High frequency stability and low phase noise are two critical metrics for evaluating the performance of optical frequency combs. Highly stable femtosecond optical frequency combs play a significant role in frontier fields such as precision measurement physics, spectroscopy, optical clocks, and attosecond science. In recent years, the figure-9 fiber cavity configuration has emerged as the preferred design for low-noise fiber-based frequency combs. Research efforts have focused on suppressing phase noise, narrowing linewidth, and improving overall stability. Significant progress in reducing phase noise and linewidth has been achieved through techniques including suppression of pump laser current noise, control of femtosecond laser dispersion, and feedback control using fast actuators, meeting the requirements for most time-frequency applications. Regarding long-term stability, while considerable engineering optimizations and temperature drift control measures have been implemented, there remains room for further improvement.
Building upon this foundation, this paper presents a highly stable erbium-doped fiber optical frequency comb with a long-term stability of 10^-21 level, implemented based on a nonlinear amplifying loop mirror mode-locking technique. A self-built, 100 MHz repetition rate (f_r) erbium (E_r) doped fiber femtosecond laser outputs 290 mW, 67 f_s pulses. A carrier-envelope offset (f_ceo) signal with a signal-to-noise ratio of approximately 35 dB is detected using a collinear f-2f self-referencing technique. Both f_ceo and the beat note signal with a continuous-wave laser are simultaneously locked to a microwave reference using phase-locked loops that control a fast intra-cavity electro-optic modulator, a piezoelectric transducer, and the pump current. After locking, the phase noise of f_ceo is 421 mrad, with an in-loop relative frequency stability of 5.24×10^-17 at 1 s. The beat note exhibits a phase noise of 129 mrad and an in-loop relative frequency stability of 1.73×10^-18 at 1 s, which further improves to 5.30×10^-21 at 20,000 seconds. This high-stability, low-noise fiber comb system provides an ideal tool for research in high-precision optical clocks, optical frequency comparisons, and time-frequency transfer.