Laser synchronization and timing distribution through a fiber

Laser synchronization and timing distribution through a fiber network using femtosecond modelocked lasers Kevin Holman JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado, USA Co-workers Funding David Jones (UBC) Jun Ye (JILA) Steve Cundiff (JILA) Jason Jones (JILA) Leo Holberg et al (NIST) Erich Ippen (MIT) NIST, NSERC, ONR-MURI

Why Synchronization? Desired in next generation light sources • Synchronize X-rays with beamline endstation lasers for pump-probe experiments • Synchronize accelerator RF with electron bunches Master clock laser + RF • Relative timing jitter of a few fs over ~1 km FEL seed lasers Linac RF Beamline endstation lasers

Outline Synchronization of multiple fs lasers • Underlying technology –Pulse synchronization –Phase coherence • Applications –Coherent anti-Stokes Raman spectroscopy (CARS) –Remote optical frequency measurements/comparisons/distribution . . . but first how to measure performance of frequency synchronization of two oscillators? • Allan Deviation • Timing jitter

Allan Deviation -typically used by metrology community as a measure of (in)stability -evaluates performance over longer time scales (> 1 sec or so) -can distinguish between various noise processes -indicates stability as a function of averaging time Phase Lock Loop Master Oscillator Device Under Test Frequency Counter

Timing Jitter Timing jitter -typically used by ultrafast community -can be measured in time domain (direct cross correlation) or frequency domain (via phase noise spectral density of error signal) -must specify frequency range Relative timing jitter leads to amplitude jitter in SFG signal Sum frequency generation fs laser #1 fs laser #2 Single side band phase noise spectral density Timing jitter spectral density Spectrum analyzer

Methods for Synchronization Radio frequency lock • Detect high harmonic of lasers’ repetition rates • Implement phase lock loop • Able to lock at arbitrary (and dynamically configurable) time delays Optical frequency lock • Use very high harmonic (~106) for increased sensitivity • Can be more technically complex than RF lock • Can lock to high finesse cavity or CW reference laser • Similar advantages for arbitrary time delay Optical cross correlation • Nonlinear correlation of pulse train • Use fs pulse’s (steep) rising edge for increased sensitivity • Small dynamic range…must be used with RF lock • Time delays are “fixed”

Experimental Setup for RF Locking SHG fs Laser 2 Delay SFG fs Laser 1 BBO SHG 100 MHz Sampling scope 14 GHz 50 ps Phase shifter 14 GHz Loop gain 100 MHz Loop gain Phase shifter SFG intensity analysis Laser 1 repetition rate control

1 Top of cross-correlation curve (two pulses maximally overlapped) Timing jitter 1. 75 fs (2 MHz BW) Timing jitter 0. 58 fs (160 Hz BW) (two pulses offset by ~ 1/2 pulse width) Total time (1 s) 0 2 Noise spectrum (fs /Hz) 30 fs Cross-Correlation Amplitude Timing Jitter via Sum Frequency Generation 10 10 0 Locking error signal -2 Mixer noise floor -4 -6 0 20 40 60 80 100 Fourier Frequency (k. Hz) Ma et al. , Phys. Rev. A 64, 021802(R) (2001). Sheldon et al. Opt. Lett 27 312 (2002).

Synchronization via Optical Cavity Lock Optical Cavity Bartels et al. , Opt. Lett. 28 663 (2003).

Synchronization via Optical Cross Correlation Output (650 -1450 nm) Δt Cr: fo Ti: sa (1/496 nm = 1/833 nm+1/1225 nm). SFG Rep. -Rate Control SFG 0 V 3 mm Fused Silica Schibli et al Opt. Lett, 28, 947 (2003)

Balanced Cross-Correlator Output (650 -1450 nm) Δt Cr: fo -GD/2 Ti: sa Rep. -Rate Control 0 V + Δt (1/496 nm = 1/833 nm+1/1225 nm). + - SFG 3 mm GD Fused Silica

