  We study tunable optomechanically induced transparency by controlling the
dark-mode effect induced by two mechanical modes coupled to a common cavity
field. This is realized by introducing a phase-dependent phonon-exchange
interaction, which is used to form a loop-coupled configuration. Combining this
phase-dependent coupling with the optomechanical interactions, the dark-mode
effect can be controlled by the quantum interference effect. In particular, the
dark-mode effect in this two-mechanical-mode optomechanical system can lead to
a double-amplified optomechanically induced transparency (OMIT) window and a
higher efficiency of the second-order sideband in comparison with the standard
optomechanical system. This is because the effective mechanical decay rate
related to the linewidth of the OMIT window becomes a twofold increase in the
weak-coupling limit. When the dark-mode effect is broken, controllable double
transparency windows appear and the second-order sideband, as well as the light
delay or advance, is significantly enhanced. For an N-mechanical-mode
optomechanical system, we find that in the presence of the dark-mode effect,
the amplification multiple of the linewidth of the OMIT window is nearly
proportional to the number of mechanical modes, and that the OMIT with a single
window becomes the one with N tunable windows by breaking the dark-mode effect.
The study will be useful in optical information storage within a
large-frequency bandwidth and multichannel optical communication based on
optomechanical systems.
