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Multipoint Joint Time and Frequency Dissemination in Delay-Stabilized Fiber Optic Links Ł. Śliwczyński, Member, IEEE, and P. Krehlik Abstract—This paper presents the system for dissemination of both the RF frequency (e.g., 5, 10, or 100 MHz) and time (pulse per second) signals using an actively tapped fiber-optic link with electronic stabilization of the propagation delay. In principle several nodes for accessing the time/frequency signals may be added without the degradation of the dissemination in the main link. We are discussing the algorithm of determining the propagation delay from the local end of the link to the access node that is required for calibration of the time dissemination. Performed analysis shows that the uncertainty of the time calibration at the access node may in practice be dominated by the dependence of the propagation delay of the receivers on impinging optical powers and is only weakly affected by the distance between the local and access modules. The uncertainty is, however, still low, being only about two times higher compared with the calibration uncertainty of the main link. Experimental results performed on several spooled fibers show that the accuracy of described calibration procedures, expressed as a difference from the results of direct measurement, is not worse than 35 ps.

I. Introduction

R

ecently the idea of using optical fibers to convey the signals generated by atomic sources has drawn considerable attention of many scientists and researchers working actively in the time and frequency community. Several various techniques and solutions have been proposed for such purposes, such as phase-stabilized coherent links for transferring an optical carrier [1]–[3] or an optical comb [4]. For transferring RF signals, techniques were developed based on so-called phase conjugators [5]–[6] and delay-stabilized links exploiting variable delay modules, realized either in the optical [7] or electrical domain [8]–[9]. Ideas of implementing time transfer in stabilized coherent links using phase modulation [10] or linear chirp [11] were also recently investigated. Stabilized fiber optic links offer not only the highest currently available stability of the transfer but also make the possibility of dissemination (i.e., delivering the highstability frequency signals to some remote location), requiring synchronization with an atomic source. This is in

Manuscript received October 9, 2014; accepted January 4, 2015. This work supported in part by the European Metrological Research Programme EMRP under SIB-02 NEAT-FT and by the Polish National Science Centre under the decision DEC-2011/03/B/ST7/01833. The authors are with the Electronics Department, AGH University of Science and Technology, Mickiewicza 30, Krakow, Malopolska 30-059, Poland (e-mail: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2014.006773

opposite to traditional, satellite-based methods of time and frequency transfer [12]–[13] that are only suited for comparing atomic sources and applying off-line corrections to synchronize distant clocks. Stabilized optical fiber links also create the possibility of multipoint dissemination of the signals from the same atomic source to many users. It was first demonstrated for an optical carrier in the phase-stabilized links [14], further extended in [15] and [16]. The idea was also implemented in multipoint links for dissemination of RF signals [17]. Tapping of the signal is based on a general observation that at any point (called the access point) of a bidirectional phase-stabilized link the variations of the phases (denoted as ΔφA and ΔφB, respectively) of the signals propagating in both directions over the same fiber are opposite (Fig. 1). Thus using a device allowing obtaining the mean phase of these two counter-propagating signals (e.g., a balanced mixer followed by a frequency divider for RF signals) assures the stable phase at the access point as well. In our previous papers, we demonstrated the multipoint dissemination in the fiber-optic links with active delay stabilization exploiting variable electronic delay lines [18] as well as an extension of this basic idea to the system with side-branches, allowing dissemination of the RF frequency signal in a more flexible tree-like topology [19]. In [20] we presented a brief description and preliminary experiments with the multipoint time dissemination. In this paper, we are presenting an in-depth analysis of proposed system together with the procedure of determining the propagation delay between the reference point of pulse per second (PPS) signal at the local module and the PPS output at the access node, supplemented with the uncertainty analysis characterizing the limitations of described technique. Presented concepts are verified and the results of numerous experiments performed with the spooled fibers of various lengths are shown. II. Architecture of the System With an Access Node The general block diagram of the system for multipoint joint time and frequency dissemination is presented in Fig. 2. The basis of the system is the main link realizing the transmission of time and frequency signals from the local module to the remote one. Along the trunk fiber, several

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terval measuring equipment, such as time interval counter (TIC) or oscilloscope. In one of our previous experiments we successfully used this approach to reduce the jitter of the SR620 time interval counter [23]. Fig. 1. Phase relations in the access point of stabilized fiber optic link.

