All-passive multiple-place optical phase noise cancellation
Liang Hu, Ruimin Xue, Xueyang Tian, Guiling Wu, Jianping Chen
LLetter preprint 1
All-passive multiple-place optical phase noisecancellation L IANG H U , R UIMIN X UE , X UEYANG T IAN , G UILING W U , AND J IANPING C HEN State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University,Shanghai 200240, China Shanghai Key Laboratory of Navigation and Location-Based Services, Shanghai 200240, China * Corresponding author: [email protected] February 25, 2021
We report on the realization of delivering coherent opti-cal frequency to multiple places based on passive phasenoise cancellation over a bus topology fiber network.This technique mitigates any active servo controller onthe main fiber link and at arbitrary access places as op-posed to the conventional technique, in which an activephase compensation circuit has to be adopted to stabi-lize the main fiber link. Although the residual fiberphase noise power spectral density (PSD) in the pro-posed technique turns out to be a factor of 7 higher thanthat of in the conventional multiple-access techniquewhen the access place is close to the end of the fiberlink, it could largely suppress the phase noise intro-duced by the servo bumps, improve the response speedand phase recovery time, and minimize hardware over-head in systems with many stations and connectionswithout the need of the active servo circuits includingphase discriminators and active compensators. The pro-posed technique could considerably simplify future ef-forts to make precise optical frequency signals avail-able to many users, as required by some large-scale sci-ence experiments. © 2021 Optical Society of America http://dx.doi.org/10.1364/XX.XX.XXXXXX
Atomic optical clocks have rapidly grown in the last decadeand are proving to be a powerful tool for investigation of fun-damental and applied physics [1–5]. Precision clock networksare of particular interest in precision measurements and funda-mental physics tests, such as general relativity, temporal varia-tion of the fundamental constant [6], searching for dark matter,gravitational waves and physics beyond the Standard Model[7–10], as well as providing innovative quantum technologiesfor other branches of science [11]. Most of the applicationsmentioned above require high-precision clock networks withmultiple places over fiber links. To achieve this aim, activecompensation schemes as first demonstrated in 1994 by Ma etal. have been proposed to cancel the fiber-induced phase driftand implement highly stable optical frequency distribution [12],which generally utilizes the phase error from a round-trip probesignal to achieve the feedback control of a voltage-controlled oscillator (VCO) via a servo controller [12]. One intriguing ques-tion is how to distribute a reference optical frequency to manyusers simultaneously in a cost-effective and robust way.In the past years, many works have demonstrated that co-herence optical phase can be delivered to multiple users withthe help of servo controllers. Grosche et al. have first proposedand demonstrated to extract the ultrastable signal for multipleusers along the active phase stabilized main link [13], enablingto tap the fiber anywhere with the same precision level as thatachieved at the main link output. Alternatively, a branchingoptical fiber network with phase noise correction at each out-put end has been proposed and experimentally demonstrated[14, 15]. All these existing demonstrators for the multiple-accessapplications have to adopt at least one active servo controllerfor the main fiber link [13, 16–18] or for each branch fiber link[14, 15, 19]. Consequently, the overall performance of the abovementioned techniques is mainly dependent on whether the servocontroller’s parameters set properly [20]. For example, there willbe occasional interruptions where a phase lock temporarily loseslock, corresponding to unpredictable jumps in the optical signals.These interruptions will reduce the effective averaging time tobias the measurement [12]. Moreover, the effect of the servobumps on the main fiber link will pass to each access place andcorrupt the spectral purity received by each place.In our previous work, we have demonstrated optical fre-quency transfer with passive phase stabilization over a bus ora ring fiber network [19, 21]. The technique possesses the ad-vantages of an unlimited compensation precision and a fastcompensation speed and free from the effect of servo bumpson the spectral purity [19, 21]. However, the feasibility andadaptability of the passive phase noise cancellation techniquefor the multiple-access application needs to be theoretically andexperimentally studied. Therefore, the investigation of the novelmultiple-access optical frequency transfer scheme which imple-ment alternative phase correction techniques other than the morecommonly used conventional, active, phase correction techniqueis seeing increasing demand. Improving the robustness and sen-sitivity of multiple-access optical frequency transfer devices, aswell as understanding and characterizing the limitations of thenovel multiple-access optical frequency transfer scheme withpassive phase correction is an important step towards the goal ofheralding a new generation of viable precision optical frequency a r X i v : . [ phy s i c s . i n s - d e t ] F e b etter preprint 2 Fig. 1.
