Raman Energy Density (RED) in the Context of Acousto-Plasmonics

Interactions between elementary excitations are of great interest from a fundamental aspect and for novel applications. While plasmon-exciton have been extensively studied, the interaction mechanisms between acoustic vibrations (phonons) and localized surface plasmons (LSPs) remain quite unexplored. Here, we present a new theoretical framework for the investigation of the interaction between confined acoustic vibrations and LSPs involved in resonant acoustic Raman scattering. We express the Raman scattering process in the framework of Fermi's golden rule and introduce the concept of Raman energy density (RED). Similarly to the Raman-Brillouin electronic density (RBED) introduced for semiconductors, this physical quantity is used as a theoretical tool for the interpretation of resonant Raman scattering mediated by LSPs in metallic nanoparticles. The RED represents the electromagnetic energy density excited in the Raman scattering process and modulated by the acoustic vibrations of the nanoparticle. We show that, similarly to the LDOS and the RBED, the RED can be mapped in the near-field region, and provides a clear picture of the interaction between LSPs and acoustic vibrations giving rise to inelastic scattering measurable in the far-field. We use the newly introduced RED concept to investigate elastic (an)isotropy effects and extract the Raman selection rules of spherical nanoparticles embedded in a dielectric environment.