  Three-mode parametric interactions can occur in triply-resonant
opto-mechanical systems in which two orthogonal optical modes are coupled with
an appropriate mechanical mode. Using an optical cavity with a membrane inside,
we report the first observation of three-mode parametric instability in a
Fabry-Perot cavity, a phenomenon predicted to occur in long baseline advanced
gravitational wave detectors. We present a large signal model for the
phenomenon, which predicts exponential growth of mechanical oscillation
followed by saturation. Our experimental results are consistent with this
model. Contrary to expectations, parametric instability does not lead to loss
of cavity lock, a fact which may make it easier to implement control techniques
in Advanced gravitational wave detectors.
