The Simplest Laser-Based Optoelectronic Oscillator: An Experimental and Theoretical Study

We present a theoretical and experimental study of the most simple autonomous optoelectronic oscillator (OEO) with a delayed feedback loop. Contrarily to the overwhelming majority of OEOs, our OEO does not use an external intensity-or phase-modulator to translate the electrical radio-frequency signal into the optical domain. Instead, we show that the electric signal can simply be used as a driving pump current of the laser that is seeding the oscillator. With this architecture, the intensity modulation is performed through the piecewise-linear (that is, nonlinear) power-intensity transfer function of the laser-diode, instead of the sinusoidal transfer function of the usual Mach-Zehnder modulators. We provide a model to investigate the dynamics of this simple architecture of OEO. This model is an integro-differential delay equation which is characterized by three time scales as in the conventional OEO, namely the low/high-cut off frequencies of the wide band filter and the time delay. The stability analysis of our OEO reveals a complex bifurcation behavior which critically depends on the gain of the feedback loop. In particular, we show that a sequence of Hopf bifurcations may lead to fast-scale oscillations with a period which is the double of the time-delay, or to slow-scale oscillations with a period which depends on the three aforementioned timescales. Our theoretical results are shown to be in excellent agreement with numerical simulations and the experimental measurements.