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In this paper, we propose and demonstrate a scheme to achieve point-to-multipoint dissemination of radio frequency (RF) signals in a local area fiber optic network with tree topology based on wavelength-division multiplexing (WDM) technique. The phase changes caused by the fluctuations of the transfer links are passively canceled at remote end instead of at local end, which makes it feasible to flexibly build a tree-topology local area dissemination network with great cost-effectiveness. For the first time, we study the limit of long-term performance which is caused by temperature-induced variation of group velocity dispersion (TIVGVD) in dissemination networks using WDM techniques. In the proof-of-concept experiments, 38.5 km and 50 km fiber links are established to disseminate a 1 GHz frequency signal with fractional instability of 10−17 order after 104 s averaging time. Then 17.4 nm wavelength spacing is introduced between local carrier and user carrier to verify the theoretical analysis. Under a controlled fiber temperature variation of about 21 °C, the obtained overlapping Allan deviation (ADEV) agrees well with the simulation results after 104 s time scales, which proves the validity of our theory. The theory has practical values in predicting and optimizing the capacity and performance of a WDM-based local area RF dissemination network.
© 2015 Optical Society of America
1. Introduction
Due to their low loss, high reliability and wide bandwidth, fiber optic links are viewed as excellent alternatives of the traditional satellite links for stable frequency dissemination which plays an important role in many research and application fields, such as the comparison of atomic clocks, geodesy, and cosmology [1–3 ]. Many groups have proposed various schemes to overcome the fluctuations of the transmission delay caused by temperature variation [4–9 ]. The point-to-point optical frequency transfer, state of the art, has achieved stabilization of over 1,000 km fiber links at a level of 10−19 with integration time less than 104 s [4, 6 ]. The idea to realize point-to-multipoint frequency dissemination was first proposed in [10] and several developed methods were also demonstrated in recent years [11–14 ]. In consideration of the complexity and scalability, there are two main concerns in the design of the point-to-multipoint dissemination scheme. One is to enable the users to share all or part of the transfer links, occupying less optical fiber links. The other one is to devise a common stabilization scheme that could be shared (or partly shared) by users without causing mutual interference. Apart from the schemes proposed in aforementioned works, as we think, the WDM technique is also a viable choice to realize point-to-multipoint frequency dissemination. By using different wavelengths, users are able to discriminate from each other and therefore can be supported by a common stabilization scheme via common fiber links.
In general, the short-term fractional instability of a transferred RF signal is determined by signal to noise ratio (SNR) [15], which is usually limited by the noise in fiber optic system, such as the relative intensity noise (RIN), shot noise and mechanical vibration. The long-term fractional instability is mainly restricted by changes in group delay caused by environmental variations, especially the temperature variation [16]. Having been well studied in optical communication system, the SNR of the frequency signal can be improved by noise compression methods or by using better devices, while the stabilization of group delay strongly relies on phase stabilization schemes in which symmetric round-trip delays are presumed. However, in a multi-wavelength system, wavelength difference between local carrier and users’ carriers will bring about asymmetry in group delays due to group velocity dispersion (GVD). This residual asymmetry of group delay changes with temperature and cannot be eliminated by phase stabilization schemes, which induces an intrinsic systematic error and finally sets a limit on the achievable long-term fractional instability of the transferred RF signal. In a WDM-based dissemination network, such problem is especially prominent because a variety of wavelengths are needed to support multi-user.
In this paper, we propose and demonstrate a WDM-based dissemination scheme to distribute RF signal to multi-user in tree topology. Phase fluctuations of the RF signal are canceled at remote ends by a passive stabilization scheme. No active servo at remote ends is needed to control voltage-controlled oscillators (VCO) or piezoelectrical transducers (PZT), which simplifies the system structure and reduces the cost. Laser diodes (LD) with different WDM wavelengths are used in each terminal to avoid mutual interference. In addition, we theoretically analyze the asymmetry in group delays that results from TIVGVD, and simulate the resulting overlapping ADEV under sinusoidal temperature variation to explore the long-term performance floor of a WDM-based dissemination system. Both our scheme and theory are verified by experiments. Based on the experimental results, for the first time to the best of our knowledge, the capacity of a WDM-based local area RF dissemination network is discussed.
