  We study the directional amplification of an optical probe field in a
three-mode optomechanical system, where the mechanical resonator interacts with
two linearly-coupled optical cavities and the cavities are driven by strong
optical pump fields. The optical probe field is injected into one of the cavity
modes, and at the same time, the mechanical resonator is subject to a
mechanical drive with the driving frequency equal to the frequency difference
between the optical probe and pump fields. We show that the transmission of the
probe field can be amplified in one direction and de-amplified in the opposite
direction. This directional amplification or de-amplification results from the
constructive or destruction interference between different transmission paths
in this three-mode optomechanical system.
