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Basic Concepts and Formalism

Chapter
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Part of the Springer Series in Optical Sciences book series (SSOS, volume 230)

Abstract

The book aims to present a systemic and self-contained guide to the canonical electromagnetic and electrostatic boundary-value problems in metallic nanostructures. In this way, the conduction electrons of a metallic medium are modeled as a degenerate electron gas, whose dynamics may be described by means of the hydrodynamic theory. Therefore, at first we need to know something about the hydrodynamic model of an electron gas. Then, we need to know something about the basic concepts and formalism of electromagnetic and electrostatic theories of an electron gas that will be used later in the book. For brevity, in many sections of this chapter the \(\exp (-i\omega t)\) time factor is suppressed. Furthermore, all media under consideration are nonmagnetic and attention is only confined to the linear phenomena.

Keywords

Electron gas Hydrodynamic model Maxwell’s equations Bohm potential Poynting’s theorem Boundary condition Spatial nonlocal effect Nanostructure 

References

  1. 1.
    P. Drude, Zur ionentheorie der metalle. Phys. Z. 1, 161–165 (1900)zbMATHGoogle Scholar
  2. 2.
    I. Villo-Perez, Z.L. Mišković, N.R. Arista, Plasmon spectra of nano-structures: a hydrodynamic model, in Trends in Nanophysics, ed. by A. Barsan, V. Aldea (Springer, Berlin, 2010)Google Scholar
  3. 3.
    C. Ciraci, J.B. Pendry, D.R. Smith, Hydrodynamic model for plasmonics: a macroscopic approach to a microscopic problem. ChemPhysChem 14, 1109–1116 (2013)Google Scholar
  4. 4.
    S. Raza, S.I. Bozhevolnyi, M. Wubs, N.A. Mortensen, Nonlocal optical response in metallic nanostructures. J. Phys. Condens. Matter 27, 183204 (2015)ADSGoogle Scholar
  5. 5.
    D. Pines, D. Bohm, A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions. Phys. Rev. 85, 338–353 (1952)zbMATHGoogle Scholar
  6. 6.
    M. Kupresak, X. Zheng, G.A.E. Vandenbosch, V.V. Moshchalkov, Comparison of hydrodynamic models for the electromagnetic nonlocal response of nanoparticles. Adv. Theory Simul. 1, 1800076 (2018)Google Scholar
  7. 7.
    M. Kupresak, X. Zheng, G.A.E. Vandenbosch, V.V. Moshchalkov, Appropriate nonlocal hydrodynamic models for the characterization of deep-nanometer scale plasmonic scatterers. Adv. Theory Simul. 3, 1900172 (2020)Google Scholar
  8. 8.
    R. Ruppin, Optical properties of a plasma sphere. Phys. Rev. Lett. 31, 1434–1437 (1973)ADSGoogle Scholar
  9. 9.
    R. Ruppin, Optical properties of small metal spheres. Phys. Rev. B 11, 2871–2876 (1975)ADSGoogle Scholar
  10. 10.
    R. Ruppin, Extinction properties of thin metallic nanowires. Opt. Commun. 190, 205–209 (2001)ADSGoogle Scholar
  11. 11.
    V. Datsyuk, O.M. Tovkach, Optical properties of a metal nanosphere with spatially dispersive permittivity. J. Opt. Soc. Am. B 28, 1224–1230 (2011)ADSGoogle Scholar
  12. 12.
    C. David, F.J. Garcia de Abajo, Spatial nonlocality in the optical response of metal nanoparticles. J. Phys. Chem. C 115, 19470–19475 (2011)Google Scholar
  13. 13.
    S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, N.A. Mortensen, Unusual resonances in nanoplasmonic structures due to nonlocal response. Phys. Rev. B 84, 121412 (2011)ADSGoogle Scholar
  14. 14.
    G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S.I. Bozhevolnyi, N.A. Mortensen, Nonlocal response in plasmonic waveguiding with extreme light confinement. Nanophotonics 2, 161–166 (2013)ADSGoogle Scholar
  15. 15.
    A. Moreau, C. Ciraci, D.R. Smith, Impact of nonlocal response on metallodielectric multilayers and optical patch antennas. Phys. Rev. B 87, 045401 (2013)ADSGoogle Scholar
  16. 16.
    S. Raza, W. Yan, N. Stenger, M. Wubs, N.A. Mortensen, Blueshift of the surface plasmon resonance in silver nanoparticles: substrate effects. Opt. Express 21, 27344–27355 (2013)ADSGoogle Scholar
  17. 17.
    T. Christensen, W. Yan, S. Raza, A.-P. Jauho, N.A. Mortensen, M. Wubs, Nonlocal response of metallic nanospheres probed by light, electrons, and atoms. ACS Nano 8, 1745–1758 (2014)Google Scholar
  18. 18.
    A. Moradi, E. Ebrahimi, Plasmon spectra of cylindrical nanostructures including nonlocal effects. Plasmonics 9, 209–218 (2014)Google Scholar
  19. 19.
    M. Wubs, Classification of scalar and dyadic nonlocal optical response models. Opt. Express 23, 31296–31312 (2015)ADSGoogle Scholar