2. Principle
2.1 Phase stabilization scheme of RF signal for multi-users
Figure 1 shows the principle of the phase stabilization scheme. The RF signal, denoted by cos(ωt), is transferred to the remote end. A phase change φp1 is induced due to the time delay of the fiber links, which can be expressed as cos(ωt + φp1). Then part of the signal is split out and fed into the fiber by a different wavelength for a round trip, as is shown by the blue dashed line. The phase changes induced in the second and third trip are φp2 and φp3. So the accumulated phase change after the third trip is φp1 + φp2 + φp3. At remote end, the single-trip signal is converted to its triple-frequency version. The output, cos(3ωt + 3φp1), then is mixed with the returned signal, named triple-trip signal and written as cos(ωt + φp1 + φp2 + φp3), to produce an intermediate frequency signal cos(2ωt + 2φp1-φp2-φp3). Because the variation of the time delay and TIVGVD are negligible during the flight time of the optical signal if the transfer is accomplished by adjacent-wavelength carriers [17], an approximation can be made as φp1≈φp2≈φp3. Therefore the last three terms in bracket are canceled. Under this hypothesis, the intermediate frequency signal cos(2ωt) is theoretically phase-stabilized and a stable RF signal cos(ωt) can be obtained at the remote end by frequency division.
Since the phase stabilization is carried out at the remote end, this principle can be easily applied to support more users and construct a point-to-multipoint RF dissemination network, as is illustrated in Fig. 2 . Such topology is quite common in the end of a dissemination system where users are irregularly distributed in a local area. It not only can be used as a local sub-network of the backbone dissemination network but also can incorporate with other topologies, like the linear or circle topology, to form a flexible compound network. To run this network, local station broadcasts the frequency signal to users by an exclusive WDM channel (λ0). After receiving the broadcasted signal, users choose WDM channels (λ1, λ2… λN) that are different from each other to send the single-trip signal back for a round trip. They then extract the returned signal in their own channels and stabilize the delivered RF signal by the proposed scheme. As long as the power consumption of the system is properly budgeted, the configurations of local station do not have to upgrade as the number of the users changes. New users just need to couple out part of the forward optical signal at any nearby junction of the fiber network and select different WDM channels to perform the stabilization scheme. No cascaded structures are needed for users like C, D, and F who have no direct access to the trunk link. Therefore the dissemination system also has good scalability.
2.2 Long-term performance limit caused by TIVGVD
In a WDM-based RF dissemination system, each user monopolizes one WDM channel to stabilize the phase of the RF signal. It is predictable that there will be increasing wavelength gap between local carrier and users’ carriers when the number of users increases. And the TIVGVD cannot be neglected anymore.
Taking the case in Fig. 2 for example, due to the effect of GVD, the difference in single-trip group delays of carrier λ0 and λN can be expressed as
where D(λ) is the group dispersion parameter, L is the length of optical fiber and Δλ is the wavelength spacing between λ0 and λN. If Δx is a fixed value, the asymmetry in laser wavelengths will not deteriorate the delivered RF signal because it just introduces a constant phase difference. In reality, however, D(λ) and L usually change with the environment. Here we consider the temperature, which is a major contributor to the variation of Δx. Then the delay difference Δx derivative with respect to the temperature T is C is the coefficient of thermal expansion and contraction, 7 ppm/°C. The value of D(λ) around 1550 nm is 17 ps/nm/km. And the chromatic dispersion thermal coefficient dD(λ)/dT is −1.4 fs/nm/km/°C for G.652 optical fiber based on the experimental results of [18]. So the value of parameter α can be obtained, −1.3 fs/nm/km/°C. Typically daily temperature variations are approximately periodic and can be roughly modeled as a sinusoidal function [16].ΔT is the peak to peak temperature change and PT is the variation period (usually 24 h).We simulate the relative phase drifts of a 50 km fiber link under a sinusoidal temperature variation using Eq. (2) and (4) , and plot the overlapping ADEV in Fig. 3 . Since the period of temperature variation is at the order of 104 s and no other short or medium term factors are considered in simulation, the restriction on overlapping ADEV is expected to be prominent around 104 s time scales. Figure 3(a) shows how overlapping ADEV at 104 s time scale varies as ΔT and Δλ. Generally the fractional instability degrades linearly as ΔT and Δλ increase. Taking 50 km frequency transfer with 30 nm wavelength gap for example, the overlapping ADEV (104 s) is expected to be restricted to 8.01 × 10−16 if the temperature sinusiodally varies 30°C peak to peak. Such large temperature variation is quite possible when the fiber links consist of aerial optical cables under direct sunlight. And it will be even worse for longer-distance transfer. In this case, TIVGVD will become the dominant restriction and lead to a performance floor. For buried fiber cables whose daily temperature variation is usually less than 1 °C [16], a 0.4 nm (50GHz) wavelength-spacing link of 50 km just exhibits a performance floor at the order of 10−19. In addition, the simulations of the overlapping ADEV at time scales from 1 s to 105 s are also given in Fig. 3(b) in which ΔT is assumed to be 20 °C. The figure shows that the TIVGVD noise floor is low at short and medium term. It grows up with the averaging time, peaks at the time scales around 2 × 104 s to 4 × 104 s and then declines rapidly. It is expected that the overlapping ADEV of the system will be restricted to 10−16 order at time scales from 104 s to 4 × 104 s for the links whose wavelength spacing is larger than 8 nm, while that for links with smaller wavelength spacing is still at the order of 10−17.
