Frequency domain computation of steady state modes of optoelectronic oscillators with stability analysis

A frequency domain approach for computing all of the steady state modes of single-loop optoelectronic oscillators (OEOs) corresponding to the exact parameter values, especially the fiber length, is presented. Computing these modes is useful in analyzing their effects on the phase noise performance as well as in designing single-mode OEOs. This computation is also useful in analyzing injection-locked OEO systems where the locking state depends on the values of oscillation frequencies and power levels of the steady state modes of the OEOs involved. The proposed steady state computation approach requires a much smaller amount of run-time compared to time domain methods; however, its results have to be checked for stability. Two stability analysis schemes, one based on the frequency domain Nyquist stability analysis and the other based on solving a slowly varying perturbation system in the time domain, are presented. The validities of these schemes are verified by comparing their results with each other, with full time domain integrations, and with previously published results. It is shown that the modes of a single-loop OEO computed by the presented approach are either stable or unstable, which justifies the need to use the proposed stability analysis schemes. Simulations show that the unstable modes ultimately converge to the dominant mode, i.e., the one with the largest small-signal loop gain. The effect of exciting any mode on the phase noise is also investigated through simulations.