Passive Optical Phase Stabilization on a Ring Fiber Network
Liang Hu, Xueyang Tian, Long Wang, Guiling Wu, Jianping Chen
JJOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 1
Passive Optical Phase Stabilization on a Ring FiberNetwork
Liang Hu,
Member, IEEE,
Xueyang Tian, Long Wang, Guiling Wu,
Member, IEEE, and Jianping Chen
Abstract —Optical frequency transfer provides the means forhigh-fidelity frequency transfer across thousands of kilometers. Acritical step in the further developing optical frequency transferis its capability to transfer a high spectral purity feature fromultrastable lasers or optical clocks to any remote locations and,at the same time, its adaptability to incorporate the opticalfrequency transfer technique into any existing communicationnetworks with different topologies. Here we for the first timereport a technique that delivers optical-frequency signals to mul-tiple independent remote hubs along a ring optical-fiber networkwith passive phase stabilization. The technique automaticallycorrects optical-fiber length fluctuations of arbitrary hubs alongthe loop by mixing and shifting optical signals. Without thehelp of an active phase tracker and a compensator, it couldsignificantly mitigate some technical problems such as the limitedcompensation speed and phase recovery time, the phase jittercontamination caused by the servo bump in conventional phasenoise cancellation. Moreover, by transmitting optical signals alongboth directions using the same optical source, it can improvethe signal-to-noise ratio at each hub. This technique maintainsthe same delay-limited phase noise correction capability as inconventional techniques and, furthermore, improves the phasejitter by a factor of 3, opening a way to a broad distribution ofan ultrastable frequency reference with high spectral purity andenabling a wide range of applications beyond metrology over aring fiber network with the naturally impressive reliability andscalability.
Index Terms —Optical clock, optical frequency transfer, passivephase stabilization, ring fiber network, metrology.
I. I
NTRODUCTION P RECISION timekeeping is a prerequisite for so manyapplications, ranging from navigation [1], [2], commu-nication networks, radio astronomy [3], [4] to searching forbeyond-standard-model physics [5], [6]. Today’s most preciseclocks are optical clocks with trapped atoms or ions, whichuse the ultrastable lasers to detect the optical frequency ofan electron transitioning between two atomic states as thetimebase [7], [8], [9]. The outstanding performance makes theoptical clocks and ultrastable lasers become ideal tools for
Manuscript received xxx xxx, xxx; revised xxx xxx, xxx. This workwas supported in part by the National Natural Science Foundation ofChina (NSFC) (61627871, 61535006, 61905143), and in part by sci-ence and technology project of State Grid Corporation of China (No.SGSHJX00KXJS1901531). (
Corresponding author: Liang Hu and GuilingWu )The authors are with the State Key Laboratory of Advanced Optical Com-munication Systems and Networks, Department of Electronic Engineering,Shanghai Jiao Tong University, Shanghai 200240, China, with ShanghaiInstitute for Advanced Communication and Data Science, Shanghai JiaoTong University, Shanghai 200240, and also with Shanghai Key Laboratoryof Navigation and Location-Based Services, Shanghai 200240, China (e-mail: [email protected]; [email protected]; wl − [email protected]; [email protected]; [email protected]) precision measurements and fundamental physics tests, suchas general relativity, temporal variation of the fundamentalconstant [10], searching for dark matter, chronometric geodesy[11], and gravitational waves [12], [13], [14]. However, theseclocks and ultrastable lasers are cumbersome and expensiveand only available at national metrology institutes and severaluniversities [7], [8], [15]. This causes a strong motivationto develop effective systems for comparing and distributingthese sources of ultraprecise frequency signals. Among them,the fiber-optic frequency dissemination technique has beenrecognized as an ideal solution for ultra-long haul dissemi-nation because of fiber-optic’s particular advantages of broadbandwidth, low loss, and high immunity to environmentalperturbations, etc [16].Solutions based on fiber transmission have been aiming forsuppressing the fiber-induced phase noise to retrieve precisefrequency information at remote locations. To achieve this aim,active compensation schemes as first demonstrated in 1994by Ma et al. have been proposed to cancel the fiber-inducedphase drift and implement highly stable optical frequencydistribution [16], [17], [18], [19]. It generally utilizes thephase error from a round-trip probe signal to achieve thefeedback control of compensators. The compensators mainlyinclude variable delay lines [20] and phase-locked loops (PLL)[16]. Although this scheme can accomplish very high phasestability, the response speed and phase recovery time arerestricted by the compensators’ parameters and optimization.Moreover, much attention has paid into the relative long-term frequency instability and accuracy, while little into highspectral purity of the transferred light. The possibility oftransferring the spectral purity of an ultrastable laser acrossdifferent locations is beneficial to the increasing requirementof high frequency stability lasers for optical atomic clocksand high-resolution spectroscopy [21], [22]. Optical frequencytransfer with high spectral purity enables such performances tobe copied to any laser in any locations, with a simplificationof the experimental setup. This is especially relevant whenseveral ultrastable lasers at different locations are needed, butonly one ultrastable cavity or clock exists.In order to surmount the above mentioned barriers, passivephase noise cancellation has drawn extensive attention forfiber-optic radio frequency transfer [23], [24]. The passivephase noise cancellation technique can realize rapid and end-less phase fluctuation compensation, and also get rid of com-plicated phase error detection and feedback circuits. However,the passive phase noise cancellation technique used for RFfrequency transfer is not directly applicable for fiber-basedoptical frequency dissemination by multiplying and dividing a r X i v : . [ phy s i c s . i n s - d e t ] F e b OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 2
