Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios

Localized surface plasmons (LSPs) of metallic nanoparticles decay either radiatively or via an electron-hole pair cascade. In this work, the authors have experimentally and theoretically explored the branching ratio of the radiative and nonradiative LSP decay channels for nanodisks of Ag, Au, Pt, and Pd, with diameters D ranging from 38 to 530 nm and height h = 20 nm, supported on a fused silica substrate. The branching ratio for the two plasmon decay channels was obtained by measuring the absorption and scattering cross sections as a function of photon energy. The former was obtained from measured extinction and scattering coefficients, using an integrating sphere detector combined with particle density measurements obtained from scanning electron microscopy images of the nanoparticles. Partly angle-resolved measurements of the scattered light allowed the authors to clearly identify contributions from dipolar and higher plasmonic modes to the extinction, scattering, and absorption cross sections. Based on these experiments they find that absorption dominates the total scattering cross section in all the examined cases for small metallic nanodisks (D<100 nm). For D>100 nm absorption still dominates for Pt and Pd nanodisks, while scattering dominates for Au and Ag. A theoretical approach, where the metal disks are approximated as oblate spheroids, is used to account for the trends in the measured cross sections. The field problem is solved in the electrostatic limit. The spheroid is treated as an induced dipole for which the dipolar polarizability is calculated based on spheroid geometry and the (bulk) dielectric response function of the metal the spheroid consists of and the dielectric medium surrounding it. One might expect this model to be inappropriate for disks with D>100 nm since effects due to the retardation of the incoming field across the metallic nanodisk and contributions from higher plasmonic modes are neglected. However, this model describes quite well the energy dependence of the dipolar resonance, the full width at half maximum, and the total extinction cross section for all four metallic systems, even when 100<D<500 nm, indicating that the combined contribution of the effects not included in the model is small for the systems studied. For this reason the authors have extended the use of the same model to study scattering/absorption branching ratios. The main conclusions include the following. (i) Both the magnitude and peak position in extinction cross section are well accounted for by the model. (ii) The branching ratio for radiative and nonradiative decay is reasonably well accounted for. (iii) The model fails to account for the correct magnitudes of the measured absorption and scattering cross sections for larger particles in the case of Ag and Au. Possible reasons for this discrepancy are discussed.