Highly-stable frequency transfer via fiber link with improved electrical error signal extraction and compensation scheme Jianye Zhao,∗ Dawei Li, Bo Ning, Shuangyou Zhang, and Wei Duan Department of Electronics, Peking University, Beijing 100871, China ∗ [email protected]
Abstract: In this paper, we demonstrate a radio frequency dissemination system via fiber link. An electric phase-shifter is used to active compensate the phase error in the transfer process. Furthermore, an improved error signal extraction component is used to extract the phase error induced via the fiber link. The system can compensate large phase range fluctuation rapidly and precisely. An experiment has been demonstrated with this structure to disseminate a 100 MHz frequency through 100 km. The relative frequency stability is 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. It means this scheme can be used to transfer the most stable microwave sources through fiber link. © 2015 Optical Society of America OCIS codes: (060.2360) Fiber optics links and subsystems; (120.5050) Phase measurement.
References and links 1. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link,” Science 319(5871), 1808–1812 (2003). 2. A. Matveev, C. G. Parthey, K. Predehl, J. Alnis, A. Beyer, R. Holzwarth, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, G. Grosche, O. Terra, T. Legero, H. Schnatz, S. Weyers, B. Altschul, and T. W. Hansch, “Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link,” Phys. Rev. Lett. 110, 230801 (2013). 3. F.-L. Hong, M. Musha, M. Takamoto, H. Inaba, S. Yanagimachi, A. Takamizawa, K. Watabe, T. Ikegami, M. Imae, Y. Fujii, M. Amemiya, K. Nakagawa, K. Ueda, and H. Katori, “Measuring the frequency of a Sr optical lattice clock using a 120 km coherent optical transfer,” Opt. Lett. 34(5), 692–694 (2009). 4. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007). 5. S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hansch, H. Schnatz, G. Grosche, and R. Holzwarth, “Opticalfrequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013). 6. M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011). 7. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012). 8. D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, “High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979 (2014). 9. A. Bercy, F. Stefani, O. Lopez, C. Chardonnet, P. E. Pottie, and A. Amy-Klein, “Two-way optical frequency comparisons at 5 × 10−21 relative stability over 100-km telecommunication network fibers,” Phys. Rev. A 90, 061802 (2014). 10. S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent Optical Phase Transfer over a 32-km Fiber with 1 s Instability at 10−17 ,” Phys. Rev. Lett. 99, 153601 (2007).
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8829
11. G. Marra, H. S. Margolis, and D. J. Richardson, “Dissemination of an optical frequency comb over fiber with 3 × 10−18 fractional accuracy,” Opt. Express 20(2), 1775–1782 (2012). 12. B. Ning, S. Zhang, D. Hou, J. Wu, Z. Li, and J. Zhao, “High-precision distribution of highly stable optical pulse trains with 8.8 × 10−19 instability,” Sci. Rep. 4, 5109 (2014). 13. O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F.Narbonneau, M.Lours, and G. Santarelli, “86-km optical link with a resolution of 2 × 10−18 for RF frequency transfer,” Eur. Phys. J. D 48, 35–41 (2008). 14. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949 (2009). 15. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5 × 10−19 accuracy level,” Sci. Rep. 2, 556 (2012). 16. L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133 (2013). 17. O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B 98(4), 723–727 (2010). 18. L. Primas, G. Lutes, and R. Sydnor, “Fiber optic frequency transfer link,” in Proceeding of Frequency Control Symposium, 478–484 (1988). 19. B. Ning, D. Hou, T. Zheng, and Jianye Zhao, “Hybrid analog-digital fiber-based radio-frequency signal distribution,” Phot. Tech. Lett 25, 1551–1554 (2013). 20. G. Lutes, “ Development of optical fiber frequency and time distribution systems,” in Proceeding of Precise Time and Time Interval Applications and Planning Meeting,(1981). 21. J. Shen, G. Wu, L. Hu, W. Zou, and Jianping Chen, “Active phase drift cancellation for optic-fiber frequency transfer using a photonic radio-frequency phase shifter,” Opt. Lett. 39(8), 282798 (2014).
