Abstract

We report a long-distance phase-stabilized millimeter-wave distribution over optical fibers, where the optical-link-induced phase noise is compensated with a high-precision photonic-generated millimeter-wave (mm-wave) voltage-controlled oscillator (VCO). The mm-wave VCO is realized based on pre-filtering and re-modulating optical spectral lines of an optical frequency comb (OFC). By adjusting the frequency spacing of the optical spectral lines extracted from the OFC, the phase error of the transmitted optical mm-wave signal can be compensated precisely. Using the mm-wave VCO, we demonstrate a distribution of a 100.02 GHz signal over spooled optical fibers and the fractional frequency instability of the system at different transmission distances is exhibited. The residual phase noise of the remote mm-wave signal after being transferred through a 160-km fiber link is measured to be −59 dBc/Hz at 1 Hz frequency offset from the carrier, and the RMS timing jitter in the frequency range from 0.01 Hz to 1 MHz reaches 62 fs. The long-term fractional frequency instability of 4.1 × 10−17 at 10000 s averaging time is achieved, and the maximum timing drift is within 0.93 ps (peak to peak) during 4 hours.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Long-distance distribution of a local ultra-stable millimeter wave (mm-wave) signal to remote ends is indispensable in various applications, including very long baseline interferometry [1,2], deep-space exploration [3,4], astronomy and distributed coherent aperture radar [5–8]. For instance, in the Atacama Large Millimeter Array (ALMA) project [9,10], its detecting frequency exceeds 950 GHz. To obtain a phase-coherent array, the antennas at each site require a highly synchronized and stable high-frequency reference for the signal detection and combination. The low attenuation, high reliability and immunity to electromagnetic interference of optical-fiber make it potential to disseminate the highly stable mm-wave frequency standards over long distances.

However, the mechanical perturbation and temperature variation along the fiber will give rise to transmission delay fluctuations that would induce phase fluctuation of the received signals at remote ends. In order to attain the high phase stability of the receiving mm-wave signal at remote ends, a phase noise detection and compensation set-up is necessary to eliminate the effect of fluctuations in the propagation delay. The round-trip delay correction mechanism is usually applied in the phase noise compensation system, which adjusts the fiber propagation delay or compensates the phase of the transmitting signal. One popular method is based on applying a fiber stretcher [11–15]. With the frequency-independent compensation of a fiber stretcher, stabilized mm-wave signals can be distributed directly. Nonetheless, the small compensation range and slow response of the fiber stretcher would limit system’s loop bandwidth and applications in long-distance distribution whose delay suffers large and fast variations. Voltage-controlled oscillator (VCO) has been widely used in long-distance distribution systems owing to its infinite compensation range and fast response. Several researches employing VCOs have been reported over the years [16–19]. However, it is difficult to detect and compensate the phase error of an mm-wave signal precisely owing to the fact that traditional electronic approaches suffer from limited frequency range of phase detection and insufficient phase control accuracy of compensation. In [20], we detected and compensated the phase error of the optical mm-wave signal induced by the fiber delay fluctuations by applying a dual-heterodyning phase error transfer (DHPT) scheme and an acousto-optic frequency shifter (AOFS), respectively. The mm-wave signal was distributed via a 60-km standard single-mode fiber (SSMF) link and the phase noise induced by the transmission delay variations was suppressed. However, when the mm-wave signal is generated and controlled, the extracted two optical spectral lines travel along separate loose optical links where the two carriers of the transmitted optical mm-wave signal experience uncorrelated optical paths. The excess phase noise induced by the uncorrelated loose fiber links degraded the long-term frequency stability of the remote signals [21,22].

In this paper, we present a photonic-generated mm-wave voltage-controlled oscillator (VCO) which compensates the phase noise of the optical mm-wave based on pre-filtering and re-modulating optical spectral lines of an OFC. By applying the pre-filtering and re-modulating process, the two optical spectral lines which carry the mm-wave signal stay in the same optical path, preventing the excess phase noise induced by the separate loose optical links from being imparted onto the transmitted signal. Thus, a higher phase-stabilized mm-wave signal distribution can be achieved over the long term at long transmission distance compared to the AOFS-based system [20]. Then, we demonstrate a 100.02 GHz optical mm-wave signal distribution system over a 160-km standard SSMF employing the proposed mm-wave VCO. With the active phase compensation, the residual phase noise of the remote mm-wave signal is −15 dBc/Hz and −59 dBc/Hz at 0.01 Hz and 1 Hz frequency offset from the carrier, respectively. The RMS timing jitter in the frequency range from 0.01 Hz to 1 MHz is 62 fs and the long-term fractional frequency instability of 4.1 × 10−17 at 10000 s averaging time is achieved. The maximum timing drift is about 0.93 ps (peak to peak) during 4 hours.

