Effect of Time Delay on the Stability of Optoelectronic Oscillators Based on Whispering-Gallery Mode Resonators

Optoelectronic oscillators (OEOs) are microwave photonic systems intended to generate ultra-pure radio-frequency signals for aerospace and communication engineering applications. Typically, a long optical fiber delay line is inserted in the feedback loop as an energy storage element intended to improve the phase noise performance. An ultra-high Q whispering-gallery mode resonator can be inserted as well in order to filter-out the spurious ring-cavity peaks arising in the radio-frequency spectrum. However, dynamical instabilities induced by a relatively large delay have never been analyzed for these OEOs. In this paper, we systematically investigate the stability of the generated microwaves as a function of the effective OEO loop gain and delay. We find that close enough to the oscillation threshold, the generated microwaves are unconditionally stable, but as the gain is increased, their stability becomes dependent on the ratio between the time delay and the overall photon lifetime of the resonator. Our results allow an optimal design for these OEOs, leading to both enhanced spectral stability and phase noise performance.