  We investigate radiation-pressure induced generation of the frequency
components at the difference-sideband in an optomechanical system, which beyond
the conventional linearized description of optomechanical interactions between
cavity fields and the mechanical oscillation. We analytically calculate
amplitudes of these signals, and identify a simple square-root law for both the
upper and lower difference-sideband generation which can describe the
dependence of the intensities of these signals on the pump power. Further
calculation shows that difference-sideband generation can be greatly enhanced
via achieving the matching conditions. The effect of difference-sideband
generation, which may have potential application for manipulation of light, is
especially suited for on-chip optomechanical devices, where nonlinear
optomechanical interaction in the weak coupling regime is within current
experimental reach.