1.
Introduction
Optical fiber links are the most precise technique to transfer frequency signals, which benefits modern science and practical applications, such as the comparison of optical clocks, fundamental physics measurement and antenna arrays [1-4]. Distinct demands require different signals to be transferred. Several groups have done remarkable work on optical frequency [5-9], frequency comb [10-12] and radio frequency [13-16]. All the three methods propose a strategy to compensate for the phase perturbation caused by vibration and temperature changes. In following discussion, we will focus on the phase noise suppression in the radio frequency transfer scheme. Several techniques, both in optical domain and electrical domain, are realized to compensate phase fluctuation. As to the optical domain method, optical group-delay actuators are applied to compensate the fiber-induced phase noise by adjusting the optical length of fiber link [17]. By this method, high transfer performance has been achieved. However, the scheme also suffers two disadvantages. The first disadvantage is the contradiction of compensation range and compensation speed. For thermally controlled fiber spool and optical delay line, although they have a large compensation range, they are often limited by the speed. While, for piezoelectric transducer (PZT), it has quick response but with limited phase range. These actuators need to be used together for highly-stable transmission which increase the complexity of the compensation scheme. The second disadvantage is that both the thermally controlled spool scheme and PZT scheme will take up a lot of space. Hence it is difficult to integrate the scheme. In electrical domain, phase conjugation methods has been studied for more than 25 years. By changing the phase of the transferred microwave frequency, phase noise induced by the environmental perturbation is actively compensated [14,18,19]. By this method, the system complexity is sharply reduced and the portability of the system is greatly enhanced. However, the compensate scheme faces its own pain point. For optical scheme, the phase fluctuation is cancelled by adjusting the optical length of the fiber link, thereby the phase of the transferred signal is changed forward and backward symmetrically. But for electrical method, it is impossible to find a pair of compensation devices to compensate the phase noise forward and backward symmetrically. It presents a challenge for error signal detecting and phase compensating. In this paper, we proposed a compensation scheme based on an electrical phase shifter and #232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8830
a modified error signal detection structure. An experiment has been demonstrated with this structure to transfer a 100 MHz frequency through 100 km. The relative frequency stability is measured as 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. 2.
Theory analysis
Figure 1(a) shows the basic frequency transmission scheme [20]. The reference signal has an initial phase. It can be expressed as v1 (t) = A1 cos(ω t + φ0 ).
(1)
Where ω represents the transferred radio frequency and φ0 represents the initial phase. After a phase shifter, a compensation phase φc is brought in to active compensate the phase fluctuation. The phase shifted signal can be given by v2 (t) = A2 cos(ω t + φ0 + φc ).
(2)
The phase shifted signal is divided into two parts. One part is used for detecting the error signal. The other part is transferred to the remote end. Because of the environment perturbation, a phase fluctuation is added to the transferred signal, which can be expressed as v3 (t) = A3 cos[ω (t − τ ) + φ0 + φc − φ p ].
(3)
Where φ p presents the phase fluctuation caused by vibration and temperature changes in the fiber link and τ presents the time delay in the optical fiber. The signal is divided into two parts. The major part is transferred back along the same fiber link for actively compensating the phase fluctuation. As the variation faster than the time delay of the round trip time cannot be compensated by the system, an assumption can be made that the forward and backward signal are corrupted by the same perturbation. Then the round-trip signal can be given by v4 (t) = A4 cos[ω (t − 2τ ) + φ0 + φc − 2φ p ].
(4)
Then the signal is mixed with by down-conversion mixer and after a low pass filter, the error signal can be acquired (5) v5 (t) = A5 cos(2ωτ + 2φ p ). The signal v5 (t) is used for controlling the phase shifter to suppress the phase fluctuation induced by fiber link. where τ is decided by the length of the fiber link and A5 can be set by amplifier. In another word, the active compensation phase φc is determined by φ p . However, the exact relationship between φc and φ p is hard to obtain because φ p and v5 (t) are not linearly oneto-one match while it is the same for the generation of φc by a voltage-controlled phase shifter. In the light of phase locking loop theory, it is necessary to establish a structure containing of φc − φ p and keep it constant.
