Nonlinear dynamics of miniature optoelectronic oscillators based on whispering-gallery mode electrooptical modulators.

We propose a time-domain model to analyze the dynamical behavior of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. In these systems, the whispering-gallery mode resonator features a quadratic nonlinearity and operates as an electrooptical modulator, thereby eliminating the need for an integrated Mach-Zehnder modulator. The narrow optical resonances also eliminate the need for both an optical fiber delay line and an electric bandpass filter in the optoelectronic feedback loop. The architecture of miniature OEOs therefore appears as significantly simpler than the one of their traditional counterparts and permits us to achieve competitive metrics in terms of size, weight, and power. Our theoretical approach is based on the closed-loop coupling between the optical intracavity modes and the microwave signal generated via the photodetection of the output electrooptical comb. The resulting nonlinear oscillator model involves the slowly-varying envelopes of the microwave and optical fields, and its stability analysis permits the analytical determination the critical value of the feedback gain needed to trigger self-sustained oscillations. This stability analysis also allows us to understand how key parameters of the system such as cavity detuning or coupling efficiency influence the onset of the radiofrequency oscillation. Our study is complemented by time-domain simulations for the microwave and optical signals, which are in excellent agreement with the analytical predictions.