  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.
