Development of a photoelectric phase-locked loop model to better synchronize frequency combs and microwaves

The high phase coherence between ultralow-noise microwaves and ultrahigh-stable optical frequency combs (OFCs) is of both scientific and technological relevance for telecommunication, timekeeping, astronomy, and metrology. Here, a photoelectric phase-locked loop (PLL) model with ultralow phase noise based on the optical-microwave phase detector technique has been proposed and experimentally demonstrated. A detailed mathematical model for tight, real-time phase synchronization of OFCs and microwaves is developed to investigate the feasibility and analyze the characteristics of the phase-coherent system. We fabricate a compact PLL circuit with a proportional-integral-derivative regulator for the synchronization of an OFC to a microwave reference. Once synchronized, the long-term stability of the OFC agrees to 2.4×10^-14 at a 1000 s averaging time, which is enhanced by more than 4 orders of magnitude. Besides, the OFC almost acquires the same frequency stability as the microwave source. The ability to better phase synchronize OFCs and microwaves enables a wide range of applications beyond the laboratory.