Theoretical Investigation of Optoelectronic Oscillators Near Bifurcation for Radio-Frequency Sensing

Motivated by our recently reported experimental results of a sub-threshold narowband OEO subject to RF injection, we analytically and numerically investigate the steady-state and dynamic behavior of an OEO in the free-running and RF injected cases. This system is analyzed near the bifurcation operating points with a focus on the zeroth-order bifurcation corresponding to threshold. We utilize stability analysis, linearization, and a slowly-varying envelope approach around bifurcations to investigate the time signatures of the OEO response, in particular, the role of the filter bandwidth and external time delay. The influence of the time delay on the trajectory of a period doubling route is analytically and numerically characterized. Near the zeroth-order free-running bifurcation, we model injected RF signal perturbations and investigate the steady-state and transient response. The RF amplification is analytically characterized below and near the zeroth-order free-running bifurcation of the OEO, focusing on the influence of the gain and external time delay. Finally, in the presence of a pulsed RF signal, we derive an analytic model that replicates the transient response of the OEO, which exhibits a series of diminishing steps leading to saturation. This approach exhibits excellent agreement with the recently reported experimental and numerical results.