Injection locking and pulling phenomena in an optoelectronic oscillator

Abstract

Injection locking and pulling characteristics of a long-loop optoelectronic oscillator (OEO) that has a large number of closely-spaced longitudinal modes are theoretically analyzed and experimentally evaluated. A differential phase equation that relates the phase difference between the OEO and the injected microwave signal to its instantaneous beat angular frequency is derived in the time domain. Based on the differential phase equation, both the locking and pulling characteristics of an injection-locked OEO are studied, and the phase noise performance is analyzed. It is found that the locking and pulling performance depends upon three parameters, the initial frequency difference between the frequency of the signal generated by the free-running OEO and frequency of the injected microwave signal, the voltage ratio between the signal generated by the free-running OEO and the injected microwave signal, and the Q factor of the free-running OEO. The phase noise performance depends upon the locking range, the phase noise performance of the free-running OEO as well as that of the injected microwave signal. The analysis is validated experimentally. Excellent agreement is found between the theoretical analysis and the experimental demonstration.