arXiv physics/98090381998-09-26physics.optics

具有悬置反射镜的法布里-珀罗谐振腔的动力学。I.非线性耦合振子

Dynamics of Fabry-Perot resonators with suspended mirrors. I. Nonlinear coupled oscillators

M. Rakhmanov, A. Arodzero

备注：: LaTeX 2e, 39 pages, 14 figures

摘要：

描述了悬置镜法布里-珀罗腔的动力学特性。悬置反射镜是非线性振荡器，通过在腔内循环的激光相互作用。自由度在法向坐标中解耦，法向坐标是质心的位置和腔的长度。我们引入了两个参数，并研究了这些参数的动态变化。第一个参数指定辐射压力的强度。它决定了谐振腔是否是多稳态的。第二个参数是控制参数，它决定腔平衡态的位置。当控制参数在较大范围内变化时，平衡态表现出滞后现象。我们分析了平衡态的稳定性，并确定了不稳定区域。的不稳定性解释的有效电位：稳定状态对应于当地的最小值的有效电位和不稳定状态对应于当地的最大值。有效电势的最小值定义了腔长度的振荡的谐振频率。我们找到频率，并分析如何调整它们。从伺服势的角度分析了带反馈控制系统的谐振腔的多稳态性。所得结果具有普遍性，适用于所有带悬镜的法布里-珀罗腔。

英文摘要：

The dynamics of Fabry-Perot cavity with suspended mirrors is described. The suspended mirrors are nonlinear oscillators interacting with each other through the laser circulating in the cavity. The degrees of freedom decouple in normal coordinates, which are the position of the center of mass and the length of the cavity. We introduce two parameters and study how the dynamics changes with respect to these parameters. The first parameter specifies how strong the radiation pressure is. It determines whether the cavity is multistable or not. The second parameter is the control parameter, which determines location of the cavity equilibrium states. The equilibrium state shows hysteresis if the control parameter varies within a wide range. We analyze stability of the equilibrium states and identify the instability region. The instability is explained in terms of the effective potential: the stable states correspond to local minima of the effective potential and unstable states correspond to local maxima. The minima of the effective potential defines the resonant frequencies for the oscillations of the cavity length. We find the frequencies, and analyze how to tune them. Multistability of the cavity with a feedback control system is analyzed in terms of the servo potential. The results obtained in this paper are general and apply to all Fabry-Perot cavities with suspended mirrors.

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