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8831
Fig. 1. (a) Basic frequency transmission schematic. (b) Contrast frequency transmission schematic. (c) Improved frequency transmission schematic. Ref: reference signal. OC: optical circulator. PD: photodetector.
The signal extraction structure, shown in Fig. 1(b), has once been proposed [16-17]. In this scheme, the reference signal v1 (t) is mixed with phase shifted signal v2 (t) and round-trip signal v4 (t), respectively. After low pass filters, two error signals are obtained v6 (t) = A6 cos(φc ).
(6)
v7 (t) = A7 cos(φc − 2φ p − 2ωτ ).
(7)
And then, a differential amplifier is used to get t he amplitude difference of v6 (t) and v7 (t). When the two cosine functions both work at their linear area with relatively high slope and A6 equals A7 , the output signal v8 (t) can represent the phase relationship of φc − φ p . By adjusting the control voltage of phase shifter thereby adjusting φc , it is possible to keep v8 (t) constant. Hence, φc − φ p can be considered constant. In this way, the environment-induced phase noise is compensated at the remote end. However, this error signal detection structure has two defects. First, it is not a trivial task to keep A6 and A7 the same. Second, by keeping v8 (t) constant, it is not always effective to lock the phase φc − φ p well. As at the maximum value of v6 (t) and v7 (t), the voltage-phase
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8832
resolution is low, and the output signal v8 (t) is the differential value of v6 (t) and v7 (t) and it is difficult to control v6 (t) and v7 (t) at high voltage-phase resolution segment. In order to overcome this problem, an improved error signal detection structure is induced and is shown in Fig. 1(c) [21]. The phase shifted signal v2 (t) is mixed with the round-trip signal v4 (t) through an up-conversion mixer, the output signal, processed by a band pass filter, can be expressed as v9 (t) = A9 cos[2ω (t − τ ) + 2φ0 + 2φc − 2φ p ].
(8)
In the meantime, the frequency of reference signal is doubled by a frequency multiplier to get a signal expressed as (9) v10 (t) = A10 cos(2ω t + 2φ0 ). The two signals mix together and pass through a low pass filter, the output signal can be expressed as (10) v11 (t) = A11 cos(2φc − 2φ p − 2ωτ ). The fluctuation of this signal is used for adjusting the control voltage of phase shifter. Hence, the active compensation phase φc is changed according to the fluctuation of v11 (t) thereby keeping the phase of the signal constant at the remote end. The compensation of the environment fluctuation is therefore realized. 3.
Experiment setup
Fig. 2. Experiment setup of frequency dissemination system with improved phase detection structure. PD: photodetector; BPF: band pass filter; Amp: amplifier; EDFA: erbium-doped fiber amplifier; DFB: distributed feedback laser; LF amp: low frequency amplifier;
Based on the error signal extraction scheme, an experimental frequency dissemination system, illustrated in Fig. 2, is set up. A signal generator is used as the reference to generate the 100 MHz transfer signal. It is phase shifted by a phase shifter and then modulates the intensity of a distributed feedback laser diode. After an optical circulator, the signal is fed into a 100 km optical fiber spool without being isolated by any means to the temperature fluctuation. Then the signal is transferred to the remote end. At the remote end, another optical circulator is used. The received signal is split into two optical paths. One part is detected by a fast photodetector #232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8833
for analysis. The signal-noise ratio of the signal is about 52 dB and the analysis of the transfer performance is realized by comparing the transferred signal with the reference. The phase difference is detected in term of voltage fluctuation and recorded by a high resolution voltage acquisition instrument. The measurement bandwidth is 3 Hz. While the major part is fed back to optical circulator and transferred back to local end along the same optical fiber link. At the local end, the round-trip signal is amplified by an erbiumdoped fiber amplifier (EDFA) after optical circulator and then detected by a photodetector. Then the signal is used to extract the error signal. The procedure has been analysed above. The signal-noise ratio of the output signal of the up-mixer is about 35 dB. Then this signal is mixed with the multiple signal of the reference and get the error signal. The error signal is used to compensate the phase fluctuation by adjusting the phase shifter. The control system is based on a DSP module and the bandwidth of the control loop is 1 kHz. 4.
