Plasmon-plasmon interaction in nanoparticle assemblies: role of the dipole-quadrupole coupling

Area of Science:

• Nanophotonics
• Plasmonics
• Condensed Matter Physics

Background:

• Metallic nanoparticle assemblies offer sub-wavelength light control via surface plasmons.
• Understanding plasmon energy dispersion is key to their photonic properties and physical nature.
• The role of quadrupole contributions in plasmon coupling needs further investigation.

Purpose of the Study:

• To compare numerical and semi-analytical models for plasmon energy dispersion.
• To determine the validity of dipole-only vs. dipole-quadrupole models.
• To analyze the influence of quadrupole contributions, especially at small lattice spacings.

Main Methods:

• Numerical calculation of low-lying energy dispersion from a general plasmon mode model.
• Development of a tractable minimal model including dipoles and quadrupoles.
• Application of semi-analytical Bogoliubov transformation to access energy bands.
• Quantitative comparison of model validity against a full-plasmon-mode Hamiltonian.

Main Results:

• The low-lying energy dispersion from the general model agrees with the minimal dipole-quadrupole model.
• The dipole-quadrupole model provides a semi-analytical approach to experimentally relevant energy bands.
• The dipole-quadrupole model is sufficient for low-energy physics in most experimental scenarios.
• Quadrupole contributions become dominant near the Brillouin zone center for small lattice spacings.

Conclusions:

• The dipole-quadrupole model offers a tractable and accurate method for studying plasmon dispersion in metallic nanostructures.
• This model is crucial for understanding and controlling light-matter interactions at the nanoscale.
• The findings provide quantitative limits for simpler models and highlight the importance of quadrupole effects in specific regimes.