Unmixing system-wide and geometry-specific plasmon modes in faceted nanoparticle trimers using a two-step matrix factorization

Abstract

Plasmonic modes in coupled nanoparticle systems are shaped by both interparticle interactions and geometry-specific features, such as facets and vertices. However, standard decomposition techniques, such as non-negative matrix factorization (NMF), often fail to individually isolate modes that are localized. This limitation arises because the factorization process relies solely on spectral data, without incorporating spatial context. To address this, we apply factorization in two steps. First, NMF identifies bulk and coupled system-wide contributions, that can then be removed in spectral reconstruction to isolate localized geometry-specific modes. Then, we perform region-based NMF on spatially-selected areas of a silica-shelled silver-nanoparticle trimer to identify subtle energy shifts between vertex and facet modes at different locations on the nanoparticles. Our approach thus enables the identification of global plasmonic modes extending across the entire dimer or trimer system, as well as geometry-specific modes arising from the faceted structure of individual nanoparticles. By reintroducing spatial context, we further distinguish between different localized modes, even within the same nanoparticle, revealing the influence of subtle geometric variations on plasmonic resonances and the potential for partial coupling between geometry-specific modes.