  20. 20.
    C. Tserkezis, J.R. Maack, Z. Liu, M. Wubs, N.A. Mortensen, Robustness of the far-field response of nonlocal plasmonic ensembles. Sci. Rep. 6, 28441 (2016)ADSGoogle Scholar
  21. 21.
    F. Sauter, Der einfl uss von plasmawellen auf das refl exionsverm o gen von metallen (I). Z. Phys. 203, 488–494 (1967)ADSGoogle Scholar
  22. 22.
    R. Ruppin, Optical properties of spatially dispersive dielectric spheres. J. Opt. Soc. Am. 71, 755–758 (1981)ADSGoogle Scholar
  23. 23.
    R. Ruppin, Mie theory with spatial dispersion. Opt. Commun. 30, 380–382 (1979)ADSGoogle Scholar
  24. 24.
    R. Ruppin, Optical properties of a spatially dispersive cylinder. J. Opt. Soc. Am. B 6, 1559–1563 (1989)ADSGoogle Scholar
  25. 25.
    S.I. Pekar, The theory of electromagnetic waves in a crystal in which excitons are produced. J. Phys. Chem. Solids 6, 785–796 (1958)MathSciNetzbMATHGoogle Scholar
  26. 26.
    F. Forstmann, R.R. Gerhardts, Metal Optics Near Plasma Frequency (Springer, Berlin, 1986)Google Scholar
  27. 27.
    K.L. Kliewer, R. Fuchs, Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence. Phys. Rev. 172, 607–624 (1968)ADSGoogle Scholar
  28. 28.
    D.L. Johnson, P.R. Rimbey, Aspects of spatial dispersion in the optical properties of a vacuum-dielectric interface. Phys. Rev. B 14, 2398–2410 (1976)ADSGoogle Scholar
  29. 29.
    A. Moradi, Quantum nonlocal effects on optical properties of spherical nanoparticles. Phys. Plasmas 22, 022119 (2015)ADSGoogle Scholar
  30. 30.
    A. Moradi, Quantum effects on propagation of bulk and surface waves in a thin quantum plasma film. Phys. Lett. A 379, 1139–1143 (2015)ADSzbMATHGoogle Scholar
  31. 31.
    A. Moradi, Plasmon modes of spherical nanoparticles: the effects of quantum nonlocality. Surf. Sci. 637, 53–57 (2015)ADSGoogle Scholar
  32. 32.
    A. Moradi, Maxwell-Garnett effective medium theory: quantum nonlocal effects. Phys. Plasmas 22, 042105 (2015)ADSGoogle Scholar
  33. 33.
    A. Moradi, Quantum nonlocal polarizability of metallic nanowires. Plasmonics 10, 1225–1230 (2015)Google Scholar
  34. 34.
    Y.-Y. Zhang, S.-B. An, Y.-H. Song, N. Kang, Z.L. Mišković, Y.-N. Wang, Plasmon excitation in metal slab by fast point charge: the role of additional boundary conditions in quantum hydrodynamic model. Phys. Plasmas 21, 102114 (2014)ADSGoogle Scholar
  35. 35.
    H.G. Booker, Cold Plasma Waves (Martinus Nijhoff Publishers, Dordrecht, 1984)Google Scholar
  36. 36.
    G. Manfredi, How to model quantum plasmas. Fields Inst. Commun. 46, 263–287 (2005)MathSciNetzbMATHGoogle Scholar
  37. 37.
    M. Bonitz, N. Horing, P. Ludwig, Introduction to Complex Plasmas (Springer, Berlin, 2010)zbMATHGoogle Scholar
  38. 38.
    F. Haas, Quantum Plasmas: An Hydrodynamic Approach (Springer, New York, 2011)Google Scholar
  39. 39.
    U. Kreibig, C. von Fragstein, The limitation of electron mean free path in small silver particles. Z. Phys. 224, 307–323 (1969)ADSGoogle Scholar
  40. 40.
    J. Euler, Ultraoptische eigenschaften von metallen und mittlere freie weglange der leitungselektronen. Z. Phys. 137, 318–332 (1954)ADSGoogle Scholar
  41. 41.
    D. Pines, Elementary Excitations in Solids (Benjamin, New York, 1963)zbMATHGoogle Scholar
  42. 42.
    P. Halevi, Hydrodynamic model for the degenerate free-electron gas: generalization to arbitrary frequencies. Phys. Rev. B 51, 7497–7499 (1995)ADSGoogle Scholar
  43. 43.
    Z.A. Moldabekov, M. Bonitz, T.S. Ramazanov, Theoretical foundations of quantum hydrodynamics for plasmas. Phys. Plasmas 25, 031903 (2018)ADSGoogle Scholar
  44. 44.
    P. Halevi, Spatial dispersion in solids and plasmas, in Electromagnetic Waves: Recent Developments in Research, ed. by P. Halevi, vol. 1 (North-Holland, Amsterdam, 1992)Google Scholar
  45. 45.
    J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962)zbMATHGoogle Scholar
  46. 46.
    W.D. Jones, H.J. Doucet, J.M. Buzzi, An Introduction to the Linear Theories and Methods of Electrostatic Waves in Plasma (Plenum Press, New York, 1985)Google Scholar
  47. 47.
    A. Moradi, Propagation of electrostatic energy through a quantum plasma. Contrib. Plasma Phys. 59, 173–180 (2019)ADSGoogle Scholar
  48. 48.
    L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1971)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Kermanshah University of TechnologyKermanshahIran

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