Fig. 3 The simulations of the overlapping Allan deviation of a 50 km fiber link (a) after 104 s averaging time, (b) at time scales from 1s to 105 s with 20°C temperature variation peak to peak.
As far as we know, the restriction caused by TIVGVD cannot be alleviated by dispersion compensation, because it generally compensates a fixed dispersion value and doing real-time adjustments is difficult. The dispersion-shift fiber (DSF), already studied in [19], also has a similar chromatic dispersion thermal coefficient dD(λ)/dT, −1.21 × 10−3 ps/nm/km/°C, at 1550 nm. Therefore it still suffers the same problem as the standard G. 652 fiber. Theoretically this is a systematic performance limit not only in the proposed scheme but also in other multi-wavelength dissemination system. As a result, this scheme maybe not the best solution for long-haul and extensive dissemination, but is more suitable for a local area dissemination network where the number of users and transfer distance are limited.
3. Experiments and results
The proof-of-concept experiments consist of two parts. First, we test the point-to-multipoint dissemination performance of the proposed scheme with 0.8 nm (100 GHz) wavelength spacing between carriers to verify the effectiveness of our scheme. Then based on the same testbed, we increase the wavelength spacing to 17.4 nm and control the temperature of the fiber spool to examine the TIVGVD limited performance.
3.1 RF dissemination with 0.8 nm wavelength spacing
The experimental setup is shown in Fig. 4 . Some of the components, such as RF bandpass filters and amplifiers, are not presented in figure for clarity. We depict the structure of User A elaborately and take it as an example to illustrate how our scheme works. Both the local end and remote ends are located in our lab for the convenience of performance characterization.
Fig. 4 The schematic of the radio frequency dissemination system. OC: optical circulator. OBSF: optical bandstop filter, centering at λ0. PD: photon detector. OBPF: optical bandpass filter. OSC: oscilloscope. Frequency convertor: × 3, ÷ 2.
In the beginning, we test the point-to-point performance of the system when only User A is connected. At the local end, a 1 GHz analog signal V0 is provided by a vector signal generator (Agilent N5182A), which is referred to an atomic clock (FS725 Rubidium frequency standard). By directly modulating a distributed feedback laser diode (DFB0), the frequency signal is fed into a G.652 fiber spool of 50 km and transferred to the remote user. The laser wavelength at local end is 1547.72 nm (λ0), corresponding to the 37th channel of the DWDM system. We set the incident power below 0 dBm to prevent nonlinear effect because the typical threshold power of Brillouin Scattering is about 0 dBm for optical fiber links of 50 km [20].
At the remote end, the optical signal is filtered out by an optical bandpass filter (OBPF1) whose center wavelength is λ0. After detected by a photon detector (PD1), a portion of the RF signal V1 is tapped out for the characterization of the unstabilized link. One of the other two branches is directly modulated on DFB1 and then is transferred back through the same optical fiber with a different wavelength of 1546.92 nm (λ1, Channel 38). DFB1 is also tuned at a low power level in order to prevent Brillouin Scattering. The backward optical signal suffers about 17 dB power loss in total and exports from Port 3 of the optical circulator (OC1). An optical bandstop filter (OBSF) that centers at λ0 is inserted behind to eliminate the Rayleigh scattering interference from the local carrier, following an erbium-doped fiber amplifier (EDFA) to boost the optical power by 20 dB. Afterwards, the output laser is coupled into the fiber link again by a 2 × 1 optical coupler for a third trip. At remote end, we extract the triple-trip signal by OBPF2 and recover the RF signal V2 by PD2. To carry out the phase stabilization scheme, the third branch of V1 is sent to a passive frequency tripler (Mini-Circuits ZX90-3-452-S +) to perform frequency up-conversion. The obtained triple-frequency signal V3 is amplified by subsequent electronic amplifier and then mixed with V2. We filter out the 2 GHz RF signal and use a frequency divider (HMC361S8G) to divide its frequency by 2. Then a stable 1 GHz RF signal V5 can be obtained by User A.
