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.
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