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Surface Plasmon Resonance Damping in Spheroidal Metal Particles: Quantum Confinement, Shape, and Polarization Dependences

Abstract : A key parameter for optimizing nanosized optical devices involving small metal particles is the spectral width of their localized surface plasmon resonances (LSPR). In the small size range the homogeneous LSPR line width is to a large extent ruled by the spatial confinement-induced broadening contribution which, within a classical description, underlies the popular phenomenological limited mean free path model. This unavoidable contribution to the LSPR line width is basically a quantum finite-size effect rooted in the finite extent of the electronic wave functions. This broadening reflects the surface-induced decay of the coherent collective plasmon excitations into particle–hole (p–h) excitations (Landau damping), the signature of which is a size-dependent fragmented LSPR band pattern which is clearly evidenced in absorption spectra computed within the time-dependent local density approximation (TDLDA). In this work we analyze the spatial confinement-induced LSPR damping contribution in the framework on an exact Hamiltonian formalism, assuming for convenience a jellium-type ionic density. In resorting to the harmonic potential theorem (HPT), a theorem stating that in the case of a harmonic external interaction the electronic center-of-mass coordinates separate strictly from the intrinsic motions of the individual electrons, we derive a simple approximate formula allowing to (i) quantify the size dependence of the LSPR damping in spherical nanoparticles (1/R law, where R is the sphere radius) and (ii) bring to the fore the main factors ruling the confinement-induced LSPR broadening. Then the modeling is straightforwardly generalized to the case of spheroidal (prolate or oblate) metal particles. Our investigations show that the LSPR damping is expected to depend strongly on both the aspect ratio of the spheroidal particles and the polarization of the irradiating electric field, that is, on the nature—transverse or longitudinal—of the collective excitation. It is found that the magnitude of the damping is tightly related to that of the LSPR frequency which rules the number of p–h excitations degenerate with the plasmon energy. Qualitative analysis suggests that the results are quite general and probably hold for other nonspherical particle shapes. In particular, in the case of elongated particles, as rods, the enlargement of the longitudinal LSPR band by the confinement effects is predicted to be much smaller than that of the transverse LSPR band.
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Jean Lerme, Christophe Bonnet, Marie-Ange Lebeault, Michel Pellarin, Emmanuel Cottancin. Surface Plasmon Resonance Damping in Spheroidal Metal Particles: Quantum Confinement, Shape, and Polarization Dependences. Journal of Physical Chemistry C, American Chemical Society, 2017, 121 (10), pp.5693-5708. ⟨10.1021/acs.jpcc.6b12298⟩. ⟨hal-02289046⟩



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