Experimental results and discussions
Fig. 3. Frequency stability measured at remote end. The free running relative frequency stability, the performance based on the structure of Fig. 1(b) and the performance based on the improved structure are presented in the figure.
The relative frequency stability is expressed in Overlapping Allan Deviation (its formula can be found in Handbook of Frequency Stability Analysis, Page 21) and is illustrated in Fig. 3. Thanks to the compensation scheme which is illustrated in Fig. 1(c), the relative frequency stability reaches 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. In order to make a comparison, an experiment based on Fig.1 (b) is demonstrated and relative frequency stability is 9 × 10−14 at 1 s and 2 × 10−16 at 4000 s while the free run relative frequency stability is 1 × 10−13 at 1 s and 9 × 10−15 at 4000 s. The signal sideband (SSB) phase noise at the remote end of the compensation scheme illustrated in Fig. 1(c) is about -106 dBc/Hz at 1 Hz offset of the 100 MHz carrier signal while the SSB phase noise of the compensation scheme illustrated in Fig. 1(b) is about -102 dBc/Hz at 1 Hz offset. The SSB phase noise of the compensation scheme illustrated in
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8834
Fig. 1(c) is better from 1 Hz to 1 kHz as the control loop bandwidths of the two compensation schemes are both 1 kHz. The data has been shown in Fig. 4.
Fig. 4. SSB phase noise at the romote end of the compensation scheme based on the structure of Fig. 1(b) and the improved structure of Fig. 1(c) are presented in the figure.
Compared with the free running performance, both the two compensation schemes work effectively to keep the fiber link stable in long term. Furthermore, the improvement of the scheme of Fig. 1(c) benefits from the promotion of the error signal extraction component. First, for the scheme of Fig. 1(b), it is very difficult to keep A6 and A7 the same even though power control circuits are used in the system. Second, for the scheme of Fig. 1(b), as it is shown in Fig.5, the differences of v6 (t) and v7 (t) presented in black line and red line are the same while the phase differences accordingly change a lot. If it is lucky enough that v6 (t) and v7 (t) are always around zero, the phase resolution is the highest. It means φc − φ p is limited in a narrow range thereby the phase noise at the remote end is well controlled. However, when v6 (t) and v7 (t) are at the peak of the cosine, φc − φ p can fluctuate in a wide range hence the phase noise at the remote end is not controlled effectively. The problem is φc − φ p is presented in the form of v8 (t) and is the differential value of v6 (t) and v7 (t). It is hard to recognize whether v6 (t) and v7 (t) are around zero or at the peak of the cosine curve. Therefore the lock range of φc − φ p cannot be controlled well. On the contrary, by the scheme demonstrated in Fig. 1(c), the two input signals can be controlled to mix with each other orthogonally thereby achieving precise phase difference without the influence of amplitude noise. Hence it is easier and more precise to extract the error signal between the reference and the feedback signal thereby achieving more accurate compensation both in short term and long term.
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8835
Fig. 5. Error signal extraction analysis for the scheme of Fig. 1(b). The ranges of voltage presented in black and red line are the same while the range of phase accordingly vary a lot.
5.
Conclusion
In conclusion, we proposed a radio frequency distribution system via optical fiber link. In this scheme, the phase noise induced by environment is cancelled by an electric phase shifter with the help of an improved error signal extraction scheme. The compensation structure is very simple but of high performance. Besides, the structure is all made up of electronic components and all the components can be integrated on a single printed circuit board, which makes it portable and robust alike. An experiment has been demonstrated with this structure to transfer a 100 MHz frequency through 100 km fiber link. The relative frequency stability is measured as 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. This is relatively the best microwave transfer performance to be reported at the averaging time of 4000 s. It means that the dissemination of the most accurate microwave standard via fiber link is available, not only inside the laboratories but also in outdoor condition. Acknowledgment This work is funded by National Natural Science Foundations of China (No. 61371074).
