An optical fiber-based frequency and timing distribution system based on the principle of heterodyne interferometry has been in development at LBNL for several years. The fiber drift corrector has evolved from an RF-based to an optical-based system, from mechanical correctors (piezo and optical trombone) to fully electronic, and the electronics from analog to fully digital, all using inexpensive off-the-shelf commodity fiber components. Short-term optical phase jitter and long-term phase drift are both in the femtosecond range over distribution paths of 2 km or more

Byrd, J.

Doolittle, L.

Huang, G.

Staples, J. W.

Wilcox, R.

UNT Digital Library

A FEMTOSECOND-LEVEL FIBER-OPTICS TIMING DISTRIBUTIONSYSTEM USING FREQUENCY-OFFSET INTERFEROMETRY∗J. W. Staples, J. Byrd, L. Doolittle, G. Huang and R. Wilcox, LBNL, Berkeley, California, USAAbstractAn optical fiber-based frequency and timing distributionsystem based on the principle of heterodyne interferome-try has been in development at LBNL for several years.The fiber drift corrector has evolved from an RF-based toan optical-based system, from mechanical correctors (piezoand optical trombone) to fully electronic, and the electron-ics from analog to fully digital, all using inexpensive off-the-shelf commodity fiber components. Short-term opticalphase jitter and long-term phase drift are both in the fem-tosecond range over distribution paths of 2 km or more.Future Accelerator Timing RequirementsThe next generation of accelerators, spread over an areameasured in kilometers, will require femtosecond-levelsynchronization of RF cavities, lasers, photoinjectors anddiagnostic devices. Phase-stabilized optical fiber is well-suited for this, along with its immunity to electrical inter-ference, gigaHertz bandwidth, low loss and easy installa-tion in wireways.Commodity-level single-mode glass fiber, such as Corn-ing SMF-28, optimized for 1300-1550 nm wavelength, ex-hibits about the same phase velocity dependence on tem-perature as copper, although the mechanism is temperaturedependence of the glass dielectric constant. All fiber com-ponents used are inexpensive off-the-shelf devices devel-oped for the telecommunications industry.The stabilization system developed at LBNL uses thetechnique of frequency-offset interferometry.As shown in Figure 1, the optical output of a 1550 nmCW laser is split between the short arm of a Michaelsoninterferometer and the long fiber to a remote receiver. Theshort arm of the interferometer is temperature-controlledto a variation of less than 0.01 C. At the end of the longfiber arm, an acousto-optical modulator (AOM) excited at50 MHz up-shifts the 195 THz laser frequency by 50 MHz,where it is then reflected by a 50% Faraday rotator mirror.The shift of the laser frequency is phase coherent with the50 MHz RF drive of the AOM. The reflected laser signal isagain upshifted by 50 MHz by its return passage throughthe AOM, resulting in a 100 MHz total frequency shiftwhere it returns along the long fiber, and combines witha sample of the original laser frequency from the interfer-ometer short arm in the splitter.The variation of the phase length of the fiber is phasecoherent to the phase variation of the 100 MHz upshiftedreturn signal. The original laser frequency, from the short∗This work is supported by the Director, Office of Science, U.S. Dept.of Energy under Contract No. DE-AC02-05CH11231arm and the upshifted laser frequency are transmitted alonga second fiber, the error signal fiber, to a photodiode at thestabilizer where they produce a 100 MHz beat note which iscompared to the 100 MHz reference oscillator. Any changein the phase length of the long fiber is reflected in a phaseshift of the 50 MHz signal to the AOM, derived from the100 MHz reference oscillator, which adds or subtracts thesame number of optical cycles in the AOM. The result-ing error signal is integrated, the integral representing thechange of phase length of the fiber, which shifts the phaseof the 50 MHz drive signal to the AOM. All these func-tion are combined in a single chip field-programmable gatearray (FPGA) controller.AOMMixer Integrator Phase ShifterRotatorMirrorFaradaySplitterError Fiber50% FaradayRotator MirrorReference Oscillator1550 nmLaserFiberStabilizedSender Stabilizer/Receiverdivideby 2Figure 1: Frequency-Offset Stabilizer ConfigurationThe fiber that carries the error signal to the stabilizerneeds no stabilization itself, as it is providing optical phaseinformation down-converted to 100 MHz. The 100 MHzbeat note is phase-coherent with changes in optical phasein the stabilized fiber, but the frequency ratio of 195 THz(1550 nm wavelength) and 100 MHz is 2 × 106, so a 1nanosecond change in the error signal fiber produces