2. Principle of the mm-wave distribution system

Figure 1 illustrates the frequency distribution system employing the photonic generated mm-wave VCO which is based on pre-filtering and re-modulating the optical spectral lines of an OFC. The mm-wave VCO is composed of an intermediate frequency (IF) VCO, an electrical single-sideband modulator (SSBM), an optical Mach–Zehnder modulator (MZM), an optical band-pass filter (OBPF) and two cascaded inter-leavers. The IF VCO is used to achieve accurate phase compensation, and the SSBM is applied to identically transfer the IF phase compensation to radio frequency (RF) driven signal of the MZM. The MZM is used to identically transfer the RF phase correction to the optical carriers to compensate the optical mm-wave signal precisely. The OBPF is applied to filter out three adjacent optical spectral lines of the OFC and the two cascaded inter-leavers are used to filter out the transmitted optical mm-wave signal.

 figure: Fig. 1

Fig. 1 Experimental set up for the phase-stabilized millimeter-wave signal distribution system based on the photonic generated mm-wave VCO. OFCG, optical frequency comb generator; mm-wave, millimeter-wave; PMC, polarization-maintaining coupler; EDFA, erbium-doped optical fiber amplifier; OBPF, optical bandpass filter; MZM, Mach-Zehnder modulator; SSBM, single sideband modulator; VCO, voltage controlled oscillator; IF, intermediate frequency; LF, loop filter; PFD, digital phase and frequency detector; AOFS, acousto-optic frequency shifter; SSMF, standard single-mode fiber; DHPT, dual heterodyne phase error transfer; PD, photo-detector; PC, polarization controller; PT, polarization tracker; OC, optical coupler; C, circulator; M, mixer.

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In the frequency distribution system, the local and the remote ends are connected with spooled SSMF. At the local end, a 25 GHz microwave synthesizer (Keysight model E8267D), which is synchronized to a 10 MHz rubidium (Rb) oscillator, is divided into two parts with a power splitter. One part of the RF signal is launched to drive an optical frequency comb generator (OFCG) generating a low phase noise OFC with 25 GHz frequency interval. The other part is single-sideband modulated by the 10 MHz VCO signal with the SSBM in the mm-wave VCO. The OFC is divided into three branches by passing through polarization maintained couplers (PMCs). One branch is the reference for detecting the phase error induced by the transmission fiber link; another one is used to analyze the residual phase noise of the remote mm-wave signal. The third branch which carries 90% output of the OFC is fed to the mm-wave VCO.

In the mm-wave VCO, the OFC passes through the appropriately configured OBPF to filter out three adjacent optical spectral lines which are subsequently re-modulated by the MZM with the SSBM’s output RF signal. The MZM is biased at the transmission null to realize the carrier suppressed modulation. Then the output signal passes through two cascaded inter-leavers (25-50 GHz, 50-100 GHz respectively). Afterwards, a 100.02 GHz photonic generated mm-wave signal whose phase can be precisely controlled is achieved, which can be expressed as

EmmVCO(t)=exp{j[(ωs2ωRFωVCO)tφv(t)]}+exp{j[(ωs+2ωRF+ωVCO)t+φv(t)]},
where ωs=2πfs,ωRF=2πfRF and ωVCO=2πfVCO. fs, fRF and fVCO are the frequencies of the OFCG’s seed laser, the microwave synthesizer and the 10 MHz VCO, respectively; φv(t) is the instantaneous phase of the 10 MHz VCO.

Then the photonic generated mm-wave signal is transmitted to the remote end over fiber link. Two erbium-doped fiber amplifiers (EDFAs) are applied before and after transmission to compensate for the power loss caused by the transmission link. The forward and backward travelling optical carriers are separated using optical circulators (C1, C2).

