Abstract

We describe the use of fiber Brillouin amplification (FBA) for the coherent transmission of optical frequencies over a 480 km long optical fiber link. FBA uses the transmission fiber itself for efficient, bi-directional coherent amplification of weak signals with pump powers around 30 mW. In a test setup we measured the gain and the achievable signal-to-noise ratio (SNR) of FBA and compared it to that of the widely used uni-directional Erbium doped fiber amplifiers (EDFA) and to our recently built bi-directional EDFA. We measured also the phase noise introduced by the FBA and used a new and simple technique to stabilize the frequency of the FBA pump laser. We then transferred a stabilized laser frequency over a wide area network with a total fiber length of 480 km using only one intermediate FBA station. After compensating the noise induced by the fiber, the frequency is delivered to the user end with an uncertainty below 2 × 10−18 and an instability σy(τ) = 2 × 10−14 /(τ/s).

©2010 Optical Society of America

1. Introduction

The development of optical frequency standards (optical clocks), is expected eventually to lead to a new definition of the second [1]. One prerequisite for a future redefinition is a suitable method to disseminate such ultra-stable optical frequencies over long distances. Optical fibers are particularly suited to transfer such frequencies to a distant user, provided that the attenuation of the signal and frequency fluctuation introduced by the acoustic and thermal fluctuations on the fiber are compensated. Such a compensation scheme requires part of the light to be reflected back to the transmitting station to form a phase detection interferometer, which means that part of the light has to travel twice the distance to the destination [2]. In optical frequency transfer applications, Erbium doped fiber amplifiers (EDFA) are currently used to amplify the signal coherently. Typically, one uni-directional EDFA is used to amplify light in each direction [3]. The problem of using two separate EDFA is not only that the system will become more complex but also that the assumption that the forward and the return directions have the same noise will break down. Thus uncompensated residual noise will increase. To avoid this, we have recently built a bi-directional EDFA using the same gain medium for amplification of light in both directions [4,5]. However, we have observed saturation of the gain medium and lasing effects caused mainly by Rayleigh scattering [6]. As a consequence the gain of the bi-directional EDFA has to be kept below 25 dB. For a typical attenuation of 0.2 dB/km for an optical fiber, the distance between two bi-directional EDFAs is therefore limited to about 120 km. In consequence, the number of intermediate amplifier stations in an envisaged 900 km fiber link in Germany [7,8] will increase, as well as the effort of controlling and maintaining these stations.

In order to keep the number of intermediate stations as low as possible, we have investigated the use of fiber Brillouin amplification (FBA) [911] as an alternative technique. This technique enables the amplification of a very small input signal (a few nano Watt) by more than 50 dB in a single gain step, with relatively low pump powers (about 30 mW). Moreover, it enables bi-directional amplification because it uses the fiber itself as the gain medium and different sections of the same fiber for each direction.

In section 2 we give a brief overview about the main properties of FBA, describe a test setup used to compare the amplification and signal-to-noise ratio (SNR) of FBA with that of our home-made bi-directional EDFA. We describe a measurement of the phase noise introduced by FBA and a new and simple method to stabilize the pump frequency for FBA, using the DC power of the stimulated Brillouin scattering (SBS) signal. In section 3 we demonstrate, for the first time, an optical frequency transfer over 480 km fiber link of a wide area network using FBA. In this case different parts of this fiber link act as gain medium for the FBA process and pump lasers were installed at the local and user ends, and at one intermediate station. The instability, the accuracy and the residual phase noise of the transmitted optical frequency are presented.

2. Fiber Brillouin amplification (FBA)

Stimulated Brillouin scattering (SBS) is a nonlinear process which results from the interaction of light with stimulated acoustic waves. In fused silica single mode fibers, acoustic waves with velocity vA (vA ≈6 × 103 m/s) back-scatter light and shift down its frequency by the Brillouin frequency of (νB = 2 n vA / λ). This shift frequency νB is about 11 GHz for a refractive index n = 1.451, and a wavelength of λ = 1.5 μm. The threshold power for SBS is given by [1214]:

Pcrit=21AγLeff(1+ΔνlaserΔνB)
where A is the effective mode area of the fiber (1 × 10−10 m2), and γ is the gain coefficient of the nonlinear process (5 × 10−11 m/W). The effective gain length is Leff = (1-e-αL)/α, therefore L eff ≈21 km for an attenuation coefficient of α = 0.2 dB/km. The Brillouin linewidth depends on the life time of the scattered excitation (τB), ΔνB = 1/πτB Hz. For a 148 km long fiber we measured ΔνB ≈10 MHz. We used a laser with linewidth of about Δνlaser = 5 kHz, which is much narrower than ΔνB. Therefore, the SBS threshold power is only 2 mW according to Eq. (1).

