Plasmon-Plasmon Interaction in Nanoparticle Assemblies: Role of the Dipole-Quadrupole Coupling
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arXiv
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| Format: | Preprint |
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2025
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| author | Masset, Olivier Bastardis, Roland Vernay, Francois |
| author_facet | Masset, Olivier Bastardis, Roland Vernay, Francois |
| contents | The synthesis of metallic nanoparticle assemblies is nowadays well-controlled, such that these systems offer the possibility of controlling light at a sub-wavelength scale, thanks, for instance, to surface plasmons. Determining the energy dispersion of plasmons likely to couple to light within these nanostructures is, therefore, a necessary preliminary task on the way to understanding both their photonic properties and their physical nature, namely the role of the quadrupole contribution. Starting with a general model that takes account of all energy modes, we show that its low-lying energy dispersion gained numerically, can be compared to that of a minimal model that treats dipoles and quadrupoles on the same footing. The main advantage of the latter relies on the fact that its formulation is tractable, such that a semi-analytical Bogoliubov transformation allows one to access the experimentally relevant energy bands. Based on this semi-analytical derivation, we determine quantitatively the limit of validity of the dipole-only model, the presently proposed dipole and quadrupole model, compared to a full-plasmon-mode Hamiltonian. The results show that the dispersion relation, which includes dipoles and quadrupoles, is sufficient to capture the low-energy physics at play in most experimental situations. Besides, we show that at small lattice spacing, the contribution of quadrupoles is dominant around the Brillouin zone center. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Plasmon-Plasmon Interaction in Nanoparticle Assemblies: Role of the Dipole-Quadrupole Coupling Masset, Olivier Bastardis, Roland Vernay, Francois Mesoscale and Nanoscale Physics Optics The synthesis of metallic nanoparticle assemblies is nowadays well-controlled, such that these systems offer the possibility of controlling light at a sub-wavelength scale, thanks, for instance, to surface plasmons. Determining the energy dispersion of plasmons likely to couple to light within these nanostructures is, therefore, a necessary preliminary task on the way to understanding both their photonic properties and their physical nature, namely the role of the quadrupole contribution. Starting with a general model that takes account of all energy modes, we show that its low-lying energy dispersion gained numerically, can be compared to that of a minimal model that treats dipoles and quadrupoles on the same footing. The main advantage of the latter relies on the fact that its formulation is tractable, such that a semi-analytical Bogoliubov transformation allows one to access the experimentally relevant energy bands. Based on this semi-analytical derivation, we determine quantitatively the limit of validity of the dipole-only model, the presently proposed dipole and quadrupole model, compared to a full-plasmon-mode Hamiltonian. The results show that the dispersion relation, which includes dipoles and quadrupoles, is sufficient to capture the low-energy physics at play in most experimental situations. Besides, we show that at small lattice spacing, the contribution of quadrupoles is dominant around the Brillouin zone center. |
| title | Plasmon-Plasmon Interaction in Nanoparticle Assemblies: Role of the Dipole-Quadrupole Coupling |
| topic | Mesoscale and Nanoscale Physics Optics |
| url | https://arxiv.org/abs/2503.13645 |