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Quantum Effects of Nonlocal Plasmons in Epsilon-Near-Zero Properties of a Thin Gold Film Slab

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Abstract

Dispersion properties of metals and propagation of quantum plasmons in the high photon energy range are studied. The nonlocal dielectric permittivity of a metal is determined by the quantum plasma effects and is calculated by taking into account collisions between free charge carriers and the lattice. The properties of epsilon-near-zero material are investigated in a thin gold film slab. The spectrum and the damping rate of the quantum plasmons are obtained for a wide range of energies, and the electron’s wave function is calculated in both classical and quantum limits. It is shown that the quantum plasmons exist with a propagation length of 1–10 nm, which strongly depends on the electron energy. The propagation length is found to be much larger than the propagation length in the classical regime, where the former is comparable to the atomic radius and the average inter-particle distance. It is found that the spatial localization of the electron wave function is extended due to the quantum effects. It is also shown that the damping of electromagnetic waves in the high photon energy range decreases when the photon energy decreases which is opposite to the conclusions obtained from the classical Drude model in this range.

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References

  1. Nguyen VH, Nguyen BH (2014) Quantum theory of plasmon energy spectra in electron gases of bulk metal and metallic nanostructures. Adv Nat Sci: Nanosci Nanotechnol 5:035004

    Google Scholar 

  2. Tame MS, McEnery KR, Ozdemir SK, Lee J, Maier SA, Kim MS (2013) Quantum plasmonics. Nat Phys 9:329–340

    Article  CAS  Google Scholar 

  3. Scholl JA, Koh AL, Dionne JA (2012) Quantum plasmon resonances of individual metallic nanoparticles. Nature 483:421–427

    Article  CAS  Google Scholar 

  4. Ostrikov K, Neyts EC, Meyyappan M (2013) Plasma nanoscience: from nano-solids in plasmas to nano-plasmas in solids. Adv Phys 62:113–224

    Article  CAS  Google Scholar 

  5. Luo J, Xu P, Gao L, Lai Y, Chen H (2012) Manipulate the transmissions using index-near-zero or epsilon-near-zero metamaterials with coated defects. Plasmonics 7:353–358

    Article  Google Scholar 

  6. Edwards B, Alu` A, Young M, Silveirinha M, Engheta N (2008) Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys Rev Lett 100:033903

    Article  Google Scholar 

  7. Akimov YA, Koh WS (2011) Design of plasmonic nanoparticles for efficient subwavelength light trapping in thin-film solar cells. Plasmonics 6:155–161

    Article  CAS  Google Scholar 

  8. Pile D (2013) Exploiting loss. Nat Photonics 7:167

    Google Scholar 

  9. Akimov YK, Ostrikov K, Li EP (2009) Surface plasmon enhancement of optical absorption in thin-film silicon solar cells. Plasmonics 4:107–113

    Article  CAS  Google Scholar 

  10. Akimov YA, Koh WS, Ostrikov K (2009) Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes. Opt Express 17:10195

    Article  CAS  Google Scholar 

  11. Yajadda MMA, Muller KH, Farrant DI, Ostrikov K (2012) Partial rectification of the plasmon-induced electrical tunnel current in discontinuous thin gold film at optical frequency. Appl Phys Lett 100:211105

    Article  Google Scholar 

  12. Yajadda MMA, Ostrikov K (2013) Thermal effect of plasmon oscillations on the tunnel current in gold nanoisland thin film at low laser intensity. Appl Phys Lett 102:111115

    Article  Google Scholar 

  13. Kritcher AL, Neumayer P, Castor J, Doppner T, Falcone RW, Landen OL, Lee HJ, Lee RW, Morse EC, Ng A, Pollaine S, Price D, Glenzer SH (2008) Ultrafast X-ray Thomson Scattering of shock-compressed matter. Science 322:69–71

    Article  CAS  Google Scholar 

  14. Lee HJ, Neumayer P, Castor J, Doppner T, Falcone RW, Fortmann C, Hammel BA, Kritcher AL, Landen OL, Lee RW, Meyerhofer DD, Munro DH, Redmer R, Regan SP, Weber S, Glenzer SH (2009) X-Ray Thomson-scattering measurements of density and temperature in shock-compressed beryllium. Phys Rev Lett 102:115001

    Article  CAS  Google Scholar 

  15. Silveirinha M, Engheta N (2006) Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials. Phys Rev Lett 97:157403

    Article  Google Scholar 

  16. Alu` A, Silveirinha M, Salandrino A, Engheta N (2007) Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern. Phys Rev B 75:155410

    Article  Google Scholar 

  17. Alu` A, Engheta N (2008) Light squeezing through arbitrarily shaped plasmonic channels and sharp bends. Phys Rev B 78:035440

    Article  Google Scholar 

  18. Shen NH, Koschny T, Kafesaki M, Soukoulis CM (2012) Optical metamaterials with different metals. Phys Rev B 85:075120

    Article  Google Scholar 

  19. Johnson PB, Christy RW (1972) Optical constants of the noble metals. Phys Rev B 6:4370

    Article  CAS  Google Scholar 

  20. Melnyk AR, Harrison MJ (1970) Theory of optical excitation of plasmons in metals. Phys Rev B 2:835

    Article  Google Scholar 

  21. Anderegg M, Feuerbacher B, Fitton B (1971) Optically excited longitudinal plasmons in potassium. Phys Rev Lett 27:1565