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8836
Abstract: In this paper, we demonstrate a radio frequency dissemination system via fiber link. An electric phase-shifter is used to active compensate the phase error in the transfer process. Furthermore, an improved error signal extraction component is used to extract the phase error induced via the fiber link. The system can compensate large phase range fluctuation rapidly and precisely. An experiment has been demonstrated with this structure to disseminate a 100 MHz frequency through 100 km. The relative frequency stability is 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. It means this scheme can be used to transfer the most stable microwave sources through fiber link. © 2015 Optical Society of America OCIS codes: (060.2360) Fiber optics links and subsystems; (120.5050) Phase measurement.
References and links 1. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link,” Science 319(5871), 1808–1812 (2003). 2. A. Matveev, C. G. Parthey, K. Predehl, J. Alnis, A. Beyer, R. Holzwarth, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, G. Grosche, O. Terra, T. Legero, H. Schnatz, S. Weyers, B. Altschul, and T. W. Hansch, “Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link,” Phys. Rev. Lett. 110, 230801 (2013). 3. F.-L. Hong, M. Musha, M. Takamoto, H. Inaba, S. Yanagimachi, A. Takamizawa, K. Watabe, T. Ikegami, M. Imae, Y. Fujii, M. Amemiya, K. Nakagawa, K. Ueda, and H. Katori, “Measuring the frequency of a Sr optical lattice clock using a 120 km coherent optical transfer,” Opt. Lett. 34(5), 692–694 (2009). 4. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007). 5. S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hansch, H. Schnatz, G. Grosche, and R. Holzwarth, “Opticalfrequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111, 110801 (2013). 6. M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011). 7. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012). 8. D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, “High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979 (2014). 9. A. Bercy, F. Stefani, O. Lopez, C. Chardonnet, P. E. Pottie, and A. Amy-Klein, “Two-way optical frequency comparisons at 5 × 10−21 relative stability over 100-km telecommunication network fibers,” Phys. Rev. A 90, 061802 (2014). 10. S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent Optical Phase Transfer over a 32-km Fiber with 1 s Instability at 10−17 ,” Phys. Rev. Lett. 99, 153601 (2007).
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8829
11. G. Marra, H. S. Margolis, and D. J. Richardson, “Dissemination of an optical frequency comb over fiber with 3 × 10−18 fractional accuracy,” Opt. Express 20(2), 1775–1782 (2012). 12. B. Ning, S. Zhang, D. Hou, J. Wu, Z. Li, and J. Zhao, “High-precision distribution of highly stable optical pulse trains with 8.8 × 10−19 instability,” Sci. Rep. 4, 5109 (2014). 13. O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F.Narbonneau, M.Lours, and G. Santarelli, “86-km optical link with a resolution of 2 × 10−18 for RF frequency transfer,” Eur. Phys. J. D 48, 35–41 (2008). 14. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949 (2009). 15. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5 × 10−19 accuracy level,” Sci. Rep. 2, 556 (2012). 16. L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133 (2013). 17. O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B 98(4), 723–727 (2010). 18. L. Primas, G. Lutes, and R. Sydnor, “Fiber optic frequency transfer link,” in Proceeding of Frequency Control Symposium, 478–484 (1988). 19. B. Ning, D. Hou, T. Zheng, and Jianye Zhao, “Hybrid analog-digital fiber-based radio-frequency signal distribution,” Phot. Tech. Lett 25, 1551–1554 (2013). 20. G. Lutes, “ Development of optical fiber frequency and time distribution systems,” in Proceeding of Precise Time and Time Interval Applications and Planning Meeting,(1981). 21. J. Shen, G. Wu, L. Hu, W. Zou, and Jianping Chen, “Active phase drift cancellation for optic-fiber frequency transfer using a photonic radio-frequency phase shifter,” Opt. Lett. 39(8), 282798 (2014).
1.