Fig. 1. A prospect hybrid ring and bus fiber topologies for the dissemination of optical frequency to academic labs, industrial and scientific applications usedfor navigation, communication networks, radio astronomy and precise test of relativistic geodesy. A ring is created with some number of optical frequencyhubs. Each hub on the ring then acts as the center of the star with multiple point-to-point links emanating and terminating at various remote nodes. the frequency of the transferred optical carrier, such as 1550nm, itself. In our previous work, we have extended the passivephase noise cancellation technique in optical frequency trans-fer by detecting and compensating optical phase noise withdifferent optical signals along the single path [25]. The maindrawback related to this technique is the different frequenciesbetween the detection and the compensation beam, leading tothat two different frequencies will be received at the remotesite and, therefore, a narrow bandpass optical filter has tobe adopted to remove the undesired signal, which may causeadditional decoherence on the transferred light.Over the last decade, extensions have been proposed thatcan provide stabilized optical-frequency signals at interme-diate sites along the length of optical fiber [26], [27], [28],[29]. However, as phase stabilization at the intermediate sitesachieved by mixing signals received from the source and thefar end of the fiber, this approach is limited to fiber linkswith a bus topology. Moreover, if the stabilization servo ofthe main link fails, then transfer to all downstream remotesites will cease to be stabilized. To overcome this maindrawback, ultrastable optical frequency dissemination schemeson a star topology optical fiber network have been proposedand demonstrated [29], [30], [31]. Using this method, a highlysynchronized optical signal itself can be recovered at arbitraryremote locations by actively compensating the phase noise ofeach fiber link at each user end [29], [30], [31]. However, themaximum node accommodation capability will be limited bythe radio frequency (RF) bandwidth of AOMs to distinguishthe optical frequency between the accommodated nodes andthe bandwidth of the electrical bandpass filters. Moreover, theexisting schemes to support optical communication based onbus and star topologies have limited scalability and reliability[32], [33], [34]. On the contrary, because of the self-healingcharacteristic of the ring network, in particular, the dual-fiberring, has a natural advantage in the network reliability [35].Although the number of fibers required in the dual-fiber ringdoubles that in the single-fiber ring, the dual-fiber ring networkhas a protection mechanism and can carry out the protection of multiple faults, resulting in shortening the recovery timeand possessing higher reliability [36], [37]. In addition, bydeploying optical amplifiers in remote nodes, the scale of thering network can be increased dramatically [38]. With thecontinuous extension of the optical frequency transfer network,the reliability and scalability will become more important[33], [34], [30]. Owing to the prominent advantages, theperformance and compatibility of optical frequency transferon a fiber ring network have to be investigated theoreticallyand experimentally.In this paper, a passive arbitrary-access stable optical phasedelivery scheme based on a ring fiber network is proposed andexperimentally demonstrated. In comparison with the previousschemes [16], [17], [18], [19], precise phase correction isobtained by embedding the phase information into an RFsignal and shifting a copy of the optical frequency signalwith the amount of phase noise introduced by the fiber loopto avoid having to actively stabilize the optical frequencysignal. The scheme we proposed largely simplifies the setupat the central station and the hubs simultaneously, and leavesthe hubs to independently control the fiber noise cancellationsystems as performed in [29], [30], [31]. Moreover, with theproposed configuration, one of the directions will only provideone optical signal at each hub’s output instead of two opticalsignals [25].The proposed technique together with optical frequencytransfer over a star topology [29], [30], [31] provides a promis-ing way to implement a robust optical frequency transfernetwork as illustrated in Fig. 1. Depending on the size anddistance of the network, a ring can be created with some num-ber of optical frequency hubs which are all connected togetherto keep failure rate as low as possible. At the same time, thevarious hubs on the ring then act as the center of the starwith multiple point-to-point links, emanating and terminatingat various remote nodes. These individual remote nodes maybe subject to failure, so they are generally located at non-critical positions and can accept occasional outages. The ring,on the other hand, keeps the hubs communicating constantly
OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 3
Fig. 2. Schematic diagram of our optical frequency transfer over a ring fiber network with passive phase stabilization. We tapped bidirectional lights with theassistance of a × optical coupler at each hub. The optical phase introduced by environment perturbations on the fiber links is passively compensated ateach hub. Electrical bandpass filters are not shown for conciseness. AOM: acousto-optic modulator, FM: Faraday mirror, DDS: direct-digital synthesizer, PD:photo-detector, FD: frequency divider, PC: power combiner. The solid and dashed arrows represent the light propagation along the clockwise and anticlockwisedirections, respectively. and makes the overwhelming majority of the network fault-free [33], [34], [30]. This hybrid optical frequency transfernetwork could be used in probes of fundamental physics anddetection of submarine earthquakes by means of deep-sea fibercables [39], among other applications [10], [11], [12], [13],[14]. At the same time, with the assistance of optical combs,stable and accurate microwave signals can be obtained andcan be used in a variety of areas including communication,navigation, radar, radio astronomy, and fundamental physicsresearch as illustrated in Fig. 1.The article is organized as follows. We illustrate the conceptof coherent optical phase dissemination with passive opticalphase stabilization on a ring fiber link in Sec. II and present inSec. III the delay limited phase-noise power spectral density(PSD). We discuss the experimental set-up and experimentalresults in Sec. IV and illustrate representative features relatedto the proposed scheme in V. Furthermore, we briefly presenta discussion in Sec. VI. Finally, we conclude in Sec. VII bysummarizing our results.II. C ONCEPT OF OPTICAL FREQUENCY TRANSFER ON ARING FIBER NETWORK
