  Here, we study the controllable optical responses in a two-cavity
optomechanical system, especially on the $\mathit{perfect}$ optomechanically
induced transparency (OMIT) in the model which has never been studied before.
The results show that the perfect OMIT can still occur even with a large
mechanical damping rate, and at the perfect transparency window the long-lived
slow light can be achieved. In addition, we find that the conversion between
the perfect OMIT and optomechanically induced absorption can be easily achieved
just by adjusting the driving field strength of the second cavity. We believe
that the results can be used to control optical transmission in modern optical
networks.
