Vlasov theory of Mie resonance broadening in metal clusters

  • Fomichev S
  • Zaretsky D
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Dynamical electromagnetic properties of metal clusters with radii R < 10
nm have been theoretically considered in the dipole approximation in a
jellium model taking into exact account the spatial dispersion of free
electron gas. The Vlasov equation for the plasma electron distribution
function inside a spherical cluster exposed to a low-intensity external
electromagnetic field is solved analytically in the linear response
approximation for the cases of both diffuse and mirror reflection of
electrons from the cluster boundary. The solution found is used to
obtain the non-local relation between the current density and the
electric field inside the cluster, which is substituted into the Maxwell
equations and boundary conditions for the electromagnetic field. In the
diffuse reflection case the complete set of field equations is reduced
to a single integral equation which has been solved numerically to
obtain the distributions of both the electric field and the electron
density inside the cluster, as well as the cluster dynamical electric
polarizability and the photoabsorption and photoscattering cross
sections. It has been found, from the cluster photoabsorption spectra
calculated, that in the considered model the width of the dipole Mie
resonance is mainly due to the electron reflection from the cluster
boundary, it slightly depends on the permittivity epsilon(0) of the
environment, and in the case of clusters in vacuum it is described with
a good accuracy by the conventional expression gamma (R) =
gamma(infinity) + bv(F)/R with b approximate to 1.0, v(F) being the
electron Fermi velocity.

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  • S. V. Fomichev

  • D. F. Zaretsky

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