A schematic diagram of the proposed technique is illustratedin Fig. 2. Here we briefly describe the principle of our opticalfrequency transfer on a ring fiber link. An optical-frequencysignal ν is divided into 2. The two parts are, respectively, sentfrom the signal source to the central site along the clockwiseand anticlockwise directions over a ring fiber link. The laserfrequency ν propagating clockwise is again split into 2. Onepart is reflected by a Faraday mirror as a reference signal andthe remaining one is downshifted by an angular frequency ω s with an acousto-optic modulator (AOM) denoted as AOM c .The laser frequency propagating anticlockwise is directlyinjected into the fiber loop, passes through the fiber loop andthen returns back in the AOM c located at the central site. Thesingle-trip signal propagating along the anticlockwise directionis mixed with the input ultrastable laser onto a photodetector 1 (PD1). The beat-note frequency is ω s , exhibiting the single-trip fiber phase noise, − φ p . After mixing with an anotherfrequency of ω a ( ω a > ω s ) with the assistance of a frequencymixer, the lower sideband signal is extracted and then appliedto the RF port of the AOM c together with ω s , resulting in adesirable clockwise optical signal with the angular frequencyof ν − ω a + ω s .Now we consider the extraction of the ultrastable signalalong the fiber loop with a × optical coupler, enabling usto extract both the clockwise and anticlockwise signals fromthe loop fiber link, at a distance L a from the central site alongthe clockwise direction and L b from the central site along theanticlockwise direction with the total fiber link length of L ( L = L a + L b ). The anticlockwise signal has a frequency ν and exhibits the phase fluctuation of φ b , and the desirableclockwise signal with the angular frequency ν − ω a + ω s atarbitrary hubs exhibits the phase fluctuations − φ p + φ a = − φ b ,where φ a and φ b are the phase noise of the fiber sections L a and L b , respectively. To compensate the phase noise ofthe anticlockwise wave, we detect the beat-note of the twoextracted signals onto the PD2. The beat-note frequency isthus ω a − ω s , exhibiting a phase fluctuation of φ b . Thesignal frequency is divided by 2, filtered, and drives an AOM(AOM a , − order) to correct the phase fluctuations of theextracted anticlockwise signal. The frequency of the extractedanticlockwise signal, after passing through the AOM a , is thusdownshifted to ν − . ω a − ω s ) and its phase fluctuation iscancelled. With this configuration, the anticlockwise directiononly includes one phase stabilized optical signal. Compared toour previous passive phase noise cancellation schemes [25],this represents another advantage, that is, no optical filtersare required to remove the unwanted optical signal. Similarcompensation can be obtained on the extracted clockwisesignal with a positive optical frequency shifter. However, inthis case, the clockwise direction signal includes two opticalfrequencies and needs an optical filter after the AOM a to selecta stable optical frequency signal, which could introduce an OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 4 additional decoherence effect [25].We can clearly see that the optical signal received atarbitrary hubs has the same phase with the standard opticalsignal at the central station. Therefore, the phase noise ofthe optical signal is effectively reduced by simply mixing andshifting optical signals.III. D
ELAY - LIMITED PHASE NOISE
PSDIn Sec. II, the description does not take the propagationdelay of the fiber sections into account. The capability ofthe phase noise rejection will be limited by the propagationdelay as first pointed out by Williams et al. [40]. By adoptingthe similar procedure performed in [28], [40], we find thatthe residual phase noise power spectral density (PSD) atan arbitrary hub along the fiber section L b in terms of thesingle-pass free-running phase noise PSD, S fiber ( ω ) , and thepropagation delay of the fiber loop, τ , can be calculated as, S E,b − ( ω ) = F E,b − ( ωτ ) S fiber ( ω )= ( ωτ ) (cid:32) − L b L τ b τ + 2 L b L (cid:18) τ b τ (cid:19) (cid:33) S fiber ( ω ) . (1)where τ b is the proragation delay along the fiber section L b .This coefficient factor F E,b − is zero for L b = L , then increasesup to one at L b = 0 . Following the same procedure, if weapply the phase correction for the clockwise light, the residualphase noise PSD at arbitrary hubs can have a form of, S E,a + ( ω ) = F E,a + ( ωτ ) S fiber ( ω )= ( ωτ ) (cid:32) − L a L τ a τ + 2 L a L (cid:18) τ a τ (cid:19) (cid:33) S fiber ( ω ) . (2)where τ a is the proragation delay along the fiber section L a .IV. E XPERIMENTAL APPARATUS AND RESULTS
A. Experimental apparatus
We have demonstrated this technique by using the simplestconfiguration as shown in Fig. 2. The interferometer is builtwith fiber optics. The proposed scheme was tested using anarrow-linewidth optical source (NKT X15) at a frequencynear 193 THz with a linewidth of 100 Hz. The signal wastransmitted along a 100 km fiber link loop. × optical cou-plers were used to extract both clockwise and anticlockwiselight at the most symmetric position, 50/50 km ( L a /L b ), and arelative most asymmetric one, 30/70 km, over the 100 km ringfiber link. Here we set ω s = 2 π × MHz and ω a = 2 π × MHz. Before dividing the frequency of the beatnote at thehub, we mix the beatnote with an assistant frequency of
