRevLett.78.1667ADSCrossRefGoogle Scholar
  64. 64.
    Haes AJ, Haynes CL, McFarland AD, Schatz GC, Van Duyne RP, Zou S (2005) MRS Bull 30(5):368–375.  https://doi.org/10.1557/mrs2005.100CrossRefGoogle Scholar
  65. 65.
    Mayer KM, Hafner JH (2011) Chem Rev 111(6):3828.  https://doi.org/10.1021/cr100313vCrossRefGoogle Scholar
  66. 66.
  67. 67.
    Chikkaraddy R, de Nijs B, Benz F, Barrow SJ, Scherman OA, Rosta E, Demetriadou A, Fox P, Hess O, Baumberg JJ (2016) Nature 535(7610):127.  https://doi.org/10.1038/nature17974ADSCrossRefGoogle Scholar
  68. 68.
    Brongersma ML, Halas NJ, Nordlander P (2015) Nat Nanotechnol 10(1):25.  https://doi.org/10.1038/nnano.2014.311ADSCrossRefGoogle Scholar
  69. 69.
    Zhou L, Swearer DF, Zhang C, Robatjazi H, Zhao H, Henderson L, Dong L, Christopher P, Carter EA, Nordlander P et al (2018) Science 362(6410):69.  https://doi.org/10.1126/science.aat696ADSCrossRefGoogle Scholar
  70. 70.
    Russell KJ, Liu TL, Cui S, Hu EL (2012) Nat Photonics 6:459.  https://doi.org/10.1038/nphoton.2012.112ADSCrossRefGoogle Scholar
  71. 71.
    Koenderink AF (2010) Opt Lett 35(24):4208.  https://doi.org/10.1364/OL.35.004208ADSCrossRefGoogle Scholar
  72. 72.
    Kern AM, Martin OJF (2012) Phys Rev A 85:022501.  https://doi.org/10.1103/PhysRevA.85.022501ADSCrossRefGoogle Scholar
  73. 73.
    Filter R, Mühlig S, Eichelkraut T, Rockstuhl C, Lederer F (2012) Phys Rev B 86:035404.  https://doi.org/10.1103/PhysRevB.86.035404ADSCrossRefGoogle Scholar
  74. 74.
    Rivera N, Kaminer I, Zhen B, Joannopoulos JD, Soljačić M (2016) Science 353(6296):263.  https://doi.org/10.1126/science.aaf6308ADSMathSciNetCrossRefGoogle Scholar
  75. 75.
    Dung HT, Knöll L, Welsch DG (2002) Phys Rev A 65:043813.  https://doi.org/10.1103/PhysRevA.65.043813ADSCrossRefGoogle Scholar
  76. 76.
    Wubs M, Vos WL (2016) New J Phys 18(5):053037.  https://doi.org/10.1088/1367-2630/18/5/053037CrossRefGoogle Scholar
  77. 77.
    Ren J, Wu T, Yang B, Zhang X (2016) Phys Rev B 94:125416.  https://doi.org/10.1103/PhysRevB.94.125416ADSCrossRefGoogle Scholar
  78. 78.
    Cesar CL, Fried DG, Killian TC, Polcyn AD, Sandberg JC, Yu IA, Greytak TJ, Kleppner D, Doyle JM (1996) Phys Rev Lett 77:255.  https://doi.org/10.1103/PhysRevLett.77.255ADSCrossRefGoogle Scholar
  79. 79.
    Hayat A, Ginzburg P, Orenstein M (2008) Nat Photonics 2(4):238.  https://doi.org/10.1038/nphoton.2008.28CrossRefGoogle Scholar
  80. 80.
    Nevet A, Berkovitch N, Hayat A, Ginzburg P, Ginzach S, Sorias O, Orenstein M (2010) Nano Lett 10(5):1848.  https://doi.org/10.1021/nl1005806ADSCrossRefGoogle Scholar
  81. 81.
    Barnett SM, Loudon R (1996) Phys Rev Lett 77:2444.  https://doi.org/10.1103/PhysRevLett.77.2444ADSCrossRefGoogle Scholar
  82. 82.