If a pump laser with a power (Ppump) is injected in the fiber, it will cause a peak Brillouin gain [9] of:

g=γLeffPpumpA

If the pump laser with a frequency νpump is injected in the opposite direction to a signal laser with a frequency νsig, it will be amplified by a process called fiber Brillouin amplification (FBA) [10,11], if the pump frequency νpump = νsig + νB. Due to the high gain of the Brillouin process (9 dB /mW) [Eq. (2)], very weak signals can be amplified with a very high gain using only few mW of pump power.

2.1 Amplification and signal-to-noise ratio

For measuring the amplification due to FBA we performed a simple test. We used a 25 km spool of single mode fiber (SMF28) as FBA gain medium and narrow linewidth fiber lasers as pump and signal lasers. These lasers have a wavelength of λ = 1542 nm, a linewidth of about 5 kHz, up to 100 mW output power and a tuning range of about 2 nm. As described in [15], the signal laser is stabilized to our optical frequency reference to reach a linewidth of about 10 Hz.

With our 10 GHz resolution optical spectrum analyzer it is not possible to resolve the amplification caused by FBA, because ΔνB is only about 10 MHz. Therefore, we constructed a Mach-Zehnder interferometer with the 25 km fiber spool in the measurement arm and an AOM in the reference arm, as shown in Fig. 1 The AOM introduces a frequency shift (55 MHz) in the reference arm to produce heterodyne beat at the photo detector. A variable attenuator is installed in the front of the 25 km arm to adjust the input power for the 25 km fiber without changing the power in the reference arm. The pump laser is injected from the opposite end of the fiber, with a power around 20 mW and with frequency up-shifted by νpump - νsig = νB = 10.972 GHz. We tuned the variable attenuator at the input of the 25 km fiber to inject different signal powers into the FBA, to simulate different fiber lengths. The pump power is optimized to obtain the maximum amplification for every signal power. This allows the gain and the SNR of the device to be measured electrically using RF spectrum analyzer. The measurement is recorded with 100 kHz analyzer filter bandwidth.

 figure: Fig. 1

Fig. 1 Set-up to measure the gain of FBA or EDFA: VA: variable attenuator, PD: photodetector, signal: signal laser with isolator, pump: pump laser, AOM: acousto-optic modulator, a 25 km fiber is used as gain medium for FBA.

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For comparison we performed the same measurement for a bi-directional EDFA and a commercial single-pass EDFA and include the result in Fig. 2 . Note, the latter is not usable in the optical frequency transfer scheme, since bi-directional operation is required to compensate the fiber phase noise.

 figure: Fig. 2

Fig. 2 FBA in comparison to EDFAs (uni-directional and bi-directional) for different signal powers received at the output of a 25 km fiber: (a) gain (b) SNR. The spectrum analyzer bandwidth is 100 kHz.

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Figure 2 shows the gain (Fig. 2a) and the SNR (Fig. 2b) for different signal powers for the devices under test. Although both the bi-directional EDFA and FBA achieve almost the same SNR, the gain of FBA is significantly higher than that of the bi-directional EDFA. This is especially true for low signal powers. As an example, the gain of FBA is about 1000 times higher than that of the bi-directional EDFA for signal powers less than 50 nW. For a transparent network, the amplifier gain has to compensate the loss in each section of the network. FBA with 50 dB gain compensates the loss of a 250 km long fiber with a typical attenuation coefficient of 0.2 dB/km. In contrast, a bi-directional EDFA with a gain of 25 dB only allows a span of about 120 km.

