  We demonstrate micromechanical reflectors with a reflectivity as large as
99.4% and a mechanical quality factor Q as large as 7.8*10^5 for optomechanical
applications. The reflectors are silicon nitride membranes patterned with
sub-wavelength grating structures, obviating the need for the many dielectric
layers used in conventional mirrors. We have employed the reflectors in the
construction of a Fabry-Perot cavity with a finesse as high as F=1200, and used
the optical response to probe the mechanical properties of the membrane. By
driving the cavity with light detuned to the high-frequency side of a cavity
resonance, we create an optical antidamping force that causes the reflector to
self-oscillate at 211 kHz.
