  We theoretically study radiation pressure induced generation of the frequency
components at the sum sideband in an optomechanical system containing an
optical parametric amplifier (OPA). It is shown that an OPA inside a cavity can
considerably enhance the amplitude of sum sideband even with low power input
fields. We find a new matching condition for the upper sum sideband generation.
The height and width of the new peak can be adjusted by the nonlinear gain of
the OPA. Furthermore, the lower sum sideband generation can be enhanced with
several orders of magnitude by tuning the nonlinear gain parameter and the
phase of the field pumping the OPA. The enhanced sum sideband may have
potential applications to the manipulation of light in a on-chip optomechanical
device and the sensitively sensing for precision measurement in the weak
optomechanical coupling regime.
