  We investigate the control field phase-dependent output field transmission
from a red detuned ring cavity optomechanical system. Our scheme displays a
double transparency window in the presence of a strong control and a weak probe
field. Additionally, we invoke an external mechanical pump to one of the
movable mirrors to modulate its vibration. Complete control over the output
field transmission can be achieved due to the combined effect of the amplitudes
and the phases of the mechanical pump and the control field. Further, a tunable
group delay of the probe pulse propagation can be obtained by the tailoring of
the control field phase in the presence of a suitable mechanical drive. We
further discuss the effect of control field phase on Stokes field generation
via the four-wave mixing process. This scheme may find potential applications
in weak signal sensing and all-optical communication purposes.
