  We study the spectrum of single-photon emission and scattering in a mixed
optomechanical model which consists of both linear and quadratic optomechanical
interactions. The spectra are calculated based on the exact long-time solutions
of the single-photon emission and scattering processes in this system. We find
that there exist some phonon sideband peaks in the spectra and there are some
sub peaks around the phonon sideband peaks under proper parameter conditions.
The correspondence between the spectral features and the optomechanical
interactions is confirmed, and the optomechanical coupling strengths can be
inferred by analyzing the resonance peaks and dips in the spectra.