access nodes may be located, forming the multipoint joint time and frequency disseminating structure. In its simplest form the tapping of an optical signal at some access node may be realized using a fiber directional coupler for extracting both the forward and backward propagating optical signals. When the signal at some access node is weak, it may be boosted using the bidirectional optical amplifier [18]. It is important to note that the presented method is transparent for the propagation of signals in the trunk fiber, adding only small attenuation because of tapping of optical signals. Using the scheme we developed in principle any RF may be disseminated (e.g., 5, 10 or 100 MHz). Similarly, the PPS signal may take any number of pulses per second; in our experiments we successfully transmitted standard 1 PPS [21], [22] and also 100 PPS [23]. The only requirement is that the frequency and time signals must be phase-coherent to be correctly transferred from the local end to the remote one. The advantage of using higher than standard 1 PPS rates is that one may gain on greater averaging that allows to reduce the noise of the time in-

A. Main Delay-Stabilized Fiber Link Assuming that the same optical fiber is used for transferring the optical signals in both directions and that the two electronic variable delay lines in the local module are closely matched, the propagation delay of this main link is stabilized as shown in [8] and [21]. For time transfer, a PPS embedder is added in the local module that modulates the PPS pulses onto the frequency signal [22]. The reverse operation in the remote module is done by the PPS de-embedder, which extracts both PPS and frequency signals. One more PPS de-embedder in the local module is necessary to allow determining the propagation delay of the main link accordingly to the formula [22]:



τ IN → OUT = τ IN → REF (1) 1 + [τ REF → RET + (τ F _ F − τ F _ B) + τ C], 2

where τIN→OUT is (calculated) delay between the PPS input and output of the main link, τIN→REF is (measured) delay between the PPS input and the reference output of the local module, τREF→RET is (measured) round-trip delay, and τC is the hardware calibration constant, related

Fig. 2. Block diagram of the system for multipoint dissemination of time and frequency (a) and the structure of the access module (b). OT and OR stand for optical transmitter and receiver, respectively.

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Fig. 3. Timing diagram of the link with an access node.

to any asymmetry of the signal path between the forward and backward directions of the local and remote modules. The difference of the propagation delay τF_F − τF_B between the forward and backward directions of the optical fiber connecting the local and remote modules may be determined using the equation:

τ F _ F − τ F _ B = (λF − λB)D + τ PMD ±

4ωAE , (2) c2

where λF − λB is the difference of the wavelengths propagating in the forward and backward directions, D is the accumulated chromatic dispersion of the fiber connecting the local and remote modules, τPMD accounts for the birefringence of the fiber. The last term accounts for the Sagnac effect [24], where ω is the angular speed of the Earth rotation, c is the speed of light in vacuum and AE is the area of the equatorial projection of the contour swept by the vector extending from the center of the Earth and moving along the path of the fiber. Using the set of (1) and (2), it is possible to calculate the propagation delay of the main link with the uncertainty of some picoseconds, as verified by numerous experiments, using both spooled and field-deployed fibers [21], [23]. B. Access Nodes for Time Dissemination The block diagram of the access node for multipoint joint time and frequency dissemination is shown in Fig. 2(b). Its core part is formed by two precisely matched electronic variable delay lines and the phase detector (processing the 10 MHz frequency signal). As we have already demonstrated [18], the middle point of two cascaded delay lines (marked as N) provides a phase-stabilized signal. To extract the PPS pulses that are transmitted by the local module of the main link, it is enough to supplement the access module with the PPS de-embedder. However, to determine the propagation delay between the reference point of the local module and the output of the access module, which is mandatory for calibrated time dissemination, two

additional PPS de-embedders are required, together with their auxiliary PPS outputs: one located in the backward path (PPS AuxB) and one at the output of delay-lines chain (PPS AuxA). It will be shown in the next section that such structure offers similar self-calibration feature (i.e., calibration without referring to some additional calibrated link, based only on the local measurements) just as it is in the main link.