This opens two possibilities: using an additional fiber spool as discrete FBA-module is a suitable solution when operational or safety requirements forbid injecting more than a few mW optical power into the transmission fiber. However, when higher power levels are allowed in the installed transmission fiber, this fiber itself can be used as gain medium. In order to test this option of a distributed amplifier further, we performed measurements using the FBA and the bi-directional EDFA on 148 km and 332 km of installed, commercial fibers. The installed dark fiber is buried and part of a wide-area network connecting PTB with other research institutes in Germany [7].

The 148 km fiber link consists of two 74 km fibers connecting Physikalisch-Technische Bundesanstalt (PTB) at Braunschweig to Institute of Quantum Optics (IQ) at Hanover. The 332 km link consists of two 166 km fibers which go from PTB, Braunschweig, south-east to a network node near Coermigk/Halle, more details are found in section (3). The results shown in Fig. 3 are obtained by replacing the 25 km fiber spool by either the 148 km link or the 332 km link, in the setup shows in Fig. 1. The measurements show that for the 148 km link, intrinsic FBA achieves 18 dB more gain than our bi-directional EDFA. For the 332 km link, the difference is even larger: FBA gives 45 dB more gain than the EDFA. This result shows that the FBA is especially suitable for long fiber links. The Brillouin frequency (νB) is measured to be 10.974 GHz and 10.970 GHz for the 148 km and the 332 km fiber link, respectively, with only 4 MHz difference.

 figure: Fig. 3

Fig. 3 Detected heterodyne beat power (RF) obtained with FBA and with EDFA, when 5 mW signal power are injected into (a) 148 km fiber (P pump = 20 mW, νB = 10.974 GHz) and (b) 332 km fiber (P pump = 40 mW, νB = 10.970 GHz).

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2.2 Phase noise

One of the most important aspects in frequency transfer applications is how much additional phase noise is introduced by the amplifier to the signal propagating through the fiber. We used the Mach-Zehnder interferometer shown in Fig. 1 to measure the phase noise of the bi-directional EDFA and FBA. Figure 4a shows the measured phase noise for the free-running interferometer without (black line) and with installed EDFA (red circles ο). At low Fourier frequencies (f < 30 Hz) the EDFA possibly adds a small amount of phase noise – this is still less than 0.1 rad2/Hz at f = 1 Hz. We attribute this phase noise to the approximately 6 m fiber used as gain medium inside the amplifier.

 figure: Fig. 4

Fig. 4 (a) Phase noise of the free-running interferometer without (black line) and with a bi-directional EDFA (red ο). (b) Phase noise of 25 km spooled SMF28 fiber without (black line) and with using FBA (blue ο).

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To measure the phase noise introduced by FBA, a 25 km fiber spool is used as FBA gain medium. Such a spool is quite sensitive to environmental perturbations, which results in additional phase noise. To reduce this effect, we put the spool inside an acoustic isolation box. Still, the measured phase noise for the unstabilized 25 km fiber (black line in Fig. 4b) exceeds one rad2/Hz at frequencies below 10 Hz. With the pump laser turned on, we then measured the phase noise of FBA (blue circles ο). The phase noise due to the FBA process is less than that of the 25 km fiber alone, since both curves coincide. The total phase noise is less than that encountered on long fiber links. It can therefore be compensated with the standard technique [2,5] if we assume that light traveling in either direction will experience the same phase noise. An experiment over a 480 km link demonstrating this is described in section 3.

2.3 Pump laser stabilization

The maximum amplification is achieved when the pump frequency matches the condition νpump = νsig + νB. Therefore, the pump laser frequency has to be stabilized. If pump and signal lasers are at the same site, a beat between the signal and the pump laser can be detected with a fast photodetector (bandwidth > 11 GHz). The beat signal is then locked to a microwave reference. But this technique needs complex and expensive equipment, which handles GHz frequencies. Furthermore, this technique will not be applicable if the pump laser is located at an intermediate station.

We have developed a simpler method based on the observation that the back-scattered pump power increases when the pump frequency is equal to sig + νB). Figure 5a , shows the system used to measure the scattered and transmitted pump powers when the pump is injected in the opposite direction of the signal in the 148 km fiber. Although the signal power is less than 1 μW at the output of the 148 km fiber the back-scattered pump power increased when the pump frequency is swept around (νsig + νB), see Fig. 5b. The transmitted pump power is decreased also by the same amount. A small modulation of the pump laser frequency and lock-in detection was used to monitor this change in the scattered pump power and stabilize the pump laser frequency at νsig + νB.

 figure: Fig. 5

Fig. 5 (a) Measurement setup for the scattered and transmitted pump power changes. The pump is injected in the opposite direction to the signal laser. CIR: circulator and OPM: optical power meter. (signal power is about 1 μW after 148 km fiber) (b).The change of the scattered pump power when the pump frequency is swept around sig + νB) and a Gaussian fit.

