Quantifying Additive and Multiplicative Noise in Optoelectronic Oscillators: An Experimental and Theoretical Analysis

Optoelectronic oscillators are nonlinear time-delayed microwave photonic systems capable of producing exceptionally pure microwave signals. In order to improve the spectral purity of the generated microwaves, it is important to investigate the origin and magnitude of the noise that drive the oscillator away from optimal operation. This task appears to be challenging above threshold because some of the noise sources are nonlinearly mixed with the signal, and it is very difficult to disambiguate them. In this study, we take advantage from the fact that the signal is expected to be null under the threshold, so that any detected oscillation in the sub-threshold range is solely the result of the noise fluctuations that we need to characterize. We develop the theoretical framework for this approach and obtain a set of stochastic differential equations, allowing us to characterize these noise sources that can thereby be lumped as additive and multiplicative fluctuation terms. We perform experimental measurements that confirm the validity of this approach and offer a generic pathway for the characterization of noise in certain classes of oscillators.