III. Calibration of the Time Transfer at the Access Nodes The timing model of the system where an access node is located between two fiber parts (characterized by time delays τF1 and τF1) is shown in Fig. 3. It was constructed basing on the block diagram shown in Fig. 2 by identifying time delays associated with particular components of the system. The inputs of the phase comparators (one in the local and the second one in the access module) showing constant delay for PPS signal are marked using the symbol Δ = 0, emphasizing that there are no fluctuations between related terminals. All delays denoted using a letter t are regarded as constant and are associated with the propagation delays of some electronic components, coaxial cables, fiber pigtails, etc. The symbol t1 denotes the propagation delay from the output of the PPS de-embedder to the PPS Reference auxiliary output, t2 is the delay of the PPS de-embedder in the remote module, t3 is the delay from the midpoint between two matched electronic delay lines (marked as point N) and the output of 1 PPS signal in the access module, and t4 and t5 are the constant delays between the inputs of the phase comparator and the PPS auxiliary outputs A and B in the access module. Symbols tOTL and tOTR denote delays concerned with the laser transmitters OTL and OTR in the local and remote modules (they include delays of optical circulators and associated optical pigtails).

Śliwczyński and krehlik: delay-stabilized fiber optic links

The symbol τ is used to denote the delays that may vary, as the delays associated with optical fibers connecting local, access, and remote modules (τF1_F, τF2_F, τF1_B, and τF2_B; indices F and B denote forward and backward direction, respectively) and delays of variable delay lines (τD and τN; ΔτD and ΔτN account for mismatches resulting from imperfections of the manufacturing of the variable delay lines). τEMB is the delay associated with the process of mapping the incoming PPS pulses into the 10 MHz signal [22]. The delays related to the optical receivers in the local (ORL), remote (ORR), and the access module (ORA and ORB), denoted as τORL, τORR, τORA, and τORB, respectively, are considered also as variable in the described model, because of residual influence of the optical power level on the delay of the receiver. The symbols using an arrow in the subscript denotes the propagation delays between various external terminals of the system that may be determined using a time interval counter (TIC) or equivalent equipment. These delays are used in the calibration procedure (τREF→RET, τA→B) and its verification (τREF→OUT, τIN→OUT, τREF→OUT_N, and τIN→OUT_N), as it will be described further in the text. Using the model from Fig. 3 the propagation delay between the input and the output of the access module may be written as

τ IN → OUT _ N = τ IN → REF + τ REF → OUT _ N. (3)

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where τCN defined as τ CN = − t 1 + 2t 3 − t 4 + t 5 + t OTL − ∆τ D − ∆τ N   

I τ CN

− (τ −τ ORL − τORA ORB) 

(8)

II τ CN

is the pre-installation calibration constant of the access node (similar to the constant τC for the main link) that have to be determined at the manufacturing stage of the system. For convenience, (8) was divided into two parts: II τ CN groups the power-dependent propagation delays of I the optical receivers, whereas τ CN combines remaining delays, including mismatches of the coupled delay lines in the local and access modules. Eq. (7), valid for any point located along the fiber link, may be regarded as a generalized version of (1), which is true only at the end of the link. To use it one has to know the value of τREF→RET measured at the terminals of the local module and the value of τA→B measured at the terminals of the access module. It is interesting to note that τREF→OUT_N depends on the difference of the forward and backward propagation delays of the first part of the optical fiber only, connecting the local module with the access one. In an analogy to (2) it may be written as

τ F1 _ F − τ F1 _ B = (λF − λB)D1 + τ PMD1 ±

4ωAE1 , (9) c2

The first term in (3), namely τIN→REF, may be measured between the terminals of the local module using a TIC, whereas the second term (τIN→REF) may be calculated using the timing model:

where an index 1 is added to denote the first part of the fiber. To determine the calibration constant τCN it is necessary to place the local and access modules in the same τ REF → OUT _ N = τ D + τ N + τ F1 _ F − t 1 + t 3 + t OTL + τ ORA. laboratory, connecting them using short fiber patchcords. (4) This way one may neglect the term τF1_F − τF1_B in (7), that leads to the formula: Two delays τD and τN associated with the variable deτ CN = 2 ⋅ τ ′REF → OUT _ N − τ ′REF → RET − τ ′A → B, (10) lay lines may be written as depending on other measur- able delays τREF→RET and τA→B (i.e., the delays that may be measured in the working system using a TIC or equiva- where primes at the right hand side are used to denote lent equipment in the situation where the local, remote, calibration measurements done in the laboratory. It is worth noting that to determine τCN it is not necessary and access modules are placed in distant locations): to have the remote module on the same laboratory bench together with the local and access modules. This feature 1 τ D = (τ REF → RET − ∆τ D − τ F _ F − τ F _ B (5) allows adding the access nodes to some already installed 2 link—such operation requires only a short break necessary + t 1 − t OTL − t OTR − τ ORL − τ ORR), for calibrating the access module and its further installa1 tion in the final location. τ N = (τ A → B − ∆τ N + τ F2 _ F 2 (6) + τ F2 _ B − t 4 + t 5 − τ ORA + τ ORB). IV. Uncertainty Budget at the Access Node Combining (4)–(6), one may arrive to the final calibration formula in the form:



