This paper presents a combined theoretical and experimental method for noise suppression in the repetition frequency (f_r) locking of erbium-doped fiber optical frequency combs (OFCs). This study proposed a novel mathematical model to bridge the noise relationship of f_r between the free-running and locked modes, and analyzed this relationship from two perspectives: the additional phase noise and the frequency stability. In addition, to integrate theoretical modeling with experimental validation, this study designed f_r locking strategy that uses a phase-locked loop (PLL) with PFD + PIID (a phase frequency detector and a proportional, first-order integer, second-order integer, first-order differential controller). Under synchronization of the f_r with a microwave reference (REF), this study achieved OFC additional frequency stabilities of 2.81 × 10⁻¹⁵@1 s and 8.08 × 10⁻¹⁹@10,000 s at 200 MHz fundamental frequency locking and 4.25 × 10⁻¹⁶@1 s and 1.91 × 10⁻¹⁹@10,000 s at 1200 MHz harmonic locking. The simulated and experimental results are in good agreement, confirming the consistency of the theoretical model and experiment. This work provides a reliable theoretical model that can be used to predict stability for OFC locking and significantly improves the additional frequency stability of OFCs.

Microwave sources based on ultrastable lasers and optical frequency combs (OFCs) exhibit ultralow phase noise and ultrahigh-frequency stability, which are important for many applications. Herein, we present a microwave source that is phase-locked to an ultrastable continuous-wave laser, with a relative frequency instability of 7 × ${10}^{-16}$ at 1 s. An Er:fiber-based OFC and an optic-to-electronic converter with low residual noise are employed to confer optical frequency stability on the 9.6 GHz microwave signal. Instead of using the normal cascaded Mach–Zehnder interferometer method, we developed a microwave regeneration method for converting optical pulses into microwave signals to further suppress the additional noise in the optic-to-electronic conversion process. The microwave regeneration method employs an optical-to-microwave phase detector based on a fiber-based Sagnac loop to produce the error signal between a 9.6 GHz dielectric resonator oscillator (DRO) and the OFC. The 9.6 GHz microwave (48th harmonic of the comb’s repetition rate) signal with the frequency stability of the ultrastable laser was achieved using a DRO that was phase-locked to the optical comb. Preliminary evaluations showed that the frequency instability of the frequency synthesizer from the optical to the 9.6 GHz microwave signal was approximately 2 × ${10}^{-15}$ at 1 s, the phase noise was $-106$ dBc Hz⁻¹ at 1 Hz, and the timing noise was approximately 9 as Hz^−1/2 (phase noise approx. $-125$ dBc Hz⁻¹). The 9.6 GHz signal from the photonic microwave source exhibited a short-term relative frequency instability of 2.1 × ${10}^{-15}$ at 1 s, which is 1.5 times better than the previous results.