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To determine the change of the Brillouin frequency (νB) with temperature [16], we measured the temperature dependence of the 25 km fiber in the range from 16 °C to 25 °C. The Brillouin frequency temperature dependence is found to be 0.4 MHz/K. Typical peak to peak diurnal temperature variations for a buried fiber (depth < 1.5 m) are well below 1 K. Even if we assume an upper limit for temperature variations of about 10 K, the stabilization circuit can easily handle a pump laser frequency shift of about 4 MHz.

3. Frequency transfer over a 480 km optical fiber

To transfer a stable optical frequency from one location to a remote user over an optical fiber link phase noise accumulated along the fiber as well as attenuation has to be compensated. In this section we describe the transfer of an optical carrier over 480 km using the fiber stabilization scheme described in [4,5] and an amplification scheme that utilizes FBAs at each end of a 480 km fiber link and in one intermediate station only.

The 480 km fiber consists of four commercial fibers with overall attenuation of 115 dB, two of them are connecting PTB, Braunschweig to Cörmigk with an attenuation of about 70 dB and the other two are connecting PTB to the Institute of Quantum Optics (IQ), Hanover with attenuation of about 45 dB. In this setup local and user end as well as the intermediate station are located at PTB, which allows for easy testing. The light is sent in the first fiber (166 km) to Cörmigk, where it is returned to the intermediate station at PTB by fiber 2. The light is amplified and sent in the third fiber (74 km) to IQ, where it is connected to a fourth fiber to return the light back to PTB (the user end).

A transfer laser is locked to an optical frequency standard with the help of a femtosecond frequency comb. The transfer laser is used to transfer the stability of the frequency standard from the local to the user end, where it is used to measure the frequency of another laser or may be used for other applications. As acoustic and thermal fluctuations on the fiber link induce phase fluctuations on the light propagating in the fiber, a part of the light is reflected using a Faraday mirror at the user end back to the local end. A beat between the reflected light and a reference arm detects the phase noise introduced by the fiber link. A phase-locked loop (PLL) is then used to control an acoustic-optic-modulator (AOM1) to compensate this phase noise. AOM2 is used to discriminate light reflected at the user end by shifting its frequency from back scattered light in the fiber and back reflected light at the local end. The compensation system is shown in Fig. 6 .

 figure: Fig. 6

Fig. 6 Brillouin amplification in a frequency transfer system, AOM: Acousto-optic modulator, PD: photodetector, FM: Faraday mirror, C1: 30/70, C2: 40/60, C3:40/60, C4:30/70 simple fiber couplers (for details see text).

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For a full round-trip in the fiber the signal accumulates 230 dB loss before it reaches the phase compensation detector PD1. In order to compensate this loss, we used two FBA amplifiers for pumping four fiber sections. A FBA amplifier is used at the intermediate station to amplify the light in the return direction with a pump power of 45 mW and in the forward direction with a pump power of 30 mW. It is also used at the local end with a pump power of 9 mW to amplify the return light and at the virtual user end with a pump power of 18 mW to amplify the forward light. Pump light is injected into the fiber using simple fiber couplers with a coupling ratio depending on the available pump powers. It compromises between signal and pump power loss. We used one amplifier for each direction because of the 80 MHz frequency difference between the forward and the return light introduced by the AOM. For the forward direction FBA2 is used with frequency νFpump = νsig + νB + 55 MHz and for the return direction FBA1 is used with frequency νRpump = νsig + νB - 25 MHz. Where νB is the Brillouin frequency and νsig is the frequency of the transfer laser (signal). A part of the Brillouin-scattered light is directed by circulators to the DC photodetectors PD (3 and 4), where it is used to stabilize the frequency of the pump laser using the method discussed in section (2.3).

