  We report a study of a cavity optomechanical system driven by narrow-band
electromagnetic fields, which are applied either in the form of uncorrelated
noise, or as a more structured spectrum. The bandwidth of the driving spectra
is smaller than the mechanical resonant frequency, and thus we can describe the
resulting physics using concepts familiar from regular cavity optomechanics in
the resolved-sideband limit. With a blue-detuned noise driving, the
noise-induced interaction leads to anti-damping of the mechanical oscillator,
and a self-oscillation threshold at an average noise power that is comparable
to that of a coherent driving tone. This process can be seen as noise-induced
dynamical amplification of mechanical motion. However, when the noise bandwidth
is reduced down to the order of the mechanical damping, we discover a large
shift of the power threshold of self-oscillation. This is due to the oscillator
adiabatically following the instantaneous noise profile. In addition to
blue-detuned noise driving, we investigate narrow-band driving consisting of
two coherent drive tones nearby in frequency. Also in these cases, we observe
deviations from a naive optomechanical description relying only on the tones'
frequencies and powers.