Introduction
Optical fiber links are the most precise technique to transfer frequency signals, which benefits modern science and practical applications, such as the comparison of optical clocks, fundamental physics measurement and antenna arrays [1-4]. Distinct demands require different signals to be transferred. Several groups have done remarkable work on optical frequency [5-9], frequency comb [10-12] and radio frequency [13-16]. All the three methods propose a strategy to compensate for the phase perturbation caused by vibration and temperature changes. In following discussion, we will focus on the phase noise suppression in the radio frequency transfer scheme. Several techniques, both in optical domain and electrical domain, are realized to compensate phase fluctuation. As to the optical domain method, optical group-delay actuators are applied to compensate the fiber-induced phase noise by adjusting the optical length of fiber link [17]. By this method, high transfer performance has been achieved. However, the scheme also suffers two disadvantages. The first disadvantage is the contradiction of compensation range and compensation speed. For thermally controlled fiber spool and optical delay line, although they have a large compensation range, they are often limited by the speed. While, for piezoelectric transducer (PZT), it has quick response but with limited phase range. These actuators need to be used together for highly-stable transmission which increase the complexity of the compensation scheme. The second disadvantage is that both the thermally controlled spool scheme and PZT scheme will take up a lot of space. Hence it is difficult to integrate the scheme. In electrical domain, phase conjugation methods has been studied for more than 25 years. By changing the phase of the transferred microwave frequency, phase noise induced by the environmental perturbation is actively compensated [14,18,19]. By this method, the system complexity is sharply reduced and the portability of the system is greatly enhanced. However, the compensate scheme faces its own pain point. For optical scheme, the phase fluctuation is cancelled by adjusting the optical length of the fiber link, thereby the phase of the transferred signal is changed forward and backward symmetrically. But for electrical method, it is impossible to find a pair of compensation devices to compensate the phase noise forward and backward symmetrically. It presents a challenge for error signal detecting and phase compensating. In this paper, we proposed a compensation scheme based on an electrical phase shifter and #232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8830
a modified error signal detection structure. An experiment has been demonstrated with this structure to transfer a 100 MHz frequency through 100 km. The relative frequency stability is measured as 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. 2.
Theory analysis
Figure 1(a) shows the basic frequency transmission scheme [20]. The reference signal has an initial phase. It can be expressed as v1 (t) = A1 cos(ω t + φ0 ).
(1)
Where ω represents the transferred radio frequency and φ0 represents the initial phase. After a phase shifter, a compensation phase φc is brought in to active compensate the phase fluctuation. The phase shifted signal can be given by v2 (t) = A2 cos(ω t + φ0 + φc ).
(2)
The phase shifted signal is divided into two parts. One part is used for detecting the error signal. The other part is transferred to the remote end. Because of the environment perturbation, a phase fluctuation is added to the transferred signal, which can be expressed as v3 (t) = A3 cos[ω (t − τ ) + φ0 + φc − φ p ].
(3)
Where φ p presents the phase fluctuation caused by vibration and temperature changes in the fiber link and τ presents the time delay in the optical fiber. The signal is divided into two parts. The major part is transferred back along the same fiber link for actively compensating the phase fluctuation. As the variation faster than the time delay of the round trip time cannot be compensated by the system, an assumption can be made that the forward and backward signal are corrupted by the same perturbation. Then the round-trip signal can be given by v4 (t) = A4 cos[ω (t − 2τ ) + φ0 + φc − 2φ p ].
(4)
Then the signal is mixed with by down-conversion mixer and after a low pass filter, the error signal can be acquired (5) v5 (t) = A5 cos(2ωτ + 2φ p ). The signal v5 (t) is used for controlling the phase shifter to suppress the phase fluctuation induced by fiber link. where τ is decided by the length of the fiber link and A5 can be set by amplifier. In another word, the active compensation phase φc is determined by φ p . However, the exact relationship between φc and φ p is hard to obtain because φ p and v5 (t) are not linearly oneto-one match while it is the same for the generation of φc by a voltage-controlled phase shifter. In the light of phase locking loop theory, it is necessary to establish a structure containing of φc − φ p and keep it constant.
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8831
Fig. 1. (a) Basic frequency transmission schematic. (b) Contrast frequency transmission schematic. (c) Improved frequency transmission schematic. Ref: reference signal. OC: optical circulator. PD: photodetector.