MHz, and the lower sideband with a frequency of 80MHz is extracted. All these RF frequencies are provided by adirect-digital-synthesizer (DDS) generator, phase locked to a10 MHz rubidium clock. With this configuration, the AOM c is simultaneously fed by MHz and MHz (downshiftedmode), and the AOM a is working at an angular frequency of 40 MHz (upshifted mode), resulting in an out-of-loop beatnoteof MHz for arbitrary hubs. To avoid the nonlinear effectin the fiber, we keep the optical power into the ring fiberlink below 5 dBm for each optical frequency: one for theanticlockwise direction ( ν ) and two for the clockwise direction( ν − π × MHz and ν − π × MHz). However, in theconventional configuration [28], the light transferred to theremote site will directly return back to the local site, resultingin the power of the returning light of − dBm at the remotesite for the 100 km fiber link when the injection power is 5dBm at the local site and fiber loss is . dB per kilometer.Consequently, we can obtain the gain of the signal-to-noiseratio of approximately 20 dB without the assistance of opticalamplifiers in the proposed scheme.To effectively measure the transfer stability at each hub,all hubs are co-located at the same optical platform as thesignal source. The out-of-loop fiber connections were keptas short as practicable and were thermally and acousticallyisolated. We use non-averaging Π -type frequency counters,which are referenced to the RF frequency source from the DDSat the central site, to record the beating frequency betweenthe fiber input light and the output light. Additionally, tomeasure the phase noise of the optical carrier frequenciesat each hub, we perform the measurement by feeding theheterodyne beat frequency together with a stable RF frequencyreference produced by the DDS to a phase detector. Thevoltage fluctuations at the phase detector output are thenmeasured with a fast Fourier transform (FFT) analyzer toobtain the phase fluctuations. B. Testing the phase noise rejection on hubs
To characterize optical transfer over the 100 km ring fiberloop, we measured the phase noise PSDs of the 50/50 kmhub and the 30/70 km hub for both the stabilized and theunstabilized cases. Typically, the phase noise PSD is usuallyparametrized as [41], [42], S φ ( f ) = (cid:88) α = − h α f α − , (3)where f α ( α = − , − , , and 2), reflecting the various con-tributions of noise in the system (i.e., random walk frequencynoise, flicker frequency noise, white frequency noise, flickerphase noise and white phase noise).The phase noise PSDs of the 50/50 km hub and the 30/70km hub are plotted in Fig. 3(a). Both hubs are very similarand typical for optical fiber links, with noise of approximately200 rad /Hz at 1 Hz and × − rad /Hz at 100 Hz witha h f − dependency, indicating that the phase noise of thefree-running loop is mainly limited by the flicker phase noise.Both compensated phase noise PSDs are below − rad /Hzbetween 1 and 10 Hz with a h f dependency, illustrating thatthe loop is mainly constrained by the white phase noise afterthe phase noise compensation. Noise is corrected up to about400 Hz, which is compatible with the theoretical bandwidth of500 Hz given by / (4 τ ) with τ being the propagation delayof fiber loop L = 100 km. This limit is the same for both hubsand is mainly determined by the longest propagation delay τ . OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 5
Fig. 3. (a) Measured phase noise PSDs of the 100km free-running fiber link (black curve) and the stabilized link with passive phase noise cancellation forthe 50/50 km hub( c , red curve) and the 30/70 km ( b , blue curve) hub. Note that strong servo bumps can be effectively eliminated in the passive phase noisecancellation scheme. The green curve is the theoretical prediction based on Eq. 1. (b) Measured fractional frequency instabilities of the 100 km free-runningfiber link (black circles) and the stabilized link for the 50/50 km (red squares) hub and the 30/70 km (blue triangles) hub. The measurement is derived fromnon-averaging ( Π -type) frequency counters expressed as ADEV. The measured noise floor of the interferometer is also shown (gray diamonds). We checked that the noise floors of both outputs were belowthese PSDs. The noise rejection of around × at 1 Hz isalso compatible with the theoretical limit given by Eq. 1 asthe green curve shown in Fig. 3(a). This shows that the noiserejection is optimized. C. Time-domain characterization
A time-domain characterization of the frequency stability interms of overlapping Allan deviation (ADEV) is shown in Fig.3(b). In this plot, black circle markers indicate the fractionalfrequency stability of optical carrier frequency disseminationover the 100 km link when passive phase noise cancellationis not activated. Curves with square and triangle markersrepresent the stability of the signals with implementing passivephase noise correction for the / km hub and the / kmhub, respectively. With the implementation of fiber noise can-cellation at the / km ( / km) hub, optical frequencytransfer achieves a fractional frequency stability of . × − ( . × − ) at the integration time of s, decreases andreaches a floor of approximately . × − ( . × − ) at , s.We can clearly see that when the fiber noise cancellationsetups are engaged, frequency fluctuations can be effectivelysuppressed and no longer dominate the instability of the opticalsignals at both hubs. In our experiment, we observe that thestability of optical frequency dissemination is improved bythree orders of magnitude at the integration time of 10,000s. Note that the noise correction is very robust and that theset-up can operate several days without any cycle slips. Asa comparison, we measured the floor of optical frequencydissemination by replacing each fiber spool with a 1 m fiberplus a 20-dB attenuator. We can observe that the floor ofoptical frequency dissemination with a stability of . × − at 1 s and . × − at 10,000 s is obtained. Consequently,the stabilized link is mainly limited by the noise floor. There are several reasons that lead to the floor in the instabilityincluding the noise of the imperfect length adjustment andthermal stabilization in the extraction optical set-up, andthe interferometric measurement set-up [43], [17], [18]. Weestimate the path length mismatch up to cm. For typicaltemperature perturbations due to our air conditioning system,with the temperature fluctuation amplitude K and cycle 3,600 s, one expects a bump of the ADEV as high as × − at approximately 1,800 s [44].As calculated by Eq. 1, the ratio of the stability of the / km and / km hubs should be R = 0 . . In our experi-ment, we obtain the ratio of R = 1 . × − / . × − =0 . , which has a large deviation from the theoretical one. Weattribute this discrepancy to the phase noise introduced by thehub itself such as the photo-detection process. We have to notethat the estimation in Eq. 1 acquired by the assumption thatthe hub will introduce negligible phase noise. In our system,the phase noise introduced by the hub itself dominates the totalphase noise of the hub at the short fiber section L b whereas theresidual phase noise of the fiber link becomes the dominationwhen the fiber section L b is long enough, enabling that themeasured results are consistent with the theoretical one asincrease of the fiber section L b . D. Frequency transfer accuracy