At the remote end, the optical signal is frequency up-shifted 40 MHz by applying an AOFS to avoid the Rayleigh backscattering. Afterwards it is power split into three parts by optical couplers (OCs). One part is used to obtain the 100.02 GHz mm-wave signal with a high-speed photo-detector (PD). Another part is used to analyze the residual phase noise; and the other one is sent back to the local end through the same fiber link. In order to alleviate the polarization varying effect, a polarization tracker (General Photonics POS-002) is used before the heterodyne detection. The remote mm-wave signal which suffers time-varying transmission delays τtrans(t) can be written as

Imm(t)=cos[(4ωRF+2ωVCO)t+φp(t)+2φv(t)],
where φp(t)=(4ωRF+2ωVCO)τtrans(t) is the phase fluctuation induced by time varying delays of the fiber link.

Ignoring the non-reciprocity of the transmission delays in optical fiber between the forward and backward directions, the returned optical carriers exhibit double of the one-way fiber-induced phase noise. In the local DHPT, the phase error induced by optical fiber transmission delay variations is mapped onto an IF signal: the round-trip signal and the local reference from the OFC are beaten in a PD generating a 30 MHz and a 50 MHz beating signal; the 50 MHz signal and the double of the 10 MHz signal output from the IF VCO are mixed to yield a 70 MHz up-converted signal, then mixed with the 30 MHz beating signal to obtain a 40 MHz IF signal. It is described as

I40MHz(t)=cos[4ωVCOt+2(φp(t)+2φv(t))],
which denotes phase fluctuation of the remote mm-wave signal. In addition, it can be seen that the phase information of IF2 is eliminated in dual heterodyne mixing process.

The 10 MHz Rb oscillator is multiplied by four with a low noise multiplying synthesizer to generate a 40 MHz output signal. Then the I40MHz(t) is discriminated with the 40 MHz output signal by using a digital phase and frequency detector (PFD) to extract the phase error signal:

Eerror(t)=4φRb[2φp(t)+4φv(t)],
where φRb is the phase of the Rb oscillator, and it is considered as a constant.

The error signal is integrated in a loop filter then fed back to control the phase of the mm-wave VCO. When the phase-locked loop is locked, the phase error is zero, i.e., Eerror(t)0. Consequently, the obtained mm-wave signal at the remote end can be expressed as

Imm(t)=cos[(4ωRF+2ωVCO)t+2φRb],
It should be noted that Imm(t) is independent of time-varying transmission delays τtrans(t) and its phase is stabilized. Thus, the phase-stable 100.02 GHz mm-wave signal can be obtained at the remote end.

3. Experimental results and analysis

The measurements of the residual phase noise and the fractional frequency instability of the distribution system are performed by analyzing the 20 MHz signal obtained from the DHPT in the measurement part shown in Fig. 1 with a phase noise analyzer (Symmetricom’s 5125A). Fig. 2 shows the measured residual phase noise (a) and the fractional frequency instability (b) of the phase locked distribution system in conditions of 1 m, 100 km, 120 km, 140 km and 160 km optical fiber links, respectively. The phase locking parameters of the phase-locked loop (PLL) in the distribution system, including the loop bandwidth and loop gain, are optimized to serve the purpose of minimizing the phase noise at different transmission distances. The optical spectrum of the under-tested 100.02 GHz signal is shown in the inset of the Fig. 2(a).

 figure: Fig. 2

Fig. 2 Single sideband phase noise (a) and fractional frequency instability (b) of the phase locked transmission system in conditions of 1 m (black), 100 km (red), 120 km (blue), 140 km (dark cyan) and 160 km (magenta) fiber link (500 Hz measurement frequency bandwidth). The inset in the Fig. 2(a) shows optical spectrum of the under-tested 100.02 GHz signal.

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The residual phase noise of the phase locked distribution system with 100 km, 120 km, 140 km and 160 km fiber links reach −22 dBc/Hz, −18 dBc/Hz, −15 dBc/Hz and −15 dBc/Hz at 0.01 Hz frequency offset from the carrier, −66 dBc/Hz, −67 dBc/Hz, −60 dBc/Hz and −59 dBc/Hz at 1 Hz frequency offset from the carrier, respectively; and the fractional frequency instability of 3.4 × 10−14, 3.8 × 10−14, 3.9 × 10−14 and 4.9 × 10−14 at 1 s averaging time, 1.1 × 10−17, 1.3 × 10−17, 2.9 × 10−17 and 4.1 × 10−17 at 10000 s averaging time are achieved, respectively. Compared to the phase locked system with shorter transmission fiber link, it can be observed that the residual phase noise of the 160-km phase locked transmission system is deteriorated with about 7 dB within the loop bandwidth, and the fractional frequency instability beyond 1000 s averaging time is degraded. The three main contributions might lead to these phenomena. Firstly, the increasing transmission distance leads to the reduction of the loop bandwidth and loop gain of the PLL, which would deteriorate the phase noise suppression capability of the PLL. Secondly, the signal-to-noise ratio at the local end and measurement part are decreasing along with the transmission distance increasing. Thirdly, the reciprocity deteriorates along with the increased transmission distance.