The signal extraction structure, shown in Fig. 1(b), has once been proposed [16-17]. In this scheme, the reference signal v1 (t) is mixed with phase shifted signal v2 (t) and round-trip signal v4 (t), respectively. After low pass filters, two error signals are obtained v6 (t) = A6 cos(φc ).
(6)
v7 (t) = A7 cos(φc − 2φ p − 2ωτ ).
(7)
And then, a differential amplifier is used to get t he amplitude difference of v6 (t) and v7 (t). When the two cosine functions both work at their linear area with relatively high slope and A6 equals A7 , the output signal v8 (t) can represent the phase relationship of φc − φ p . By adjusting the control voltage of phase shifter thereby adjusting φc , it is possible to keep v8 (t) constant. Hence, φc − φ p can be considered constant. In this way, the environment-induced phase noise is compensated at the remote end. However, this error signal detection structure has two defects. First, it is not a trivial task to keep A6 and A7 the same. Second, by keeping v8 (t) constant, it is not always effective to lock the phase φc − φ p well. As at the maximum value of v6 (t) and v7 (t), the voltage-phase
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8832
resolution is low, and the output signal v8 (t) is the differential value of v6 (t) and v7 (t) and it is difficult to control v6 (t) and v7 (t) at high voltage-phase resolution segment. In order to overcome this problem, an improved error signal detection structure is induced and is shown in Fig. 1(c) [21]. The phase shifted signal v2 (t) is mixed with the round-trip signal v4 (t) through an up-conversion mixer, the output signal, processed by a band pass filter, can be expressed as v9 (t) = A9 cos[2ω (t − τ ) + 2φ0 + 2φc − 2φ p ].
(8)
In the meantime, the frequency of reference signal is doubled by a frequency multiplier to get a signal expressed as (9) v10 (t) = A10 cos(2ω t + 2φ0 ). The two signals mix together and pass through a low pass filter, the output signal can be expressed as (10) v11 (t) = A11 cos(2φc − 2φ p − 2ωτ ). The fluctuation of this signal is used for adjusting the control voltage of phase shifter. Hence, the active compensation phase φc is changed according to the fluctuation of v11 (t) thereby keeping the phase of the signal constant at the remote end. The compensation of the environment fluctuation is therefore realized. 3.
Experiment setup
Fig. 2. Experiment setup of frequency dissemination system with improved phase detection structure. PD: photodetector; BPF: band pass filter; Amp: amplifier; EDFA: erbium-doped fiber amplifier; DFB: distributed feedback laser; LF amp: low frequency amplifier;
Based on the error signal extraction scheme, an experimental frequency dissemination system, illustrated in Fig. 2, is set up. A signal generator is used as the reference to generate the 100 MHz transfer signal. It is phase shifted by a phase shifter and then modulates the intensity of a distributed feedback laser diode. After an optical circulator, the signal is fed into a 100 km optical fiber spool without being isolated by any means to the temperature fluctuation. Then the signal is transferred to the remote end. At the remote end, another optical circulator is used. The received signal is split into two optical paths. One part is detected by a fast photodetector #232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8833
for analysis. The signal-noise ratio of the signal is about 52 dB and the analysis of the transfer performance is realized by comparing the transferred signal with the reference. The phase difference is detected in term of voltage fluctuation and recorded by a high resolution voltage acquisition instrument. The measurement bandwidth is 3 Hz. While the major part is fed back to optical circulator and transferred back to local end along the same optical fiber link. At the local end, the round-trip signal is amplified by an erbiumdoped fiber amplifier (EDFA) after optical circulator and then detected by a photodetector. Then the signal is used to extract the error signal. The procedure has been analysed above. The signal-noise ratio of the output signal of the up-mixer is about 35 dB. Then this signal is mixed with the multiple signal of the reference and get the error signal. The error signal is used to compensate the phase fluctuation by adjusting the phase shifter. The control system is based on a DSP module and the bandwidth of the control loop is 1 kHz. 4.
Experimental results and discussions
Fig. 3. Frequency stability measured at remote end. The free running relative frequency stability, the performance based on the structure of Fig. 1(b) and the performance based on the improved structure are presented in the figure.
