Abstract
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.
Highlights
Optoelectronic oscillators (OEOs) have emerged as competitive microwave photonic sources for the generation of ultra-stable radiofrequency signals [1], [2]. In their most simplest architecture, they feature a closed optoelectronic feedback where the nonlinear element is an electrooptical (EO) Mach-Zehnder modulator, the energy storage element is a few-km-long optical delay line, and the frequency-selection element is a radiofrequency filter [3]. Such conventional OEOs have been shown to achieve remarkably high phase noise performances, with a record st to −163 dBc/Hz at 6 kHz offset from a 10 GHz carrier [4]
We conveniently introduce the reduced azimuthal order l = − 0 so that the whispering-gallery mode (WGM) of interest are symmetrically labeled as l = 0, ±1, ±2, · · ·, with l = 0 being the pumped mode
We have investigated the stochastic dynamics of an architecture of miniature OEO
Summary
Optoelectronic oscillators (OEOs) have emerged as competitive microwave photonic sources for the generation of ultra-stable radiofrequency signals [1], [2] In their most simplest architecture, they feature a closed optoelectronic feedback where the nonlinear element is an electrooptical (EO) Mach-Zehnder modulator, the energy storage element is a few-km-long optical delay line, and the frequency-selection element is a radiofrequency filter [3]. Such conventional OEOs have been shown to achieve remarkably high phase noise performances, with a record st to −163 dBc/Hz at 6 kHz offset from a 10 GHz carrier [4].
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