Figure 3 shows the timing drift of the received mm-wave signal in the free running and phase locking dissemination system at different transmission distances over 4 hours. It is shown in Fig. 3(a) that the propagation delay fluctuation spans over about 2.2 ns within 4 hours in the condition of 100 km free-running transmission link. In Fig. 3(b) which shows magnified plot of the timing drift of the phase locked system, the timing drift is confined well below 0.38 ps, 0.46 ps, 0.56 ps and 0.93 ps peak-to-peak at the 100 km, 120 km, 140 km and 160 km transmission distances, respectively. It can be observed that the phase noise induced by the propagation delay variations is effectively suppressed by the proposed system. While the suppression capability of the compensation system is declined at longer transmission distances.

 figure: Fig. 3

Fig. 3 (a) Timing drift of the remote 100.02 GHz signal in 100 km free-running and 100 km, 120 km, 140 km, 160 km phase-locked transmission system. (b) Magnified plot of timing drift in the phase locked transmission system. The inset in Fig. 3(a) shows the detailed timing drift in 100 km free running system.

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The comparative measurement between the phase locked transmission system with the proposed mm-wave VCO and the AOFS-based concept [20] is conducted under the equal conditions. The proposed system is still stable at the transmission distance of 160 km, while the AOFS-based concept in [20] can hardly get locked at the transmission distance longer than 120 km. And the results are shown in Fig. 4. It can be seen in Fig. 4(a) that the Allan deviation of the phase locked 120 km transmission system with the proposed mm-wave VCO (blue triangles) are 3.8 × 10−14 at 1 s averaging time and 3.3 × 10−17 at 4000 s averaging time, while that of the phase locked 120 km transmission system with the AOFS-based concept (red circles) are 7.9 × 10−14 at 1 s averaging time and 8.4 × 10−17 at 4000 s averaging time. It is shown in Fig. 4(b) that the RMS timing jitter of the phased locked system with the mm-wave VCO (pink diamonds), which is calculated by integrating the phase noise over the frequency range from 0.01 Hz to 1 MHz, at 120 km transmission distance is about 38 fs, while that of the system with the AOFS-based concept (olive stars) is about 72 fs. However, the RMS timingjitter of the proposed system with 160 km fiber link is still 62 fs. This demonstrates that, by applying the proposed mm-wave VCO scheme, the distribution system exhibits a capability of high phase stability over the long term at long transmission distance.

 figure: Fig. 4

Fig. 4 (a) Fractional frequency instability of phase locked 120 km (black squares), 160 km (blue triangles) transmission system with the mm-wave VCO and phase locked 120 km transmission system with the AOFS-based concept [20] (red circles). (b) The transmission induced RMS timing jitter of phase locked system with the mm-wave VCO (pink diamonds) and the AOFS-based concept (olive stars).

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4. Conclusion

In summary, we present a phase-stabilized mm-wave distribution system employing a photonic generated mm-wave VCO which compensates the phase noise of the optical mm-wave signal based on pre-filtering and re-modulating optical spectral lines of an OFC. Preventing the excess noise induced by the separate loose optical links from being imparted onto the transmitted mm-wave signal, the distribution system can achieve high phase stability at long transmission distance over the long term. We experimentally demonstrate a 100.02 GHz mm-wave signal with high phase stability over a 160-km SSMF. With the active phase compensation, the residual phase noise of the remote mm-wave signal is −59 dBc/Hz at 1 Hz frequency offset from the carrier and the fractional frequency instability of 4.1 × 10−17 at 10000 s averaging time is achieved. The timing drift of the phase locked system is within 0.93 ps peak-to-peak over 4 hours and the RMS timing jitter in the frequency range from 0.01 Hz to 1 MHz is about 62 fs. The frequency of the transmitted mm-wave signal in the distribution system could be flexible by applying an optical dual band-pass filter with specific shapes. The proposed system is suitable for the demand of distributing the high frequency signal over long-distance fiber with high phase stability.

