  We discuss the possible cooling of different phonon modes via three wave
mixing interactions of vibrational and optical modes. Since phonon modes
exhibit a variety of dispersion relations or frequency spectra with diverse
spatial structures, depending on the shape and size of the sample, we formulate
our theory in terms of relevant spatial mode functions for the interacting
fields in any given geometry. We discuss the possibility of Dicke like
collective effects in phonon cooling and present explicit results for
simultaneous cooling of two phonon modes via the anti-Stokes up conversions. We
show that the bimodal cooling should be observable experimentally.
