  Cavity optomechanical phenomena, such as cooling, amplification or
optomechanically induced transparency, emerge due to a strong imbalance in the
dissipation rates of the parametrically coupled electromagnetic and mechanical
resonators. Here we analyze the reversed dissipation regime where the
mechanical energy relaxation rate exceeds the energy decay rate of the
electromagnetic cavity. We demonstrate that this regime allows for
mechanically-induced amplification (or cooling) of the electromagnetic mode.
Gain, bandwidth, and added noise of this electromagnetic amplifier are derived
and compared to amplification in the normal dissipation regime. In addition, we
analyze the parametric instability, i.e. optomechanical Brillouin lasing, and
contrast it to conventional optomechanical phonon lasing. Finally, we propose
an experimental scheme that realizes the reversed dissipation regime using
parametric coupling and optomechanical cooling with a second electromagnetic
mode enabling quantum-limited amplification. Recent advances in high-Q
superconducting microwave resonators make the reversed dissipation regime
experimentally realizable.