    Blum C, Zijlstra N, Lagendijk A, Wubs M, Mosk AP, Subramaniam V, Vos WL (2012) Phys Rev Lett 109:203601.  https://doi.org/10.1103/PhysRevLett.109.203601ADSCrossRefGoogle Scholar
  83. 83.
    Sanders S, Manjavacas A (2018) ACS Photonics 5:2437.  https://doi.org/10.1021/acsphotonics.8b00225CrossRefGoogle Scholar
  84. 84.
    Shim H, Fan L, Johnson SG, Miller OD (2019) Phys Rev X 9:011043.  https://doi.org/10.1103/PhysRevX.9.011043CrossRefGoogle Scholar
  85. 85.
    Chew WC (1995) Waves and fields in inhomogenous media. Wiley-IEEE PressGoogle Scholar
  86. 86.
    Prigogine I, Rice SA (eds) (1978) Advances in chemical physics, vol XXXVII. Wiley, New YorkGoogle Scholar
  87. 87.
    Carminati R, Cazé A, Cao D, Peragut F, Krachmalnicoff V, Pierrat R, Wilde YD (2015) Surf Sci Rep 70(1):1.  https://doi.org/10.1016/j.surfrep.2014.11.001ADSCrossRefGoogle Scholar
  88. 88.
    Chew H (1987) J Chem Phys 87(2):1355.  https://doi.org/10.1063/1.453317ADSCrossRefGoogle Scholar
  89. 89.
  90. 90.
    Cohen-Tannoudji C, Diu B, Laloe F (1978) Quantum mechanics, vol 2. Wiley, New YorkzbMATHGoogle Scholar
  91. 91.
    Wiese WL, Smith MW, Glennon BM (1966) Atomic transition probabilities, vol 1. NIST. https://www.govinfo.gov/app/details/GOVPUB-C13-d53059923643c9d4d7265eb9e770b013
  92. 92.
    Wiese WL, Fuhr JR (2009) J Phys Chem Ref Data 38(3):565.  https://doi.org/10.1063/1.3077727ADSCrossRefGoogle Scholar
  93. 93.
    Andersen ML, Stobbe S, Sørensen AS, Lodahl P (2011) Nat Phys 7(3):215.  https://doi.org/10.1038/nphys1870CrossRefGoogle Scholar
  94. 94.
    Peřina J (ed) (2001) Coherence and statistics of photons and atoms. Wiley, New YorkGoogle Scholar
  95. 95.
    Scheel S, Buhmann S (2008) Acta Phys Slovaca 58(5):675ADSCrossRefGoogle Scholar
  96. 96.
  97. 97.
    Selvin PR (2000) Nat Struct Biol 7:730–734.  https://doi.org/10.1038/78948CrossRefGoogle Scholar
  98. 98.
    Lakowicz JR (ed) (2000) Principles of fluorescence spectroscopy, 3rd edn. Springer, New YorkGoogle Scholar
  99. 99.
    Andrew P, Barnes WL (2004) Science 306(5698):1002.  https://doi.org/10.1126/science.1102992ADSCrossRefGoogle Scholar
  100. 100.
    Lunz M, Gerard VA, Gun’ko YK, Lesnyak V, Gaponik N, Susha AS, Rogach AL, Bradley AL (2011) Nano Lett 11(8):3341.  https://doi.org/10.1021/nl201714yADSCrossRefGoogle Scholar
  101. 101.
    Govorov AO, Lee J, Kotov NA (2007) Phys Rev B 76:125308.  https://doi.org/10.1103/PhysRevB.76.125308ADSCrossRefGoogle Scholar
  102. 102.
    Persson BNJ, Zaremba E (1984) Phys Rev B 40:5669.  https://doi.org/10.1103/PhysRevB.30.5669ADSCrossRefGoogle Scholar
  103. 103.
    Göppert-Mayer M (1931) Ann Phys 401(3):273.  https://doi.org/10.1002/andp.19314010303CrossRefGoogle Scholar
  104. 104.
    Rivera N, Rosolen G, Joannopoulos JD, Kaminer I, Soljačić M (2017) Proc Natl Acad Sci USA 114(52):13607.  https://doi.org/10.1073/pnas.1713538114ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Center for Nano OpticsUniversity of Southern DenmarkOdense MDenmark

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