Stochastic Analysis of Miniature Optoelectronic Oscillators Based on Whispering-Gallery Mode Electrooptical Modulators

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.