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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1775–1782
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Dissemination of an optical frequency comb over fiber with 3 × 10−18 fractional accuracy

Giuseppe Marra, Helen S. Margolis, and David J. Richardson  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1775-1782 (2012)
http://dx.doi.org/10.1364/OE.20.001775


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Abstract

We demonstrate that the structure of an optical frequency comb transferred over several km of fiber can be preserved at a level compatible with the best optical frequency references currently available. Using an optical phase detection technique we measure the noise introduced by the fiber link and suppress it by stabilizing the optical path length. The measured fractional frequency stability of the transferred optical modes is 2 × 10−18 at a few thousand seconds and the mode spacing stability after optical-microwave conversion is better than 4 × 10−17 over the same time scale.

© 2011 OSA

1. Introduction

A decade after the optical frequency comb technique transformed the field of frequency metrology, these devices have already found applications in other science areas as diverse as spectroscopy [1

1. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006). [CrossRef] [PubMed]

3

3. J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nature Photon. 3, 99–102 (2009). [CrossRef]

], attosecond physics [4

4. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009). [CrossRef]

] and astrophysics [5

5. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008). [CrossRef] [PubMed]

, 6

6. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008). [CrossRef] [PubMed]

]. When combined with atomic references, tests of fundamental physics that would have been unthinkable only a few years ago, and whose outcome could open a whole new era for physics, can now be performed [7

7. 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, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008). [CrossRef] [PubMed]

, 8

8. “STE-QUEST, Space-Time Explorer and QUantum Equivalence Principle Space Test,” http://sci.esa.int/ste-quest.

]. With optical frequency standards currently exhibiting a fractional accuracy better than 10−17 [9

9. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104, 070802 (2010). [CrossRef] [PubMed]

] and optical frequency combs making this accuracy available across a wide spectrum [10

10. L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 level,” Science 303, 1843–1845 (2004). [CrossRef] [PubMed]

], new experiments could be devised in a wide range of research fields if ultra accurate optical frequencies were to be made available beyond the walls of metrology laboratories.

2. Fiber noise suppression principle

Fig. 1 Experimental setup. The detection stage (fb det.) consists of a photodiode, a filter and cascaded amplifiers. MLL: mode-locked laser; CIR: circulator; FS: fiber stretchers; TCS: thermally controlled spool; Integr.: integrator; AOM: acousto-optic modulator; SMF: single-mode fiber; DCF: dispersion compensating fiber.

The Doppler-induced frequency shift on the optical comb mode fp = pfr + f0, due to environmental perturbations on the fiber, can be written as
δfp=1cd[n(fp)l]dtfp
(1)
where n(fp) and d[n(fp)l]/dt are the refractive index of the fiber and the instantaneous rate of change of the optical path length at frequency fp, and c is the speed of light in vacuum. This frequency shift can be measured by detecting any of the beat frequencies fbp,m arising from interference between the optical modes fm and fp of the AOM-shifted and unshifted combs respectively:
fbp,m=fAOM(fpfm)1cd[n(fp)l]dtfp
(2)
where we have assumed that the optical frequencies generated by the mode-locked laser are constant over the round trip time so that no noise is detected due to the self-heterodyne effect. This assumption is reasonable when the self-heterodyne noise is lower than the phase noise introduced by enviromental perturbations to the fiber link, which is the case in our experiment for frequencies within the feedback bandwidth of approximately 2 kHz.

These detected beats give rise to a current from the photodetector that can be described as
i(t)m=m1m2p=p1p2cos2π[fAOM(pm)fr1cd[n(fp)l]dtfp]t
(3)
where m1, m2, p1 and p2 define the range of comb modes that contribute to the signal. Equation (3) illustrates the gain in sensitivity achieved using optical rather than microwave phase detection techniques; the frequency shift due to changes in the optical path length is greater by a factor fp/fr ∼ 106. In our experiment fAOM was 104 MHz, fr was 100 MHz and we chose to detect the lowest frequency beat such that p = m + 1, in which case
i(t)p=p1p2cos2π[fAOMfr1cd[n(fp)l]dtfp]t.
(4)

The lowest frequency beat, 4 MHz in our experiment, is amplified and phase compared with a maser-referenced synthesizer, generating an error signal which, after integration, is applied to two fiber stretchers and a thermally controlled fiber spool to compensate for fast (up to a few kHz) and slow phase fluctuations respectively.

