  We model optomechanical systems as linear optical amplifiers. This provides a
unified treatment of diverse optomechanical phenomena. We emphasize, in
particular, the relationship between ponderomotive squeezing and
optomechanically induced transparency, two foci of current research. We
characterize the amplifier response to quantum and deliberately applied
fluctuations, both optical and mechanical. Further, we apply these results to
establish quantum limits on external force sensing both on and off cavity
resonance. We find that the maximum sensitivity attained on resonance
constitutes an absolute upper limit, not surpassed when detuning off cavity
resonance. The theory can be extended to a two-sided cavity with losses and
limited detection efficiency.
