Periodic and quasiperiodic dynamics of optoelectronic oscillators with narrow-band time-delayed feedback

We present a detailed study of instabilities arising in optoelectronic oscillators with a single narrow-band time-delayed feedback loop. Such optoelectronic oscillators produce periodic solutions and may be useful as high-purity signal generators, but their nonlinear dynamics sets limits on available signal amplitudes. Starting from an integrodifferential model, we utilize approximate analytic solutions to find the stability boundaries of the periodic solutions as well as regions of multistability. Our analytical predictions are confirmed by numerical simulations and experiments.