We test the fractional instability of the transferred RF signal while the transfer delay is drifting as the outdoor environment changes. To measure the phase fluctuations of the stabilized link, the homodyne signal between the reference and the recovered RF signal serves as an error signal after passing a lowpass filter with 1.9 MHz cutoff frequency. The voltage of the error signal, which is expected to be DC, is sampled, digitalized, and converted to phase fluctuations. It should be noted that this phase measurement scheme will suffer phase confusion when the phase of the RF signal shifts 2π. Since normally the stabilized RF signal is stable enough to avoid this problem whereas the relative phase drifts of the unstabilized link are usually very large in long-term measurement, we take the advantage of the measuring precision of this frequency-mixing scheme to measure the phase fluctuations of the stabilized link, but use an oscilloscope to measure the relative phase drifts of the unstabilized link. The corresponding overlapping ADEV is shown in Fig. 5 . Curve (1) is the noise floor of the transfer system which is measured by replacing the fiber spool with 1m optical fiber. The red curve gives the fractional instability of the unstabilized link by directly comparing the single trip signal and the reference signal. The overlapping ADEV is 6.61 × 10−13 for 1 s averaging time, and then it gradually grows up after 100 s. Under a daily temperature variation of about 10 °C, its long-term fractional instability reaches 3.59 × 10−13 after 104 s averaging time. When the stabilization scheme is activated, as is shown by curve (3), an obvious improvement of fractional instability is observed, leading to overlapping ADEV of 6.3 × 10−17 after 104 s averaging time. Error bars after 104 s are given in the inset for clarity.
Fig. 5 The fractional instability of (1) noise floor, (2) unstabilized link A with single user accessed, (3) stabilized link A with single user accessed, (4) stabilized link A with multi-user accessed, (6) stabilized link B with multi-user accessed.
Then we test the point-to-multipoint dissemination performance to study whether adding new user will cause adverse effect to the existed user. An optical coupler functions as an optical splitter and combiner to form a network in tree topology. User B is connected by a fiber spool of 38.5 km and has the same structure as User A. To distinguish from User A, it chooses a different wavelength of λ2 (1548.52 nm) which also has 0.8 nm wavelength spacing to local carrier. Simultaneous phase measurements of the recovered RF signals are carried out at both users’ sites. Fractional instability is also calculated and shown in Fig. 5, which is 7.67 × 10−17 for the 50 km link and 5.39 × 10−17 for the 38.5 km link after 104 s averaging time. Noting that the fractional instability of User A is very close to that when A is exclusively served by local end, it is reasonable to draw a conclusion that the system is free of mutual interference among users.
3.2 RF dissemination with 17.4 nm wavelength spacing
In the aforementioned experiments, there is only 0.8 nm wavelength difference between local and users’ carriers. According to theoretical simulation in Fig. 3(a), the TIVGVD-induced limit of overlapping ADEV under 10 °C sinusoidal temperature variation is 7.12 × 10−18 at 104 s time scale. This is even better than the noise floor that we have achieved. Therefore the impact of TIVGVD is not noticeable in Fig. 5. To verify our theory and demonstrate how TIVGVD will limit the long-term performance of a WDM-based system, we introduce 17.4 nm wavelength spacing between local and user carrier. The schematic diagram of the proof-of-concept experiment is shown in Fig. 6 . The laser wavelength of User B is adjusted to 1530.33 nm to gain a 17.4 nm wavelength gap whereas User A keeps unchanged to serve as a contrast counterpart. User A and User B share a common fiber spool of 50 km so that they will endure the same change of the transfer link. The fiber spool is put into a temperature-controlled chamber to go through quasi-sinusoidal temperature variation.
Figure 7(a) gives the measured temperature variation in chamber. We control the period of temperature variation to be approximate 24 h with peak to peak value of 21 °C. Simultaneous phase measurements are done by the frequency-mixing scheme. The results are shown in Fig. 7(b). It is apparent that the relative phase drifts of User B show great consistency with temperature variation, while that of User A also has the same trend but is smaller in amplitude. The actual peak to peak relative phase drifts are respectively 0.018 rad and 0.152 rad for User A and B.
Fig. 7 (a) The temperature variation in chamber. (b) The phase fluctuations of the transferred RF signals.