3. Results

To test the precision with which the full structure of the optical frequency comb can be preserved when transmitted over several-km-scale fiber links, two comb parameters must be measured: the repetition rate fr (mode spacing) and the frequency of a selected optical mode.

The measurement of the mode spacing stability, accuracy and phase noise is performed by phase comparing the 80th harmonic (8 GHz) of fr at the receiver end of the fiber with that detected directly at the output of the laser using a microwave mixer (Fig. 2a). The power spectral density of the phase noise fluctuations between 0.1 Hz and 100 kHz was measured with an FFT analyser. When the noise cancellation is activated, the measured phase noise is −91 dBc/Hz at 1 Hz offset from the carrier (Fig. 3a), very close to the noise measured when the 7.7 km SMF and the DCF are replaced by a 2 m fiber and an attenuator set to provide the same overall loss. We observe suppression of both the thermally induced fiber noise at low offset frequencies (by up to 20 dB) and the acoustic noise around a few hundred hertz. By integrating the phase noise between 1 Hz and 100 kHz we calculate the timing jitter to be less than 17.5 fs. The measurement of the frequency stability was achieved by converting the output voltage of the microwave mixer, logged every 0.5 s with a digital voltmeter (measurement bandwidth 7 Hz), into phase changes. The measured stability is shown in Fig. 3b. The Allan deviation of the data taken within the first two hours is 1.8×10−15 at 1 s and 7×10−17 at 100 s. Over longer periods, the signal-to-noise ratio (SNR) of the error signal degrades due to changes in the polarization of the returned optical signal with respect to that of the local signal. When the SNR falls below approximately 25 dB (in a 10 kHz bandwidth), we notice a degradation of the fractional frequency stability to 2.2 × 10−15 at 1 s and 1 × 10−16 at 100 s. This problem could be alleviated by using an optical amplifier to increase the power of the returned optical signal in order to maintain the SNR above this level. An alternative approach could be to insert an automatic polarization control system on the returned pulse train. However, even with the SNR degradation the fractional transfer stability is better than 4×10−17 at 1000 s, corresponding to a timing jitter of 40 fs.

Fig. 2 Experimental setups for phase noise and frequency stability measurement of the mode spacing (a) and transferred optical modes (b). The detection stages floc and frem consist of a fast photodiode, a narrow bandpass filter and microwave amplifiers.
Fig. 3 Single sideband phase noise (a) and frequency stability (b) of the 80th harmonic (8 GHz) of the fundamental frequency spacing measured at the remote end. a) blue: fiber noise not suppressed; red: fiber noise suppressed; grey: measurement noise floor. b) Open blue squares: fiber noise not suppressed; open red circles: fiber noise suppressed; filled red circles: fiber noise suppressed, first two hours; filled grey squares: measurement noise floor.

Fig. 4 Phase noise (a) and frequency stability (b) of the sample optical mode at the remote end. a) suppression inactive (blue); active (red). Inset: phase evolution over time of the optical mode when the suppression is active. b) Without (open blue squares) and with noise suppression, 7 Hz (filled red circles) and 200 kHz (open red circles) measurement bandwidth; open grey squares: measurement noise floor.

