Nonlinear dynamics of the dual-loop optoelectronic oscillator based on polarization multiplexing

This paper focuses on the temporal dynamics of the dual-loop optoelectronic oscillator (OEO) based on polarization multiplexing. The delay-differential equation (DDE) for the dual-loop OEO system is presented for the first time. After employing microwave envelope method to simplify the DDE, the envelope signal equation describing the system dynamics is obtained. Stability analysis of the static solution of the envelope signal equation is also performed, and the gain thresholds for the system to exhibit various dynamic behaviours are calculated. Moreover, the proposed nonlinear dynamics approach reveals the stability of microwave envelope in detail as a function of the feedback gain and coupling coefficient, which indicates that there is not monotonously incremental relationship between envelope amplitude of the ultrapure microwave and the feedback gain. Finally, the experimental measurements confirm the results obtained from the theoretical and numerical analysis.