Theoretical and Experimental Analysis of Optical Frequency Combs Synchronized to a Microwave Reference Achieving 10−19-Level Additional Stability
Abstract
:1. Introduction
2. Theoretical Model and Experimental Implement
2.1. Theoretical Model
2.1.1. Model of Additional Phase Noise and Frequency Stability
2.1.2. Model of the n-th Harmonic Locking
2.2. Experimental Implement
- Measured the OFC background phase noise SFree(f) utilizing a phase noise meter and the corresponding background frequency stability utilizing a frequency meter (Figure 2a);
- Simulated phase noise SLocked(f) and stability using Formulas (2) and (4) in the locked mode.
- Connected both PFD inputs to REF and measured the output voltage with a DMM (Figure 2b);
- Simulated the equivalent PFD background phase noise SPDF(f) and frequency stability via Formulas (A10)–(A12).
- Combine SFree(f), , SPDF(f), and in Formulas (5)–(6) to simulated overall additional phase noise Soverall(f) and frequency stability ;
- For n-th harmonic locking, simulated the overall additional phase noise Sn-overall(f) and frequency stability via Formulas (8)–(9).
3. Experimental Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
OFCs | Optical frequency combs |
PLL | Phase-locked loop |
PFD | Phase frequency detector |
PIID | A phase frequency detector and a proportional, first-order integer, second-order integer, first-order differential controller |
PSF | Phase noise suppression factor |
SSF | Stability suppression factor |
REF | Radio frequency |
RF | Microwave reference |
SNR | Signal-to-noise ratio |
NALM | Nonlinear amplification loop mirror |
Appendix A
Appendix A.1
Appendix A.2
References
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Locking Strategy | 1 Hz | 1 Hz (Harmonic) |
---|---|---|
PFD + PIID | −168.7 dBc/Hz | −182.3 dBc/Hz Δ |
Multiplier + PI [22] | −96 dBc/Hz | −138 dBc/Hz * |
Improvement ratio | 72.7 dB | 44.3 dB |
Locking Strategy | τ = 1 s | τ = 8000 s | τ = 1 s (Harmonic) | τ = 8000 s (Harmonic) |
---|---|---|---|---|
PFD + PIID | 2.81 × 10−15 | 2.72 × 10−19 | 4.25 × 10−16 Δ | 2.80 × 10−19 Δ |
Multiplier + PI [22] | 4.54 × 10−14 | 1.67 × 10−16 | 1.46 × 10−14 * | 4.85 × 10−17 * |
Improvement ratio | 16.2 | 614.0 | 34.4 | 173.2 |
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Chen, X.; Li, M.; Rao, B.; Yang, X.; Hu, Z.; Dong, R.; Zhang, S.; Zhang, P. Theoretical and Experimental Analysis of Optical Frequency Combs Synchronized to a Microwave Reference Achieving 10−19-Level Additional Stability. Photonics 2025, 12, 195. https://doi.org/10.3390/photonics12030195
Chen X, Li M, Rao B, Yang X, Hu Z, Dong R, Zhang S, Zhang P. Theoretical and Experimental Analysis of Optical Frequency Combs Synchronized to a Microwave Reference Achieving 10−19-Level Additional Stability. Photonics. 2025; 12(3):195. https://doi.org/10.3390/photonics12030195
Chicago/Turabian StyleChen, Xin, Mingkun Li, Bingjie Rao, Xiguang Yang, Zhenyuan Hu, Ruifang Dong, Shougang Zhang, and Pan Zhang. 2025. "Theoretical and Experimental Analysis of Optical Frequency Combs Synchronized to a Microwave Reference Achieving 10−19-Level Additional Stability" Photonics 12, no. 3: 195. https://doi.org/10.3390/photonics12030195
APA StyleChen, X., Li, M., Rao, B., Yang, X., Hu, Z., Dong, R., Zhang, S., & Zhang, P. (2025). Theoretical and Experimental Analysis of Optical Frequency Combs Synchronized to a Microwave Reference Achieving 10−19-Level Additional Stability. Photonics, 12(3), 195. https://doi.org/10.3390/photonics12030195