We also performed an evaluation of the accuracy of fre-quency transfer at arbitrary hubs. Figure 4 shows the fre-quency deviation of the beat-note’s data for the 50/50 kmhub, recorded with a 1 s gate time and Π -type counters,over successive 180,300 s (green point, left axis) and thearithmetic mean of all cycle-slip free 100 s intervals (blackdots, right axis). Histograms (brown bars) and Gaussian fits(red curves) of a frequency deviation for the hub after 50km are also illustrated in Fig. 4(b) and (c). According to theGaussian fit in Fig. 4(c), the calculated results demonstrate OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 6
Fig. 4. (a) Two-day frequency comparison between sent and transferredfrequencies after 50 km over the 100 km ring fiber. Data were taken withdead-time free Π -type frequency counters with a 1 s gate time (green points,left axis). We calculated unweighted mean ( Π -type) values for all cycle-slipfree 100 s long segments, resulting in 1,803 data points (black dots, rightfrequency axis, enlarged scale). Histograms (brown bars) and Gaussian fits(red curves) for (b) frequency values as taken with Π -type frequency counterswith one second gate time and (c) 1,803 phase coherent 100-second frequencyaverages with a mean of . × − and a standard deviation of . × − .Taking the long-term stability shown in Fig. 3(b) into account, we determinethe statistical uncertainty to be × − . that the mean frequency is shifted by 435 µ Hz ( . × − ).The standard deviation of the 100 s data points is . mHz( . × − ) which is a factor of 100 smaller than the ADEVat 1 s as expected for this Π -type evaluation. Consideringthe long-term stability of frequency transfer as illustrated inFig. 3(b) mainly limited by the flicker frequency noise, weconservatively estimate the accuracy of the transmitted opticalsignal as shown in the last data point of the ADEV, resultingin a relative frequency accuracy of × − .Following the same procedure, the mean frequency offsetfor the 30/70 km hub was calculated using the total 40,069 Π -type counter data to be -812 µ Hz ( − . × − ) and astandard deviation of the 100 s points is . mHz ( . × − ).Considering the long-term ADEV at 10,000 s of the dataset for the 30/70 km hub of . × − , we conservativelyestimate that the mean frequency offset is − . × − witha statistical uncertainty of . × − for the 30/70 km hub.We can conclude that there is no systematic frequency shiftarising in the extraction setup at a level of a few − .V. R EPRESENTATIVE FEATURES IN THE PROPOSEDTECHNIQUE
The above section is mainly devoted to characterizingthe results of our scheme from the perspective of conven-tional optical frequency transfer parameters consisting of thefractional frequency stability, the phase noise PSD and theaccuracy as performed in most existing research work [16],[17], [18], [19]. In this section, we will theoretically study and experimentally demonstrate the representative features ofour proposed scheme, that is, a ring fiber network with passivephase stabilization, including the lower phase jitter and fasterphase recovery capability.
A. Lower phase noise and timing jitter
For active phase noise cancellation system similar with[40], the closed-loop transfer function at arbitrary hubs alongthe anticlockwise direction in the frequency domain can beexpressed as, H A ( ω ) = F E,b − (cid:90) L dz exp( − iω ( τ + z/c n )) × (cid:20) exp( − iω ( z/c n )) − cos( ωτ − ωz/c n )cos( ωτ ) G ( ω )1 + G ( ω ) (cid:21) (4)where G ( ω ) is the open-loop transfer function of the compen-sation system, L is the fiber link length and c n is the speedof light in the fiber.With the same procedure adopted in [40], [28], the transferfunction in our passive phase stabilization set-up at arbitraryhubs along the anticlockwise direction can be calculated as, H P ( ω ) = F E,b − (cid:20) − cos( ωτ ) − sinc ( ωτ ) + 12 sinc (2 ωτ ) (cid:21) (5)Figure 5(a) shows the calculated phase noise PSDs for thestabilized link at the 50/50 km hub by using active (blue solidcurve) and passive (red dashed curve) phase noise cancellationsystem with the phase noise PSD of the 100 km free-runninglink of /f rad /Hz. In typical servo controllers, the gainhas to be tuned large enough to maintain a sufficient phasenoise rejection capability. The infinite gain will lead to thedivergence of the gain for frequencies equal to integer multipleof f = 1 / (4 τ ) = 500 Hz. Here the servo bandwidth ismainly limited by the total fiber length instead of the fibersections ( L a and L b ). It is interesting to note this issue isautomatically disappeared in the passive phase stabilizationset-up with the optimized gain. To calculate the ratio ofthe phase jitter between the active and passive phase noisecancellation technique, we integrate the phase noise from 1 Hzto 1 kHz as shown in Fig. 5(b). We can see that more than oneorder of magnitude of the reduction of the phase jitter can beachieved for the proposed phase noise cancellation technique.Note that the integration results for the active phase noise PSDare dependent on the frequency resolution of the simulation.Here the frequency resolution is 1 Hz and the phase jitter willincrease more as improving the frequency resolution due tothe diverged bump effect.To experimentally verify the calculated results, we used theset-up shown in Fig. 2 as the passive phase noise system. Theactive phase noise system we used is similar with our previousmultiple-access optical frequency transfer system [45]. Figure5(c) shows the residual phase noise PSDs at the / kmhub over the 100 km fiber link with passive ( a , red dashedcurve) and active ( b , blue solid curve) phase cancellation. Inactive phase noise cancellation, the residual phase noise isessentially limited by the residual fiber noise in the range from OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 7