Balanced Cross-Correlator

Experimental result: Residual timing-jitter The residual out-of-loop timing-jitter measured from 10 m. Hz to 2. 3 MHz is 0. 3 fs (a tenth of an optical cycle)

Outline cont… Synchronization of two fs lasers • Underlying technology –Pulse synchronization –Phase coherence • Applications –Coherent anti-Stokes Raman spectroscopy (CARS) –Remote optical frequency measurements/comparisons/distribution

Time/Frequency Domain Pictures of fs Pulses Time domain Df E(t) 2 Df t 1/ frep = t F. T. Df = 2 p fo/ frep Frequency domain I(f) frep Phase accumulated in one cavity round trip Derivation details: Cundiff, J. Phys. D 35, R 43 (2002) fo D. Jones et. al. Science 288 (2000) nn = n frep + fo f

Requirements for Coherent Locking of fs Lasers 1/ frep 1 = t 1 E(t) For successful phase locking: fs laser • Pulse repetition rates must be synchronized with pulse jitter << an optical cycle (at 800 nm << 2. 7 fs) t Pulse envelopes are locked • Carrier envelope phase must evolve identically (fo 1=fo 2) Evolution of carrier-envelope phases are locked E(t) fs laser t fo 1 I(f) fo 2 1/ frep 2 = t 2 frep f

Experimental Setup Phase lock: fo 1 -fo 2 = 0 (Interferometric) Cross-Correlation Auto-Correlation Spectral interferometry Delay AOM SHG fs Laser 2 SFG Delay fs Laser 1 BBO SHG 100 MHz Sampling scope 14 GHz 50 ps Phase shifter 14 GHz Loop gain 100 MHz Loop gain Phase shifter Laser 1 repetition rate control

Locking of Offset Frequencies fo 1 – fo 2 5 MHz Phase lock activated (fo 1 – fo 2) Hz 1. 0 60 d. B R. B. 100 k. Hz sdev = 0. 15 Hz (1 -s averaging time) 0. 5 0. 0 -0. 5 -1. 0 0 200 400 Time (s) 600 800

Spectral Interferometry (Linear Unit) Spectral Interferometry - Laser 1 spectrum - Laser 2 spectrum - Both lasers, not phase locked - Both lasers, phase locked (a) 700 750 800 Wavelength (nm) 850 900 R. Shelton et. al. Science 293 1286 (2001)

Outline cont… Synchronization of two fs lasers • Underlying technology –Pulse synchronization –Phase coherence • Applications –Coherent anti-Stokes Raman spectroscopy (CARS) –Remote optical frequency measurements/comparisons/distribution

Coherent Anti-Stokes Raman Scattering Microscopy • Four-wave mixing process with independent pump/probe and Stokes lasers (2 wp-ws=was) • First demonstrated as imaging technique by Duncan et al (1982)* Prepare coherent (resonant) Convert molecular coherent molecular state vibrations to anti-Stokes photon wp ws wp was n=1 Molecular vibration levels n=0 • Capable of chemical-specific imaging of biological and chemical samples *M. D. Duncan, J. Reinjes, and T. J. Manuccia, Opt. Lett. 7 350 (1982).

CARS Microscope APD Stokes Laser Forward Detection was Filter Sample Pump/Probe Laser 3 -D scanner NA=1. 4 Objective wp, ws Dichroic mirror was APD Epi (Reverse) Detection

Synchronization Performance Stokes Laser (Master) To CARS microscope Pump/Probe Laser (Slave) 14 GHz 100 MHz Feedback Loop FFT Spectrum Analyzer Jitter Spectral Density Lasers are Coherent Mira ps Ti: sapphire lasers Noise floor of mixer/amplifiers

Experimental Setup Sum Frequency Generation (SFG) used to measure relative timing jitter SFG BBO Bragg Cells used to decimate rep. rate Bragg Cell Stokes Laser (Master) Bragg Cell Pump/Probe Laser (Slave) Polystyrene beads in aqueous solution 80 MHz 14 GHz Loop gain Phase Shifter DBM 3 -D scanner 14 GHz Phase Shifter wp, ws Dichroic mirror was APD

