Nonlinear dynamics of optoeletronic oscillators based on whispering-gallery mode resonators

To overcome the drawbacks of fiber-based opto-electronic oscillators (OEO), it has previously been proposed to replace the fiber delay line with a high-Q whispering-gallery mode (WGM) resonator. In such a resonator, photons are trapped inside the dielectric by total internal reflection, hence performing optical energy storage. For a Q-factor in the 10⁹ range, the photon lifetime in the cavity T_ph = Q/C0o is of the order of 1 μs with a corresponding linewidth of 100 kHz. According to Leeson theory, such a linewidth allows one to obtain superior phase noise performances in comparison to traditional radio-frequency systems. In order to investigate the behavior of this this OEO, we propose to use a nonlinear dynamics framework based on the slowly-varying amplitude of the generated microwave. We build a model showing that saddle-node bifurcations sequentially arise in the system as the feedback gain is increased. The stability of the various oscillatory states of the system is studied, and we perform numerical simulations to confirm this analysis. Experiments are also conducted, and the time-domain evolution of the generated microwave is successfully compared with the simulations.