4. Conclusion

These results demonstrate that it is possible to preserve the overall structure of an optical frequency comb when it is transferred over several-km lengths of optical fiber, at a level better than the best optical frequency standards currently available. We measure the stability of the optical frequency of a sample mode of the comb to be comparable to that achieved when only a single optical frequency is transferred [13

13. G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett. 34, 2270–2272 (2009). [CrossRef] [PubMed]

17

17. F. Kéfélian, O. Lopez, H. Jiang, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “High-resolution optical frequency dissemination on a telecommunications network with data traffic,” Opt. Lett. 34, 1573–1575 (2009). [CrossRef] [PubMed]

] rather than the tens of thousands transferred in our experiment. This frequency comb transfer technique could potentially be used over much longer distances (>100 km) by adding optical amplifiers, possibly bidirectional, to compensate for the extra loss of the fiber. We note that, employing a different phase detection technique, we have previously transferred a microwave frequency over 86 km of installed fiber using a frequency comb [20

20. G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett. 36, 511–513 (2011). [CrossRef] [PubMed]

]. Microwave stability similar to that demonstrated in this paper was achieved in that earlier work, although the stability of optical modes was not measured. As for other frequency transfer techniques, the performance could be degraded by the longer round trip time which limits the fiber noise cancellation bandwidth. However, the degree of degradation will depend on the measurement bandwidth required by the user. For a similar measurement bandwidth to that used in this experiment (7 Hz), transfer over many hundreds of km would be possible.

The results make it possible to envisage the dissemination of highly stable and accurate optical frequency combs from metrology laboratories to other remotely located users. Simultaneous distribution to multiple users can be implemented easily and at low cost since only one AOM is required regardless of the number of fiber links. The availability of a wide comb of optical frequencies with stability and accuracy matching that of state-of-the-art optical clocks and, equivalently, an optical pulse train with ultra-low timing jitter could enable researchers from different scientific areas to devise new experiments and further extend the applications of optical frequency combs in the years to come.

This work was funded by the UK National Measurement System as part of the Pathfinder Metrology programme. We thank Radan Slavík from the University of Southampton for lending us some of the equipment for this experiment and for useful discussions. DJR acknowledges partial support for his contribution to this research from the UK Engineering and Physical Sciences Research Council through grant number EP/I01196X/1.

References and links

1.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006). [CrossRef] [PubMed]

2.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007). [CrossRef] [PubMed]

3.

J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nature Photon. 3, 99–102 (2009). [CrossRef]

4.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009). [CrossRef]

5.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008). [CrossRef] [PubMed]

6.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008). [CrossRef] [PubMed]

7.

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, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008). [CrossRef] [PubMed]

8.

“STE-QUEST, Space-Time Explorer and QUantum Equivalence Principle Space Test,” http://sci.esa.int/ste-quest.

9.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104, 070802 (2010). [CrossRef] [PubMed]

10.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 level,” Science 303, 1843–1845 (2004). [CrossRef] [PubMed]

11.

G. Grosche, K. Predehl, S. M. F. Raupach, H. Schnatz, O. Terra, S. Droste, and R. Holzwarth “High performance frequency comparisons over optical fibre,” IQEC/CLEO Pacific Rim 2011, Technical Digest CD-ROM (Sydney, Australia, 2011)

12.

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, 723–727 (2010). [CrossRef]

13.

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett. 34, 2270–2272 (2009). [CrossRef] [PubMed]

14.

H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25, 2029–2035 (2008). [CrossRef]

15.

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, 1284–1293 (2008). [CrossRef]

16.

M. Musha, F.-L. Hong, K. Nakagawa, and K. Ueda, “Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network,” Opt. Express 16, 16459–16466 (2008). [CrossRef] [PubMed]

17.

F. Kéfélian, O. Lopez, H. Jiang, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “High-resolution optical frequency dissemination on a telecommunications network with data traffic,” Opt. Lett. 34, 1573–1575 (2009). [CrossRef] [PubMed]

18.

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, 021101 (2007). [CrossRef] [PubMed]

19.

K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett. 30, 1225–1227 (2005). [CrossRef] [PubMed]

20.

