## Abstract

A frequency domain algorithm is proposed for deriving all of the possible steady state modes of dual injection-locked optoelectronic oscillators (DIL-OEOs), corresponding to the detailed system parameters, such as the fiber lengths, small signal open loop gains, radio frequency filters’ bandwidths, phase shifting values, and injection parameters. It is shown that some or all of the modes computed by the new approach may be unstable; these are just mathematical solutions of the steady state equations. Therefore, it is necessary to check the stability of these modes. A stability analysis approach is proposed, which is based on simulating the slowly varying time domain dynamic governing the perturbation variables. The steady state and stability analysis approaches enable one to predict the required injection parameters for having a reliable steady state injection-locked mode in the DIL-OEO system. The new method requires a much smaller runtime compared to the corresponding time domain methods. In addition, it avoids many simplifying assumptions of the corresponding frequency domain approaches presented in the literature. The validities of the steady state and stability analysis methods are verified by comparing their results with full time domain integrations and with other predictions regarding the required injection parameters for phase locking, as presented in the literature.

© 2017 Optical Society of America

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