  A laser beam directed at a mirror attached onto a flexible mount extracts
thermal energy from its mechanical Brownian motion by Doppler effect. For a
normal mirror the efficiency of this Doppler cooling is very weak and masked by
laser shot-noise. We find that it can become very efficient using a Bragg
mirror at the long wavelength edge of its band stop. The opposite effect of
cooling opens new routes for optical pumping of mechanical systems: a laser
pointing at a Bragg mirror and tuned at its short wavelength edge induces
amplification of the vibrational excitation of the mirror leading eventually to
its self-oscillation. This new effects rely on the strong dependency of the
Bragg mirror reflectivity on the wavelength.