We give the corresponding overlapping ADEV based on the measured relative phase drifts in Fig. 8 . The magenta curve represents the performance of User A, which starts at 4.47 × 10−13 and averages down to 4.13 × 10−17 after 2 × 104 s. This result is comparable to that of the previous experiment. However, by contrast, the overlapping ADEV of the 17.4 nm-wavelength-spacing link turns up at 104 s (3.02 × 10−16) and keeps going upward until 3.82 × 10−16 at 2 × 104 s. The red dashed curve is the simulation of user B based on our theory when all conditions are set as same as the experimental conditions, i.e. 17.4 nm wavelength gap, 21°C temperature variation peak to peak and 50 km transfer distance. The variation trend after 104 s agrees well with the experimental curve, showing that TIVGVD has become the dominant restriction of fractional instability around this term. In this case, the overlapping ADEV cannot be improved by further suppression of other restricting factors and the red dashed curve therefore indicates the limit of the fractional instability of User B. Interestingly, fluctuations with period of 100 s order are observed in Fig. 7(b) for both User A and B. This may result from the temperature-induced polarization evolution of the optical signals [21]. And the larger wavelength spacing of User B is speculated to lead to larger amplitude of the fluctuations and worse fractional instability around this term.
4. Discussion
Having been verified by experiments, our theory manifests that for users who have certain laser wavelengths, the TIVGVD-induced fractional instability limit is determined by both the transfer distance and temperature variation. Whereas, when the highest demand of the users in a network is determined and the temperature variation within a period is also predictable, we can use the theory to get the maximum tolerable wavelength gap Δλ max for a certain transfer distance, and then further estimate the TIVGVD-induced capacity limit of the dissemination system. The capacity is given by
where λ s is the channel spacing. The principle can be illustrated by Fig. 9 , which gives the relation between transfer distance L and Δλ max under different system performance. ΔT is assumed to be 10 °C and λ s is 0.4 nm. Points beyond 100 km are not given in the figure because we focus on a local area dissemination network and there will be other factors that may dominate the limit of system performance when conducting long-haul transfer, for example, the Rayleigh scattering of the users’ light. Within the margin of our experimental results, as can be approximately represented by the red curve, to achieve fractional instability of 7.7 × 10−17 at 104 s, the largest wavelength deviation from the local wavelength is 8.4 nm for RF transfer of 50 km. The 21 red circles (including 10 circles not marked in figure) on the left of the magenta dashed line represent the channels whose TIVGVD-induced fractional instability limit is better than the required performance. Since there are symmetric channels on the both sides of local carrier, the total number are twofold. Assuming the fractional instability is the same for 0.4 nm spacing as it is for 0.8 nm spacing, the network can support 42 users 50 km away in total with the performance that our experiments have achieved. Similar marks are also made at the blue curve and green curve, which respectively represent fractional instability equal to one-tenth of the state of art stability of Cesium frequency standard [22] and H-maser frequency standard [23]. Generally, frequency transfer with such fractional instability can be considered as stability-lossless transfer of the corresponding frequency standard. It shows that the TIVGVD-induced capacity is 66 for Cesium frequency standard dissemination of 50 km range, while it is limited to just 10 for more stable H-maser frequency standard dissemination. Clearly, higher performance demand will lead to smaller network capacity. But this can be alleviated by adding more local carriers. For example, if the center station simultaneously broadcasts the frequency signal by a second channel, which is marked by a black circle in the figure, another 10 users (between the two black lines) then can be supported by the H-maser frequency standard. By adding broadcasting channels every other 4.4 nm spacing, capacity of the dissemination network can be further improved.In actual situations, users usually are randomly distributed and have different demands of performance. To make full use of the system resources, the system manager can allocate the wavelengths that are nearby λ0 to remote or high-demand users and allocate the greater-spacing ones to those with short distance or low performance demand, so that the system can support more users. Also, actual temperature variation should also be considered in the optimization of the dissemination network.
7. Conclusion
In summary, we have demonstrated a WDM-based scheme that provides simple and flexible access to stable RF signal for multi-user in local area fiber optic networks with tree topology. Experimentally, fractional instability of 7.67 × 10−17 and 5.39 × 10−17 for 50 km and 38.5 km fiber link is simultaneously achieved at 104 s time scale. It is definitely a helpful complement to the previous dissemination scheme and can be developed as the sub-network of a terrestrial frequency dissemination network. In addition, we have studied the performance limit caused by TIVGVD, which is also verified on the proposed scheme. The theoretical and experimental results show that the TIVGVD will become the dominant restriction of fractional instability after 104 s averaging time for WDM-based RF dissemination networks with a great number of users and large temperature variation. Therefore in the management of such a dissemination network, wavelengths should be properly allocated based on the transfer distance, temperature variation, and the demand of performance.
Acknowledgments
The work was supported in part by the National Natural Science Foundation of China under Grant with No. 61371121, No.61177065, No.61174199, No. 61032005, the National Basic Research Program of China (No. 2012CB315603), and the Nature Science Foundation of Jiangsu Province of China (No. BK2012058). All the authors contributed equally to this work.
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