A beat signal at the user end between the forward light and the light from a reference arm (out-of-loop beat) indicates the 480 km fiber link stability. The signal is analyzed in the frequency domain with a FFT spectrum analyzer; in the time domain we use a Π-type frequency counter with zero dead time.

The phase noise of the out-of-loop beat is measured before and after applying the compensation scheme by detecting the phase changes with respect to a reference oscillator using a digital phase detector, after division by a suitable ratio to keep the phase changes below one radian [17]. Figure 7 shows the phase noise in (rad2/Hz) for the out-of-loop signal measured before and after applying the compensation. The phase noise reduction is 39 dB at 1 Hz, which is near to the theoretical limit of 41 dB at 1 Hz predicted by Williams et al. [18], SD (f) = (1/3) (2π)2 τ 2 delay f 2 Sφ (f) = 7.5 × 10−5 f 2 Sφ (f), where Sφ (f) is the phase noise of the free-running fiber, τdelay is the time for a one-way trip in the fiber and f is the Fourier frequency. It is close to optimal (green ο in Fig. 7) within the theoretical compensation bandwidth; the phase noise is suppressed up to Fourier frequencies of about 50 Hz.

 figure: Fig. 7

Fig. 7 Phase noise of the out-of-loop signal (OL) before (black dashed), and after (red solid) compensation. The green curve (ο) gives the theoretical compensation limit according to [18].

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We used a Π-type frequency counter with 1 second gate time to measure the frequency of the out-of-loop signal at the user end in the time domain and used the Allan deviation (ADEV) as a statistical measure of the frequency stability [19]. Figure 8 shows the ADEV of the out-of-loop signal before (black ) and after (red ο) the phase compensation. After applying the compensation, the stability of the transferred frequency reaches σy(τ) = 2 × 10−14 /(τ/s). This value is in good agreement with the value calculated from the phase noise (see Fig. 7). The ADEV curve follows a 1/τ slope and reaches a value of 2 × 10−18 at 8200 s (a bit over 2 hours). Comparing the achieved instability for this 480 km stabilized link with our previous measurements over 146 km [4], we observe excellent agreement with the scaling law (σy ~L 3/2) derived in [18]. Thus the new measurements support our prediction [5] that we can achieve an instability of ~5 × 10−14/(τ s−1) for a 900 km link connecting PTB Braunschweig and MPQ Garching.

 figure: Fig. 8

Fig. 8 Out-of-loop signal (OL) with compensated (red ο) and uncompensated phase noise (black ■).

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The mean value of the transmitted frequency is shifted from that of the reference laser by 64 μHz with a statistical uncertainty of 54 μHz. This shift corresponds to fractional frequency deviation of 3 × 10−19. The statistical uncertainty is obtained by dividing the standard deviation of the measurement by N since it is white phase noise and not by N, as discussed in [20], where N = 65000 is the total number of data points.

4. Conclusion

We have presented a fiber Brillouin amplifier (FBA) as an alternative to the currently used EDFA amplifier in frequency transmission applications. A FBA offers bi-directional amplification with a SNR ratio comparable to that of the currently used EDFA and with high gain of about 50 dB, especially when the signal is very small (several nW). FBA phase noise was measured, and a simple and new method for stabilizing the FBA pump laser was discussed. Finally, FBAs at the user and local ends and at one intermediate station only, were used to transfer an optical carrier frequency over 480 km fiber. The relative instability of the fiber link is σy(τ) = 2 × 10−14 /(τ/s) and reaches 2 × 10−18 after about two hours. Thus, the link will not limit a frequency comparison between today’s best optical clocks. Moreover, this is to our knowledge the largest distance bridged using only one intermediate amplifier station and with the lowest instability reported so far.

Acknowledgment

The authors would like to thank Katharina Predehl and Thomas Legero for technical assistance, as well as Piet Schmidt and Fritz Riehle for helpful comments. The work was partly supported by DFG through the Centre for Quantum Engineering and Space-Time Research, QUEST. Osama Terra is supported by a scholarship from the Egyptian National Institute of Standards (NIS) and is a member of the Braunschweig International Graduate School of Metrology, IGSM. Osama Terra’s home address is National Institute of Standards (NIS), Tersa St., Haram-Giza, Egypt, P. O. Box: 136 Giza, Postal code:12211; and his home email address is osama.terra@nis.sci.eg.