Relative Timing Jitter Pulse delay is adjusted to overlap at half-maximum point of cross-correlation Timing jitter is converted to Stokes amplitude fluctuations Relative jitter via SFG Pump/ Probe SFG Relative jitter via CARS With 80 MHz lock, rms jitter is ~700 fs Switching to 14 GHz lock, rms jitter is 21 fs Bandwidth is 160 Hz

Images of 1 mm Diameter Polystyrene Beads Raman shift = 1600 cm-1 Pump 0. 3 m. W @ 250 k. Hz Stokes 0. 15 m. W @ 250 k. Hz Counts 80 -MHz lock ~770 fs timing jitter 14 -GHz lock ~20 fs timing jitter 2 mm

Outline cont… Synchronization of two fs lasers • Underlying technology –Pulse synchronization –Phase coherence • Applications –Coherent anti-Stokes Raman spectroscopy (CARS) –Remote optical frequency measurements/comparisons/distribution

Synchronization of Remote Sources Compare optical standards for tests of fundamental physics Increasing stability Required in next generation light sources • Synchronize X-rays with beamline endstation lasers for pump-probe experiments • Synchronize accelerator RF with electron bunches • Relative timing jitter of a few fs over ~1 km Telecom network synchronization • Low timing-jitter: dense time-division multiplexing • Frequency reference from master clock allows dense wavelength-division multiplexing

Distribution of frequency standards Optical standard Optical atomic clock Noise added by fiber must be detected and minimized Optical frequency standard 1/t fs Ti: sapphire comb 1. 5 -mm transmitting comb t RF standard Holman et al. Opt. Lett. 28, 2405 (2003) Jones et al. Opt. Lett. 28, 813 (2003) End user Optical fiber network End user Degradation of signal during detection minimized End user

3. 45 km fiber link between JILA and NIST Trapped Sr Boulder Regional Administrative Network Iodine clock L. Hollberg C. Oates J. Bergquist D. Wineland Single Hg+ ion

RF transfer: modulated CW source RF standard Counter 3. 5 km 1310 nm laser diode Modulator J. Ye et al. J. Opt. Soc. Am. B 20, 1459 (2003) Performance similar to NASA/JPL work on frequency distribution system for radio telescopes

RF transfer: mode-locked laser Pulses vs. simple sine-wave modulation? • Easier to transfer optical stability transmitting laser (all optical)

RF transfer: mode-locked laser Pulses vs. simple sine-wave modulation? • Easier to transfer optical stability transmitting laser (all optical) • More sensitive derivation of error signal (optical pulse cross-correlation)

RF transfer: mode-locked laser Pulses vs. simple sine-wave modulation? • Easier to transfer optical stability transmitting laser (all optical) • More sensitive derivation of error signal (optical pulse cross-correlation) • Time gated transmission (immune to some noise, e. g. spurious reflections)

RF transfer: mode-locked laser Pulses vs. simple sine-wave modulation? • Easier to transfer optical stability transmitting laser (all optical) • More sensitive derivation of error signal (optical pulse cross-correlation) • Time gated transmission (immune to some noise, e. g. spurious reflections) • Simultaneously transmit optical and microwave 1/t Optical standard RF standard

RF transfer: mode-locked laser Pulses vs. simple sine-wave modulation? • Easier to transfer optical stability transmitting laser (all optical) • More sensitive derivation of error signal (optical pulse cross-correlation) • Time gated transmission (immune to some noise, e. g. spurious reflections) • Simultaneously transmit optical and microwave 8 th harmonic Frequency / time domain analysis End user 8 th harmonic Frequency reference Mode locked fiber laser Local 3. 5 km

Transfer with mode-locked pulses Pulses minimize instability of photodetection: • Average power ; SNR but … • Dispersion broadens pulse (~ 1 ns) more power to maintain SNR so … • Reduce bandwidth • Recompress pulse Power SNR Spectral Width (nm) 660 m. W 80 d. B 12. 0 ( ) 160 m. W 30 m. W 80 d. B 85 d. B 5. 5 ( ) Noise floor ( ) 30 m. W 85 d. B Noise floor ( ) Holman et al. Opt. Lett. 29, 1554 (2004)