Fig. 5. (a) Blue solid curve and red dashed curve show, respectively, the residual phase noise PSDs with the active and passive phase noise cancellationsystem for the phase noise PSD of the free-running fiber link /f rad /Hz. To maintain a sufficient phase noise rejection capability, the gain has to betuned large enough, leading to the divergence of the gain amplitude for frequencies equal to integer multiple of f = 1 / (4 τ ) . (b) The phase jitter integratedfrom 1 Hz to 1 kHz for the active (blue solid curve) and passive (red dashed curve) phase noise cancellation system, respectively. (c) Measured phase noisePSD at the 50/50 km hub over the 100-km optical link with passive ( a , red dashed curve) and active ( b , blue solid curve) phase cancellation. Black linesrepresent the extrapolated noise components. Active phase noise cancellation appears a strong servo bump compared to passive phase cancellation. (d) Thephase jitter integrated from 1 Hz to 1 kHz is ∼ . rad and ∼ . rad for the active (blue solid curve) and passive (red dashed curve) phase noise cancellationsystem, respectively. As a comparison, the phase jitter integrated from 1 Hz to 100 Hz for the active ( d , blue dashed dot curve) and passive ( c , red longdashed curve) phase noise cancellation systems, respectively is also shown. ∼ Hz, with a strong bump appearing significantlyat 300 Hz. The shifted bump position from f = 500 Hzcould be from the insufficient gain in the servo controller. Onthe contrary, the spectral analysis does not report any strongnoise contribution in the 300 Hz range with passive phasenoise cancellation, allowing that the bump does not play arole in our passive optical phase noise cancellation concept.The total integrated phase noise (1 Hz to 1 kHz) of the datain Fig. 5(d) for active (blue solid curve) and passive (reddashed curve) phase noise cancellation are 3.2 rad and 1.0rad, which corresponds to temporal jitters of ∼ f s and825 as, respectively, enabling the reduction of the phase jitterby a factor of about 3 by adopting passive phase stabilization.As a comparison, the phase jitter integrated from 1 Hz to 100Hz is almost identical for both cases as shown in Fig. 5(d).The main bottleneck of our detection scheme is the round-trippropagation delay, limiting the servo bandwidth. This can besolved by dividing the fiber link into several sub-links whichcould serve to further reduce the round-trip propagation delay,resulting in the improvement of the signal-to-noise ratio in ourscheme [46]. B. Faster response speed and phase recovery time
To examine the characterization of the faster response speedand phase recovery time, we compared two kinds of opticalfrequency transfer schemes described above over a 20 km fiber link as performed in [25]. To simulate the interruption, weinset one more AOM just after the laser source to switchthe light on/off. The RF port of the AOM is controlled bya TTL signal which has a rising time of ∼ ns, which canbe neglected. Both systems’ output was analyzed based onthe voltage generated by mixing down the out-of-loop beat tothe dc. Figure 6 illustrates the phase recovery time of 20 kmoptical path length stabilization with active and passive phasecorrection. We observed that the phase recovery time of opticalpath length stabilization with active phase noise cancellationhas a few strongly damped oscillations of the phase lastingapproximately ∼ ms, whereas this time is negligible forour proposed passive phase noise cancellation. This feature isvery beneficial for the case in which the interruptions happenfrequently on the long fiber links [17], [18], [19].VI. D ISCUSSION
The above analysis has ignored the effect of the backscat-tering noise on the frequency transfer performance. Small-scale inhomogeneities of the refractive index in the fiber causeRayleigh scattering of the transferring waves. In our case,the backscattered clockwise wave returns to the access huband is superimposed upon the extracted anticlockwise wave.Similarly, the backscattered anticlockwise wave returns to theaccess hub and is superimposed upon the extracted clockwisewave. Consequently, the Rayleigh scattering effect can not
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Fig. 6. Phase recovery behaviour of the 20 km optical path length stabilizationwith active (red curve) and passive (blue curve) phase correction, respectively.A delay is introduced between the TTL signal (black curve) for switching thelight on at 0 s and the activation of the phase stabilization at τ (cid:39) µ sas indicated by the shaded green area. be completely avoided in our application. According to theresults presented in [45], the Rayleigh backscattering inducedfractional frequency instability can be as low as a few − /τ ( τ being the averaging time) over a 100 km fiber link. Thus,this effect can be neglected at our precision.Our dissemination loop can support multiple hubs si-multaneously. Although there is an insertion loss at everyhub, proper optical amplifiers such as erbium-doped-fiber-amplifiers (EDFA) and electrical amplifiers can be used toamplify the desired optical signals and detected RF signals.Thus, it ensures that multiple hubs can be mapped properlyalong the optical loop link. Though N copies of hardwarefor frequency recovery are needed if N hubs are required, allof these copies have the same configuration including fixedoptical and electronic components with no tunable parts. Itshould be noted that several intermediate hubs along the fiberloop were tested besides the 50/50 km and 30/70 km hubs.Because of the similarity among the test results of differenthubs, we just show the test results of the two representativehubs selected in the loop fiber link, the most symmetric one(50/50 km) and a relative most asymmetric one (30/70 km).VII. C ONCLUSION
