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Cascade Brillouin scattering as a mechanism for photoluminescence from rough surfaces of noble metals

In surface-enhanced Raman scattering experiments that use plasmonic nanostructures as substrates, the scattering spectrum contains a broad background usually associated with photoluminescence. This background exists above and below the frequency of the incident wave. The low-frequency part of this background is similar to the scattering spectrum of a plasmon nanoparticle, while the high-frequency part follows the Gibbs distribution. We develop a theory that explains experimentally observed features in both the high- and low-frequency parts of the photoluminescence spectrum from a unified point of view. We show that photoluminescence is attributed to the cascade Brillouin scattering of the incident wave by metal phonons under the plasmon resonance conditions. The theory is in good agreement with our measurements over the entire frequency range of the background.