Schematic diagram of our multi-access optical frequency dissemination with passive phase correction over a fiber link. Weevaluate the system performance by measuring the beatnote between the local light reference and the output of the access place.AOM: acousto-optic modulator, FRM: Faraday mirror, FM: frequency mixer, EDFA: erbium-doped fiber amplifier, OC: optical cou-pler, FD: frequency divider, PD: photo-detector, PC: power combiner, DDS: direct digital synthesizer. The black solid and dashedarrows represent the directions of the forward and backward lights, respectively. The blue solid arrows are the direction of the RFsignals.transfer devices. Theses devices could be employed in the abovementioned applications [1–11].In this article, we extend the study of the optical frequencytransfer technique based on our previous passive phase cor-rection technique [19, 21], demonstrating its application as amultiple-access optical frequency transfer technique. We experi-mentally study the optical frequency transfer stabilities, phasenoise power spectral densities (PSDs) and accuracies for thetwo access places at the most symmetric 50/50 km ( L a / L b ) oneand the relative asymmetric 70/30 km one, over a total fiberlink of L =
100 km. In comparison with our previous work[19, 21, 22], in which we have demonstrated multiple-place op-tical frequency transfer over the star and ring fiber networkswith the passive phase noise cancellation technique, here wedemonstrated that a high performance multiple-place opticalfrequency transfer over the widely adopted bus fiber topologywith all-passive phase noise cancellation at the access places andthe main fiber link. The proposed technique could increase theadaptability to incorporate the optical frequency transfer tech-nique into any existing communication networks with differenttopologies.Figure 1 shows the schematic diagram of multiple-place op-tical frequency transfer with a simple extraction along the pas-sively stabilized main link. The main optical link aims at regen-erating a coherent optical phase at the output end of the fiber[21] and at any places along the fiber as the input end of the fiber.The principle of passively stabilizing the main fiber link can befound in [19, 21]. In brief, an ultrastable reference ν at the localsite is upshifted by frequency of ω l with an acousto-optic modu-lator (AOM) denoted as AOM1 and then injects into the fiber. Atthe output, the light is downshifted by frequency of ω r with theAOM2 (here ω l > ω r ), and part of light is sent back with a Fara-day mirror (FRM). The round-trip signal is mixed with the inputultrastable laser using an interferometer consisting of an opticalcoupler (OC) and another FRM. The beatnote radio frequency(RF) signal is twice the sum of the AOMs’ frequencies and ex-hibits the round-trip phase noise, 2 φ p , with φ p = φ a + φ b , where φ a and φ b are the noise of the fiber spans of length of L a and L b , respectively. Afterwards, we divide the beatnote with a factor of2 and then mix the divided signal with an assistant frequencyof ω s . The lower sideband of the mixed signal, ω s − ω l + ω r ,is used. Afterwards, the mixed signal together with ω l is fedinto the electrical port of the AOM1. Finally at the output end,the phase fluctuations of the optical frequency ν + ω s − ω l areautomatically cancelled.At each access place, the configuration is similar with the onepresented in [13], at a distance L a from the input end and L b from the output end, a 2 × S F ( ω ) ∝ cos (( ν + ω l ) t + φ a )+ cos (( ν + ω s − ω l + ω r ) t − φ p + φ a ) . (1) Similarly, the backward signal has a form of S B ( ω ) ∝ cos (( ν − ω r + ω l ) t + φ p + φ b )+ cos (( ν + ω s − ω l − ω r ) t + φ b ) . (2) The beatnote frequencies between ν + ω l and ν − ω r + ω l and between ν + ω s − ω l + ω r and ν + ω s − ω l − ω r , result in thesame frequency of 2 ω r with the phase fluctuation 2 φ b . The signalis divided by a factor of 2, filtered, and drives an AOM (AOM3)in order to correct for the frequency and phase fluctuations ofthe forward signal. The forward signal after passing through theAOM3, is thus downshifted to, S F (cid:48) ( ω ) ∝ cos (( ν − ω r + ω l ) t + φ p )+ cos (( ν + ω s − ω l ) t ) . (3) A similar phase noise cancelled signal can be obtained on thebackward extracted signal with an opposite frequency shifter.Thus, the phase noise of the remote site and the access sites areautomatically cancelled.As demonstrated by Williams et al. , the phase noise rejectioncapability is limited by the propagation delay [23]. The residualphase noise PSD, S access ( f ) , at each access place in terms ofthe single-pass free-running phase noise PSD, S fiber ( f ) , and the etter preprint 3 single-pass fiber link L propagation delay, τ , by compensatingthe forward optical signal can be expressed as [22, 23], S access ( f ) (cid:39) ( π f τ ) (cid:34) + L a L − (cid:18) L a L (cid:19) (cid:35) S fiber ( f ) . (4) Note that, in comparison with the conventional multiple-access technique, the phase noise rejection capability of both theconventional and proposed techniques is proportional to τ andthe uncompensated single-pass fiber phase noise PSD, S fiber ( ω ) .Although, the residual fiber phase noise PSD in the proposedtechnique turns out to be a factor of 7 worse than that of inthe conventional multiple-access scheme at the output of thefiber link ( L a = L ) [16, 19], it could largely suppress the phasenoise introduced by the servo bumps (see Fig. 2), which couldsignificantly increase as the increase of the fiber link [24], andsimplify the hardware overhead in systems with many stationsand connections [21]. - 5 - 4 - 3 - 2 - 1 f e Phase noise PSD [rad2/Hz]
O f f s e t f r e q u e n c y [ H z ] a bcd a b c d e f Fig. 2.