G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett. 36, 511–513 (2011). [CrossRef] [PubMed]

21.

C.-W. Kang, T.-A. Liu, R.-H. Shu, C.-L. Pan, and J.-L. Peng, “Simultaneously transfer microwave and optical frequency through fiber using mode-locked fiber laser,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest, (Optical Society of America, 2009), p. JWA70.

22.

Y.-F. Chen, J. Jiang, and D. J. Jones, “Remote distribution of a mode-locked pulse train with sub 40-as jitter,” Opt. Express 14, 12134–12144 (2006). [CrossRef] [PubMed]

23.

E. Ivanov, S. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control 52, 1068–1074 (2005). [CrossRef]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.3940) Instrumentation, measurement, and metrology : Metrology
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: October 25, 2011
Revised Manuscript: December 2, 2011
Manuscript Accepted: December 10, 2011
Published: January 11, 2012

Citation
Giuseppe Marra, Helen S. Margolis, and David J. Richardson, "Dissemination of an optical frequency comb over fiber with 3 × 10−18 fractional accuracy," Opt. Express 20, 1775-1782 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1775


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References

  1. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science311, 1595–1599 (2006). [CrossRef] [PubMed]
  2. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature445, 627–630 (2007). [CrossRef] [PubMed]
  3. J. Mandon, G. Guelachvili, and N. Picqué, “Fourier transform spectroscopy with a laser frequency comb,” Nature Photon.3, 99–102 (2009). [CrossRef]
  4. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009). [CrossRef]
  5. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature452, 610–612 (2008). [CrossRef] [PubMed]
  6. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321, 1335–1337 (2008). [CrossRef] [PubMed]
  7. 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, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008). [CrossRef] [PubMed]
  8. “STE-QUEST, Space-Time Explorer and QUantum Equivalence Principle Space Test,” http://sci.esa.int/ste-quest .
  9. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett.104, 070802 (2010). [CrossRef] [PubMed]
  10. L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 level,” Science303, 1843–1845 (2004). [CrossRef] [PubMed]
  11. G. Grosche, K. Predehl, S. M. F. Raupach, H. Schnatz, O. Terra, S. Droste, and R. Holzwarth “High performance frequency comparisons over optical fibre,” IQEC/CLEO Pacific Rim 2011, Technical Digest CD-ROM (Sydney, Australia, 2011)
  12. 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. B98, 723–727 (2010). [CrossRef]
  13. G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett.34, 2270–2272 (2009). [CrossRef] [PubMed]
  14. H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B25, 2029–2035 (2008). [CrossRef]
  15. 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. B25, 1284–1293 (2008). [CrossRef]
  16. M. Musha, F.-L. Hong, K. Nakagawa, and K. Ueda, “Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network,” Opt. Express16, 16459–16466 (2008). [CrossRef] [PubMed]
  17. F. Kéfélian, O. Lopez, H. Jiang, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “High-resolution optical frequency dissemination on a telecommunications network with data traffic,” Opt. Lett.34, 1573–1575 (2009). [CrossRef] [PubMed]
  18. 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, 021101 (2007). [CrossRef] [PubMed]
  19. K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett.30, 1225–1227 (2005). [CrossRef] [PubMed]
  20. G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett.36, 511–513 (2011). [CrossRef] [PubMed]
  21. C.-W. Kang, T.-A. Liu, R.-H. Shu, C.-L. Pan, and J.-L. Peng, “Simultaneously transfer microwave and optical frequency through fiber using mode-locked fiber laser,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest, (Optical Society of America, 2009), p. JWA70.
  22. Y.-F. Chen, J. Jiang, and D. J. Jones, “Remote distribution of a mode-locked pulse train with sub 40-as jitter,” Opt. Express14, 12134–12144 (2006). [CrossRef] [PubMed]
  23. E. Ivanov, S. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control52, 1068–1074 (2005). [CrossRef]

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