an er-ror of only 0.5 femtosecond to the correction.In previous implementations of the stabilizer, the AOMphase was fixed, and mechanical phase shifters (piezo andmotor-driven optical trombone) were placed in series withthe stabilized fiber. These suffered from a finite range ofcorrection and the usual problems with devices using mov-ing parts. The transition to an all-electronic system sig-nificantly simplified the system with a smaller parts count,essentially unlimited range of correction, and increased re-liability.The frequency reference for the system is the 195 THzlaser frequency itself, which must be stabilized to 1 part in109 for the system to provide 1 femtosecond stability withwith variations of the long fiber of 1 nanosecond. The CWlaser is stabilized by taking a sample of the laser, doublingits frequency, and locking it to a saturated absorption linein a Rubidium cell using a Pound-Drever-Hall (PDH) [2]stabilizer configuration. To verify its operation, two inde-pendent PDH-stabilized 1550 nm lasers were beat againsteach other with measured drifts in the 200 kHz range.To measure the effectiveness of the stabilizer itself, twoindependent stabilizers were built, operating from a com-mon laser, and the out-of-loop optical beat note measuredbetween the outputs of the 50% Faraday mirrors at the farend of the long fibers of the independent stabilizers. TheAOMs may operate by shifting the laser light either upwardor downward, so one channel has an up-shifting AOM andthe other uses a down-shifting AOM, giving a 100 MHzdifference in the laser light between the two channels (theone-way shift in each channel is up or down 50 MHz). Theresultant difference in optical frequency of the laser lightexiting each of the 50% Faraday mirrors in the indepen-dently stabilized channels is then compared directly to the100 MHz reference oscillator and represents the residualdifferential optical phase error between the two channels.1550 nm Laser SplitterResidualErrorSignalSenderSenderStabilizer−AOM+AOMStabilized Fiber 1Error Signal 1Stabilized Fiber 2Error Signal 2Stabilizer100 MHz Reference OscillatorFigure 2: Two independent channels with out-of-loop mon-itor.We tested the stabilizer performance in two venues: thelong fiber at LBNL is a 2 km loop, part of the LBNL datanetwork backbone which runs under roads and through sev-eral buildings, and a 2.8 km fiber loop in the SLAC klystrongallery, exposed to full ambient temperature variation andthe acoustic perturbation of the klystron modulators. Mea-surement were taken with a stabilized reference short fiberin one channel and the long fiber in the other. Figure 2shows a block diagram of the differential phase measure-ment setup, with a long fiber in channel 1 and a short fiberin the channel 2. Figure 3 shows the results for a 232hour data run of the 2.8 km fiber in the SLAC klystrongallery. The black trace shows the phase length changeof the gallery fiber, 2184 picoseconds peak-to-peak due todiurnal temperature variation, and the red trace is the resid-ual error after correction, drifting 31.5 femtoseconds in 232hours, or less than 0.14 fsec per hour. The p-p short-termjitter is less than 2 femtoseconds.Figure 4 shows the noise spectrum on the stabilizedklystron gallery fiber, measured on the 50 MHz drive tothe AOM, from 10 Hz to 100 KHz with the loop open (red)and closed (black). The noise suppression at 10 Hz is 60dB. The feedback loop consists of a simple integrator witha 1/f gain curve. As the correction is phase-coherent tothe optical frequency, the integration of the power spec-trum from 10 Hz to 1 MHz gives an rms jitter of the opticalcarrier of 0.95 femtosecond.-100001000Fiber Transit Time Variation (psec)0 50 100 150 200 2500102030Differential Time Error (fsec)Fiber Transit Time Variation (psec) and Differential Error Timing (fsec)Figure 3: 2.8 km SLAC klystron gallery phase variation(black trace, right-hand scale), and residual error after cor-rection (red trace, left-hand scale) for a 232 hour data run.10 100 1000 10000 100000Frequency (Hz)-100-80-60-40-200Noise Power (dBc)Open, Closed Loop Noise SpectrumFigure 4: Loop noise with control loop open (red) andclosed (black).Group-Phase Velocity CorrelationThe system corrects the phase variation of the fiber. Totransmit a stabilized RF signal, the group velocity mustalso be stabilized. There is a monotonic relationship be-tween the two, which is experimentally determined. cite-group This requires the modulation of the laser by RF, re-covery of the RF at the far end of the fiber with a photodi-ode and measuring the group velocity variation, and com-paring it to the optical phase velocity variation of the fiber.The optical level to the photodiode is set to the level