    Article  CAS  Google Scholar 

  22. Maas R, Parsons J, Engheta N, Polman A (2013) Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths. Nat Photonics 7:907–912

    Article  CAS  Google Scholar 

  23. Manfredi G (2005) How to model quantum plasmas. Fields Inst Commun 46:263–288

    Google Scholar 

  24. Akimov AV, Mukherjee A, Yu CL, Chang DE, Zibrov AS, Hemmer PR, Park H, Lukin MD (2007) Generation of single optical plasmons in metallic nanowires coupled to quantum dots. Nature 450:402–406

    Article  CAS  Google Scholar 

  25. Silveirinha M (2009) Artificial plasma formed by connected metallic wires at infrared frequencies. Phys Rev B 79:035118

    Article  Google Scholar 

  26. Hecker NE, Hopfer RA, Sawaki N, Maier T, Strasser G (1999) Surface plasmon enhanced photoluminescence from a single quantum well. Appl Phys Lett 75:1577–1579

    Article  CAS  Google Scholar 

  27. Martino GD, Sonnefraud Y, Kena-Cohen S, Tame M, Ozdemir SK, Kim MS, Maier SA (2012) Quantum statistics of surface plasmon polaritons in metallic stripe waveguides. Nano Lett 12:2504–2508

    Article  Google Scholar 

  28. Zayats AV, Smolyaninov II, Maradudin AA (2005) Nano-optics of surface plasmon polaritons. Phys Rep 408:131–314

    Article  CAS  Google Scholar 

  29. Roppin R (1975) Optical properties of small metal spheres. Phys Rev B 11:2871

    Article  Google Scholar 

  30. Akimov YA (2012) Impact of nonuniform electron density on plasmonic properties of metal nanoparticles. Plasmonics 7:495–500

    Article  CAS  Google Scholar 

  31. Alexandrov AF, Bogdankevich LS, Rukhadze AA (1984) Principles of plasma electrodynamics. Springer-Verlag, Berlin Heidelberg. http://www.springer.com/gp/book/9783642692499

  32. Domps A, Reinhard PG, Suraud W (1997) A Fermionic Vlasov description of Coulomb systems. Ann Phys 260:171–190

    Article  CAS  Google Scholar 

  33. Bohm D (1952) A suggested interpretation of the quantum theory in terms of “Hidden” variables. Phys Rev 85:166–179

    Article  CAS  Google Scholar 

  34. Bohm D, Pines D (1953) A collective description of electron interaction: III. Coulomb interactions in a degenerate electron gas. Phys Rev 92:609–625

    Article  CAS  Google Scholar 

  35. Eliasson B, Shukla PK (2010) Dispersion properties of electrostatic oscillations in quantum plasmas. J Plasma Phys 76:7–17

    Article  CAS  Google Scholar 

  36. Bathnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511–525

    Article  Google Scholar 

  37. Tyshetskiy Y, Kompaneets R, Vladimirov SV (2012) Surface pasmon polaritons in a semi-bounded degenerate plasma: role of spatial dispersion and collisions. Phys Plasmas 19:112107

    Article  Google Scholar 

  38. Roppin R (2005) Non-local optics of the near field lens. J Phys Condens Matter 17:1803

    Article  Google Scholar 

  39. David C, de Abajo FJG (2001) Spatial nonlocality in the optical response of metal nanoparticles. J Phys Chem C 115:19470

    Article  Google Scholar 

  40. Yajadda MMA, Farrant DI, Levchenko I, Muller KH, Ostrikov K (2011) Demonstration of nonlinear absorption in Au semi-continuous film by electrical measurement. Opt Express 19:17167

    Article  CAS  Google Scholar 

  41. Gather MC, Meerholz K, Danz N, Leosson K (2010) Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer. Nat Photonics 4:457–461

    Article  CAS  Google Scholar 

  42. Moaied M, Tyshetskiy Y, Vladimirov SV (2013) High-frequency electromagnetic surface waves in a semi-bounded weakly ionized plasma. Phys Plasmas 20:022116

    Article  Google Scholar 

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Acknowledgments

M. Moaied thanks the University of Sydney for the Australian Postgraduate Award and the CSIRO for the financial support through the OCE PhD Scholarship Top-up Scheme. This work was partially supported by the Australian Research Council and CSIRO’s Science Leadership Scheme.

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Authors and Affiliations

  1. School of Physics, The University of Sydney, Sydney, NSW, 2006, Australia

    Modjtaba Moaied & Kostya (Ken) Ostrikov

  2. Commonwealth Scientific and Industrial Research Organisation (CSIRO), PO Box 218, Lindfield, NSW, 2070, Australia

    Modjtaba Moaied, Mir Massoud Aghili Yajadda & Kostya (Ken) Ostrikov

  3. School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD, 4000, Australia

    Kostya (Ken) Ostrikov

Authors
  1. Modjtaba Moaied
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  2. Mir Massoud Aghili Yajadda
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  3. Kostya (Ken) Ostrikov
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Correspondence to Modjtaba Moaied.

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Moaied, M., Yajadda, M.M.A. & Ostrikov, K.(. Quantum Effects of Nonlocal Plasmons in Epsilon-Near-Zero Properties of a Thin Gold Film Slab. Plasmonics 10, 1615–1623 (2015). https://doi.org/10.1007/s11468-015-9951-0

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  • DOI: https://doi.org/10.1007/s11468-015-9951-0

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