Funding

National Natural Science Foundation of China (NSFC) (61690193).

References and links

1. K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000). [CrossRef]  

2. H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” J. Geodyn. 61, 68–80 (2012). [CrossRef]  

3. J. Ye, J. L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003). [CrossRef]  

4. M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007). [CrossRef]  

5. J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006). [CrossRef]  

6. B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005). [CrossRef]  

7. K. Y. Lau, F. L. George, and L. T. Robert, “Ultra-stable RF-over-fiber transport in NASA antennas, phased arrays and radars,” J. Lightwave Technol. 32(20), 3440–3451 (2014). [CrossRef]  

8. J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998). [CrossRef]  

9. B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

10. A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006). [CrossRef]  

11. H. Kiuchi, “Highly stable millimeter-wave signal distribution with an optical round-trip phase stabilizer,” IEEE Trans. Microw. Theory Tech. 56(6), 1493–1500 (2008). [CrossRef]  

12. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006). [CrossRef]  

13. O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

14. 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). [CrossRef]  

15. 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). [CrossRef]   [PubMed]  

16. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008). [CrossRef]  

17. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009). [CrossRef]   [PubMed]  

18. M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010). [CrossRef]   [PubMed]  

19. 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(1), 556 (2012). [CrossRef]   [PubMed]  

20. D. Sun, Y. Dong, H. Shi, Z. Xia, Z. Liu, S. Wang, W. Xie, and W. Hu, “Distribution of high-stability 100.04 GHz millimeter wave signal over 60 km optical fiber with fast phase-error-correcting capability,” Opt. Lett. 39(10), 2849–2852 (2014). [CrossRef]   [PubMed]  

21. G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013). [CrossRef]  

22. D. S. Wu, D. J. Richardson, and R. Slavik, “Optical Fourier synthesis of high-repetition-rate pulses,” Optica 2(1), 18–26 (2015). [CrossRef]  

References

  • View by:

  1. K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
    [Crossref]
  2. H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” J. Geodyn. 61, 68–80 (2012).
    [Crossref]
  3. J. Ye, J. L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003).
    [Crossref]
  4. M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
    [Crossref]
  5. J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
    [Crossref]
  6. B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005).
    [Crossref]
  7. K. Y. Lau, F. L. George, and L. T. Robert, “Ultra-stable RF-over-fiber transport in NASA antennas, phased arrays and radars,” J. Lightwave Technol. 32(20), 3440–3451 (2014).
    [Crossref]
  8. J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
    [Crossref]
  9. B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).
  10. A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006).
    [Crossref]
  11. H. Kiuchi, “Highly stable millimeter-wave signal distribution with an optical round-trip phase stabilizer,” IEEE Trans. Microw. Theory Tech. 56(6), 1493–1500 (2008).
    [Crossref]
  12. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
    [Crossref]
  13. O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).
  14. 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).
    [Crossref]
  15. 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).
    [Crossref] [PubMed]
  16. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
    [Crossref]
  17. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009).
    [Crossref] [PubMed]
  18. M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010).
    [Crossref] [PubMed]
  19. 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(1), 556 (2012).
    [Crossref] [PubMed]
  20. D. Sun, Y. Dong, H. Shi, Z. Xia, Z. Liu, S. Wang, W. Xie, and W. Hu, “Distribution of high-stability 100.04 GHz millimeter wave signal over 60 km optical fiber with fast phase-error-correcting capability,” Opt. Lett. 39(10), 2849–2852 (2014).
    [Crossref] [PubMed]
  21. G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
    [Crossref]
  22. D. S. Wu, D. J. Richardson, and R. Slavik, “Optical Fourier synthesis of high-repetition-rate pulses,” Optica 2(1), 18–26 (2015).
    [Crossref]

2015 (1)

2014 (2)

2013 (1)

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

2012 (4)

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(1), 556 (2012).
[Crossref] [PubMed]

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” J. Geodyn. 61, 68–80 (2012).
[Crossref]

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).
[Crossref] [PubMed]

2010 (2)

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).
[Crossref]

M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (3)

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
[Crossref]

H. Kiuchi, “Highly stable millimeter-wave signal distribution with an optical round-trip phase stabilizer,” IEEE Trans. Microw. Theory Tech. 56(6), 1493–1500 (2008).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

2007 (1)

M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[Crossref]

2006 (3)

J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

2005 (1)

B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005).
[Crossref]

2003 (1)

2000 (1)

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

1998 (1)

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Amy-Klein, A.