τ REF → OUT _ N = τ IN → REF

(7) 1 + (τ REF → RET + τ A → B + τ F1 _ F − τ F1 _ B + τ CN), 2

The uncertainty analysis of the propagation delay τIN→OUT_N between the input of the system and the output of the access node may be performed using (7)–(9). Resulting uncertainty budget presented in Table I is, in general, similar to the budget for the main link [22]. However, a larger value of combined uncertainty may be ex-

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Fig. 4. Variation of the propagation delay of the optical receiver versus impinging optical power. The inset shows the resulting histogram (bars) and its approximation using the arcsin(∙) probability distribution (dashed line).

pected because processing of the signal inside the access module is substantially more complex (e.g., additional delay lines, two optical receivers, three PPS de-embedders, etc.). The rows 1 to 3 list the uncertainty components related to the measurement of time intervals; the 5 ps value adopted in Table I assumes the oscilloscope-based measurement, featuring much lower uncertainty compared with typical TIC [21]. The row 3 shows the uncertainty of τA→B that is specific for calibration of the access node. The main difference, however, compared with the main link uncertainty, is the necessary modification of the uncertainty of the calibration constant τCN that is affected by the dependence of the receiver propagation delays on II the level of impinging optical power [included in τ CN in (8)]. It may be expected that determining the τCN during the laboratory calibration of the system will be certainly carried out under different optical powers than those that will drive the receivers in the final destination of the ac-

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cess module. Measurements we performed revealed that this may contribute substantially to the combined uncertainty—see Fig. 4 showing variations of the propagation delay of the receivers we used in our setup in the order of 36 ps peak-to-peak. To estimate the contribution of this effect to the uncertainty of τCN we assumed that the probability distribution of the dispersion of the delay may be reasonably well approximated by the arcsin(∙) distribution (inset in Fig. 4). This is characterized by the standard deviation of 0.5∆ PP 2 , giving the contribution of all involved receivers (ORL, ORA, and ORB) a square root of three larger, i.e., equal to ∆ PP 6 4 (row 4b). The uncertainty of the first part of the calibration conI stant τ CN (row 4a), that includes the mismatch of two pairs of variable delay lines, may be estimated taking a value of 7.2 ps as the standard uncertainty for one line (determined in our previous experiments [8], [21]) and increasing it by 2 because of uncorrelated impact of each pair. The last four rows in Table I (numbered from 5 to 8) list the uncertainties related to the fiber chromatic dispersion, birefringence, the local and remote optical transmitter detuning, and the Sagnac effect, respectively. All the contributions that are length dependent take into account only the part of the fiber connecting the local and access modules. Example budgets reveals the fact that the uncertainty of the time calibration of the access node is quite independent on its distance from the local module; the value of the uncertainty is in practice dominated by the uncertainty of the calibration constant τCN, which is length independent. Comparing to the uncertainty of the time dissemination in the main link we may observe about two times increase for 100 km long link (compare Fig. 4 in [21], showing a value of approximately 8 ps). Reduction of this value is possible, e.g., by implementing a feedback system keeping the powers at the inputs of the optical receiver equal or, better,

TABLE I. One Uncertainty Analysis of the Calibration of the Access NodeWith Example Budget. Standard uncertainty No.

Uncertainty source

Sensitivity coefficient

Length independent

1 2 3 4a 4b

τIN→REF τREF→RET τA→B I τ CN II τ CN

1 0.5 0.5 0.5 0.5

5 ps 5 ps 5 ps 7.2 ps ⋅ 2 ∆ PP 6 4 a

5

D1

0.5(λF − λB)

6 7 8

τPMD1 λF − λB AE1

aAssuming

0.5 0.5 D1 2ω/c2

Length dependent

— — — — — ∂D ∂T ⋅ ∆T ⋅ L1 5 ps/nm 12 — LDV ⋅ L1 5 pm — — 10−3∙AE1 Combined standard uncertainty:

Budget L1 = 10 km

L1 = 100 km

5 ps 2.5 ps 2.5 ps 5 ps 11 ps

5 ps 2.5 ps 2.5 ps 5 ps 11 ps

2.1 psb

2.3 psb

psc

0.3 psc 4.3 psd 0.3 pse 15 ps

0.2 0.4 psd 0.03 pse 14 ps

three contributions of three independent receivers (ORL, ORA, and ORB). assuming lasers detuning equal to 100 GHz (conforming to standard ITU DWDM grid), taking ∂D/∂T = 4 fs/(nm∙km∙K) and ΔT =

bCalculated

25°C. cAssumed typical link design value (LDV) equal to 0.05 ps∙km−1/2 for currently used fibers. dChromatic dispersion of G.652 standard single mode fiber assumed, equal to 17 ps/(nm∙km) at 1550 nm. eThe path of the fiber is assumed to travel along the 50th parallel of north latitude.

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using fiber optic receivers with much weaker dependence of their propagation delay on the level of received optical signal (e.g., [25]).

V. Experimental Results To verify the ideas presented in the previous sections, we performed several experiments in which we focused on determining the stability of the dissemination of time and frequency signals at the access node and on verification of the calibration procedure of the delay between the local module and the access node. The results of these experiments are presented below. A. Dissemination Stability The setup we used to determine the stability of the transfer is presented in Fig. 5. For the tests with the time transfer we decided to use 100 PPS, instead of standard 1 PPS, to gain from the reduction of the jitter of the oscilloscope thanks to the possibility of higher averaging. The 100 PPS signal was derived from the 10 MHz signal using a chain of digital synchronous dividers. Both the local and access modules were placed in our laboratory, to have the access to the input and output connectors of the system and to the reference signals (100 PPS and 10 MHz) in the same place. The length of the fiber connecting the local and remote modules was equal to 160 km, composed of two spools of fiber (49 km each) placed in the thermal chamber and the field-deployed part, running along the Krakow beltway from our laboratory at AGH in Krakow to Skawina and back (62 km in total). Two single path bidirectional

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amplifiers (SPBA) [26] used to compensate the attenuation of the fiber and to boost the power levels at the optical inputs of the access module completed the link. The access module used one more SPBA as its part, working simultaneously as the in-line amplifier (see [18] for the discussion of possible structures of the access modules). The thermal chamber forced the temperature variations of 5 K with a daily period that, together with the temperature fluctuations affecting the field-deployed fiber, resulted in observed variations of the propagation delay of the fibers in the order of 20 ns peak-to-peak (see the plot in the right bottom corner of Fig. 5). The results of a three-day measurement session are shown in Figs. 6(a) and 6(b), presenting the time deviation (TDEV) of 100 PPS pulses and the overlapping Allan deviation (ADEV) for 10 MHz signal, respectively. The record of the phase fluctuations, which were used to calculate respective TDEV and ADEV curves, are plotted above the relevant stability plots. Omitting the higher level of a high-frequency noise, one may notice similarity of presented phase fluctuation curves. This results from the principle of operation of our dissemination system, where the frequency signal is used to convey the information about the PPS pulses. For the averaging times greater than about 100 s the value of TDEV is below 600 fs, reaching its minimum around 300 fs near 1000 s. The plot of ADEV shows almost monotonic decrease proportional to the inverse of the averaging time with the value at one day averaging around 2.3∙10−17. It may be noted that the fluctuations of the propagation delay of the fiber induced by the thermal chamber with daily period are only slightly visible on the stability plots as small bumps near the averaging time of 43 000 s (compare with the open-loop performance shown in the insets).

Fig. 5. Laboratory setup used for determining the stability of time and frequency signals at the access module. For stability analysis we applied A7MX frequency/phase difference comparator (Quartzlock) for 10 MHz and DSO81004A real-time digital oscilloscope (10 GHz bandwidth, 40 Gs/s sampling rate) for 100 PPS. The 10 MHz signal was supplied from SMB100A signal oscillator equipped with the oven-controlled crystal oscillator reference.

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Fig. 6. Stability measured at the outputs of the access module: TDEV of 100 PPS output (a) and overlapping ADEV (red) of 10 MHz output (b). In the upper part of the figure, the evolution of the phase drift of relevant signals is plotted. Open loop stability plots are shown in the insets. The averaging for oscilloscope measurement was 5 s, whereas the bandwidth in case of A7MX phase comparator was limited to 10 Hz.

