  We investigate a theoretical demonstration of perfect frequency conversion in
an optomechanical system in the weak coupling regime without a Stokes
side-band. An optomechanical cavity illuminated by a weak probe field generates
two side-modes, differentiating from the original signal by a phonon frequency.
We report the presence of a special combination of parameters in the
weak-coupling regime, where Stokes side-mode vanishes exactly. Only the
anti-Stokes mode is observed with a few hundreds Hz spectral bandwidth of the
probe field. Emergence of this special point is totally unrelated with the
electromagnetically induced transparency (EIT) condition, where absorption
(dip) cancellation is limited with the damping rate of the mechanical
oscillator. Emergence is independent of the cavity type, i.e. single or
double-sided, and takes place only for a single value of the effective coupling
strength constant which is specific to the system parameters. At a specific
effective coupling strength between the mirror and the cavity field, which can
be tunable via the coupling field, only the anti-Stokes band is generated. At
that specific coupling there appears no Stokes field. Hence, a filter, to
eliminate the Stokes field, does not necessitate.
