Kevin Holman

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

2. 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 • Relative timing jitter of a few fs over ~1 km Master clock laser + RF FEL seed lasers Beamline endstation lasers Linac RF

3. 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

4. Allan Deviation 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 Device Under Test Master Oscillator Frequency Counter

5. 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

6. 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”

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

8. Timing Jitter via Sum Frequency Generation /Hz) 0 2 10 Locking error signal -2 10 Mixer noise floor Noise spectrum (fs -4 10 -6 10 0 20 40 60 80 100 Fourier Frequency (kHz) 1 Top of cross-correlation curve (two pulses maximally overlapped) Timing jitter 1.75 fs (2 MHz BW) 30 fs Cross-Correlation Amplitude Timing jitter 0.58 fs (160 Hz BW) (two pulses offset by ~ 1/2 pulse width) Total time (1 s) 0 Ma et al., Phys. Rev. A 64, 021802(R) (2001). Sheldon et al. Opt. Lett 27 312 (2002) .

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

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

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

12. Balanced Cross-Correlator

13. Experimental result: Residual timing-jitter The residual out-of-loop timing-jitter measured from 10mHz to 2.3 MHz is 0.3 fs (a tenth of an optical cycle)

14. 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

15. Time/Frequency Domain Pictures of fs Pulses Df Frequency domain 2Df Time domain E(t) fo I(f) frep t f nn=n frep+ fo 1/ frep= t Phase accumulated in one cavity round trip Df = 2p fo/ frep F.T. Derivation details: Cundiff, J. Phys. D 35, R43 (2002) D. Jones et. al. Science 288 (2000)

16. Requirements for Coherent Locking of fs Lasers fo2 fo1 I(f) frep f 1/ frep1= t1 E(t) • For successful phase locking: • Pulse repetition rates must be synchronized with pulse jitter << an optical cycle (at 800 nm << 2.7 fs) • Carrier envelope phase must evolve identically (fo1=fo2) fs laser t Pulse envelopes are locked Evolution of carrier-envelope phases are locked E(t) fs laser t 1/ frep2= t2

17. Experimental Setup Delay Delay Phase lock: fo1 -fo2 = 0 (Interferometric) Cross-Correlation Auto-Correlation Spectral interferometry AOM SHG fs Laser 2 SFG fs Laser 1 BBO SHG 100 MHz Sampling scope 14 GHz 14 GHz 50 ps Phase shifter 14 GHz Loop gain Laser 1 repetition rate control 100 MHz Loop gain Phase shifter

18. Locking of Offset Frequencies 1.0 R.B. 100 kHz 0.5 0.0 -0.5 -1.0 200 400 600 800 0 5 MHz 60 dB fo1 – fo2 Phase lock activated sdev = 0.15 Hz (1-s averaging time) (fo1 – fo2) Hz Time (s)

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

20. 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

21. Coherent Anti-Stokes Raman Scattering Microscopy • Four-wave mixing process with independent pump/probe and Stokes lasers (2wp-ws=was) • First demonstrated as imaging technique by Duncan et al (1982)* Prepare coherent (resonant) molecular state Convert molecular coherent 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).

22. CARS Microscope APD Stokes Laser was Filter Pump/Probe Laser Sample 3-D scanner NA=1.4 Objective Dichroic mirror wp,ws was APD Forward Detection Epi (Reverse) Detection

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

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

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

26. Images of 1mm Diameter Polystyrene Beads Raman shift = 1600 cm-1 Pump 0.3 mW @ 250 kHz Stokes 0.15 mW @ 250 kHz • 80-MHz lock • ~770 fs timing jitter • 14-GHz lock • ~20 fs timing jitter • 2 mm • Counts • Counts

27. 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

28. Synchronization of Remote Sources Compare optical standards for tests of fundamental physics • 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 Increasing stability

29. Distribution of frequency standards Optical atomic clock Optical standard Optical frequency standard fs Ti:sapphire comb 1/t t RF standard Noise added by fiber must be detected and minimized 1.5-mm transmitting comb Optical fiber network Holman et al. Opt. Lett. 28, 2405 (2003) Jones et al. Opt. Lett. 28, 813 (2003) End user End user End user Degradation of signal during detection minimized

30. 3.45 km fiber link between JILA and NIST Single Hg+ ion Boulder Regional Administrative Network Trapped Sr Iodine clock L. Hollberg C. Oates J. Bergquist D. Wineland

31. RF transfer: modulated CW source Counter 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 standard 3.5 km 1310 nm laser diode Modulator

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

33. 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)

34. 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)

35. 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

36. 8th harmonic Frequency / time domain analysis End user 8th harmonic Local Frequency reference 3.5 km Mode locked fiber laser 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

37. Transfer with mode-locked pulses Power Power SNR SNR Spectral Width (nm) Spectral Width (nm) • Dispersion broadens pulse (~ 1 ns) more power to maintain SNR but … 660 mW 660 mW 80 dB 80 dB 12.0 ( ) 12.0 ( ) 160 mW 80 dB 5.5 () 30 mW 85 dB Noise floor ( ) so … • Reduce bandwidth 30 mW 85 dB Noise floor ( ) • Recompress pulse • Pulses minimize instability of photodetection: • Average power ; SNR Holman et al. Opt. Lett.29, 1554 (2004)

38. Use dispersion shifted fiber in link • Active stabilization: free-space delay arm in-line with DSF • Not limited by receiver noise • Reduce Allan deviation to noise floor Conditions at Receiver

39. 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)

41. Compensate dispersion of installed fiber Dispersion compensation fiber 3.5 km End user Frequency reference Local Mode locked fiber laser 3.5 km 81st harmonic • Eliminate low frequency noise on • installed fiber network • Dispersion compensation • Avg. power ; SNR

42. Cell Image 5 µm • Human Epithelial cell • Image size is 50 by 50 microns • Total acquisition time: 8 seconds • Raman shift = 2845 cm-1 • Pump 0.6 mW @ 250 kHz • Stokes 0.2 mW @ 250 kHz • Image taken by Dr. Eric Potma and Prof. Sunney Xie at Harvard University with synchronization system commercialized by Coherent Laser Inc. Slice

43. 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

44. Phase Coherent Transmission of Optical Standard Detection of Roundtrip Signal 3.45 km fiber +1 order corrected standard at NIST Nd:YAG AOM 1 AOM 2 -1 order • Adjustment of AOM 1, shifts center frequency of Nd:YAG to compensate fiber perturbations • AOM 2 differentiates local and roundtrip signals JILA I2 Atomic Clock

45. Fiber phase noise FWHM: compensated 0.05 Hz 20 dB 1 kHz Fiber phase noise uncompensated Transmission of Iodine Standard

46. 30 Fiber phase noise uncompensated 20 10 Beat Frequency (Hz) 0 -10 -20 sdev (1-s) 5.4 Hz -30 0 200 400 600 800 Time (s) 30 Digital phase lock 20 10 Beat Frequency (Hz) 0 -10 sdev (1-s) 0.9 Hz -20 -30 0 200 400 600 800 Time (s) Transmission of Iodine Standard

47. 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)

48. Self-Referenced Locking Technique fo I(f) nm frep f 0 nn = n frep + fo x2 n2n = 2n frep + fo fo • need an optical octave of bandwidth! D. Jones et. al. Science 288 (2000)

49. Single Side Band Generator