In our experiments we were unable to analyze the signals at the access node simultaneously with the signals at the end of the main link. For the comparison we may, however, use the results of our previous measurements performed in similar conditions over the links of similar lengths. Relevant curves are shown in Figs. 6(a) and 6(b) with dotted lines. As a reference for ADEV we used the data from 124-km-long link, composed of two fiber spans connected in series, running from Krakow to Skawina and back, with one SPBA in the middle [21]. For TDEV comparison we used the data obtained from 149 km long link running from Braunschweig to Hannover and back, with one SPBA in the middle [23]. Both reference curves are below the curves determined in current experiments that suggests that somewhat worse stability of the signals at the access node may be expected compared with the stability of the signals at the end of the link. The degradation of the stability is reasonable, especially noting the fact that the signal chain to the output of the access module is substantially more complex, including additional variable delay lines, two optical receivers, and three PPS deembedders, each adding its own fluctuations to the signals processed. B. Time Calibration To test the time calibration procedure we used the measurement setup shown in Fig. 7. As in the previous point, we used 100 PPS signal for time transfer. We applied the same method as described in our previous paper [22], relying on comparing directly measured propagation delay between the reference output of the local module and the PPS output of the access module with the value τREF→OUT_N calculated accordingly to (7). In this

approach, we did not take into account the propagation delay between the output of the clock source and the reference output of the local module that includes delay of the embedder τEMB. This delay depends on the phase relation at the inputs of the local module between the 10 MHz and 100 PPS pulses and is constant as long as the lengths of the cables used to bring these signals to the local module are constant. Knowing the propagation delay of the cable used to connect 100 PPS signal with the input of the link, the value of τIN→REF may be determined by measuring the propagation delay between the output of the disseminated clock and the reference output of the local module [21]. In our measurement setup we used a self-developed digital PPS generator having two 100 PPS outputs: the direct one, connected with the PPS input of the local module, and the delayed one, connected with the trigger input of the oscilloscope (DSO81004A). The delay between these two outputs is settable with well-defined granularity of 10 μs, derived directly from the 10 MHz reference signal supplying the PPS generator. Setting appropriate delay value guaranties that the time interval measured by the oscilloscope is not longer than ± 5 μs that limits the influence of the inaccuracy of the timebase of the oscilloscope and allows keeping the uncertainty of a measured time interval at the level of 5 ps. All the measurements were performed relatively to the reference output of the local module using the same piece of microwave coaxial cable (Belden 1671A), so instead of measuring the delay τA→B directly we determined its value from two separate measurements of τREF→A and τREF→B. After initial calibration of the measurement setup (i.e., taking the delay to the local reference point as zero) we determined accordingly to (10) the value of the calibration constant τCN connecting the local, access, and remote

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VI. Conclusion

Fig. 7. Experimental setup used for testing time calibration at the access node.

modules with short patchcords and adding 5 dB fixed optical attenuators to not overdrive the optical receivers. The results of 11 tests performed using various lengths and types of the fiber (G.652, G.655, and G.653 with standard, reduced, and zero chromatic dispersion, respectively) and various locations of the access module are collected in Table II. In some measurements we added a fixed optical attenuator with a piece of the optical fiber (rows 2 and 3) to vary the level of the optical signals reaching the receivers in the local and access modules. For longer links (rows 10 and 11) we used one more SPBAs to compensate the attenuation of the fiber (one SPBA was used all the times as it made the part of the access module). The difference between the calculated and measured propagation delay shown in the last column of Table II does not exceed 35 ps in the worst case and is consistent with expanded uncertainty (two times the standard uncertainty) of this difference equal to 36 ps. This proves that the described system for multipoint joint dissemination of time and frequency and the method of the calibration may be used for distributed applications requiring picosecond accuracy of time dissemination.

In the paper we described the structure and the principle of operation of the system for multipoint joint dissemination of time and RF frequency signals. The access module, being the key element of such system, utilizes the same basic components as used in the main stabilized link (i.e., the coupled electronic delay lines and the PPS deembedders) that facilitates the design and implementation of such system. In principle the number of access modules is not limited and they may be placed in any location on the fiber route between the local and remote modules. To determine the propagation delay between the source of 1 PPS signal and the output of the access module it is necessary to determine the calibration constant τCN first. To do this it is enough to collect only the local and access modules in one place and connect them using a short fiber patchcord. The location of the remote module is unimportant for this calibration process that may be important when installing the access node on a live link (i.e., one that is already used to disseminate signals between two distant points). The experiments we performed with verifying our calibration formula (7) showed good agreement with the actually measured propagation delay; however, the difference is generally slightly worse compared with the calibration of the main link with similar length. A possible reason of observed deterioration is the dependence of the propagation delay of the optical receiver on the power of impinging signal. This is not so important in the main link, where such influence greatly cancels out because the powers received by the local and remote receivers are quite similar (assuming similar output powers of local and remote transmitters). Using the receivers with smaller dependence of the propagation delay or stabilizing the optical powers at the inputs of the receivers will allow reducing the uncertainty of calibration of the access nodes substantially (Table I, row 4b).