Use dispersion shifted fiber in link Conditions at Receiver Photodiode Power SNR Instability (1 s) 40 m. W 85 d. B 6 e-14 ( ) 40 m. W 85 d. B 6 e-15 ( ) • Active stabilization: free-space delay arm in-line with DSF • Not limited by receiver noise • Reduce Allan deviation to noise floor

Summary / Future Work… Techniques and technology of: • Synchronization of ultrafast lasers • Delivering frequency standards over fiber networks Can be applied to synchronization efforts at next generation light sources Shorter time scales with < 10 fs jitter at multiple locations will require: • Optical delivery of clock signal • Active stabilization of optical fiber network • Some combination of RF and all-optical error signal generation (depends on frequency range of interest) Main message: No showstoppers on synchronization (financial or technical)

Compensate dispersion of installed fiber Dispersion compensation fiber Frequency reference 3. 5 km Mode locked fiber laser End user Local 3. 5 km 81 st harmonic • Dispersion compensation Avg. power ; SNR • Eliminate low frequency noise on installed fiber network

Cell Image • Human Epithelial cell • Image size is 50 by 50 microns • Total acquisition time: 8 seconds • Raman shift = 2845 cm-1 Pump 0. 6 m. W @ 250 k. Hz Stokes 0. 2 m. W @ 250 k. Hz Image taken by Dr. Eric Potma and Prof. Sunney Xie at Harvard University with synchronization system commercialized by Coherent Laser Inc. Slice 5 µm

Distribution over Fiber Networks Optical Fiber Network Master Clock End User Noise added by fiber must be detected and minimized End User Degradation of signal during detection minimized

Phase Coherent Transmission of Optical Standard Detection of Roundtrip Signal Nd: YAG AOM 1 -1 order JILA I 2 Atomic Clock 3. 45 km fiber er ord +1 AOM 2 corrected standard at NIST • Adjustment of AOM 1, shifts center frequency of Nd: YAG to compensate fiber perturbations • AOM 2 differentiates local and roundtrip signals

Transmission of Iodine Standard Fiber phase noise compensated Fiber phase noise uncompensated 20 d. B FWHM: 0. 05 Hz 1 k. Hz

Beat Frequency (Hz) Transmission of Iodine Standard 30 Fiber phase noise uncompensated 20 10 0 -10 -20 sdev (1 -s) 5. 4 Hz -30 Beat Frequency (Hz) 0 200 400 600 800 Time (s) 30 Digital phase lock 20 10 0 -10 sdev (1 -s) 0. 9 Hz -20 -30 0 200 400 600 Time (s) 800

Summary/Future Work… Techniques and technology of: • Synchronization of ultrafast lasers • Delivering frequency standards over fiber networks can be (easily) applied to synchronization efforts at next generation light sources Shorter time scales with <10 fs jitter at multiple locations will require: • Optical delivery of clock signal • Some combination of RF and all-optical error signal generation (depends on frequency range of interest)

Self-Referenced Locking Technique I(f) 0 fo nm frep f nn = n frep + fo x 2 n 2 n = 2 n frep + fo fo • need an optical octave of bandwidth! D. Jones et. al. Science 288 (2000)

Single Side Band Generator

Outline • Why transfer highly stable frequency standards? • Current method for transfer of RF standard • Mode-locked laser for RF transfer • Active stabilization of transfer network

Instability of optical amplifier (EDFA) Jitter spectral analysis (FFT) Frequency reference Mode locked fiber laser 8 th harmonic End user Local 3. 5 km EDFA

Conclusions • 10 x improvement with mode-locked pulses for RF transfer • Reducing temporal stretching of pulse • Active stabilization implemented noise floor frequency transfer • EDFA jitter well within stabilization loop bandwidth optical power ; SNR instability = measurement