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).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Asari, K.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Bai, Y.

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(1), 556 (2012).
[Crossref] [PubMed]

Beasley, A. J.

A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006).
[Crossref]

Behrend, D.

H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” J. Geodyn. 61, 68–80 (2012).
[Crossref]

Bergquist, J. C.

Bize, S.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

J. Ye, J. L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003).
[Crossref]

Brito, R.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Calhoun, M.

M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[Crossref]

Castro, J.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Chardonnet, C.

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).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Chardonnet, Ch.

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

Chen, W. L.

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(1), 556 (2012).
[Crossref] [PubMed]

Clairon, A.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Cliché, J.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

D’Addario, L.

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Daussy, C.

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Diddams, S. A.

Dong, Y.

Drouin, B. J.

B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005).
[Crossref]

Emerson, D. T.

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Feng, Y. Y.

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(1), 556 (2012).
[Crossref] [PubMed]

Fujieda, M.

M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010).
[Crossref] [PubMed]

M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009).
[Crossref] [PubMed]

Gao, C.

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(1), 556 (2012).
[Crossref] [PubMed]

George, F. L.

Grammer, W.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Hall, J. L.

Hara, T.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Hollberg, L. W.

Holman, K. W.

Hosokawa, M.

Hu, W.

Huang, S.

M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[Crossref]

Jacques, C.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Jones, D. J.

Jones, R. J.

Kawano, N.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Kerr, A. R.

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Kitching, J.

Kiuchi, H.

H. Kiuchi, “Highly stable millimeter-wave signal distribution with an optical round-trip phase stabilizer,” IEEE Trans. Microw. Theory Tech. 56(6), 1493–1500 (2008).
[Crossref]

Kuji, S.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Kumagai, M.

M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010).
[Crossref] [PubMed]

M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009).
[Crossref] [PubMed]

Lau, K. Y.

Li, T. C.

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(1), 556 (2012).
[Crossref] [PubMed]

Liu, Z.

Lopez, O.

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).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Lours, M.

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).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Ma, L. S.

Maiwald, F. W.

B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005).
[Crossref]

Margolis, H. S.

Marra, G.

Masui, Y.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Meadows, J.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Miao, J.

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(1), 556 (2012).
[Crossref] [PubMed]

Murakowski, J. A.

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

Murowinski, R.

A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006).
[Crossref]

Nagano, S.

M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010).
[Crossref] [PubMed]

M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009).
[Crossref] [PubMed]

Narbonneau, F.

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Newbury, N. R.

Nishio, M.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Payne, J. M.

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Pearson, J. C.

B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecular spectroscopy,” Rev. Sci. Instrum. 76(9), 093113 (2005).
[Crossref]

Peng, J. L.

Prather, D. W.

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

Richardson, D. J.

Robert, L. T.

Robertsson, L.

Santarelli, G.

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).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Sato, K.

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

Schneider, G. J.

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

Schuetz, C. A.

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

Schuh, H.

H. Schuh and D. Behrend, “VLBI: A fascinating technique for geodesy and astrometry,” J. Geodyn. 61, 68–80 (2012).
[Crossref]

Shi, H.

Shi, S.

G. J. Schneider, J. A. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radiofrequency signal-generation system with over seven octaves of continuous tuning,” Nat. Photonics 7(2), 118–122 (2013).
[Crossref]

Shillue, B.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

J. M. Payne, L. D’Addario, D. T. Emerson, A. R. Kerr, and B. Shillue, “Photonic local oscillator system for the millimeter array,” Proc. SPIE 3357, 143–151 (1998).
[Crossref]

Slavik, R.

Sun, D.

Swann, W. C.

Tarenghi, M.

A. J. Beasley, R. Murowinski, and M. Tarenghi, “The Atacama large millimeter/submillimeter array: overview and status,” Proc. SPIE 6267, 626702 (2006).
[Crossref]

Tjlelker, R. L.

M. Calhoun, S. Huang, and R. L. Tjlelker, “Stable photonic links for frequency and time transfer in the deep space network and antenna arrays,” Proc. IEEE 95(10), 1931–1946 (2007).
[Crossref]

Treacy, R.