TABLE II. Results of Verification of the Calibration of Time Dissemination. Fiber section 1

Fiber section 2

100 PPS delay

No.

Length [km]

Dispersion [ps/(nm∙km)]

Length [km]

Dispersion [ps/(nm∙km)]

[ps]

[ps]

Calculated – measuredc [ps]

1 2 3 4 5 6 7 8 9 10 11

49 49 49 (+10  dB attn.) 49 69 20 67 69 107 147 (+2 × SPBA) 147 (+2 × SPBA)

813 813 813 813 786 −27 1117 786 1164 2389 2389

49 49 (+10  dB attn.) 49 69 49 49 49 67 49 18 49

813 813 813 786 813 813 813 1117 813 304 813

247 969 016 247 969 016 247 969 016 247 978 998 347 738 999 100 018 705 337 539 119 347 749 000 535 469 145 744 049 590 744 029 582

247 969 009 247 969 005 247 969 000 247 978 993 347 738 981 100 018 705 337 539 095 347 748 982 535 469 110 744 049 578 744 029 561

7 9 16 5 18 0 24 18 35 12 21

aCalculated

Measuredb

Difference

Calculateda

using (7); estimated standard uncertainty 17 ps for maximum length of section 1 equal to 150 km. standard uncertainty of measured delay equal to 5 ps, including only the contribution of the oscilloscope. cEstimated standard uncertainty of difference equal to 18 ps. bEstimated

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The ideas shown in this paper may be further extended to multipoint dissemination systems operating in the sidebranch configuration [19]. Such systems may be used to disseminate the time and frequency signals from a single atomic source to many distant users, requiring precise time/frequency synchronization, i.e., calibration facilities for industry, synchronization of telecom networks, or large-scale scientific experiments, such as low-frequency array for radio astronomy (LOFAR; a few LOFAR stations are to be built in the near future in Poland). Fiberbased stabilized links may also find use as a backup synchronization network for commonly used satellite methods exploiting GPS, which may become important in the future for safety or redundancy reasons. References [1] K. Predehl, G. Grosche, S. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. Hänsch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science, vol. 336, no. 6080, pp. 441–444, 2012. [2] O. Lopez, A. Haboucha, B. Chanteau, Ch. Chardonet, A. AmyKlein, and G. Santarelli, “Ultrastable long distance optical frequency distribution using the Internet fiber network,” Opt. Express, vol. 20, no. 21, pp. 23518–23526, 2012. [3] D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, “High-accuracy coherent optical frequency transfer over a double 642-km fiber link,” Appl. Phys. B, vol. 117, no. 3, pp. 979–986, 2014. [4] G. Marra, H. S. Margolis, and D. J. Richardson, “Dissemination of an optical frequency comb over fiber with 3×10−18 fractional accuracy,” Opt. Express, vol. 20, no. 2, pp. 1775–1782, 2012. [5] M. Fujieda, M. Kumagi, and S. Nagano, “Coherent microwave transfer over 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 57, no. 1, pp. 168– 174, 2010. [6] Y. He, B. J. Orr, K. G. H. Baldwin, M. J. Wouters, A. N. Luiten, G. Aben, and R. B. Warrington, “Stable radio-frequency transfer over optical fiber by phase-conjugate frequency mixing,” Opt. Express, vol. 21, no. 16, p. 18754–18764, 2013. [7] O. Lopez, A. Amy-Klein, M. Lours, Ch. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B, vol. 98, no. 4, pp. 723–727, 2010. [8] Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas., vol. 60, no. 4, pp. 1480–1488, 2011. [9] B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5x10−19 accuracy level,” Sci. Rep., vol. 2, art. no. 556, 10.1038/srep00556, 2012. [10] O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, Ch. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B, vol. 110, no. 1, pp. 3–6, 2013.

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