Fig. 1. Principle of the F–P cavity-assisted relative timing jitter locking scheme and comparison of offset repetition rate locking stabilities under three operating conditions. (a) The RF source provides a reference signal to lock frep directly. (c) Schematic of equivalent locking using a PS-FBG in free-running operation. (e) Schematic of F–P cavity-assisted Δfrep locking in free-running operation. (b), (d), and (f) Schematic representations of the frequency deviation corresponding to the three cases.

Fig. 2. Schematic diagram of the experimental setup. (a) Two free-running combs pass through the sample, PS-FBG, and F–P cavity synchronously. Three optical streams are captured by a low-speed PD array and recorded through a three-channel ADC card. A commercial OSA is employed to record transmission spectra of the F–P cavity simultaneously. All signals are processed on a computer. (b) Output spectra of the OFCs. OC, optical coupler.

Fig. 3. Block diagram of the online calibration process. Raw data recorded [(a), (b)] by the ADC card and (c) by the OSA. The subscript of the signal indicates the fiber device that passed through. Panels (d) and (e) plot the time-varying phases of (a) and (b) obtained by the HT and their difference, respectively. (f) The raw spectrum of (a) by performing the FFT. (g) Spectrum of the signal after performing phase calibration of (a) using the time-varying phase difference plot in (e). (h) Spectrum after performing wavelength calibration and spectral shaping on (g) taking (c) as the reference.

Fig. 4. Distribution of frequencies extracted from IPS-FBG (t). Calculation of Δfrep evolution over time for (a) frame 2, (b) frame 7, and (c) frame 10 out of 16 frames under free-running operation. (d)–(f) Frequency distributions calculated by each IGM selected from the corresponding frame.

Fig. 5. Comparison of (a) frequency noise PSD curves and (b) integral frequency jitter curves for two operating states calculated from the IPS-FBG(t).

Fig. 6. Characterizations of wavelength calibration results for three operating states. (a) Statistical results of absolute wavelength deviations at the resonance peak of each F–P cavity for the three conditions. (b) Standard deviation after wavelength calibration in free-running operation. (c) and (d) Allan deviations calculated after multiple coherent averaging of the resonance peaks of the F–P cavity 1520.9 nm away from and 1550.0 nm near the center wavelength, respectively.

Fig. 7. Spectroscopic measurements of the P and R branches of the hydrogen cyanide (H13C14N) gas absorption cell in free-running operation. (a) Retrieved normalized spectral absorption features of H13C14N compared to the HITRAN database. (b) and (c) Comparison of the difference before and after wavelength calibration in the R and P branches, respectively. (d) Spectral measurements of the R4 and P11 absorption lines of H13C14N molecules at different averaging times compared to the HITRAN database.