B. Shillue, W. Grammer, C. Jacques, R. Brito, J. Meadows, J. Castro, Y. Masui, R. Treacy, and J. Cliché, “The ALMA photonic local oscillator system,” SPIE 8452, 8452161 (2012).

Wang, B.

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(1), 556 (2012).
[Crossref] [PubMed]

Wang, L. J.

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(1), 556 (2012).
[Crossref] [PubMed]

Wang, S.

Williams, P. A.

Wu, D. S.

Xia, Z.

Xie, W.

Ye, J.

Zhang, J. W.

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(1), 556 (2012).
[Crossref] [PubMed]

Zhu, X.

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(1), 556 (2012).
[Crossref] [PubMed]

Appl. Phys. B (1)

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).
[Crossref]

Eur. Phys. J. Spec. Top. (1)

O. Lopez, A. Amy-Klein, C. Daussy, Ch. 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. Spec. Top. 48(1), 35–41 (2008).

IEEE Contr. Syst. Mag. (1)

J. Cliché and B. Shillue, “Precision timing control for radio astronomy, maintaining femtosecond synchronization in Atacama large millimeter array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

K. Sato, T. Hara, S. Kuji, K. Asari, M. Nishio, and N. Kawano, “Development of an ultrastable fiber optic frequency distribution system using an optical delay control module [for frequency standard and VLBI],” IEEE Trans. Instrum. Meas. 49(1), 19–24 (2000).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

H. Kiuchi, “Highly stable millimeter-wave signal distribution with an optical round-trip phase stabilizer,” IEEE Trans. Microw. Theory Tech. 56(6), 1493–1500 (2008).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

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Figures (4)

Fig. 1
Fig. 1 Experimental set up for the phase-stabilized millimeter-wave signal distribution system based on the photonic generated mm-wave VCO. OFCG, optical frequency comb generator; mm-wave, millimeter-wave; PMC, polarization-maintaining coupler; EDFA, erbium-doped optical fiber amplifier; OBPF, optical bandpass filter; MZM, Mach-Zehnder modulator; SSBM, single sideband modulator; VCO, voltage controlled oscillator; IF, intermediate frequency; LF, loop filter; PFD, digital phase and frequency detector; AOFS, acousto-optic frequency shifter; SSMF, standard single-mode fiber; DHPT, dual heterodyne phase error transfer; PD, photo-detector; PC, polarization controller; PT, polarization tracker; OC, optical coupler; C, circulator; M, mixer.
Fig. 2
Fig. 2 Single sideband phase noise (a) and fractional frequency instability (b) of the phase locked transmission system in conditions of 1 m (black), 100 km (red), 120 km (blue), 140 km (dark cyan) and 160 km (magenta) fiber link (500 Hz measurement frequency bandwidth). The inset in the Fig. 2(a) shows optical spectrum of the under-tested 100.02 GHz signal.
Fig. 3
Fig. 3 (a) Timing drift of the remote 100.02 GHz signal in 100 km free-running and 100 km, 120 km, 140 km, 160 km phase-locked transmission system. (b) Magnified plot of timing drift in the phase locked transmission system. The inset in Fig. 3(a) shows the detailed timing drift in 100 km free running system.
Fig. 4
Fig. 4 (a) Fractional frequency instability of phase locked 120 km (black squares), 160 km (blue triangles) transmission system with the mm-wave VCO and phase locked 120 km transmission system with the AOFS-based concept [20] (red circles). (b) The transmission induced RMS timing jitter of phase locked system with the mm-wave VCO (pink diamonds) and the AOFS-based concept (olive stars).

Equations (5)

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E mmVCO ( t )=exp{ j[ ( ω s 2 ω RF ω VCO )t φ v ( t ) ] } +exp{ j[ ( ω s +2 ω RF + ω VCO )t+ φ v ( t ) ] },
I mm ( t )=cos[ ( 4 ω RF +2 ω VCO )t+ φ p ( t )+2 φ v ( t ) ],
I 40MHz ( t )=cos[ 4 ω VCO t+2( φ p ( t )+2 φ v ( t ) ) ],
E error ( t )=4 φ Rb [ 2 φ p ( t )+4 φ v ( t ) ],
I mm ( t )=cos[ ( 4 ω RF +2 ω VCO )t+2 φ Rb ],

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