Measured phase noise PSDs of a the 70/30 km free-running access place (blue curve), b the 50/50 km free-running access place (orange curve), c the compensated 70/30km access place (black curve), d the compensated 50/50 kmaccess place (magenta curve), e the 70/30 km theoretical delay-limited value (gray curve), and f the 50/50 km theoreticaldelay-limited value (cyan curve). Strong servo bumps can beeffectively removed in the proposed scheme.We implement the proposed extraction scheme in Fig. 1 on a100 km fiber link. The signal source that has been adopted in thisexperiment is a narrow-linewidth optical source (NKT X15) at afrequency of near 193 THz with a typical linewidth of 100 Hz.At an arbitrary access place, a 2 × L a / L b ), andthe relative asymmetric one, 70/30 km. To compensate the totalloss of 23 dB of the 100 km fiber link system, we implement ahome-made bidirectional Erbium-doped fiber amplifier (EDFA)at the middle of the fiber link. The angular frequencies at thelocal and remote sites are ω l = π ×
75 MHz, ω r = π × ω s = π ×
115 MHz, respectively. The AOM1 issimultaneously supplied by two angular frequencies of 2 π ×
85 MHz and 2 π ×
75 MHz, and the AOM3 is supplied by theangular frequency of 2 π ×
45 MHz. Consequently, the beatnotesbetween the input and extracted sites have a frequency of 2 π ×
40 MHz. This beatnote is recorded simultaneously with a dead-time free counter with a gate time of 1 s and non-averaging Π -type operation. At the same time, we implement the phasenoise measurement by feeding the heterodyne beatnote signaltogether with a stable frequency reference to a phase detector.The phase fluctuations S φ ( ω ) at the phase detector output aremeasured with a fast Fourier transform (FFT) analyzer [22, 25]. - 1 9 - 1 8 - 1 7 - 1 6 - 1 5 - 1 4 ADEV
A v e r a g i n g t i m e [ s ]
Fig. 3.
Measured fractional frequency instability, calculatedfrom Π -type data with the overlapping Allan deviation(ADEV), of the 100-km free-running main link (red triangles),the stabilized 70/30 km access place output (black squares),the compensated 50/50 km access place output (blue cicles),and the noise floor, in which the fiber links are replaced by theshort fibers, of the access place output (gray diamonds)Figure 2 shows the phase noise power spectral densities(PSDs) of the stabilized 70/30 km access place ( c , black curve)and the stabilized 50/50 km access place ( d , magenta curve),respectively. The phase noise PSDs of the free-running 70/30 kmaccess place ( a , blue curve) and the 50/50 km access place ( b , or-ange curve) are also shown. The free-running curve is typical foroptical fibre links, with a noise of approximately 100 rad /Hz at1 Hz for the 70/30 km access place, scaling down with a slopeof about f − , and reaching around 10 − rad /Hz after 100 Hz.Their noises of the free-running 70/30 km ( a , blue curve) and50/50 km access places ( b , orange curve) slightly differ becausethe two measurements are performed at different times. At thesame time, both passive phase stabilized cases are also very sim-ilar with the phase noise PSDs about 10 − rad /Hz between 1and 100 Hz. We can clearly see that the noise correction is lim-ited by the main fiber propagation delay approximately ∼ ( √ τ ) . This limit is the same for both accessplaces because the bandwidth of the extraction is limited by thelonger delay, namely the main fiber link delay [16]. More impor-tantly, we can clearly see that compared with the conventionalmultiple-access optical frequency transfer technique [13–15], thestrong servo bumps are effectively suppressed in our passivephase noise cancellation technique as observed in our previouswork [19, 21, 22].Figure 3 displays the fractional frequency stability of the etter preprint 4 free-running and passively stabilized configurations, calculatedfrom Π -type data with overlapping Allan deviation (ADEV).The stability of the 70/30 km (50/50 km) access place is 3.1 × − (2.0 × − ) at 1 s averaging time, decreases as a slope ofapproximately τ − and reaches a floor of approximately 4.1 × − (3.3 × − ) at 10 s. As calculated by Eq. 4, the ratio ofthe stability of the 50/50 km and 30/70 km places should be R = R (cid:39) × − /3.1 × − ). As a comparison, we also measuredthe noise floor for the access output as displayed in Fig. 3. Thelong-term stability is mainly attributed to the thermal noise onuncompensated fibre paths, due to imperfect length adjustmentand thermal stabilisation in the extraction optical set-up, orin the main fiber link [22, 25]. Compared with our previouswork in which we characterized the system performance at theoutput of the main fiber link [21], the ultrastable laser can bethus transferred through the secondary and main links withoutsignificant degradation. Fig. 4.
