二次耦合光力学系统的一类高维可控自持振荡行为

Self-sustained oscillation in controllable quadratic coupling opto-mechanical systems

光力学系统通常的耦合是光压耦合,是光场强度和纳米振子位移的一次耦合,但在光场很强和振子振幅较大的光力学系统中,非线性的耦合效应会变得非常明显和重要,而且其所产生的非线性效应对制造具有特殊功能的光力学器件具有重要意义.本文在二次耦合模型的基础上研究了光腔和振子之间通过二次耦合作用达到能量平衡状态时系统所产生的自持振荡现象,给出了二次耦合光力学系统的一般模型,并通过数值方法研究了系统的定态行为和远离定态的极限环动力学行为,标定了系统定态响应的稳定区域到极限环行为的分岔点.发现在调节输入场参数(改变耦合系数)以及光腔和振子的弛豫系数时,系统的相空间会出现一些稳定的高维自持振荡极限环.通过数值分析发现该四维极限环在三维相空间的投影都趋于稳定的三维周期轨道,并且该极限环轨道会随外部调控参数的改变发生扭动,出现类似二维李萨如图样的稳定纽结结构.该现象表明:通过光场与振子的能量耦合,利用一定强度的外部驱动可以有效控制振子的定态响应和振动,可以让微振子锁定在具有一定振幅和频率的自发振动上,为开发物理器件提供了可靠的光力学控制系统.

The traditional opto-mechanical coupling in an opto-mechanical system is a linear coupling which is proportional to the field intensity I and oscillator displacement x. The nonlinear spatial coupling effect becomes obvious and important in a strong cavity field with large oscillating amplitude, and then the nonlinear effect with quadratic coupling in opt-mechanical device is also significant. In this article, we find that a general opto-mechanical system with quadratic coupling will produce a stable self-sustained oscillation when the energy injected by external driving equals that of dissipations in certain parametric regions. We numerically solve the semi-classical equation of motion of the system and find high-dimensional limit circles in its phase space under the control of driving and damping. We verify the high-dimensional limit circles by the closed orbits in all the projective three-dimensional phase space and show a highly controllable topological structure of the phase orbit which is very similar to Lissajous figures formed in a two-dimensional case. The self-sustained oscillations of the driving resonator with controllable amplitudes and frequencies demonstrate a reliable physical application of opto-mechanical system under quadratic coupling.