  We describe an optomechanical device consisting of a fiber-based optical
cavity containing a silicon nitiride membrane. In comparison with typical
free-space cavities, the fiber-cavity's small mode size (10 {\mu}m waist, 80
{\mu}m length) allows the use of smaller, lighter membranes and increases the
cavity-membrane linear coupling to 3 GHz/nm and quadratic coupling to 20
GHz/nm^2. This device is also intrinsically fiber-coupled and uses glass
ferrules for passive alignment. These improvements will greatly simplify the
use of optomechanical systems, particularly in cryogenic settings. At room
temperature, we expect these devices to be able to detect the shot noise of
radiation pressure.
