Quantum spill-out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays in silver

Enok Johannes Haahr Skjølstrup, Thomas Søndergaard, Thomas Garm Pedersen

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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A gap plasmon is an electromagnetic wave propagating in a gap between two noble metal surfaces. Such gap plasmons have previously been studied using only a classical description of the noble metals, but this model fails and shows unphysical behavior for sub-nanometer gaps. To overcome this problem quantum spill-out is included in this paper by applying Density-Functional Theory (DFT), such that the electron density is smooth across the interfaces between metal and air. The mode index of a gap plasmon propagating in the gap between the two metal surfaces is calculated from the smooth electron density, and in the limit of vanishing gap width the mode index is found to converge properly to the refractive index of bulk metal. When neglecting quantum spill out in this limit the mode index shows unphysical behavior and diverges instead. The mode index is applied to calculate the reflectance of an ultrasharp groove array in silver, as gaps of a few nm are found in the bottom of such grooves. At these positions the gap plasmon field is highly delocalized implying that it mostly exists in the bulk silver region where absorption takes place. Surprisingly, when the bottom width is a few nm and the effect of spill out at a first glance seems to be negligible, strong absorption is found to take place 1-2 Å from the groove walls as a consequence of the dielectric function being almost zero at these positions. Hence quantum spill out is found to significantly lower the reflectance of such groove arrays in silver.

Original languageEnglish
Title of host publicationNanophotonics VII
EditorsDavid L. Andrews, Andreas Ostendorf, Angus J. Bain, Jean-Michel Nunzi
Number of pages12
PublisherSPIE - International Society for Optical Engineering
Publication date4 May 2018
Article number1067205
ISBN (Electronic)9781510618701
Publication statusPublished - 4 May 2018
EventSPIE Photonics Europe - Palais de la Musique et des Congrès, Strasbourg, France
Duration: 22 Apr 201826 Apr 2018


ConferenceSPIE Photonics Europe
LocationPalais de la Musique et des Congrès
Internet address
SeriesProceedings of SPIE, the International Society for Optical Engineering


  • density functional theory
  • electron spill-out
  • gap plasmons
  • metal optics
  • mode index
  • ultrasharp grooves


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