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.PACS numbers: 03.65. Ta, 42.50.Wk Resonantly enhanced feedback-backaction of optomechanical coupling [1] has attracted great interest recently and the strong interaction between cavity fields and mechanical motion has been demonstrated experimentally [2]. This emerging subject leads to many potential applications for both optics and physics, including achieving high precision measurement [3], on-chip manipulation of asymmetric light propagation [4,5], and optomechanically induced transparency [6][7][8]. Optomechanically induced transparency is an interesting analog of electromagnetically induced transparency, where the control field induces a transmission window for the probe field when the resonance condition is met [9][10][11]. Optomechanically induced transparency can be well understood through the linearization of the semiclassical evolution equations [12,13].In view of the nonlinear nature of the interaction between light and mechanical motion via radiation pressure, many interesting phenomena and applications have been revealed. A perturbative analysis of output optical spectrum in the parameter configuration of optomechanically induced transparency reveals spectral components at the second order sideband that arises from nonlinear optomechanical interactions and exhibits a prominent feature of nonlinear optomechanically induced transparency [14]. Recently, nonlinear optomechanical dynamics have emerged as an interesting frontier in cavity optomechanics [15][16][17]. In the semiclassical mechanism, sideband generation and optomechanical chaos have been studied in various contents, including coherent-mechanical pumped optomechanical systems [18], optomechanical system with second-order coupling [19], hybrid electro-optomechanical systems [20,21], and photonic molecule optomechanical system [22]. Delaying or advancing higher-order sideband signals [23] have also been revealed which may be important in optical information processing techniques.In the present work, we consider that the optomechanical system is double driven: two probe fields with different frequencies (ω 1 and ω 2 , respectively) perturb the...