References and Links

1. S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004). [CrossRef]   [PubMed]  

2. L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19(21), 1777–1779 (1994). [CrossRef]   [PubMed]  

3. 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 × 1018 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008). [CrossRef]  

4. O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009). [CrossRef]  

5. 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(15), 2270–2272 (2009). [CrossRef]   [PubMed]  

6. E. Desurvire, Erbium-doped fiber amplifiers: principle and applications, (Wiley-Interscience publication, 1994).

7. H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010). [CrossRef]  

8. K. Predehl, R. Holzwarth, T. Udem, T. W. Hänsch, O. Terra, G. Grosche, B. Lipphardt, and H. Schnatz, “Ultra Precise Frequency Dissemination across Germany - Towards a 900 km Optical Fiber Link from PTB to MPQ,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuS2.

9. N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986). [CrossRef]  

10. R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989). [CrossRef]  

11. M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994). [CrossRef]  

12. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972). [CrossRef]   [PubMed]  

13. E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972). [CrossRef]  

14. G. Agrawal, Applications of Nonlinear Fiber Optics, (Academic Press, 2001).

15. G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008). [CrossRef]  

16. J. Geng, S. Staines, M. Blake, and S. Jiang, “Distributed fiber temperature and strain sensor using coherent radio-frequency detection of spontaneous Brillouin scattering,” Appl. Opt. 46(23), 5928–5932 (2007). [CrossRef]   [PubMed]  

17. F. Walls, A. Clements, C. Felton, M. Lombardi, and M. Vanek, “Extending the Range and Accuracy of Phase Noise Measurements,” National Institute of Standards and Technology (NIST) Technical Note 1337, TN129 (1990).

18. W. 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 (2008). [CrossRef]  

19. E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005). [CrossRef]  

20. W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010). [CrossRef]  

References

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  1. S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
    [Crossref] [PubMed]
  2. L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19(21), 1777–1779 (1994).
    [Crossref] [PubMed]
  3. 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. D 48(1), 35–41 (2008).
    [Crossref]
  4. O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
    [Crossref]
  5. 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(15), 2270–2272 (2009).
    [Crossref] [PubMed]
  6. E. Desurvire, Erbium-doped fiber amplifiers: principle and applications, (Wiley-Interscience publication, 1994).
  7. H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
    [Crossref]
  8. K. Predehl, R. Holzwarth, T. Udem, T. W. Hänsch, O. Terra, G. Grosche, B. Lipphardt, and H. Schnatz, “Ultra Precise Frequency Dissemination across Germany - Towards a 900 km Optical Fiber Link from PTB to MPQ,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuS2.
  9. N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
    [Crossref]
  10. R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
    [Crossref]
  11. M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
    [Crossref]
  12. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
    [Crossref] [PubMed]
  13. E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
    [Crossref]
  14. G. Agrawal, Applications of Nonlinear Fiber Optics, (Academic Press, 2001).
  15. G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
    [Crossref]
  16. J. Geng, S. Staines, M. Blake, and S. Jiang, “Distributed fiber temperature and strain sensor using coherent radio-frequency detection of spontaneous Brillouin scattering,” Appl. Opt. 46(23), 5928–5932 (2007).
    [Crossref] [PubMed]
  17. F. Walls, A. Clements, C. Felton, M. Lombardi, and M. Vanek, “Extending the Range and Accuracy of Phase Noise Measurements,” National Institute of Standards and Technology (NIST) Technical Note 1337, TN129 (1990).
  18. W. 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 (2008).
    [Crossref]
  19. E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
    [Crossref]
  20. W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
    [Crossref]

2010 (2)

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[Crossref]

2009 (2)

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

2008 (3)

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. D 48(1), 35–41 (2008).
[Crossref]

W. 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 (2008).
[Crossref]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[Crossref]

2007 (1)

2005 (1)

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
[Crossref]

2004 (1)

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[Crossref] [PubMed]

1994 (2)

1989 (1)

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[Crossref]

1986 (1)

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[Crossref]

1972 (2)

Amy-Klein, A.

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. D 48(1), 35–41 (2008).
[Crossref]

Bergquist, J. C.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[Crossref] [PubMed]

Blake, M.

