Continuous-wave frequency synthesis of a laser diode based on discrete-time negative frequency feedback: II. Theory

In this paper, we present the theory for a novel lightwave frequency synthesis system demonstrated recently. The system is composed of a frequency stabilized master laser, a frequency tunable slave laser, and an active optical feedback loop with an acoustooptic frequency shifter. The reference frequency is synthesized by circulating the optical pulse from the master laser around the loop and one output pulse with the desired frequency shift is used to stabilize the frequency of the slave laser. The theoretical aspects of the frequency synthesis system are explained based on the control theory for discrete-time negative feedback. We evaluate the frequency stability numerically by means of the Allan variance for different sampling periods, and reveal the relation between the frequency fluctuation characteristics of the slave laser in its free running condition. The numerical results agree with those of the reported experiments.