  We theoretically analyze three-mode opto-acoustic parametric interactions in
a coupled Fabry-Perot cavity, where one acoustic mode interacts with two
optical modes. We show explicitly that extra degrees of freedom in a coupled
cavity allow explorations of both parametric instability and cooling regimes
with high parametric gain in a single table top experiment. This work can
motivate experimental realizations of the three-mode parametric instability
which might be an issue in next-generation gravitational-wave detectors with
high optical-power cavities, helping in the development of better models, and
in developing techniques for controls. In addition, we show that the same
scheme can be implemented in the resolved-sideband acoustic-mode cooling.