The relative frequency stability is expressed in Overlapping Allan Deviation (its formula can be found in Handbook of Frequency Stability Analysis, Page 21) and is illustrated in Fig. 3. Thanks to the compensation scheme which is illustrated in Fig. 1(c), the relative frequency stability reaches 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. In order to make a comparison, an experiment based on Fig.1 (b) is demonstrated and relative frequency stability is 9 × 10−14 at 1 s and 2 × 10−16 at 4000 s while the free run relative frequency stability is 1 × 10−13 at 1 s and 9 × 10−15 at 4000 s. The signal sideband (SSB) phase noise at the remote end of the compensation scheme illustrated in Fig. 1(c) is about -106 dBc/Hz at 1 Hz offset of the 100 MHz carrier signal while the SSB phase noise of the compensation scheme illustrated in Fig. 1(b) is about -102 dBc/Hz at 1 Hz offset. The SSB phase noise of the compensation scheme illustrated in
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8834
Fig. 1(c) is better from 1 Hz to 1 kHz as the control loop bandwidths of the two compensation schemes are both 1 kHz. The data has been shown in Fig. 4.
Fig. 4. SSB phase noise at the romote end of the compensation scheme based on the structure of Fig. 1(b) and the improved structure of Fig. 1(c) are presented in the figure.
Compared with the free running performance, both the two compensation schemes work effectively to keep the fiber link stable in long term. Furthermore, the improvement of the scheme of Fig. 1(c) benefits from the promotion of the error signal extraction component. First, for the scheme of Fig. 1(b), it is very difficult to keep A6 and A7 the same even though power control circuits are used in the system. Second, for the scheme of Fig. 1(b), as it is shown in Fig.5, the differences of v6 (t) and v7 (t) presented in black line and red line are the same while the phase differences accordingly change a lot. If it is lucky enough that v6 (t) and v7 (t) are always around zero, the phase resolution is the highest. It means φc − φ p is limited in a narrow range thereby the phase noise at the remote end is well controlled. However, when v6 (t) and v7 (t) are at the peak of the cosine, φc − φ p can fluctuate in a wide range hence the phase noise at the remote end is not controlled effectively. The problem is φc − φ p is presented in the form of v8 (t) and is the differential value of v6 (t) and v7 (t). It is hard to recognize whether v6 (t) and v7 (t) are around zero or at the peak of the cosine curve. Therefore the lock range of φc − φ p cannot be controlled well. On the contrary, by the scheme demonstrated in Fig. 1(c), the two input signals can be controlled to mix with each other orthogonally thereby achieving precise phase difference without the influence of amplitude noise. Hence it is easier and more precise to extract the error signal between the reference and the feedback signal thereby achieving more accurate compensation both in short term and long term.
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8835
Fig. 5. Error signal extraction analysis for the scheme of Fig. 1(b). The ranges of voltage presented in black and red line are the same while the range of phase accordingly vary a lot.
5.
Conclusion
In conclusion, we proposed a radio frequency distribution system via optical fiber link. In this scheme, the phase noise induced by environment is cancelled by an electric phase shifter with the help of an improved error signal extraction scheme. The compensation structure is very simple but of high performance. Besides, the structure is all made up of electronic components and all the components can be integrated on a single printed circuit board, which makes it portable and robust alike. An experiment has been demonstrated with this structure to transfer a 100 MHz frequency through 100 km fiber link. The relative frequency stability is measured as 3 × 10−14 at 1 s and 3 × 10−17 at 4000 s. This is relatively the best microwave transfer performance to be reported at the averaging time of 4000 s. It means that the dissemination of the most accurate microwave standard via fiber link is available, not only inside the laboratories but also in outdoor condition. Acknowledgment This work is funded by National Natural Science Foundations of China (No. 61371074).
#232658 - $15.00 USD (C) 2015 OSA
Received 16 Jan 2015; revised 17 Mar 2015; accepted 17 Mar 2015; published 30 Mar 2015 6 Apr 2015 | Vol. 23, No. 7 | DOI:10.1364/OE.23.008829 | OPTICS EXPRESS 8836