Frequency comparison between input and access placefrequencies after 70 km over the 100 km fiber. (b) 84,014 datapoints were taken with dead-time free Π -type frequency coun-ters with a 1 s gate time (green points, left axis). We calculatedunweighted mean ( Π -type) values for all cycle-slip free 1,000s long segments, resulting in 84 data points (black dots, rightfrequency axis, enlarged scale). Histograms (brown bars) andGaussian fits (red curves) for (a) frequency values taken withone second gate time and (c) 84 phase coherent 1,000-secondfrequency averages.Complementary to the characterization of the stability andphase noise, the accuracy has to be throughout-fully examinedby calculating the mean value of the end-to-end beatnote fre-quency offset. Figure 4(b) shows the frequency deviation of thebeatnote’s data for the 70/30 km access place, recorded witha 1 s gate time and Π -type counters, over successive 84,014 s(green point, left axis) and the arithmetic mean of all cycle-slipfree 1,000 s intervals (black dots, right axis). Histograms (brownbars) and Gaussian fits (red curves) of the frequency deviationfor the access place after 70 km are also illustrated in Fig. 4(a)and (c). According to the Gaussian fit in Fig. 4(c), the calculatedresults demonstrate that the mean frequency is shifted by -28.9 µ Hz ( − × − ). The standard deviation of the 1,000 s datapoints is 493 µ Hz (2.5 × − ), which is a factor of 1,000 smallerthan the ADEV at 1 s as expected for this Π -type evaluation.Considering the long-term stability of frequency transfer as illus- trated in Fig. 3, we conservatively estimate the accuracy of thetransmitted optical signal as shown in the last data point of theADEV, resulting in a relative frequency accuracy of 4.1 × − .Adopting the same procedure, the mean frequency offset andthe standard deviation for the 50/50 km place were calculatedusing the 1000 s point with the total 89,690 Π -type counter datato be 52.2 µ Hz (2.7 × − ) and 454 µ Hz (2.3 × − ), respec-tively. Taking into account the long-term ADEV at 10,000 s of thedata set for the 50/50 km access place of 3.3 × − , we conser-vatively estimate that the mean frequency offset is 2.7 × − with a statistical uncertainty of 3.3 × − for the 50/50 kmaccess place. We can conclude that there is no systematic fre-quency shift arising in the all-passive multiple-place phase noisecancellation setup at a level of a few 10 − .In summary, we have presented a new method, making astable optical frequency available at any arbitrary access placesalong the fiber link with passive phase noise cancellation. Incomparison with previous work, here we demonstrated thata high performance multiple-place optical frequency transferover the widely adopted bus fiber topology with the open-loopdesign, mitigating some technical difficulties in conventional ac-tive multiple-access phase noise cancellation. We experimentallydemonstrate transferring of optical frequency to two differentaccess places. After being compensated, delivering an opticalfrequency to different places with the relative frequency insta-bility in terms of ADEV measured by the Π -mode frequencycounter can be as low as 3.1 × − at 1 s and 4.1 × − at10,000 s. The frequency uncertainty of the light after transferringthrough the fiber relative to that of the input light is a few 10 − for the access places over the 100 km fiber link. Funding.
This research was supported by the National NaturalScience Foundation of China (NSFC) (61905143, 61627817).
Disclosures.
The authors declare no conflicts of interest.
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