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. D 48(1), 35–41 (2008).
[Crossref]

Chraplyvy, A.

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[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. D 48(1), 35–41 (2008).
[Crossref]

Diddams, S. A.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[Crossref] [PubMed]

Ertmer, W.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Feldmann, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Ferreira, M.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[Crossref]

Friebe, J.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Geng, J.

Grosche, G.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[Crossref]

Hall, J. L.

Hansch, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Holzwarth, R.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

Ippen, E.

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[Crossref]

Jefferts, S. R.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[Crossref] [PubMed]

Jiang, S.

Jungner, P.

Lee, W.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[Crossref]

Legero, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

Lipphardt, B.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[Crossref]

Lopez, O.

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. D 48(1), 35–41 (2008).
[Crossref]

Lours, M.

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. D 48(1), 35–41 (2008).
[Crossref]

Lu, Z.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Ma, L. S.

Mun, J.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[Crossref]

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. D 48(1), 35–41 (2008).
[Crossref]

Newbury, N. R.

Oates, C. W.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[Crossref] [PubMed]

Olsson, N.

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[Crossref]

Pape, A.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Park, C.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[Crossref]

Pinto, J.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[Crossref]

Predehl, K.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

Rasel, E.-M.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Riedmann, M.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Rocha, J.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[Crossref]

Rubiola, E.

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
[Crossref]

Santarelli, G.

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. D 48(1), 35–41 (2008).
[Crossref]

Schnatz, H.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[Crossref]

Smith, R. G.

Staines, S.

Sterr, U.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

Stolen, R.

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[Crossref]

Swann, W. C.

Terra, O.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

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(15), 2270–2272 (2009).
[Crossref] [PubMed]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

Tkach, R.

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[Crossref]

Udem, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

van der Ziel, J.

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[Crossref]

Vogt, F.

Wang, L.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Williams, W.

Wub, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[Crossref]

Ye, J.

Yu, D.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[Crossref]

Appl. Phys. Lett. (2)

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[Crossref]

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[Crossref]

Eur. Phys. J. D (2)

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Figures (8)

Fig. 1
Fig. 1 Set-up to measure the gain of FBA or EDFA: VA: variable attenuator, PD: photodetector, signal: signal laser with isolator, pump: pump laser, AOM: acousto-optic modulator, a 25 km fiber is used as gain medium for FBA.
Fig. 2
Fig. 2 FBA in comparison to EDFAs (uni-directional and bi-directional) for different signal powers received at the output of a 25 km fiber: (a) gain (b) SNR. The spectrum analyzer bandwidth is 100 kHz.
Fig. 3
Fig. 3 Detected heterodyne beat power (RF) obtained with FBA and with EDFA, when 5 mW signal power are injected into (a) 148 km fiber (P pump = 20 mW, νB = 10.974 GHz) and (b) 332 km fiber (P pump = 40 mW, νB = 10.970 GHz).
Fig. 4
Fig. 4 (a) Phase noise of the free-running interferometer without (black line) and with a bi-directional EDFA (red ο). (b) Phase noise of 25 km spooled SMF28 fiber without (black line) and with using FBA (blue ο).
Fig. 5
Fig. 5 (a) Measurement setup for the scattered and transmitted pump power changes. The pump is injected in the opposite direction to the signal laser. CIR: circulator and OPM: optical power meter. (signal power is about 1 μW after 148 km fiber) (b).The change of the scattered pump power when the pump frequency is swept around sig + νB ) and a Gaussian fit.
Fig. 6
Fig. 6 Brillouin amplification in a frequency transfer system, AOM: Acousto-optic modulator, PD: photodetector, FM: Faraday mirror, C1: 30/70, C2: 40/60, C3:40/60, C4:30/70 simple fiber couplers (for details see text).
Fig. 7
Fig. 7 Phase noise of the out-of-loop signal (OL) before (black dashed), and after (red solid) compensation. The green curve (ο) gives the theoretical compensation limit according to [18].
Fig. 8
Fig. 8 Out-of-loop signal (OL) with compensated (red ο) and uncompensated phase noise (black ■).

Equations (2)

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P c r i t = 21 A γ L e f f ( 1 + Δ ν l a s e r Δ ν B )
g = γ L e f f P p u m p A

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