Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings

Many works are based on the steady-state analysis of mean-value dynamics in electro- or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x(0) but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.