In conclusion, we demonstrated a technique for dissemina-tion of high-precision optical-frequency signals to multiple in-dependent hubs on a ring optical-fiber network. The techniqueautomatically corrects optical-fiber length fluctuations of eachhub along the loop. At the same time, using the same opticalsource propagating along both directions can significantlyimprove the signal-to-noise ratio. The results demonstraterelative frequency instabilities, expressed as overlapping Allandeviation of . × − at 1 s averaging time, scalingdown to . × − at 1,000 s with a τ − dependency atthe intermediate hub over a 100 km fiber ring. A similarperformance is also demonstrated at another hub. We find no systematic offset between the sent and transferred frequencieswithin the statistical uncertainty of about × − .This technique with passive phase compensation maintainsthe same phase noise rejection capability as in conventionaltechniques and significantly shortens the response speed andphase recovery time of optical frequency dissemination andreduces the phase jitter by a factor of 3 compared to theconventional technique, opening a way to a broad distributionof an ultrastable frequency reference with high spectral purityand enabling a wide range of applications beyond metrologyover reliable and scalable ring fiber networks.R EFERENCES[1] A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Opticalatomic clocks,”
Rev. Mod. Phys. , vol. 87, no. 2, p. 637, 2015.[2] F. Riehle, “Optical clock networks,”
Nat. Photonics , vol. 11, no. 1, pp.25–31, 2017.[3] Y. He, K. G. Baldwin, B. J. Orr, R. B. Warrington, M. J. Wouters, A. N.Luiten, P. Mirtschin, T. Tzioumis, C. Phillips, J. Stevens et al. , “Long-distance telecom-fiber transfer of a radio-frequency reference for radioastronomy,”
Optica , vol. 5, no. 2, pp. 138–146, 2018.[4] C. Clivati, R. Ambrosini, T. Artz, A. Bertarini, C. Bortolotti, M. Frittelli,F. Levi, A. Mura, G. Maccaferri, M. Nanni et al. , “A VLBI experimentusing a remote atomic clock via a coherent fibre link,”
Sci. Rep. , vol. 7,p. 40992, 2017.[5] K. Van Tilburg, N. Leefer, L. Bougas, and D. Budker, “Search forultralight scalar dark matter with atomic spectroscopy,”
Phys. Rev. Lett. ,vol. 115, no. 1, p. 011802, 2015.[6] M. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko,and C. W. Clark, “Search for new physics with atoms and molecules,”
Rev. Mod. Phys. , vol. 90, no. 2, p. 025008, 2018.[7] G. E. Marti, R. B. Hutson, A. Goban, S. L. Campbell, N. Poli, and J. Ye,“Imaging optical frequencies with µ Hz precision and . µ m resolution,” Phys. Rev. Lett. , vol. 120, p. 103201, Mar 2018.[8] M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano,K. Beloy, T. Yoon, G. Milani, D. Nicolodi, J. A. Sherman et al. , “Ul-trastable optical clock with two cold-atom ensembles,”
Nat. Photonics ,vol. 11, no. 1, pp. 48–52, 2017.[9] W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Sch¨affer, K. Beloy,D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H.Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesybelow the centimetre level,”
Nature , vol. 564, no. 7734, pp. 87–90, 2018.[10] R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. M¨uller, “Measurementof the fine-structure constant as a test of the standard model,”
Science ,vol. 360, no. 6385, pp. 191–195, 2018.[11] J. Grotti, S. Koller, S. Vogt, S. H¨afner, U. Sterr, C. Lisdat, H. Denker,C. Voigt et al. , “Geodesy and metrology with a transportable opticalclock,”
Nat. Phys. , vol. 14, no. 5, pp. 437–441, 2018.[12] S. Kolkowitz, I. Pikovski, N. Langellier, M. D. Lukin, R. L. Walsworth,and J. Ye, “Gravitational wave detection with optical lattice atomicclocks,”
Phys. Rev. D , vol. 94, no. 12, p. 124043, 2016.[13] P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Newmethod for gravitational wave detection with atomic sensors,”
Phys. Rev.Lett. , vol. 110, no. 17, p. 171102, 2013.[14] L. Hu, N. Poli, L. Salvi, and G. M. Tino, “Atom interferometry with theSr optical clock transition,”
Phys. Rev. Lett. , vol. 119, no. 26, p. 263601,2017.[15] M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical latticeclock,”
Nature , vol. 435, no. 7040, p. 321, 2005.[16] L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same opticalfrequency at two places: accurate cancellation of phase noise introducedby an optical fiber or other time-varying path,”
Opt. Lett. , vol. 19, no. 21,pp. 1777–1779, 1994.[17] K. Predehl, G. Grosche, S. Raupach, S. Droste, O. Terra, J. Alnis,T. Legero, T. H¨ansch, T. Udem, R. Holzwarth et al. , “A 920-kilometeroptical fiber link for frequency metrology at the 19th decimal place,”
Science , vol. 336, no. 6080, pp. 441–444, 2012.[18] S. Droste, F. Ozimek, T. Udem, K. Predehl, T. H¨ansch, H. Schnatz et al. ,“Optical-frequency transfer over a single-span 1840 km fiber link,”
Phys.Rev. Lett. , vol. 111, no. 11, p. 110801, 2013.
OURNAL OF LIGHTWAVE TECHNOLOGY, VOL. XXX, NO. XXX, MARCH 2020 9 [19] D. Calonico, E. Bertacco, C. Calosso, C. Clivati, G. Costanzo, M. Frit-telli, A. Godone, A. Mura, N. Poli, D. Sutyrin et al. , “High-accuracycoherent optical frequency transfer over a doubled 642-km fiber link,”
Appl. Phys. B , vol. 117, no. 3, pp. 979–986, 2014.[20] O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli,“High-resolution microwave frequency dissemination on an 86-km urbanoptical link,”
Appl. Phys. B , vol. 98, no. 4, pp. 723–727, 2010.[21] I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le Coq, C. W.Oates, Q. Quraishi, and K. o. Feder, “Coherent optical link over hundredsof metres and hundreds of terahertz with subfemtosecond timing jitter,”
Nat. Photonics , vol. 1, no. 5, p. 283, 2007.[22] B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall,C. Chardonnet, C. Daussy, B. Darqui´e, Y. Le Coq, and A. Amy-Klein,“Quantum cascade laser frequency stabilization at the sub-Hz level,”
Nat. Photonics , vol. 9, no. 7, p. 456, 2015.[23] S. Pan, J. Wei, and F. Zhang, “Passive phase correction for stable radiofrequency transfer via optical fiber,”
Photonic Netw. Commun. , vol. 31,no. 2, pp. 327–335, 2016.[24] Y. He, B. J. Orr, K. G. Baldwin, M. J. Wouters, A. N. Luiten, G. Aben,and R. B. Warrington, “Stable radio-frequency transfer over optical fiberby phase-conjugate frequency mixing,”