thatminimizes the phase-amplitude characteristic of the photo-diode itself. The ratio of group velocity to phase velocityvariation of the fiber due to temperature variation is approx-imately 1.02.Stabilized RF Phase DetectorsTo maintain better than 10 femtosecond stability in theRF domain, phase detectors operating at S-band (2856MHz) must have a stability of better than 0.01 degrees. Ina configuration where RF is transmitted over a stabilizedfiber, closed-loop controllers will include high-precisionphase detectors operating in the RF domain. This requiresactive stabilization of the RF phase detector itself.To maintain the high precision offered by stabilizationin the optical domain, a technique that continually injectsa calibration signal into the RF circuits is used [4]. As thisis a CW rather than a pulsed RF transmission system, adouble-sideband suppressed-carrier (DSSC) calibrate sig-nal is injected into the RF chain, immediately following theRF recovery photodiode and carried through the entire RFclosed-loop phase corrector. The frequency offset of thesidebands in an S-band system is on the order of 1 MHz.SUMSPLITSUMFPGA LogicReference PhaseCalibrate SignalKlystron SampleKlystronSampleRF ModulatedOptical CarrierSplitDownconversion OscillatorTo KlystronFigure 5: Phase detectors stabilized by injection of a DSSCcalibrate signal.Figure 5 shows an example where a stabilized fiber linkcarries an S-band modulated carrier to a photodiode, whichrecovers the S-band phase reference signal. The system’sgoal is to use the phase of that reference to stabilize thephase of the cavity field, and the feedback actuator is thephase of a klystron drive signal. The FPGA generates aDSSC signal and injects it as close to the photodiode andthe cavity sensor as possible. All phase shifts (includingthose that vary with temperature) in the components afterthe summing junctions will apply equally to the referenceand calibration signals, and can therefore be detected andcorrected digitally by the FPGA. The downconversion mix-ers convert S-band signals to 50 MHz that are digitized bythe FPGA circuit board.Modulation-Demodulation Noise PerformanceThe additional noise generated by the modulation-demodulation process of transmitting RF over an opticallink is measured. The RF carrier is impressed onto thelaser light with a Mach-Zehnder (M-Z) modulator. TheAM modulated carrier is then amplified with an erbium-doped diode-pumped fiber amplifier (EDFA) and transmit-ted through the stabilizer. The modulation of the laser sig-nal does not affect the operation of the stabilizer. Figure 6shows two overlaid plots of the noise power spectrum of a1 GHz oscillator that modulates the laser light through theM-Z modulator, and of the output of the photodiode.Figure 6: Noise spectrum of original RF generator (yel-low), and of photodiode output of RF modulated onto laserand demodulated (blue).In this case, the phase noise jitter of the 1.0 GHz test sig-nal was 31 femtosecond, integrated over the range of 100Hz to 100 kHz, as was the recovered 1 GHz signal from thephotodiode. The modulation-demodulation process doesnot add significant phase noise to the original RF signal.Synchronizing Mode-Locked LasersThis system is particularly well-suited to locking a re-mote mode-locked (M-L) laser to a local reference stan-dard. Two widely separate (for example, 5 THz) comb linesof the M-L laser spectrum synchronize two CW lasers,which are each transmitted over individually stabilizedfibers, which then lock the same two lines in a slave laser.This preserves the carrier-envelope-offset conditions of theslave M-L laser to that of the reference laser. In this ap-plication, only phase stabilization of the fiber stabilizers isneeded, not group velocity correction as only the unmodu-lated optical carrier frequency is used. [5]REFERENCES[1] R. B. Wilcox and J. W. Staples, Systems Design Concepts forOptical Synchronization in Accelerators, PAC2007, p.3807,Albuquerque[2] Eric. D. Black, An introduction to Pound-Drever-Hall laserfrequency stabilization, Am. J. Phys. 69, 79 (2001).[3] J. M. Byrd et al, Timing Distribution in Accelerators via Sta-bilized Optical Fiber Links, Linac06, p. 577, Knoxville[4] L. R. Doolittle, Low-Level RF Control System Design andArchitecture, APAC 2007, Indore, India[5] J. W. Staples, R. Wilcox and J. Byrd, Demonstration ofFemtosecond-Phase Stabilization in 2 km Optical Fiber,PAC07, p. 494, Albuquerque

A Femtosecond-Level Fiber-Optics Timing Distribution System Using Frequency-Offset Interferometry

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A Femtosecond-Level Fiber-Optics Timing Distribution System Using Frequency-Offset Interferometry

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