We propose a theoretical analysis of the stochastic dynamics of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. The core element in this microwave photonic oscillator is a high- $Q$ whispering-gallery mode resonator with quadratic nonlinearity, which simultaneously performs electrooptical modulation, frequency filtering and energy storage. This multi-task resonator allows the oscillator to feature improved size, weight and power metrics. In this article, we analyze how the various sources of optical and electrical noise in the oscillator are converted to output microwave signal fluctuations. We use an approach based on stochastic differential equations to characterize the dynamics of the microwave signal as a function of radiofrequency gain and laser pump power. This stochastic analysis also allows us to understand how key parameters of the resonator such as its intrinsic and extrinsic $Q$ -factors influence the system's dynamics below and above threshold. The time-domain numerical simulations for miniature OEO stochastic dynamics provides an excellent agreement with the analytical predictions.

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基于回音壁模式电光调制器的微型光电振荡器的随机分析

我们提出了基于耳语画廊模式谐振器的微型光电振荡器（OEO）随机动力学的理论分析。这种微波光子振荡器的核心元素是 $ Q $具有二次非线性的耳语画廊模式谐振器，同时执行电光调制，频率滤波和能量存储。这种多任务谐振器使振荡器具有改进的尺寸，重量和功率指标。在本文中，我们分析了振荡器中各种光学和电噪声源如何转换为输出微波信号波动的方法。我们使用基于随机微分方程的方法将微波信号的动态特性表征为射频增益和激光泵浦功率的函数。这种随机分析还使我们能够了解谐振器的关键参数，例如其固有和非固有特性。$ Q $ 因素会影响系统在阈值上下的动态变化。微型OEO随机动力学的时域数值模拟与分析预测提供了极好的一致性。