Opt. Express , vol. 21, no. 16, pp.18 754–18 764, 2013.[25] L. Hu, X. Tian, G. Wu, and J. Chen, “Passive optical phase noisecancellation,” arXiv:2003.13421 , 2020.[26] G. Grosche, “Eavesdropping time and frequency: phase noise cancel-lation along a time-varying path, such as an optical fiber,”
Opt. Lett. ,vol. 39, no. 9, pp. 2545–2548, 2014.[27] Y. Bai, B. Wang, X. Zhu, C. Gao, J. Miao, and L. Wang, “Fiber-basedmultiple-access optical frequency dissemination,”
Opt. Lett. , vol. 38,no. 17, pp. 3333–3335, 2013.[28] A. Bercy, S. Guellati-Khelifa, F. Stefani, G. Santarelli, C. Chardonnet,P.-E. Pottie, O. Lopez, and A. Amy-Klein, “In-line extraction of anultrastable frequency signal over an optical fiber link,”
J. Opt. Soc. Am.B , vol. 31, no. 4, pp. 678–685, 2014.[29] S. W. Schediwy, D. Gozzard, K. G. Baldwin, B. J. Orr, R. B. War-rington, G. Aben, and A. N. Luiten, “High-precision optical-frequencydissemination on branching optical-fiber networks,”
Opt. Lett. , vol. 38,no. 15, pp. 2893–2896, 2013.[30] L. Hu, X. Tian, G. Wu, M. Kong, J. Shen, and J. Chen, “Multi-nodeoptical frequency dissemination with post automatic phase correction,”
J. Light. Technol. , 2020.[31] L. Wu, Y. Jiang, C. Ma, H. Yu, Z. Bi, and L. Ma, “Coherence transferof subhertz-linewidth laser light via an optical fiber noise compensatedby remote users,”
Opt. Lett. , vol. 41, no. 18, pp. 4368–4371, 2016.[32] D. Breuer, F. Geilhardt, R. Hulsermann, M. Kind, C. Lange, T. Monath,and E. Weis, “Opportunities for next-generation optical access,”
IEEECommun. Mag. , vol. 49, no. 2, pp. s16–s24, 2011.[33] F. J. Effenberger, “PON resilience,”
J. Opt. Commun. Netw. , vol. 7, no. 3,pp. A547–A552, 2015.[34] P. Chanclou, A. Cui, F. Geilhardt, H. Nakamura, and D. Nesset,“Network operator requirements for the next generation of optical accessnetworks,”
IEEE Netw. , vol. 26, no. 2, pp. 8–14, 2012.[35] K. Gou, C. Gan, X. Zhang, and Y. Zhang, “A tangent-ring opticalTWDM-MAN enabling three-level transregional reconfigurations andshared protections by multipoint distributed control,”
Opt. Commun. ,vol. 410, pp. 855–862, 2018.[36] X. Li, C. Gan, Z. Liu, Y. Yan, and H. Qiao, “Novel WRM-basedarchitecture of hybrid PON featuring online access and full-fiber-faultprotection for smart grid,”
Opt. Commun. , vol. 407, pp. 69–82, 2018.[37] X. Sun, C. Chan, Z. Wang, C. Lin, and L. Chen, “A single-fiber bi-directional WDM self-healing ring network with bi-directional OADMfor metro-access applications,”
IEEE J. Sel. Areas Commun. , vol. 25,no. 3, pp. 18–24, 2007.[38] S. Zhang, W. Ji, X. Li, K. Huang, and Z. Yan, “Efficient and reliableprotection mechanism in long-reach PON,”
J. Opt. Commun. Netw. ,vol. 8, no. 1, pp. 23–32, 2016.[39] G. Marra, C. Clivati, R. Luckett, A. Tampellini, J. Kronj¨ager, L. Wright,A. Mura, F. Levi, S. Robinson, A. Xuereb et al. , “Ultrastable laserinterferometry for earthquake detection with terrestrial and submarinecables,”
Science , vol. 361, no. 6401, pp. 486–490, 2018.[40] P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stabilitytransfer of an optical frequency over long fiber-optic links,”
J. Opt. Soc.Am. B , vol. 25, no. 8, pp. 1284–1293, 2008.[41] J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E.McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. Vessot et al. ,“Characterization of frequency stability,”
IEEE Trans. Instrum. Meas. ,no. 2, pp. 105–120, 1971. [42] J. Rutman, “Characterization of phase and frequency instabilities inprecision frequency sources: Fifteen years of progress,”
Proceedings ofthe IEEE , vol. 66, no. 9, pp. 1048–1075, 1978.[43] S. M. Foreman, A. D. Ludlow, M. H. De Miranda, J. E. Stalnaker,S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1 s instability at − ,” Phys. Rev. Lett. , vol. 99, no. 15,p. 153601, 2007.[44] X. Tian, L. Hu, G. Wu, and J. Chen, “Hybrid fiber-optic radio frequencyand optical frequency dissemination with a single optical actuator anddual-optical phase stabilization,”
J. Light. Technol. , pp. 1–1, 2020.[45] L. Hu, X. Tian, G. Wu, and J. Chen, “Fundamental limitations ofRayleigh backscattering noise on fiber-based multiple-access opticalfrequency transfer,” arXiv:2003.13417 , 2020.[46] O. Lopez, A. Haboucha, F. K´ef´elian, H. Jiang, B. Chanteau, V. Roncin,C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Cascaded multiplexedoptical link on a telecommunication network for frequency dissemina-tion,”
Opt. Express , vol. 18, no. 16, pp. 16 849–16 857, 2010.
Liang Hu received the B.S. degree from Hangzhou Dianzi University, China,in 2011, and the M.S. degree from Shanghai Jiao Tong University, China,in 2014. He received the Ph.D. degree from University of Florence, Italy, in2017 during which he was a Marie-Curie Early Stage Researcher at FACTproject. He is currently a Tenure-Track Assistant Professor in the State KeyLaboratory of Advanced Optical Communication Systems and Networks,Department of Electronic Engineering, Shanghai Jiao Tong University, China.His current research interests include photonic signal transmission and atominterferometry.
Xueyang Tian received the B.S. degree from Shanghai Dianji University,China, in 2017. She is currently a graduate student in the State Key Laboratoryof Advanced Optical Communication Systems and Networks, Department ofElectronic Engineering, Shanghai Jiao Tong University, China. Her currentresearch interests include photonic signal transmission.
Long Wang received the B.S. and M.S. degrees from Harbin Institute ofTechnology, China, in 2017 and 2019, respectively. He has been admitted asa doctoral student in the State Key Laboratory of Advanced Optical Com-munication Systems and Networks, Department of Electronic Engineering,Shanghai Jiao Tong University, China. His current research interests includephotonic signal transmission.
Guiling Wu received the B.S. degree from Haer Bing Institute of Technology,China, in 1995, and the M.S. and Ph.D. degrees from Huazhong Universityof Science and Technology, China, in 1998 and 2001, respectively. He iscurrently a Professor in the State Key Laboratory of Advanced Optical Com-munication Systems and Networks, Department of Electronic Engineering,Shanghai Jiao Tong University, China. His current research interests includephotonic signal processing and transmission.